{"1": {"fulltext": "", "height": "3453", "width": "2237", "jp2-path": "elementsoflogic00copp_0001.jp2"}, "2": {"fulltext": "N^\\n-s\\nv\\n,0^^\\n\u00e2\u0080\u00a2x\\nV\\nc-0\\n.1^\\nc^^\\n1\\n:4\\n(__\\n6 S\\nV-,\\n0^\\ncP\\nO\\n-^^y.\\n\u00e2\u0080\u00a2^t^. 9 A v#", "height": "3299", "width": "2224", "jp2-path": "elementsoflogic00copp_0002.jp2"}, "3": {"fulltext": "-7-\\nI i,\\ns r\\nS\\nOO\\n,0 o^\\nDigitized by the internet ^cltive\\ni n 2Q1 1 with f u nding if fo nr\\nThe Cfbrary of Congress\\nM^\\nv\\ns\\nxX^\\nS ^^^yr^-\\n,^V ^^_.\\n7\\nV. ,^1\\nhttD:/yWww. arcin i ve b^/de^ai Is7e1emem^^", "height": "3219", "width": "2088", "jp2-path": "elementsoflogic00copp_0003.jp2"}, "4": {"fulltext": "", "height": "3284", "width": "2044", "jp2-path": "elementsoflogic00copp_0004.jp2"}, "5": {"fulltext": "", "height": "3284", "width": "2044", "jp2-path": "elementsoflogic00copp_0005.jp2"}, "6": {"fulltext": "", "height": "3284", "width": "2066", "jp2-path": "elementsoflogic00copp_0006.jp2"}, "7": {"fulltext": "ELEMENTS OF LOGIC\\nDESIGNED AS A\\nMANUAL 4W INSTEUCTIOK\\nHENRY COPPEE, A. M.,\\nPEOFESSOR OP ENGLISH LITEKATUEE IN THE UNIVERSITY OF PENNSYLVANIA; AND\\nLATE PRINCIPAL-ASSISTANT PROFESSOR OF ETHICS AND ENGLISH\\nSTUDIES IN THE UNITED STATES MILITARY ACADEMY\\nAT WEST POINT.\\nfir\\nPHILADELPHIA:\\nPUBLISHED BY E. H. BUTLEB CO.\\n1858.", "height": "3266", "width": "2023", "jp2-path": "elementsoflogic00copp_0007.jp2"}, "8": {"fulltext": "3C\\nCI\\nTHB LIBEARY\\nor CONOREti\\nWAtMmOTDlf\\nEntered, according to Act of Congress, in the year 1S57, by\\nE. H. BUTLER CO.,\\nIn the Clerk s Office of the District Court of the United States, in and for\\nthe Eastern District of Pennsylvania.", "height": "3312", "width": "2037", "jp2-path": "elementsoflogic00copp_0008.jp2"}, "9": {"fulltext": "PREFACE.\\nThe following treatise has been written in the hope\\nthat it may supply, in some degree, a real want. For\\nseveral years the author was a teacher of Logic, in\\nthe Military Academy at West Point, where the sub-\\nject was thoroughly studied by the aid of Archbishop\\nWhately s text-book.\\nHow much a manual was needed before that work\\nappeared may be known from the significant fact that,\\nas soon as it was published as an article in the Ency-\\nclopaedia Metropolitana, it was eagerly caught at\\nby the community of, teachers, and used, unaltered,\\nas a book for college instruction, on both sides of the\\nAtlantic.\\nSince the publication of that article many have\\nattempted the preparation of a manual, which should\\nhave the instruction of classes as its original design\\nbut the soundness of Whately s views and the con-\\n(3)", "height": "3275", "width": "1957", "jp2-path": "elementsoflogic00copp_0009.jp2"}, "10": {"fulltext": "IV PREFACE.\\nciseness of his expression, still give to his work the\\ngreatest circulation. Among so many endeavours the\\nauthor would venture to express the hope that his little\\nmanual may find its special purpose and mission it\\nis short it is explanative of all the difficult points so\\noften left to confuse a student the arrangement is\\nsimple, and much that in a larger treatise would be\\nof necessity included, is here omitted, so that what\\nthe student learns in the limited time of a college\\nterm, he may learn well, and retain in his memory as\\na basis for further investigations. To some persons\\nit may seem too much simplified but let it be remem-\\nbered that it is a manual for youth and that its only\\naim is to teach them the Elements of Logic, as the\\nfoundation of all reasoning.\\nThe basis of the work is Whately s Logic many\\nof the examples are taken directly from that so many\\nindeed, that the acknowledgment is here made for\\nthem all, and for much that is excellent in arrange-\\nment and in expression. As the clear expounder of\\nAristotle, and the originator of much that is valuable,\\nWhately must stand at the head of the Logicians of\\nthis age. The author would refer specially also to\\nthe material assistance obtained from Devey s", "height": "3284", "width": "2062", "jp2-path": "elementsoflogic00copp_0010.jp2"}, "11": {"fulltext": "PREFACE. Y\\nLogic, (Bolm s series), Aristotle s Post mid Prior\\nAnalytics, (Bohn s translation); NeiVs Art of Rea-\\nsoning Blahey s Historical Sketch of Logic;\\nLord Bacon s New Organon Arnauld (Logique de\\nPort Royal); J. Bentham s Book of Fallacies.\\nFrom Neil a few of the examples have been taken.\\nBesides these he has consulted a great number of\\nworks, the aid derived from which is so general that\\nthey do not require special mention.\\nUniversity of Pennsylvania, July, 1857,", "height": "3284", "width": "2062", "jp2-path": "elementsoflogic00copp_0011.jp2"}, "12": {"fulltext": "", "height": "3284", "width": "2052", "jp2-path": "elementsoflogic00copp_0012.jp2"}, "13": {"fulltext": "TABLE or CONTENTS.\\nCHAPTEB L\\nPAGE\\nSection 1. Logic; the meaning of the term and the scope of the\\nScience 13\\n2. Sources of Error 14\\n3. Logic and Philosophy 16\\n4. Objection to Logic as an Art 19\\n5. Natural Logic 21\\n6. Systematic forms of Error 22\\n7. Of Method 23\\n8. Analysis and Synthesis 26\\n9. Analysis and Synthesis as applied to Logic .30\\nProposed plan of Study 1. An Analytical View of\\nLogic. 2. A Synthesis of Formal Logic. 3. A His-\\ntorical View of Logic 31-32", "height": "3216", "width": "1922", "jp2-path": "elementsoflogic00copp_0013.jp2"}, "14": {"fulltext": "Vm TABLE OF CONTENTS.\\nCHAPTER II.\\nAnalytical View of Logic.\\nPAGE\\nSection 10. The reasoning process analyzed .33\\nThe Dictum of Ari totle 36\\nCHAPTER IIL\\nA Synthesis of Logic.\\nSection IL Of certain operations and states of the mind in the pro-\\ncess of Argument 40\\nCHAPTER IV.\\nSection 12. Of Terms 45\\n13. Division of Simple Terms 47\\n14. Quantity and Quality of Terms 49\\nCHAPTER V.\\nOf those operations in Logic which belate to Terms.\\nSection 15. Abstraction and Generalization 51\\n16. Species, Genus, and Differentia 52\\n17. Property and Accident 53\\n18. Of the different orders of Genera and Species 56\\n19. Realism and Nominalism 58\\n20. Definition of Terms 58\\n21. Nominal and Real Definitions 62", "height": "3284", "width": "2068", "jp2-path": "elementsoflogic00copp_0014.jp2"}, "15": {"fulltext": "TABLE OF CONTENTS. IX\\nPAGE\\nSection 22. Rules for Definition .63\\n23. Division 68\\n24, Recapitulation 73\\nCHAPTER VI.\\nSection 25. Propositions 75\\n26, Propositions divided into Simple and Compound 79\\n27. Quantity and Quality of Propositions .81\\n28. Of the Distribution of Terms in Propositions 85\\n29, Conversion 88\\n30, Of Opposition 94\\n31, Of the Matter of Propositions 96\\n32. Of Compound Propositions 99\\n33. The New Analytic 103\\nCHAPTER VII.\\nSection 34. Of Arguments 106\\n35, Of the Syllogism 108\\n36. Logical Axioms 109\\nCHAPTER VIII.\\nOp Figure and Moods.\\nSection 37. Figure 117\\n38. Of Mood .121\\n39. Of Reduction 134", "height": "3266", "width": "2000", "jp2-path": "elementsoflogic00copp_0015.jp2"}, "16": {"fulltext": "X TABLE OF CONTENTS.\\nPAGE\\nSection 40. Indirect Reduction i;;9\\n41. Notation of the Syllogism 142\\nCHAPTER IX.\\nOf lRRii:GULAR, Informal, and Compound Arguments.\\nSection 42. Of Abridged Syllogisms 147\\n43. The Sorites, or Chain Argument 151\\n44. Of the Epichirema 155\\n45. Of Hypothetical Syllogisms 167\\nCHAPTER X.\\nFallacies,\\nSection 46. The Meaning and Comprehension of a Fallacy 170\\n47. Of Fallacies in dictione, or Formal Fallacies 172\\n48. Material, or Informal Fallacies 175\\n49. Verbal Fallacies 188\\n50. The manner of removing Ambiguity in Terms 201\\n51. The Fallacy of Probabilities, or the Calculation of\\nChances 202\\n52. Popular Fallacies 205\\nCHAPTER XL\\nSection 53. Of certain modes in which Logic is applied .211", "height": "3284", "width": "2034", "jp2-path": "elementsoflogic00copp_0016.jp2"}, "17": {"fulltext": "TABLE or CONTENTS. XI\\nCHAPTER NIL\\nA Historical Sketch of Logic.\\nPAGE\\nSection 54. Division of the Subject 220\\n55. Aristotle 222\\n56. The Logic of Christianity 2.36\\n57. The Logic of Experimental Philosophy 252\\n58. Logic in the Eighteenth and Nineteenth Centuries 266\\n59. Of Categories and Classification 268\\n60. Conclusion 275", "height": "3284", "width": "2034", "jp2-path": "elementsoflogic00copp_0017.jp2"}, "18": {"fulltext": "", "height": "3284", "width": "2054", "jp2-path": "elementsoflogic00copp_0018.jp2"}, "19": {"fulltext": "LOGIC.\\nCHAPTER I.\\n(1.) Logic: the meaning of the Term and the\\nscope of the Science,\\nAs of all the Greek words which have been trans-\\nferred to our English speech, none is vaguer and more\\nsubtle in its meaning than the word logos (^oyoj,) so\\nof all the sciences, none is less understood both as to\\nits meaning and its scope, than the science of Logic,\\nthe name of which is taken from that word and, in\\nconsequence, no term is more erroneously applied and\\nmore frequently misapplied than the name itself.\\nAs Koyo^ means a ivord, some writers have sup-\\nposed Logic to be simply the science of spoken or\\nwritten words^ and have thus confounded it with\\nRhetoric and even with Grammar others, con-\\nsidering a word to imply not simply the written\\nsymbol or the spoken sound, but also the expres-\\n2 (13)", "height": "3216", "width": "1980", "jp2-path": "elementsoflogic00copp_0019.jp2"}, "20": {"fulltext": "14 LOGIC.\\nsion of the tJiougJit, have supposed Logic to be the\\nscience of thought, and have thus confounded it Avith\\nIntellectual Philosophy^ or the investigation of the\\nlaws of thought and mind others still, and by far the\\ngreater number, regarding it as a union of language\\nand thought in the deduction of truth, have claimed\\nthat it had to do with the subject-matter of scientific\\ninvestigation, and have thus erred more widely than\\nall by confounding Logic with the labours of physical,\\nmetaphysical, and ethical philosophy.\\nIt seems necessary then, at the beginning of a trea-\\ntise on this subject, to define the meaning of the word,\\nand the true scope of the science, before we under-\\ntake its study: to rid ourselves, as it were, of the\\nmists which surround us, before we can even see\\nclearly the field in which we are to labour.\\n(2.) Sources of Error.\\nMany accurate thinkers have confused the minds\\nof students by producing books, which, while they\\ncontain a just view of the logical system itself, attempt\\nat every step to explain the suhject-matter upon which\\nthis system is employed, and which forms no part of\\nit while many others, adopting strongly the views of\\nthose who have initiated so-called systems of logic,\\nhave, as partisans, carried forward from period to\\nperiod old errors and old perplexities and, themselves\\nignorant of the subtleties which surround them, have", "height": "3198", "width": "1940", "jp2-path": "elementsoflogic00copp_0020.jp2"}, "21": {"fulltext": "SOURCES or ERUOR. 15\\ncalled their views the true logic, and those of every\\nother writer false. Others again have endeavoured, in\\nan amiable but unscientific spirit, to harmonize all the\\nschemes of the philosophers, and to call the result,\\nfull of error and inexactness, the system of Logic.\\nThere are indeed in the systems of the great philo-\\nsophers many parts that are mutually dependent, and\\ntrue science will be found to harmonize with itself\\neverywhere. But since there is also error in them all,\\nno mere greatness of name, should exempt from the\\nscrutiny and exposure of error.\\nWe must take care to distinguish between the dif-\\nferent functions of the intellect, so as to call things\\nby their right names; not including in the name\\nLogic what belongs to Physics or Metaphysics, but\\nlaying down at the outset the limits and province of\\nthat system, which we wish to designate by the word\\nLogic. If we can do this we shall have accomplished\\nvery much at the beginning, and shall find our labour\\neasy as we proceed.\\nIf we would see how important it is rightly to\\nunderstand this fact of the ambiguity which the word\\nLogic has produced in the minds of men, we need but\\nlook for a moment at the errors into which modern\\nphilosophers have fallen, when speaking of the Logic\\nof Aristotle as compared with the Logic of Bacon.\\nIf, as we shall endeavour to demonstrate. Logic is\\nthe science which controls the universal and ultimate", "height": "3195", "width": "1923", "jp2-path": "elementsoflogic00copp_0021.jp2"}, "22": {"fulltext": "16 LOGIC.\\nprinciple of reasoning, given to man, just as speech\\nwas given to him, by a beneficent Creator, then it\\nis not Aristotle s Logic, nor Bacon s Logic, but a\\nsingle, universal Logic, given to man as the rule of\\nhis reason, which must be intelligible and harmonious\\nwherever and by whomever it is used.\\n(3.) Logic and Pliilosoj^liy\\nIn this consideration another word plays a pro-\\nminent part. The word which has been pressed into\\nservice, to denote the peculiar progress of great\\nminds in the domains of Truth, is PMloso^liy\\nbut even the word Philosopher, adopted by a wise\\nancient* as a more modest title than 504)05, as the\\nsages of Greece were called, has been productive of\\ngreat confusion. Philosophy has been made to\\nstand for a thousand sciences, and to preside in the\\nkingdoms of mind, morals, and physics, until to be a\\npliiloso pher means to pursue one of many intellectual\\npursuits, and Philosophy unqualified means every-\\nthing or nothing.\\nAnd yet this vague and inexact term Philosophy,\\nis the one which has been most frequently confoimded\\nwith Logic, and a want of clear definition and of a just\\nunderstanding in the dispute, has led to the produc-\\ntion of abominable, distorted, and monstrous systems,\\nPythagoras.", "height": "3199", "width": "1936", "jp2-path": "elementsoflogic00copp_0022.jp2"}, "23": {"fulltext": "LOGIC AND PHILOSOPHY. 17\\nboth of Philosophy and Logic, which have confused\\nthose desirous of learning, and deterred many from\\nthe difficult and perilous attempt.\\nIndeed both words, and the errors to which their\\nuse has led, indicate, at once, the yearning and the\\nweakness of the human mind, the desire of man to\\ninvestigate and systematize truth, combined with the\\nobscurity and doubt which beset his investigations at\\nevery step.\\nThe acuteness of the G-reeks, upon which had been\\ngrafted all the pov^er and attainment of the Oriental\\nworld, could reach no clearer nomenclature, than to\\ncall their studies and their inductions Philosophy\\nthe love rather than the attainment of ivisdom and\\nthe art by w^iich they reasoned from truth to truth,\\nby which they progressed from parallel to parallel in\\nthe sea of doubt and uncertainty. Logic, the art of\\nwords or discourse, the very mention of which sug-\\ngests a dubious question, and calls up, as it were, two\\nopponents in considering it.\\nIn avoiding these errors, let us agree to regard\\nPhilosophy as the investigation of truth, as to its\\nsubject-matter, the process of finding materials, and\\nof classifying and aggregating observations and ex-\\nperiments, and Logic, as the simple reasoning process\\nby which we pass from truth to truth already found,\\nand by which we guard against false arguments in\\nsuch a passage.\\n2* B", "height": "3198", "width": "1926", "jp2-path": "elementsoflogic00copp_0023.jp2"}, "24": {"fulltext": "18 LOGIC.\\nHaving thus seen that the name Logic is in a great\\ndegree arbitrary, and that we should not attain to an\\nunderstanding of the subject, if we followed, even\\nremotely, the etymology of the word, we repeat that\\nLogic has to do neither with the words themselves\\nexcept as they are arranged into propositions and\\narguments nor with their meanings, but only with\\nthe process of reasoyiing, i. e. passing from two hnoivn\\nand achnoivledged judgments to a third which is\\nderived from their combination. In general words,\\nthen, we may state a definition of the term. Logic is\\nthe Science and the Art of Reasoning.\\nOf these two terms. Science and Art^ we remark\\nthat Art is in a critical sense more extensive than\\nScience, since the practice of an Art implies the\\napplication of the principles of Science, while on the\\nother hand, Science might, indeed does exist in its\\ntheoretic state without being put to practical use.\\nThe Science would be the investigation of the prin-\\nciples upon which the human mind is based in reason-\\ning, and the Art, the application of those principles\\nto the establishment of practical rules for conducting\\nthe process. Logic may then be more simply defined\\nthe Art of Reasoning, and as such we shall consider\\nit in these pages less concerned about the composi-\\ntion of man s reason, than about the practical laws\\nand methods by which it works.\\nBefore proceeding to explain the system of Logic,", "height": "3201", "width": "1966", "jp2-path": "elementsoflogic00copp_0024.jp2"}, "25": {"fulltext": "OBJECTION TO LOGIC AS AN AET. 19\\nwhich has developed itself since the days of Aristotle,\\nlet us meet at the threshold some plausible objections\\nwhich have been brought against the establishment of\\nany system whatever.\\n(4.) Objection to Logic as an Art,\\nAs man has been universally gifted with reason by\\nmeans of which he may combine his thoughts and\\narrive at just conclusions, and with language in which\\nto communicate them, it is asserted that every man\\ncarries his own Logic within him, as the immediate\\ngift of God.\\nAll men reason, it is true, and many men are not\\naware of the logical process which they use and this\\nhas been made, even by men of acute minds, an objec-\\ntion against Logic for, they say, since men reason,\\nand reason well, without rules, and without knowing\\nthe process, a system of rules must be unnecessary.\\nThe objection is plausible, and has been fruitful of\\nevil. But as it is one which may be brought against\\nmany other arts as well as Logic, it may, we think,\\nbe most easily met, and most clearly refuted by illus-\\ntration. Many children speak with correctness and\\nprecision before they have any knowledge of Grammar\\nand there are persons of wonderful powers in arithme-\\ntical computation who have never learned Arithmetic\\nbut G-rammar and AritJimetie are not for such reasons\\ncondemned their rules are an infallible test for pre-", "height": "3195", "width": "2003", "jp2-path": "elementsoflogic00copp_0025.jp2"}, "26": {"fulltext": "20 LOO re.\\ncise speaJcing, and correct computation, and are thus\\nguides to the weaker and slower intellects, and these\\nconstitute the immense majority of mankind, to keep\\nthem from formal error. So, too, in Music and Paint-\\ning great geniuses arise in both Arts, but no one\\nwould contend that hard study, according to the estab-\\nlished systems of the great composers, and the great\\nmasters established upon the true principle of voice\\nand ear is not absolutely requisite to excellence\\nand success.\\nMany persons of clear perceptive faculties, and\\nwho form and combine their judgments rapidly, may\\nreason acutely and well without a system of rules\\nbut, in order to be certain of their correctness, others\\nmust have some invariable test on the other hand\\nthere are many, of quick but erratic minds, who rea-\\nson with such dangerous sophistry that the most deli-\\ncate logical tests alone can expose the fallacy, of\\nw^hich indeed they may not themselves be entirely\\naware. As such delicate tests have not been within\\nthe reach of the multitude, it is thus that men have\\nbecome, for want of a popular knowledge of Logic,\\nat once self-deceivers and deluders of mankind have\\nestablished illogical religious creeds, monstrous social\\nfallacies, false theories of government, w^hich are im-\\nmediately made manifest by the simple application of\\nLogic.\\nNay more since Logic is the one, universal princi-", "height": "3201", "width": "1974", "jp2-path": "elementsoflogic00copp_0026.jp2"}, "27": {"fulltext": "NATURAL LOGIC. 21\\npie of Keasoning, applied alike to every branch of\\nscience Exact or Inductive, it seems much more\\nnecessary that we should establish full and unerring\\nrules for our guidance, and thus be kept, at every\\nturn, from the manifold errors which arise from sys-\\ntems based upon such objections as those we have\\nmentioned.\\n(5.) Natural Logic.\\nThe natural laws which govern the human mind in\\nits attempts to reason, have been called by the oppo-\\nsers of Logical systems, Natural Logic. We accept\\nthe name, and are ready to allow that this instinct of\\nreason is in the main right, and originally, perfect in\\nits kind but now, in the fallen condition of man, liable\\nto be biassed by prejudice, distorted by passion, or\\ninsidiously tempted into open error. Thus many men,\\nwho reason correctly on most subjects, are swayed,\\nin one or more, by self-interest, partisanship, fashion,\\npredominance of the imagination, and such like\\ncauses and thus men of equally clear minds, in the\\nmain, from the same premises draw different conclu-\\nsions, or establish the same conclusion by very differ-\\nent premises. Thus also the same man, at different\\nperiods of his life, or swayed by various circumstances,\\nwill reason differently and from such causes, it is\\nevident that each man s natural Logic is not a suffi-\\ncient guide for his reason.", "height": "3195", "width": "1931", "jp2-path": "elementsoflogic00copp_0027.jp2"}, "28": {"fulltext": "22 LOGIC.\\nYet still it is from this natural Logic, or rather,\\nthe concurrence of the right reason of many well\\nordered minds, that the science of Logic has been\\ndeduced.\\nBy a systematic observation of such minds, as they\\nreason, taking care to remove all causes of error in\\neach particular case, we establish rules for the reason,\\nand are able to detect, by the application of these\\nrules to other cases, every fallacious argument result-\\ning from such causes of error.\\nThere must have been reason before there could be\\na system of laws to govern it, just as we know there\\nwas language before Grammar was formed. It was\\nto systematize this reason, to methodize this natural\\nLogic, and particularly to guard against errors in the\\nuse of the reasoning powers, that a canon was pre-\\npared, and that a complete science of Logic has been\\nformed.\\nWe have spoken in general terms of the confusion\\nand error which have grown out of the misapprehen-\\nsion of Logic the more special phases of it are those\\nresulting from an attempt to systematize these general\\nerroneous notions.\\n(6.) Systematic Forms of Error.\\nBy a very common misuse of language, we hear\\nsuch phrases as mathematical reasoning j moral\\nreasoning^ si/llogistio reasoning, and inductive", "height": "3199", "width": "1949", "jp2-path": "elementsoflogic00copp_0028.jp2"}, "29": {"fulltext": "OF METHOD. 23\\nreasoning which would lead us to suppose that\\ninstead of one there were many kinds of reasoning.\\nThis is a fruitful source of error.\\nThese, so-called, different kinds of reasoning are\\nonly applications of Logic to different subjects, and\\ndifferent habits of thought the Logic in each is the\\nsame, the subject-matter alone is different.\\nIt would seem unnecessary to dwell upon this point,\\nbut it has been so commonly misunderstood, and the\\nerror has been so disseminated by professed writers\\nupon Logic, that it must be plainly stated and care-\\nfully remembered.\\nWhen we speak, then, of a good mathematician, we\\nmean one who is able, most surely and rapidly, to\\naipiply Logic to the investigations of numbers and\\nquantity. When we hear of a great theologian, we\\nknow that he has amassed much theological learning,\\nand has applied Logic to it successfully. So too with\\nother sciences.\\nIn general, in which ever of the myriad fields of\\nNature and mind, ardent votaries may wander how-\\never various the stores they may amass, they must all\\ncome back with their sheaves to the great measuring-\\ncentre of Logic, and apply its dicta before they can\\ncompute or use their gathered gains.\\n(7.) Of Method.\\nMethod is the order and arrangement of facts to", "height": "3198", "width": "1854", "jp2-path": "elementsoflogic00copp_0029.jp2"}, "30": {"fulltext": "24 LOGIC.\\nproduce a certain result to establish new truth, to\\ninv estigate old, and to explain and teach both. It is\\nderived from the Greek fisO obov- which denotes the\\nwai/ through which we arrive at a certain result.\\nWhatever steps are taken to make knowledge pro-\\nfitable, to reduce theory to practice, and to give clear\\nand intelligible ideas of science, constitute Method.\\nThe extension of the term Method^ it is evident, will\\ndiffer according to the subject to which it is applied.\\nThe methods of investigation differ slightly for the\\ndifferent kinds of science, but may generally be\\nclassified under two heads, Analysis and Synthesis, of\\nAvhich the former is generally used in the private in-\\nvestigation of truth, and the latter for the purposes\\nof instruction.\\nThe successive stages in the discovery, progress\\nand establishment of any science, are three, viz.\\nthe descriptive, the inductive (also called the expe-\\nrimental), and the deductive or exact stage.\\nAs soon as, by the description of a science, the\\nstatement of its present condition, its wants, its un-\\nknown causes, c., we have a just representation of\\nit, we proceed to observation and experiment, or in-\\nduction and when by induction, or the laboured\\ncollection of many particular facts and examples, we\\nhave established general laws, we may then deduce\\nfrom thejn any particular fact or facts, which it con-\\ncerns us to know.", "height": "3222", "width": "1993", "jp2-path": "elementsoflogic00copp_0030.jp2"}, "31": {"fulltext": "ANALYSIS AND SYNTHESIS. 2b\\nThese stages of investigation belong equally to the\\nphysical and moral sciences, with the slight difference\\nin practice, that the vagueness and complexity in-\\nvolved in mental, spiritual, and social phenomena,\\nwhich all belong to the moral sciences, require more\\ndelicate and subtle agencies to trace their laws than\\nthose of the natural world around us.\\nAnd the sources of experiment are not at all ana-\\nlogous. Here we are surrounded by apparent contra-\\ndictions. The world of nature is changeable and\\nshifting, and yet it is palpable to our senses the laws\\nwhich govern it are mysterious and inscrutable, and\\nyet they are constant the moral world which is un-\\nchangeable and eternal, is vague and obscure, and\\nthe abstract conclusions to which our inductions lead\\nus, positive and incontrovertible as they are, are but\\nfew and unsatisfactory.\\nWe shall have occasion to consider the subject of\\nMethod more in detail hereafter, but at present we\\ndesign to apply it to the consideration of Logic.\\nWe speak of the Method of a single science, or a\\nMethod which is applied to all as in that which\\nleads to the Classification of the sciences. In either\\ninvestigation the division of Method into Analysis\\nand Synthesis, is a just one, as both are used in\\neither process.", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0031.jp2"}, "32": {"fulltext": "26 LOGIC.\\n(8.) Analysis and Synthesis.\\nTo illustrate more clearly the nature of these two\\nprocesses, let us take a familiar example. If we\\ndesigned to teach a person how to make and use some\\ncomplicated structure, as, for example, a ship, and if\\nthis person had never seen one, the first step in the\\nprocess would be to show him the ship completely\\nbuilt and ready to proceed to sea; fully rigged,\\nequipped and manned that he might take in at a\\nglance its finished appearance, and its ultimate design\\nand use in a word, that he might know ivhat he was\\nto learn to make. This would be the first lesson in\\nship-building. The next step would be to show it to\\nhim partially dismantled, or in effect, to take it to\\npieces before his eyes, that he might see the parts of\\nwhich it is composed, and their relative position in\\nthe structure.\\nThe third step w^ould be to show him how each part\\nwas made, and to let him see them all in minute\\ndetail lying together, according to some system, which\\nshould be preparatory to a reconstruction of the\\nship.\\nThis process of successive steps is Analysis, or a\\ndissolution of anything into its elements.\\nIn the investigation of any science, it is of primary\\navaXvoi to Separate into elements.", "height": "3201", "width": "1995", "jp2-path": "elementsoflogic00copp_0032.jp2"}, "33": {"fulltext": "ANALYSIS AND SYNTHESIS. 27\\nimportance. Showing us at first the scope and design\\nof the science, by systematic degrees it decomposes\\nit into its elements, and prepares us for intelligent\\nstudy of its many forms.\\nThis operation shows us also the simplicity of science,\\nand is evidently derived from the teachings of nature\\nfor while there are innumerable forms of animal and\\nvegetable life, the analysis of nature which is con-\\nstantly going on, shows but few parts or elements in\\nall her works, and great simplicity of combination of\\nthe same elements in different proportions, to produce\\nthe most dissimilar forms and results. So all the\\nsciences, physical, intellectual, and moral, while they\\nassume many and varying forms, are in reality com-\\nposed of a few simple elements of nature or mind, and\\nthis their analysis displays.\\nThe analysis of physical science is of course the\\nmost exact of these processes, in proportion as the\\nthings of sense are easier to comprehend and fix than\\nthose of mind and spirit: in physics, this process of\\nanalysis is carried from the grandest class, such as\\nkingdoms and high genera, to the observation and use\\nof atoms and molecules inconceivably small, which\\nare to constitute the basis-elements of a reconstruct-\\ning process. Accurate analysis is a work of patient\\nlabour. Chance experiments have indeed occasionally\\nproduced great results, but this is an argument for,\\nrather than against, careful analysis. Koger Bacon dis-", "height": "3195", "width": "1931", "jp2-path": "elementsoflogic00copp_0033.jp2"}, "34": {"fulltext": "28 LCMuc.\\ncovered a, \u00e2\u0096\u00a0fiiliuIiiatliiL!; powder when lie was not seek-\\ning it but, to be useful, this powder must cease to be\\na chance discovery; that is, it must be analyzed into\\nnitre, charcoal., and hrimstoyie, so that, these constit-\\nuents once known, we can make our fulminating\\npowder at will. Science has never proceeded upon\\nchance it moves safely cnly when it moves by in-\\nvariable but ever-extending laws.\\nIncomplete analysis has done more to establish and\\nperpetuate error, than even blind superstition. For\\nit was in the face of the latter that Copernicus and\\nGalileo established the true theory of the heliocentric\\nsystem while before their time, the incomplete,\\nfalse, and arbitrary analysis of astronomy, and the\\nbelief in stellar influences, which a just analysis would\\nliave destroj^ed, led all the writers, from the time\\nof Ptolemy, to build a false system of celestial\\nmechanics and thus to clog the wheels of true\\nscience.\\nThe process of analysis having been completed, we\\ncome naturally to Synthesis.\\nHaving taken to pieces, we proceed to the other\\ntask of rebuilding carefully examining each different\\nelement as they all lie before us, until we understand\\nthoroughly the material of which it is made and its\\nconstruction, we proceed to adjust it to its place in\\nthe structure piece by piece, perhaps slowly and pain-\\nivvrWrjiiL to place together.", "height": "3216", "width": "1973", "jp2-path": "elementsoflogic00copp_0034.jp2"}, "35": {"fulltext": "ANALYSIS AND SYNTHESIS. 29\\nfully, we build the ship, until ai length it is complete\\nnor is the labour yet finished we launch it upon the\\nwaters, spread its sails to the wind, and see it in\\npractical and successful movement, and then we may\\naccount ourselves acquainted with the structure, and\\nable to build its like whenever called upon to do so.\\nThis operation is called Synthesis it is evident\\nthat it is also continually going on in nature in the\\nreproduction out of crude materials of the many forms\\nof complicated existence.\\nMany writers, in investigating a science, begin with\\nthis latter process, entirely neglecting the former but\\nit is so evident that the analysis of a science gives\\nlarge and valuable lessons preparatory to its synthesis,\\nor real study for ourselves, that most modern treatises\\non science have adopted and followed this order of\\ninstruction. It may then be safely stated that in any\\nscience the true synthesis can only be proportional to\\na vigorous and just analysis, and there have conse-\\nquently been rules laid down for proceeding to con-\\nsider any science or art in pursuance of this method.\\nThe rules for Analysis may be reduced to these\\n1st. Not to believe any general scientific statement\\nwithout proof: that proof determined by the just\\nprinciples of evidence.\\n2d. To divide every scientific dictum into as many\\nparts or elements as shall be necessary to resolve it.\\n3d. To make a methodical arrangement of these", "height": "3195", "width": "1955", "jp2-path": "elementsoflogic00copp_0035.jp2"}, "36": {"fulltext": "30 LOGIC.\\nelements in order that we may understand them\\nclearly and the relation which they bear to each other.\\nHaving done this, the corresponding rules for Syn-\\nthesis are\\n1st. To use such terms to express the elementary\\nparts as are free from ambiguity.\\n2d. In combining these, to assume only such clear\\nprinciples or axioms as cannot be contested by any\\npersons.\\n3d. To prove, by demonstration, all the conclusions\\nat which we arrive, in the employment of the terms\\nand axioms used.\\nThese remarks upon analysis and synthesis, as the\\ntwo vital functions of Method in investigation, and as\\nthe two necessary instruments of all scientific study,\\nare designed for general application. A proper and\\nconstant application of the rules of analysis and syn-\\nthesis would cause great advancement in our studies,\\nand would go far to insure us from error, however\\nrapid that advancement might be. But we have\\nplaced the subject of Method in this place, because\\nwe design to use it in application to the study of Logic\\nitself; for, as a science to be studied. Logic comes\\nunder the rules which have been just laid down.\\n(9.) Analysis and SyntJiesis as applied to Logic,\\nNow, let us employ this method in investigating the\\nscience of Logic.", "height": "3201", "width": "1957", "jp2-path": "elementsoflogic00copp_0036.jp2"}, "37": {"fulltext": "PROPOSED PLAN OF STUDY. 31\\nThat we may study the subject profitably, making\\neach step a preliminary to the due understanding of\\nthe successive steps, we propose to divide the entire\\nsubject into the following special considerations\\n1. AN ANALYTICAL VIEW OF LOGIC.\\nIn this we regard the science in its aim and its\\nworkings, and after thus showing its design and its\\nscope, we analyze or dissolve it into its different parts,\\nshowing what those parts are which effect by their\\ncombination the purpose designed.\\n2. A SYNTHESIS OF FOEMAL LOGIC.\\nAs Synthesis is the reverse process of Analysis, and\\nas an Analysis of such a study would be in reality\\nbut a general view of the scope of that science which\\nSynthesis is to establish, we shall see that while our\\nanalytical view of Logic may be brief and general, our\\nsynthesis must be minute and careful. We must more\\nparticularly examine those parts which our analysis\\nhas given us, in order that we may be able duly to\\ncombine them in their just relations.\\nIn imparting instruction upon subjects which are\\nknown, the synthesis is evidently the more important\\nprocess, and hence must be longer and more minute\\nwhile in the investigations of an unknown science the\\nanalysis is the more important and valuable process.", "height": "3195", "width": "1931", "jp2-path": "elementsoflogic00copp_0037.jp2"}, "38": {"fulltext": "82 Lor.io.\\nIn the general syntliesis of Logic we shall also\\ndevote a chapter to the subject of Fallacies and\\nthen consider some of the ways in which the syllo-\\ngism is used, and the technical phrases which ex-\\npress these uses.\\n3. A IIISTOKICAL VIEW OF LOGIC.\\nThis historical view of Logic has been placed after\\nthe study of the formal Logic, rather than before it,\\nas is usual in most treatises, because we can appreciate\\na history only of that which we know, and we shall\\nunderstand much better the causes of error and the\\nobstacles to science which history gives us, when we\\nare beforehand aware of the true scope and relations\\nof the particular science whose history is related.\\nWhen we know what Logic is, its history is intelligible\\nand interesting, and not otherwise.\\nFor Loo^ic is so intermingled or rather entangled\\nO o o\\nwith other kinds of philosophy in almost all of its\\nprincipal epochs, that any one who should undertake\\nto read of its adventures in history without being\\nable constantly to dissociate it from its companion\\nsciences, would find it a useless and unprofitable task.", "height": "3201", "width": "1944", "jp2-path": "elementsoflogic00copp_0038.jp2"}, "39": {"fulltext": "ANALYTICAL VIEW OF LOGIC. 33\\nCHAPTER 11.\\nANALYTICAL VIEW OE LOGIC.\\n(10). The reasoning process analyzed.\\nTo apply tlie method of analysis to the study of\\nLogic as an art, we begin with the definition already\\nlaid down that Logic is the Art of Reasoning.\\nReasoning consists in the combination of two known\\njudgments to form a third, which is deduced from\\nthem. Reasoning, when expressed in language, is\\ncalled argument.\\nThe ultimate and simple form of argument, logi-\\ncally expressed, is tlie syllogism. In a more extended\\nsense, reasoning covers also the combination and suc-\\ncession of many arguments.\\nThe syllogism is an argument consisting of three\\npropositions, of which the first is called the major pre-\\nmiss, the second, the minor premiss, and the third,\\nthe conclusion.\\nMajor premiss. All A is B All men are mortal.\\nMinor premiss. All C is A All Hindoos are men.\\nConclusion. Therefore all C is B All Hindoos are mortal.\\nsvv and \\\\oyi^ojxai, more remotely Xtyw.\\nC", "height": "3198", "width": "1854", "jp2-path": "elementsoflogic00copp_0039.jp2"}, "40": {"fulltext": "34 LOGIC.\\nEach of these propositions consists of two terms,\\nthe subject and the predicate and the verb uniting\\nthem is called the copula. Men reason to satisfy\\ntheir own minds, to convey instruction, or to refute\\nerror, and in so doing, they combine many of these\\nsyllogisms, thus forming compound arguments, which\\nmay always be analyzed into the simple arguments\\nwhich compose them. In a simple syllogism, in many\\ncases, one or other of these premisses conveys a fact\\nso well known that it may be taken for granted, and\\nso it is suppressed, and thus is formed an abridged\\nargu77ient, called an entliymeme. For example\\n[Minor premiss.) Csesar was a man,\\nTherefore Coesar was mortal.\\nThis is an enthymeme w^ith the major premiss\\nsuppressed. This major premiss is, All men are\\nmortal, which is taken for granted in the conclusion,\\nwhere, because Coesar was a man, it is affirmed that\\nhe was mortal. In every case, however, if the enthy-\\nmeme appear at all doubtful, the suppressed premiss\\nmay be written out, and the validity or invalidity of\\nthe argument thus determined. Compound argu-\\nments, instead of having each syllogism fully ex-\\npressed, are usually formed of a number of enthymemes\\ncombined.\\nThe groundwork of the syllogism is the dictum of\\nAristotle, or his universal test for Argument.\\nWithout in this place entering even very briefly", "height": "3217", "width": "1975", "jp2-path": "elementsoflogic00copp_0040.jp2"}, "41": {"fulltext": "Aristotle s dictum. 35\\ninto the History of Logic a history of experiment\\nand error it is interesting to know the time of its\\nfirst decided manifestation, and the person to whom\\nwe owe it as a definite science. In that magnificent\\nperiod when the school of Plato had prepared the\\nmind of Greece for the coming of Aristotle, and the\\nenergy of Philip had opened the way for the con-\\nquests of Alexander, that system of Logic was\\nformed, which, after having passed through the\\nfiercest ordeals, has remained almost without change\\nto our day. It has been indeed covered up, and to\\nall appearance lost, in the times of European bigotry\\nand ignorance schoolmen and churchmen have alike\\nassailed it but with the vital principle of truth, it\\nhas remained untouched by the ruinous hand of\\nTime, amid exploded systems of Ethics, false specu-\\nlations of Philosophy, and the cunning allegories\\nof Heathen mythology. The Analytics of Aristotle\\nform the cyclopaedia of Logic in this age, as in all\\nformer periods.\\nAfter many years of patient investigation Aristotle\\nestablished the Dictum de omni et nullo, of which\\nthe first part, de omni, refers to all affirmative reason-\\ning, and the second, de nuUo, to all negative reason-\\ning. Stated by the use of ordinary symbols they\\nwould be written as follows", "height": "3195", "width": "1947", "jp2-path": "elementsoflogic00copp_0041.jp2"}, "42": {"fulltext": "36 LOGIC.\\nTlie Dictum of Aristotle.\\nBe omni.\\nDe nullo.\\nAll A. is B.\\nNo A. is B.\\n(1) (2)\\n(1) (2)\\nAll or some C. is A.\\nAll or some C. is A.\\n(1) (2)\\n(1)\\nTherefore all or some C.\\nisB.\\nTherefore no C. is B., or some C.\\n(2)\\nis not B.\\nOr if stated by a geometrical notation, as all syllo-\\ngisms may be stated\\nBut to explain the dictum practically, it bas been\\ntranslated thus\\nWhat eve? may he predicated of a ivhole class, may\\nalso he predicated of all or any of the individuals con-\\ntained in that class.\\nTo predicate means to affirm or deny.\\nThus in the dictum de omni. In the major premiss\\nwe predicate or affirm B. of the whole class A.\\nIn the minor premiss we assert that all or some C.\\nis- an individual or a number of individuals included\\nunder the class A.\\nAnd in the conclusion we predicate B. of the indi-\\nviduals, as we did in the major premiss of the whole\\nclass to which they belong.\\nThis simple dictum of Aristotle is the groundwork\\nof the syllogism, and the syllogism is the universal\\n^Prcedico are, not jr dico cere.", "height": "3201", "width": "1990", "jp2-path": "elementsoflogic00copp_0042.jp2"}, "43": {"fulltext": "THE DICTUM OF ARISTOTLE. 37\\nprinciple of reasoning. It is sufficient in this place\\nto state the fact it will be proven hereafter. The\\npropositions of which the syllogism is composed are\\nfurther analyzed. A proposition consists of two terms\\nand a copula, of which the first term is called the sub-\\nject, the last the predicate, and the connexion between\\nthem is the copula.\\nsuhj. cop. predic.\\n(men) (are) (mortal).\\nsubj. cop. pred.\\n(men) (are not) (trees.)\\nIt has been said that the dictum of Aristotle is the\\ngroundwork of the syllogism, and that the syllogism\\nis the universal principle of reasoning it must be also\\nremarked that every valid argument, no matter what\\nmay be its original form, may be put under the form\\nof the syllogism, and to it in that form the dictum may\\nbe directly applied and, on the other hand, if any\\nargument cannot be reduced to this form, it is invalid.\\nThus this dictum forms not only the vehicle of correct\\nreasoning, but is a sure test of error in Logic. We shall\\nconstantly recur, in considering every form of argu-\\nment, to this test.\\nThe reasons why in mathematical investigation we\\nuse letters, and in arithmetic numbers, are first, to\\nexpedite and simplify the work, and secondly, to gene-\\nralize it. For the same purposes we use symbols in\\nLogic. If, for example, I write the syllogism", "height": "3195", "width": "1939", "jp2-path": "elementsoflogic00copp_0043.jp2"}, "44": {"fulltext": "38 LOGIC.\\nAll good men are happy,\\nJohn is a good man,\\nTherefore, John is happy\\nI limit my argument entirely to the particular of John\\nbeing a good man and he{7ig happy whereas, if I write\\nAll A. is B.,\\nC. is A.,\\nTherefore C. is B.\\nI propose a general formula which will apply to\\nmany cases according to the subject and the matter\\nof inquiry. It will be well for the student to frame\\nparticular examples under the general formula, and\\nthus at once to fix the form in the mind and accustom\\nhimself to the practical applications of the system\\nof Logic to particular cases.\\nBesides the dictum of Aristotle, to the form of which\\nevery valid argument may be reduced, there will be\\ngiven hereafter a series of rules for detecting fallacy\\nand for determining the validity of an argument when\\nit is not exactly in this form, and, by means of these,\\nthe logical student may defend himself against the\\nsubtlest sophistry, holding Aristotle s dictum in re-\\nserve as a final test. Where one who is ignorant of\\nLogic is obliged to use much efi ort and circumlocution\\nto determine the validity or invalidity of an argu-\\nment, and is in great danger of error in the process,\\nthe logicia^n, at once and without inquiry into the\\nsubject-matter of discourse, applies his tests to the", "height": "3218", "width": "1979", "jp2-path": "elementsoflogic00copp_0044.jp2"}, "45": {"fulltext": "THE DICTUM OF AEISTOTLE. 39\\nframework of the reasoning, and indicates infallibly\\nthe defect in the argument. And so deciding as to\\nthe validity or invalidity of the general formula as\\nexpressed by the symbolical letters A., B., C, he has\\nonce for all decided for each particular example which\\ncan fall under that formula.\\nIn concluding this brief analysis of Logic, let us\\nrecapitulate. Logic is the Art of Reasoning there\\nis but a single universal principle of Reasoning its\\nbasis is the dictum of Aristotle, and its simple form\\nis the syllogism.\\nThe syllogism is composed of two premisses and a\\nconclusion each of these is a proposition and each\\nproposition consists of three parts, two terms and a\\ncopula. It is now our purpose to examine these con-\\nstituents of Logical formulae in the inverse order,\\nbeginning with terms.", "height": "3198", "width": "1854", "jp2-path": "elementsoflogic00copp_0045.jp2"}, "46": {"fulltext": "40\\nLOGIC.\\nCHAPTER III.\\nA SYNTHESIS OF LOGIC.\\n(11.) Of certain operations and states of the\\nmind in the process of Argument,\\nIn proceeding to the synthesis of the reasoning\\nprocess, we must first consider certain operations and\\nstates through which the mind passes in approaching\\nan argument. Logicians have enumerated many\\nwhich are so nearly related to each other, that we\\nmay reduce them to three.\\nThese are 1st. Apj^reJiension 2d. Judgment\\n3d. Reasoning, or Ratiocination. As a preparation\\nfor these in their order, Attention has been called the\\nprimary state but this is self-evident. Apprehension\\nis a pure mental consciousness of the existence of an\\nobject arising from perception perception being the\\nprocess of conveying an impression to the mind,\\nthrough the senses. We must first perceive an object\\nbefore we can apprehend it.\\nBy the five senses of the body we have a know-\\nledge of the world around us the first step in obtain-\\ning this knowledge, is sensation, or the impression on", "height": "3189", "width": "1940", "jp2-path": "elementsoflogic00copp_0046.jp2"}, "47": {"fulltext": "A SYNTHESIS OF LOGIC. 41\\nthe organ of sense; sensation is conveyed in a myste-\\nrious, inexplicable manner to the mind, to produce\\nperception and as soon as we have perceived the\\nobject by this union between the mind and the senses,\\napprehension or an intelligent knowledge of it is\\nproduced.\\nApprehension is simple or complex.\\nSimple Apprehension is the notion of one object or\\nof several which bear no relation to each other and\\nthis notion is expressed generally by one word, as\\nJohn, man, river or by many connected by conjunc-\\ntion, John and Peter the man and the hoy.\\nComplex apprehension is the notion we form of\\nseveral objects which bear a relation to each other,\\nas a man ivalking, a bundle of rods.\\nWhen an act of Apprehension is expressed in lan-\\nguage, it is called a term.\\nBut, whereas certain words, which express terms,\\nare equivocal or ambiguous, it must be observed that\\nLogic deals only with general or abstract terms, and\\nhas nothing to do with their distinctness or indistinct-\\nness. It only takes for granted that a term is dis-\\ntinct and unambiguous. A Logical term then is a\\nsimple, unequivocal act of apprehension.\\n2. Judgment.\\nJudgment is that operation of the mind, by which,\\nif we have two objects of apprehension or terms, both\\nknown to us, we declare that they agree or disagree\\n4*", "height": "3198", "width": "1939", "jp2-path": "elementsoflogic00copp_0047.jp2"}, "48": {"fulltext": "42 LOGIC.\\nwith each other. Thus, if I know who \u00e2\u0096\u00a0^John is,\\nand what a hero is, I may declare that\\nJohn is a hero.\\nOr that John is not a hero.\\nJudgment is therefore of two kinds, affirmative\\nwhen the two terms are declared to agree; and nega-\\ntive, when they are declared to disagree.\\nAn act of Judgment when expressed in language,\\nis called a proposition.\\nAnd here, also, it must be observed, that Logic\\nonly takes cognisance of abstract propositions, which\\nare expressed by logical formula, and has nothing\\nto do with their truth or falsity. It takes for\\ngranted indeed, that, when a proposition is stated, it\\nis true.\\nFor example, if the proposition be A. is B. it is\\nassumed by Logic, that A. is in reality B., and thus,\\nif, when this general formula be translated into a par-\\nticular proposition, it prove to be false. Logic is not\\nresponsible for the falsehood, nor for the error which\\nfinds its way into an argument by reason of the use of\\na false premiss. Much error has arisen through the\\nmistake of supposing that Logic had to do with Lan-\\nguage directly, and with the judgments expressed in\\nlanguage but it is just such an error as would lead\\nus to assign such values to the unknown quantities in\\nany algebraic formula, such for instance as y 2px\\n0, as would destroy the equation. Algebra pre-", "height": "3201", "width": "1989", "jp2-path": "elementsoflogic00copp_0048.jp2"}, "49": {"fulltext": "OPERATIONS OF THE MIND IN REASONING. 43\\nsupposes the equation to be just, and develops only\\nsuch values of x and y as will establish it. The\\nLogical formula is as abstract and general as this,\\nand Logical propositions are always assumed as true.\\n3. Ratiocination.\\nRatiocination is that act of the mind by which,\\nhaving two or more acts of judgment, or projjositions,\\nwe pass to another or others founded upon them and\\ngrowing out of their combination.\\nThus if we have the two propositions\\nAll men are mortal,\\nCcesar loas a man,\\nwe have, as an inference or fact implied in these two\\npropositions, and deduced from their combination, the\\nfinal proposition, QoiBar was mortal.\\nAn act of ratiocination when expressed in lan-\\nguage is called an argiivient and an argument when\\nreduced to its simple logical form is called a syllogism.\\nThat simple logical form demands a certain order in\\nthe premisses and the conclusion.\\nIf now we examine the syllogism\\nMajor premiss. A is B Men are mortal.\\nMinor premiss. C is A Ceesar is a man.\\nConclusion. C is B Csesar is mortal.\\nwe shall perceive that it consists of three propositions,\\nwhich are called the major and minor premisses and\\nthe conclusion and three terms represented by A.,", "height": "3195", "width": "1955", "jp2-path": "elementsoflogic00copp_0049.jp2"}, "50": {"fulltext": "44 LOGIC.\\nB., and C, each term being used twice in the syllo-\\ngism. The term which occurs in the major premiss\\nand the conclusion, (B.) is called the major term that\\nwhich occurs in the minor premiss and the conclusion,\\n(C.) the minor term, and that which is found in both\\npremisses (A.) the middle term.\\nExtended Ratiocination is conducted by the com-\\nbination of many of these syllogisms, or their conclu-\\nsions, according to Logical laws.", "height": "3222", "width": "2003", "jp2-path": "elementsoflogic00copp_0050.jp2"}, "51": {"fulltext": "OF TERMS. 45\\nCHAPTER IV.\\n(12.) Of Terms.\\nA TERM has been defined an act of ap2?reJiension\\nexpressed in language^ and may be either simple or\\ncomplex.\\nA simple term is the name of a single object of\\napprehension, and is generally expressed by one word,\\nas man^ house, field.\\nA complex term is the expression of several objects\\nof apprehension with the relation which they sustain\\nto each other, as a good hoy, a horse running.\\nIt is evident that the name of a term is arbitrary,\\nand of use only to convey the apprehension to another,\\nas in different languages the terms which express the\\nsame object of apprehension will be different words\\nthus we have the object we call horse, expressed in\\nFrench by the word cheval, and in Spanish by the\\nword cahdllo. Words then, it must be remembered, are\\nnot terms, but are arbitrary signs for conveying and\\nusing terms.\\nBut language, or the use of words, is necessary", "height": "3195", "width": "1931", "jp2-path": "elementsoflogic00copp_0051.jp2"}, "52": {"fulltext": "46 LOGIC.\\nto the form of reasoning, as no reasoning can bo ap-\\nplied and tested until it assumes the dress of language.\\nWhen a word is capable of being used alone as a\\nterm, it is said to be Qategorematic^^ and when it needs\\nthe assistance of other words to constitute with it a\\nte:-m, it is called Syncategorematic. Thus ma7i, horse,\\nJolin^ are categorematic words liere^ gave^ and, are\\nsyncategorematic.\\nBy a casual examination of the different parts of\\nspeech we shall find\\n1st. Of the noun That it is only categorematic\\nwhen in the nominative case the possessive mans\\nrequires another word denoting the thing possessed,\\nand the objective a word which governs it.\\n2d. Of the adjective That it is syncategorematic\\nfor, although we say John is good, w^e understand\\nman or hoy after good.\\n3d. Of the verb That it is, so to speak, more than\\ncategorematic, since it contains often the copula and\\nthe predicate as, the man walks in this sentence\\nwalks is equivalent to is walking, in which is is the\\ncopula, and walking the predicate.\\nThe infinitive mood is often in reality not a verb,\\nbut a noun in the nominative case. Thus the sen-\\ntence To die for one s country is happiness means\\nDeath for ones country is happiness; To die being\\nfully expressed by Death.\\nKarr]y6prina sometbing alleged or aflBrined.", "height": "3201", "width": "1971", "jp2-path": "elementsoflogic00copp_0052.jp2"}, "53": {"fulltext": "OF TERMS. 47\\n4th. Of the remaining parts of sjoeech we see at a\\nglance that they are syncategorematic, and are only\\nused in connexion with other words to constitute\\nterms. The word which has the form of the present\\nparticijyie is sometimes an infinitive^ and sometimes a\\nnoun; we might substitute it in the last example\\ngiven as a case of either. Dying for one s country is\\nhappiness, is equivalent to both the forms given.\\n(13.) Division of Simple Terms.\\nSimple terms are divided into singular and common.\\nA singular term is that which expresses a single\\nindividual, and is usually the name of a person, place,\\nor thing as John, Philadelphia, the Delaware.\\nA common term is that which expresses any indivi-\\ndual or individuals of a whole class as a man, the men,\\nan army. To make a common term singular, we prefix\\nthe demonstrative pronoun tliis or that, as this man,\\nthat iHver, which is equivalent to stating the name of\\nthe man or river as, This man is John That river is\\nthe Delaware. Common terms stand for classes, and\\nare sometimes called appellative, as giving name or\\nappellation to many individuals.\\nThey thus are of great aid to science, in that, when\\nmany common properties have been discovered in a\\ngreat number of individuals, and their distinctive\\npeculiarities have been discarded, they may all be\\ncalled by one name, and that name will be a common", "height": "3187", "width": "1915", "jp2-path": "elementsoflogic00copp_0053.jp2"}, "54": {"fulltext": "48 LOGIC.\\nterm when this is in view a common term is called,\\naccording to its comprehension, genus or species.\\nCommon terms are further distinguished accord-\\ning to their matter, into abstract and concrete.\\nAn abstract term is an ideal word, expressing an\\nabstract property capable of inherence in an object,\\nand yet without reference to that object. Thus hard-\\nness, length, beauty, are abstract terms, which inhere\\nin many objects, but do not indicate any particular\\none.\\nA concrete term is one which presents to the mind,\\nat once, the property and the existence of the object\\nin which it inheres. Thus hard, lo7ig, beautiful, are\\nconcrete terms, implying certain objects which are\\nhard, long, or beautiful.\\nConcrete terms are also called denotative and con-\\nnotative, because they denote the abstract proioerty,\\nwhile they connote or imply in their signification the\\nbody or object to which it belongs. Thus hardyiess,\\nbeing an abstract term, is also an ideal noun the\\nmind rests upon the vague idea, because it indicates\\nnothing farther but when hard is mentioned we feel\\nthe right to ask, what is hard f the answer is stone.\\nThus the concrete term hard has denoted the quality\\nof hardness, and connoted stone as the object in which\\nthat quality inheres.", "height": "3190", "width": "1951", "jp2-path": "elementsoflogic00copp_0054.jp2"}, "55": {"fulltext": "OF TERMS. 49\\n(14.) Quality and Quantity of Terms.\\nTerms are further divided according to their quan-\\ntity and quality.\\nThe quality of a term is the mode or manner in\\n\u00e2\u0080\u00a2which it expresses an act of apprehension.\\nTerms are said to be synonymous under this divi-\\nsion, when thej express the same act of apprehension\\nbut by common usage this exact meaning is departed\\nfrom, and synonymous terms now mean those which\\nexpress different shades of meaning thus happiness\\ndjudi felicity are synonymous terms, and yet their ety-\\nmology teaches us a difference in their meanings\\nthe former attributing pleasure to luck or fortune,\\nand the latter simply asserting a state of unalloyed\\npleasure.\\nIncompatible terms are those which cannot be used\\nas predicates of the same subject at the same time\\nthus hot and cold asleep and awaJce.\\nPositive terms are those which state the real exist-\\nence of the objects they stand for. The opposite of\\nthese are negative terms, or those which deny the\\nexistence, or assert the absence of certain objects or\\nattributes.\\nThere is a class of terms called Privative^ w^hich\\nare often confounded with negative terms but there\\nis a real and important difference between them. A\\nprivative term expresses, that some quality or attri-\\nbute usually belonging to the class, is wanting in some\\nft D", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0055.jp2"}, "56": {"fulltext": "5U LOGIC.\\nindividuals of that class thus dumb, idiotic, are pri-\\nvative terms, since their very names call to the mind\\nthe fact that man generally is gifted with speech and\\nreason.\\nTerms are divided according to their quantity into\\nmany distinct classes, according to their number and\\ndimensions.\\nThus we have the common division of numeral and\\nordinal, as twenty, a hundred, tiuo positive (in its\\ngrammatical sense), comparative and superlative terms,\\nas good, better, best and that which is more truly a\\nlogical division into distributed and undistributed:\\na distributed term being one the whole of which is\\nconsidered, and an undistributed term one in which\\nonly a part is taken, this part being usually an inde-\\nfinite part, expressed by such words as some, few,\\nseveral, c. All men is a distributed term, some men,\\nan undistributed term.", "height": "3191", "width": "1965", "jp2-path": "elementsoflogic00copp_0056.jp2"}, "57": {"fulltext": "OF TERxMS. 51\\nCHAPTER y.\\nOF THOSE OPERATIONS IN LOGIC WHICH RELATE TO\\nTERMS.\\n(15.) Abstraction and Generalization.\\nAbstraction consists in drawing off and consider-\\ning one or more of the properties of an object to the\\nexclusion of the rest. Thus we use abstraction \u00e2\u0080\u00a2when\\nwe observe the colour and odour of the rose, disregard-\\ning its other characteristics. If we abstract the\\ncolour and odour of one rose, then of another, and so\\nof many, and finding these alike for all, call them all\\nby one common name Rose^ we are said to generalize.\\nGeneralization then consists in disregarding the\\ndifferences between many objects which are alike in\\ncertaiyi properties, and calling them by a common\\nname, by reason of their resemblance or identity in\\nthese properties.\\nWe may abstract, it is evident, without performrhg\\nthe other process of generalizing, but we cannot\\ngeneralize without first abstracting in the general\\ncase, however, we abstract for the purpose of gene-\\nralizing. It is by these two processes that we obtain\\ncommon terms, or the names of classes. All these", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0057.jp2"}, "58": {"fulltext": "52 Looro.\\ncommon terms are the result of higher or lower pro-\\ncesses of generalization. Thus, by a low generaliza-\\ntion, we obtain tea-rose, by a higher, rose, by a higher\\nstill, floiver, and by one step farther, vegetable, c.\\nBut common terms, as classes, are further dis-\\ntinguished into species and genera and, as expressive\\nof certain things belonging to the species and genus,\\nthey are also divided into the differentia, property,\\nand accident. Some writers, in considering the sub-\\nstance of a term, have called the object for which it\\nstands, the essential part or the essence.\\n(16.) Species, Genus, and Differentia.\\nA species is a class obtained by generalization,\\nwhich includes only individuals or subordinate classes,\\nand is itself included in a genus as an Arabian horse\\nis a species of horse horse is a species of quadruped\\nquadimped is a species of animal. A genus is a class\\nobtained by a higher generalization, which compre-\\nhends under it two dr more species as animal is the\\ngenus alike of quadruped and biped, ciuadruped is the\\ngenus of horse, coiv, deer, c., and biped the genus of\\nman, c.\\nIt is evident that in one sense the species implies\\nmore than the genus as, for instance, if quadruped\\nbe the genus and horse the species, horse will contain\\nall the signification of quadruped, and also the dis-", "height": "3176", "width": "1941", "jp2-path": "elementsoflogic00copp_0058.jp2"}, "59": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 53\\ntinctive signification of liorse as to shape, size, habits,\\nuses, c. which latter does not belong to quadruped.\\nFor this reason the species is said to express the\\nwhole essence of the object, while the genus expresses\\nonly a part of the essence, and that the material part.\\nThus, man expresses the whole or complete essence\\nof the animal so called, while animal expresses only\\nthe comprehensive or material part of the essence\\nwhich only limits him to an animate existence.\\nThe differentia of an object is the formal or dis-\\ntinguishing part of that object, and divides it from a\\nclass to which it does not belong and, when united\\nwith the genus or material part, forms ivith it the\\nspecies or whole essence. Thus, if man be the species,\\nand animal the genus, rational would be the differ-\\n(species) (differentia) (genus)\\nentia, and we should have man rational animal.\\nBy which it appears that although the genus compre-\\nhends this species and many others, the species really\\nimplies, although in a different sense, more than the\\ngenus, viz., the genus and differentia.\\n(17.) Property and Accident.\\nThus, having shown the relations between the genus,\\nor the whole essence, the species, and the differentia,\\nparts of the essence, each of which is expressed by\\na common term, we come to consider those things\\nwhich are or may be joined to the species or essence.\\nThey are divided as follows", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0059.jp2"}, "60": {"fulltext": "54 LOGIC.\\nI. Property^ which is joined universally to the\\nessence, and thus must be asserted as belonging to\\nevery individual of the species and 2d. Accident,\\nwhich is joined only contingently, that is, to one indi-\\nvidual or certain individuals of the species, and not to\\nthe whole species.\\nProperty is of two kinds. 1st. That which is uni-\\nversal, or belonging to every individual of the species,\\nhut not peculiar to the species, as respiration, which,\\nalthough it belongs to all men, is not confined to the\\nspecies man. 2d. That which is universal and pecu-\\nliar, as the power of intelligent speech, which, while\\nman, as a species, possesses it, is peculiar to man.\\nSome writers have erred in enumerating a third kind,\\nviz. peculiar hut not universal, as, for example, to\\nhe able to he a poet. But this violates our definition,\\nsince, if it belong to some individuals and not to the\\nspecies, it ceases to be a property, and becomes an\\naccident.\\nII. Accident is something joined contingently to the\\nspecies, or belonging only to certain iiidividuals of it.\\nAccident is of two kinds separable and insep arable,\\nA separable accident is a circumstance which may be\\ndetached from the individual, without affecting his\\nidentity or altering our general conception of him as\\nJohn is walking, or is lying doivn in which examples\\nthe accidental circumstance of ivalking or lying down\\nis not a necessary part of the individual, but may be", "height": "3191", "width": "1976", "jp2-path": "elementsoflogic00copp_0060.jp2"}, "61": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 55\\ndetached from him, so that we may still conceive of\\nhim as doing neither.\\nAn inseparable accident is one which cannot be\\ndetached from the individual; as, horn in Phila-\\ndelphia; horn in 1800.\\nIt is by means of such inseparable accidents that\\na man is described or his history written but it must\\nbe remarked that this phraseology is rather conve-\\nnient than exact, for, as soon as the event which we\\ncall a separable accident occurs in the life of an indi-\\nvidual, it really becomes inseparable. Thus, if John\\nwalked to the city on a certain day, or, being unwell\\nafterwards, was It/ing down in consequence, we can\\nno more detach these facts from his history, than we\\ncan the event of his being horn in a certain place, and\\nat a certain time.\\nHaving now illustrated the meanings of genus, spe-\\ncies, essence, differentia, property, and accident, let\\nus, for convenience and clearness of illustration, write\\nout a sentence embodying all these uses of common\\nterms, as a model, by which the student will easily\\nframe other examples for himself. This sentence will\\nalso embody the diflerent processes of generalization.\\n(property, universal\\n(Individual) (species) (dififerentia) (genus) but not peculiar)\\nJohn is a Man, a rational animal, who breathes,\\n(property universal and peculiar) (separable accident)\\nhas the faculty of speech, is lying on the sofa, and was\\n(inseparable accident)\\nborn in Philadelphia.", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0061.jp2"}, "62": {"fulltext": "56 LOGIC.\\nThe logical name given to every common term re-\\npresenting a genus, S2:)ecies, differentia, property, acci-\\ndent, is predicable viz., something which may he pre-\\ndicated no other terms than these are predicable.\\n(18.) Of the different orders of Genera and\\nSpecies,\\nA summum genus or highest genus is the highest\\nclass of all, and has no genus above it.\\nA term which expresses at once 2^ genus and a species\\nis called a subaltern genus and species. For example,\\nquadruped is a genus of horse and a species of animal.\\nIn the descending scale from the summum genus, the\\nsuccessive or inferior genus is called a subaltern genus.\\nIn the ascending scale from the lowest species, it is\\ncalled the subaltern species.\\nWhen a genus is divided into its species they are\\ncalled co-ordinate or cognate species, to indicate\\nthat they are not subordinate to each other. Thus\\nif quadruped be divided into horse, cow, lion, as re-\\npresenting the equine, feline, and vaccine races, these\\nwould be cognate species.\\nA species which contains beneath it no other species,\\nbut only individuals, is called an infima or loivest spe-\\ncies. In any scientific investigation, however, ranging\\nbetween any two limits although not absolutely the\\nhighest and loivest, it is usual for convenience to call\\nthe highest limit named, summum genus, and the low-\\nest, infima species; as though we should say Let", "height": "3201", "width": "2017", "jp2-path": "elementsoflogic00copp_0062.jp2"}, "63": {"fulltext": "OPERATIOXS WHICH RELATE TO TERMS. 57\\nA be the summum genus, and C the infima species,\\nduring this investigation. There are also in pommon\\nuse the phrases proximum genus and remote genus,\\nthe first of which means the genus next above, and the\\nsecond, a genus farther removed from, the species in\\nquestion. Thus quadnqoed is the proximum, and\\nanimal the remote genus of horse. It is necessary\\nthat the proximum genus should be the genus next\\nabove the species in question but the remote genus may\\nbe any one farther removed, and not necessarily the\\nsummum genus, which is of course the 7nost remote.\\nIt must be observed that the use of a common term,\\nas either species, genus, differentia, property, or acci-\\ndent, is a relative use and because it is used with one\\nof these significations in one sentence, this does not\\ndeter us from using it with quite another meaning, on\\nanother occasion. Thus if we take the word red, we\\nshall find we can make it serve as each, in turn.\\nThe colour Red is a genus under which as species\\nare ranged pink, scai^let, crimson, vermillion, c., the\\ndiff erent kinds of Red.\\nRed is a species of the genus colour, and ranges\\nwith white, blue, yellow, c., as cognate species.\\nRed is a differentia of the Red rose, which dis-\\ntinguishes it from other roses. Red is a property of\\nhlood and an accident of a house, separable if it be\\npainted red, inseparable if it be built of Red stone.\\nAnd thus in analyzing any sentence we must be care-", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0063.jp2"}, "64": {"fulltext": "58 LOGIC.\\nfill to ascertain the real value of the common terms\\nemployed.\\n(19.) Realism and Nominalism.\\nWhile upon the subject of common terms, it is well\\nto refer to the long-standing controversy between the\\nRealists andthe Nominalists^ which, although it became\\nstrangely intermixed with theology and church polity,\\nhad its origin in the significance of a common term.\\nIt will be referred to more at length in the historical\\nview. The Realists contended that every common terra\\nwas the name of something really existing that a\\ngenus and a species were real things, while the Nomi-\\nnalists believed that we obtained common terms merely\\nto express a certain inadequate undefined notion of\\none individual, which we apply to many.\\nIt would seem to be a trivial subject for controversy,\\nbut the more w^e examine it, the more difficult and\\nsubtle it appears. Like many subtle controversies, it\\nseems to be of little consequence in which way it could\\nbe decided but it had, to the disputatious Greeks,\\nand the more disputatious Schoolmen, a charm on\\naccount of its subtlety, which its value could not\\nsecure to it.\\n(20.) Definition of Terms-\\nDefinition is applied to terms in their logical use,\\nand means describing them in such a manner as to\\ndistinguish them from all and any other terms.\\n*c?e and finio, more x am oialy finis.", "height": "3196", "width": "1988", "jp2-path": "elementsoflogic00copp_0064.jp2"}, "65": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 59\\nAs much error arises from the indistinctness of\\nterms, and the fact that different persons employ them\\nin different meanings, just definitions which may bind\\nboth parties in a controversy are very important.\\nA definition is usually put in the form of a catego-\\nrical proposition, of which the subject is. the term to\\nhe defined^ and the predicate is the description or dis-\\ntinct explanation. Thus in the example Man is a\\nrational animal^ the whole sentence is called tlie defi-\\nnition. This 13 not, however, strictly speaking, cor-\\nrect as the predicate alone rational animaV defines\\ni man, as if in answer to the question what is the\\ndefinition of man\\nThe first division of definition is into two kinds,\\nEssential and accidental Essential definitions are\\nfurther divided into physical and logical.\\nThe second division of definition is into nominal\\nand real. Eefore explaining the meaning of these\\ndivisions, we shall arrange them, for the sake of con-\\nvenient reference, into a tabular statement.\\nDEFINITION.\\n1st division (divided into) 2d division\\nN\\nEssential Accidental Nominal Real\\n(div. into)\\nPhysical Logical\\nAn essential definition is one which presents to us", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0065.jp2"}, "66": {"fulltext": "6 0 LOGIC.\\nthe principal parts of the essence of the thing defined\\nthus, a steamboat is something consisting of hull,\\nengine, wheel-houses, smoke-pipe, c. or, again, it\\nis a vessel for water transportation propelled by\\nsteam. In each case the form of our essential defi-\\nnition would, be induced by the character of the per-\\nson asking the definition, and according to the infor-\\nmation he desired, but always in terms of the essential\\n2)arts of the object for which the term stands. But\\nit must be particularly observed that these principal\\nor essential parts are of two kinds widely different\\nfrom each other physical parts or parts which are\\nactually separable by the hand^ and Logical parts, or\\nthose which are only divisible by the mind. To ex-\\nplain, ?L physical essential definition of a ship would\\nbe an object which consists of hull, masts, cordage,\\nc., being the parts into which it may be physically\\ndivided while the logical parts which would consti-\\ntute a logical esseiitial definition would be the genus,\\nviz., ocean vessel and differentia, viz., of pecu-\\nliar build; which, as we have seen, when combined\\nmake up the species ship.\\n(species) (genus) (differentia)\\nA ship is an ocean-vessel of peculiar build.\\nA logical essential definition then, in every case,\\nconsists of the genus and differentia. Logic is con-\\ncerned with logical definitions alone, but examines\\nthe others to distin2;uish between them and lo2;ical", "height": "3201", "width": "1934", "jp2-path": "elementsoflogic00copp_0066.jp2"}, "67": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 61\\ndefinitions. And it is likewise true that the physical\\nand logical definitions sometimes coincide, but this is\\nof rare occurrence.\\nAn accidental definition, or description, as it has\\nbeen technically called, consists in presenting the cir-\\ncumstances belonging to an object, and these are its\\nproperty or accident as these are generally more de-\\nscriptive of an animal or object than the material part\\nwhich is the genus, or the differentia which distin-\\nguishes the species in question only from its co-ordi-\\nnate species.\\nFrom what has been said before, it will appear that\\nin describing a species we can only use properties, as\\naccidents attach alone to individuals, while properties\\nbelong to every individual of a whole species we\\nshould use, besides, properties which are universal and\\njjecidiar, since, as they belong to every individual of\\nthe species, and to none out of it, we thus find its own\\ncharacteristics whereas if we used the properties\\nwhich were universal but not peculiar, we should only\\nknow characteristics which marked that species in\\ncommon with others, and thus not define it. Thus if\\nwe should describe man as a being who lived and\\nbreathed, this would not define or describe }i\\\\m. justly.\\nSo, too, in describing an individual, as for instance\\nin biographical notices, we should not use separable\\naccidents which are not a permanent and necessary\\npart of the object, but inseparable accidents which\\n6", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0067.jp2"}, "68": {"fulltext": "62 LOGIC.\\nbelong necessarily and permanently to it. For exam-\\nple, if we say William was the Duke of Normandy\\nwho conquered England in 1066, we describe him by\\nmeans of the inseparable accidents, viz., that he was\\nDuke of Normandy, and that he conquered England.\\n(21.) Nominal and Real Definitions.\\nWe come now to the second division of definitions,\\ninto nominal and real.\\nA nominal definition is one which gives the mean-\\ning of the term which is used as the name of the\\nthing. In brief, it defines the name. Thus, a tele-\\nscope is an instrument for viewing distant bodies.\\nThe photograph is a painting made by light on sen-\\nsitive plates. The decalogue is the table of the\\nten commandments.\\nA real definition analyzes and explains, not the\\nname of the thing, but the thing itself; enumerating,\\nbesides, all its important characteristics and proper-\\nties thus, a real definition for a telescope would be\\na treatise on the construction, powers, and uses of the\\ninstrument, and a real definition of the decalogue\\nwould be given only hg reciting all its commandments.\\nIn the investigations of science it is evident that\\nthe aim is to obtain real definitions, and the fuller\\nand more complete they are the greater their value\\nbut since in Logic we have only to do with the names\\nof things, and not with their subject-matter, or the con-\\nceptions which they convey to us, it is evident that", "height": "3220", "width": "1959", "jp2-path": "elementsoflogic00copp_0068.jp2"}, "69": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 63\\nwe only need nominal definitions and not real and\\nindeed, with regard to matters of general information,\\na nominal definition will be sufficient to settle the\\ngrounds of a controversy for while it is the name\\nthat indicates the individual or the class, the definition\\nexplains the name.\\nWe may even, sometimes, provided both parties to\\nan argument agree to do so, consider as a definition\\nsomething which is purely hypothetical^ but which still\\npartakes of the nature of a definition thus, for ex-\\nample, in an astronomical problem we say, let Q he\\nthe sun s place in the heavens; or in any case for\\npurposes of illustration, let so and so he so and so.\\nThis form of definition is purely relative for although,\\nin reality, C is not the sun s place, it is so relatively\\nto the other points on the diagram.\\nIt must also be observed that it is not necessary to\\nthe justness of a definition that it should refer to real\\nthings, as, for example, we define an unicorn to be\\nfahled animal, having hut one horn; and a phoenix to\\nbe a hird fahled to live ivithout a mate and to rise\\nfrom its own ashes.\\n(22.) Rules for Definition\\nSo important has the subject of definition been\\nconsidered, that Logicians have laid down three rules\\nfor it, to which, if we adhere, we shall insure just and\\nadequate definitions.\\n1st. The definition must give to the mind a clearer", "height": "3195", "width": "1931", "jp2-path": "elementsoflogic00copp_0069.jp2"}, "70": {"fulltext": "64\\nLOGIC.\\nconception than the name of the thing defined, or it\\nwill be useless.\\nIn most of the arts and sciences this consists in\\nputting a technicality into plain language, for those\\nwho are uninitiated but if I am asked to define cow,\\na word understood by every one, and say that cow is\\na ruminant quadruped, I violate the rule. In the no-\\nmenclature of science many technical terms give, in one\\nword, what it would require much circumlocution to ex-\\npress in common words. Accompanying this rule there\\nis the caution that the character of the definition should\\ndepend upon the subject and the persons addressed.\\n2d. The definition must be adequate that is, neither\\ninclude other things than those necessary to define, nor\\nexclude any necessary explanation of the thing defined.\\nThus, if I define bird to be an animal that moves\\nin the air by means of wings, I am too extensive in\\nmy definition as that would include other animals\\nthan birds, as bats, flying fish, c. and if I define\\nit to be a feathered animal that sings, that would be\\ntoo narrow, as some birds do not sing.\\n3d. The third rule is rather a caution which grows\\nout of the other two than a rule like them. It is, that\\nthe luords used in a definition should be sufficient and\\nof the proper kind to define the thing.\\nIf we use too many words, we confuse the meaning\\nand are liable to tautology if too few, we are liable to\\nobscurity. Thus, to say that a square is a four-sided", "height": "3222", "width": "2036", "jp2-path": "elementsoflogic00copp_0070.jp2"}, "71": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 65\\nfigure ivith equal sides, would be true but not definite,\\nas there may be drawn other parallelograms not right-\\nangled, with equal sides. If we say a parallelogram\\nis a four-sided figure ivliose opposite sides are equal and\\nparallel we use too many words, as the equality of\\nthe sides implies the parallelism, and vice versa.\\nIn the first case we err, because we do not exclude,\\nin our definition of the square, all other figures in\\nthe second, because we allow it to be supposed that\\nthere are four-sided figures whose opposite sides are\\nequal and not parallel.\\nThe examples taken are broader and more apparent\\nthan those in which faulty definitions are generally\\nused, but they render the error more obvious, and in-\\ndicate to us the character of the danger to be avoided.\\nIf we would see the practical necessity of defini-\\ntions, we need but consider a few of the vague and\\ninexact terms which we use in our ordinary speech,\\nand which it seems a prevailing fashion to distort in\\ntheir meanings. We shall recur to this subject under\\nthe general title of Verbal Fallacies, but may now\\ngive a few illustrations of the value of exact defini-\\ntions. Take for example such words as Necessity\\nand Necessary, which may mean either an accordance\\nwith the invariable law of God, or an obedience to\\nthe blind decree of fate, according to the belief or\\nscepticism of him who uses them. In its political sense,\\nthe adjective necessary has been said to be capable of\\n6* E", "height": "3195", "width": "1913", "jp2-path": "elementsoflogic00copp_0071.jp2"}, "72": {"fulltext": "(j^ LOGIC.\\ncertain degrees of comparison, as in the argument urged\\nin favour of the Bank of the United States,* in speak-\\ning of the means necessai-y for carrying out the provi-\\nsions of the Constitution, it was asserted that they may\\nbe cLassed under the three categories of necessary, very\\nnecessary, and absolutely and indispensably necessary.\\nSo also in religion, certain things are said to be gene\\nrally necessary to salvation, while others are said to bo\\nabsolutely necessa?^. Thus the technical sense of tho\\nword is entirely lost as that refers to an absolute\\ncondition, tvhich cannot but be, or cannot be otherivise,\\nand therefore does not admit of comparison. Or if we\\nwould see a strange, conglomerate example of indefi-\\nnite and erroneous terms, demanding a clear definition,\\ntake the war-cry of the French revolutionists,\\n^Liberty, .Equality, Fraternity no one word of\\nwhich can express to the people a distinct idea, or\\nwill bear the test of a clear definition.\\nIt has been a custom in nominal definitions to de-\\nfine one term by means of its synonym, borrowed\\nfrom another language. Although our language is, in\\nits structure and the great majority of its words,\\nAnglo-Saxon, still the large number of French and\\nLatin words which have been brought into it, have\\nformed terms synonymous with the original Saxon\\nbut, when they had become naturalized, as we had\\nno use for two words exactly synonymous, wisdom\\nKent s Commentaries, vol. i., Lect. 12.", "height": "3201", "width": "2042", "jp2-path": "elementsoflogic00copp_0072.jp2"}, "73": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 67\\nsuggested that they should exhibit shades of difference\\nin meaning, which did not originally belong to them\\nso that few if any words are justly defined by their\\nsynonyms. Besides, as a similar idea among any two\\npeople would have its differences drawn from their own\\npeculiarities of clime, and race, and manner of life and\\ngovernment, the synonyms when brought into the lan-\\nguage would often express great differences at once, and\\nwithout any effort on our part to cause them to do so.\\nAs a remarkable instance of this, let us see how very\\nwrong it would be to define our English word freedom^\\nby its synonym liberty^ which comes to us from the\\nLatin and yet, how many confound the two. Indeed\\nthese are historic words, and give us an insight into\\nthe times of their birth, wonderfully illustrative of\\nthe people and countries from which they came.\\nFreedom is the personal, individual independence and\\nright of every man, his free doom, i. e. free province or\\njurisdiction from his birth. Coming as it does from\\nthe Teutonic element in our language, it tells us of\\nthe free and independent Germans, who by their own\\nvalour, overturned the great fabric of the Roman\\nempire. They were men of the forest and mountain,\\ninhabiting no cities there were none in Germany till\\nafter the eighth century but only roving where were\\nthe lordliest spoils, and claiming them as the reward\\nof their personal /reec?om. On the other hand, liberty\\ntells us of the Roman cities, of the sway of the Roman", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0073.jp2"}, "74": {"fulltext": "68 Lor.rc.\\nempire, and of Roman licentiousness of a form of\\nmanumission, implying slavery; individuality merged\\nin citizenship to be a Roman citizen to have attained\\nthe post of honour, open to all advancement in diplo-\\nmacy and war. Nor is the spirit belonging to these\\nwords yet lost. While we cling like good citizens to\\nour liberty^ vouchsafed to us by the constitution of\\nthe country, as Americans, we much more desire to\\nkeep well guarded i^xdiA, freedom of opinion, of speech,\\nof action, which is our indefeasible right as men.\\nIn view of the importance of just definitions, let us\\nundertake no controversy, or expression of opinion in-\\nvolving a vague and indistinct term, without demand-\\ning a definition, and agreeing to use it during the\\ndiscussion.\\n(23.) Division.\\nIt is of great importance in the consideration of\\ncommon terms which stand for classes, that we should\\nbe able to divide them into all their several parts or\\nsignificates. An individual^ as its name indicates,*\\nis incapable of logical division. It is only a species\\nor genus, i. e. a class, in more general language,\\nwhich can be so divided.\\nDivision is of two kinds, physical and logical to\\nthese some writers add, im23roperly, numerical divi-\\nsion.\\nin and dividuus, fi-om divido, to divide.", "height": "3201", "width": "2045", "jp2-path": "elementsoflogic00copp_0074.jp2"}, "75": {"fulltext": "OPERATIONS WHICH RELATE TO TERMS. 69\\nPhysical division is the actual separation of tlie\\nphysical parts of which a thing is composed. It is\\nevident that an individual is capable of physical divi-\\nsion; thus, an individual tree^ as a certain oak, may\\nbe divided into trmik, hranclies, and these further sub-\\ndivided into hark, heart, leaves, c. an individual\\nman, as John, may be physically divided into head,\\narms, trunk, legs, c. With this kind of division\\nLogic has directly nothing to do.\\nLogical division, which cannot be applied to in-\\ndividuals, but only to classes, consists in separating a\\ngenus into its different species and a species into the\\nindividuals composing it and this in regular order\\nfrom the summum genus to the injima species. Thus,\\nthe genus tree would be logically divided into oak,\\nmaple, hemlock, fir, pine, elm, c. and the species\\noak, into red oak, white oak, live oak, scrub oak, c.\\nand each of these again into the individual trees com-\\nprising its kind.\\nIt will be evident that in a just division, each one of\\nthe parts denoting a species will be less than the\\nwhole number which make up the genus or any one\\nof the parts denoting an individual will be less than\\nthe whole number which make up the species or, as\\na test of the correctnesss of the division, we must be\\nable to predicate the summum genus of any one of\\nthe parts.\\nIf, for example, we have assumed tree to be the", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0075.jp2"}, "76": {"fulltext": "70 LOGIC.\\nsummiim genus, we must be able to predicate tree of\\noak^ or live-oak, or any individual live-oak.\\nIt is evident that the same term may be logically\\ndivided, according to race, into Caucasians, Malays,\\nc. according to creeds, into Buddhists, Jeivs, Ma-\\nhomedans, Christians, c. according to nation, into\\nAmericans, English, French, c. These cross-divi-\\nsions must not be mingled or confounded for ex-\\nample, to divide man into Caucasians, Mahomedans,\\nAmericans, c., would be false and useless division.\\nThe principle of division is best illustrated by a\\nscheme, or inverted tree, in which is arranged clearly,\\nsymmetric ally, and without arbitrariness, the different\\nparts of the division.\\nSCHEME OF DIVISION. SUMMUM GENUS.\\nTREE.\\nOak. Maple, Pine, c.\\nLive-Oak, White-Oak, Red-Oak, c. Sugar-Maple, Common-Maple.\\nIndividual Trees. Individual Trees.\\nIt may be well to observe particularly an auxiliary\\nphrase, according to, which we use to keep us from a\\nsimple but dangerous error. Man is divided not into\\nraces, creeds, nations, c., but according to these,\\ninto various parts thus\\nSUMMUM GENUS. MANKIND DIVIDED ACCORDING TO.\\nRace. Creed. Nation.\\nCaucasian, Malay, c. Jews, Christians, Mahomedans. English, French, German, c.", "height": "3201", "width": "2033", "jp2-path": "elementsoflogic00copp_0076.jp2"}, "77": {"fulltext": "DIVISION. 71\\nIt is evident that all the co-ordinate species must\\nbe on the same line or platform, that is, they must\\nhold the same relative position to the summum genus.\\nWe must be careful to omit no subaltern genus; and\\nwe must place each subaltern genus in its own rela-\\ntive grade. Thus, if we should place oak properly, in\\nthe division of tree, but should pass immediately from\\nthe genus ti ee to the species sugar maple, thus leaving\\nout the species maple, co-ordinate to oak, we should\\nmake an unequal and undue division. This would\\nbe placing one of the co-ordinate species on the same\\nlevel with one subordinate to it.\\nFrom what has been said, it will perceived that the\\nprocess of Division is exactly the opposite of Gene-\\nralization.\\nAs in Generalization, we disregarded the differ-\\nences between many individuals, or between many\\nspecies, and considered only the properties they\\nhad in common, that we might constitute them re-\\nspectively species and genus, calling them by a common\\nname; so in Division, we take the genus thus obtained\\nand add to it the several differences which we had re-\\nmoved in Generalization, and which distinguish its\\nparts, that we may call the parts thus enumerated by\\nseparate names.\\nThe two inverse processes of generalization and\\ndivision may be plainly illustrated by a scheme or", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0077.jp2"}, "78": {"fulltext": "72\\nLOGIC.\\ndouble tree and this may be made as full as we\\nplease thus, from individual trees we may generalize\\nto the genus tree or, from trees and shrubs and other\\nkinds of vegetation, we may generalize to the sum-\\nmum genus vegetable. The division will be of the\\nexact species, c., but in the inverse order.\\nSCHEME OF GENERALIZATION AND DIVISION.\\nJncHvidtial Trees. JiidividucU Trees. Individual Trees.\\nLive-Oak, Eed-Oak,, c. Sugar-Maple, Birdseye-Maple, c. Vniite-Pine, Tellow-Pine, c.\\nOak.\\nMaple.\\nPine.\\nTREE.\\nA\\nOak.\\nMaple.\\nPine.\\nLive-Oak, Red-Oak, c. Sugar-Maple, Birdseye-Maple, c. White-Pine, Tellow-Pine, o\\nIndividitaZ Trees.\\nIndividual Trocs.\\nIiidividudX Treee.\\nWhat has been called matlieraatical or numerical\\ndivision is in reality but a form of physical division\\nthus, I divide a loaf into slices, or an apple into pieces,\\nIjliysically, with or without regard to the equality of\\nthe pieces, or their sizes relatively to each other. If\\nthis equality or relation be observed, it may be called\\nnumerical division, but it is only an exact form of\\nphysical division as a half, a third, ten times as\\ngreat, c., c.", "height": "3201", "width": "2036", "jp2-path": "elementsoflogic00copp_0078.jp2"}, "79": {"fulltext": "RECAPITULATION. 73\\nBy a comparison of the subjects of Division and\\nDefinition^ it will be seen that division is, after all,\\nbut a systematic and practical kind of definition^ since\\nthere can be no better way to illustrate the meaning\\nof tree, than logically to divide it, before our eyes, into\\nall its species down to individual trees.\\nIt will be readily seen that the nature of the logical\\ndivision of terms will depend much upon the science\\nin which, they are used, and the principle according to\\nwhich they are to be classified. Thus an etlinologist\\nwould divide ??2 a; ^z^mcZ according to races; a theologian\\naccording to creeds and a statesman according to\\nnation. The principle of all the divisions would be\\nthe same, while the resulting cross-divisions, as we\\nhave seen, will be widely different.\\n(24.) Recapitulation.\\nIt will be well to recapitulate briefly what has been\\nsaid upon the subject of terms, and the various ope-\\nrations which concern them. We have shown,\\n1st. That a term is the expression of an object of\\napprehension, and have explained the different kinds\\nof terms, according to a regular division.\\n2d. That common terms are obtained by the pro-\\ncesses of Abstraction and Generalization.\\n3d. The distinction between genera^ species, and\\nindividuals, ^c.", "height": "3195", "width": "1923", "jp2-path": "elementsoflogic00copp_0079.jp2"}, "80": {"fulltext": "74 LOGIC.\\n4th. The Definition of terms, and just rules for\\ndefinition.\\n6th. Division of terms, with the difference between\\nphysical and logical division, and special considera-\\ntion of the latter.\\nThe next step will be to combine these terms into\\npropositions that is, from our knowledge of two of\\nthem to assert their agreement or disagreement.", "height": "3201", "width": "2018", "jp2-path": "elementsoflogic00copp_0080.jp2"}, "81": {"fulltext": "PROPOSITIONS. 75\\nCHAPTER YI.\\n(25.) Propositions.\\nA proposition^ is an act of judgment expressed in\\nlanguage, and consists of three parts, a subject, a\\npredicate, and a copula: the subject and the predi-\\ncate are called the terms or extremes of the propo-\\nsition.\\nThe subject, in the due order, is placed first, and is\\nthat of which something is predicated, i. e. affirmed\\nor denied.\\nThe predicate is that which is affirmed or denied of\\nthe subject.\\nThe copula is the uniting word which expresses\\nthe agreement or disagreement between the subject\\nand predicate and is always some part of the verb\\nto be. When the copula is affirmative, agreement is\\nexpressed, when negative, disagreement.\\nsub. cop. pred. sub. cop. pred.\\nA is B (Csesar) is (a tyrant.)\\nsub. cop. pred. sub. cop. pred.\\nA (is not) B (Caesar) (is not) (a tyrant.)\\nFrom propono something proposed or set forth for our acceptanca.", "height": "3195", "width": "1915", "jp2-path": "elementsoflogic00copp_0081.jp2"}, "82": {"fulltext": "76 LOGIC.\\nThe negative particle, it must be observed, is ahvays\\na part of the copula.\\nWhat appear, in our ordinary speech, to be simple\\npropositions, are sometimes inverted or elliptical forms\\nof expression, which must be put into simple logical\\nform before they can be considered as propositions.\\nThus we say I hope to see you, I desire to re-\\nmain and in these cases the subject is really placed\\nlast the true meaning being\\nsubj. cop. pred,\\n{To see you) is {the thing which Iliope^ or my\\nhope.\\\\\\nAs an example of another form of inversion, we\\nhave that which springs from the constant use of the\\nneuter pronoun it. Thus, in ordinary language, we\\nsay It is true that I think so. The true logical\\nform may be given thus\\nsubj. cop. pred.\\n(That I think so) is (a true thing).\\nMany writers have denied that there is such a thing\\nas a negative judgment and, consequently, that any\\nnegation attaches to the copula for they say that\\nthe proposition John is not happy is equivalent to\\nJohn is unhappy, w^hich indicates a positive sensation\\nor frame of mind, as well as the other but this is a\\nquibble about words, as there are propositions in which\\nthe negation cannot be thus destroyed, and such is\\nthe case with far the greater number. The positive", "height": "3201", "width": "2023", "jp2-path": "elementsoflogic00copp_0082.jp2"}, "83": {"fulltext": "PROPOSITIONS. 77\\nterm is generally limited and intelligible the nega-\\ntive unlimited and indefinite thus man^ is a term\\nwhich we can grasp, but not man^ includes all the\\nuniverse beside.\\nOf the Oopula. The copula may be always reduced\\nto the present tense of the indicative mood of the\\nverb to he, and consequently expresses neither past\\nnoY future time. Thus, Caesar ^vas the conqueror of\\nGaul, is equivalent to Caesar is the historic person-\\nage who conquered Gaul. I shall he glad to see\\nyou is the same as I am the person who will be glad\\nto see you, c. but as this reduction is in general un-\\nnecessary, we agree to call those propositions which are\\nexpressed in time other than the present. Very often\\nthe copula and predicate are expressed together in\\none word, as The sun shines here the word shines\\nmay be resolved into is shining, in which is is the\\ncopula, and shining the predicate. And sometimes,\\nin other languages, as the Latin or Greek, a proposi-\\ntion is conveyed in one single word, as amo, I love or\\nam loving, T^vrita^, I am striking but in every case,\\na proposition may easily be placed in such a form that\\nthe subject, predicate, and copula are distinctly stated.\\nBut this definition of a proposition, as a sentence\\nconsisting of a suhject, predicate, and copula, is evi-\\ndently a physical definition, and is not sufficient for\\nour purpose. The logical definition of Si j^^^oposition\\nis sentence which affirms or denies; here propo-", "height": "3195", "width": "1915", "jp2-path": "elementsoflogic00copp_0083.jp2"}, "84": {"fulltext": "78 LOGIC.\\nsition is the species^ sentence the genus, and which\\naffirms or denies is the differentia, or statement of\\nthe difference between this kind of sentence and all\\nothers. The word p7 oposition not having in its ety-\\nmology this strict meaning, it is very loosely used to\\nexpress almost every kind of sentence. We must be\\ncareful, in Logic, to limit it to the definition just\\ngiven. Hence, we should say that a categorical pro-\\nposition, in its grammatical sense, implies the indica-\\ntive mood, since absolute affirmation or denial is ex-\\npressed only by that mood. Thus are excluded, the\\nimperative mood or all commands, the subjunctive\\nmood or all hypothesis, the infinitive mood, which, as\\nits name indicates, is not a finite, uniting verb, but\\nonly a verbal noun.\\nIf we examine these moods a little more in detail\\nwe shall find, first, that even in the indicative mood,\\nquestions, or the interrogative form of that mood are\\nexcluded, for the use of a question implies that one\\nof the parts of the proposition is wanting, and that\\nwe depend upon the answer to supply it. Thus the\\nfirst and simplest form of the question is\\nIs A B z=il^ man mortal\\nif the answer be affirmative, then we have a right to\\nthe copula is, which before was wanting, and may write\\nA 2S B Man is mortal.\\nAnother form of the question is what is A? or\\nwhat is B? the answer to which will supply us with", "height": "3201", "width": "1938", "jp2-path": "elementsoflogic00copp_0084.jp2"}, "85": {"fulltext": "PROPOSITIONS. 79\\nthe predicate and subject respectively. With regard\\nto the suhjunctive mood there are, it must be observed,\\npropositions which assume that form and which are\\ncalled hypothetical, and they come under the class of\\ncompound propositions, as\\nIf A is B, Q is D.\\nIn almost every case the hypothesis is stated in the\\nindicative rather than the subjunctive mood thus\\nIf A zs B, C is J) rather than in the form\\nIf A 56 B, C ^vill he D.\\nOf the infinitive mood it may be observed that there\\nare various forms thus, to ride is pleasant, may be\\nrendered by riding is pleasant horseback exercise is\\npleasant plainly showing that with the verbal form\\nthere is a substantive value.\\n(26.) Projpositions divided into Simjple and\\nCompound,\\nIf now, we proceed to consider first the substance\\nof propositions, we shall find them divided according\\nto their substance into simple and compound.\\nA simple proposition is one which has but one sub-\\nject and predicate, united by the copula is or is not.\\nSimple propositions are also called categorical, that is\\nthere is simply affirmed or denied an agreement\\nbetween the subject and predicate.\\nA compound proposition is one which has more than\\none subject or more than one predicate, and may be\\nresolved into two or more simple propositions as", "height": "3187", "width": "1931", "jp2-path": "elementsoflogic00copp_0085.jp2"}, "86": {"fulltext": "80 LOGIC.\\nThe DeJmoare and the Schuylkill are rivers in Penn-\\nsylvania Compound propositions are further divided\\naccording to their substance into categorical, condition-\\nal, causal, and disjunctive,\\nA compound categorical proposition, like a simple\\ncategorical, affirms or denies the predicate siinj^ly and\\ncertainly of the subject; thus\\nAlexander, Ccesar, and Napoleon ivere ambitious\\nof military glory.\\nA conditional proposition consists of two simple\\ncategoricals united bj the conjunction if thus\\nIf A is B, Ois D,\\nIt is usual, for convenience, to place the conjunc-\\ntion first the first categorical A is B is then called\\nthe antecedent, and the other C is D the consequent.\\nA causal proposition is one in which the reason of\\nthe truth of a simple proposition is stated thus\\nBecause A is B, C is D.\\nA Disjunctive proposition is one in which one of\\ntwo simple propositions is asserted to be true thus,\\neither A is B, or C is D. This is done by the use\\nof the conjunctions either and or.\\nPropositions are still further divided according to\\ntwo of Aristotle s categories which will be considered\\nhereafter, i. e., according to their quantity and qua-\\nlity. In simple language Quantity considers of how\\nmuch of the subject the predicate is affirmed or\\ndenied as, some or all A is B.", "height": "3201", "width": "1932", "jp2-path": "elementsoflogic00copp_0086.jp2"}, "87": {"fulltext": "PROPOSITIONS. 81\\nAnd Quality regards the kind or manner of that\\npredication J i. e. whether it be affirmative or negative\\nwhether A is or is not B.\\n(27.) Quantity and Quality of Propositions.\\nThe quantity of a proposition is determined by the\\ncomprehension of its subject. If we assert that the\\npredicate agrees or disagrees with the whole subject,\\nthat is, all the significates which come under the\\nterm, the proposition is said to be universal^ thus,\\nAll men are mortal, No men are trees\\nare universal propositions, because the whole of the\\nsubject is considered. But if we assert the predicate\\nto agree or to disagree with only a fart of the sub-\\nject, the proposition is G2,]\\\\Qdi particular\\nSome men are hrave few men are good many\\nmen are not prudent are examples of particular pro-\\npositions.\\nThe quality of propositions we shall find also to be\\nof two kinds the quality of the subject-matter, and\\nthe quality of the expression. Propositions are divi-\\nded according to the quality of the subject-matter into\\ntrue and false,, and, according to the form of expres-\\nsion, into affirmative and negative.\\nIt is evident that with the quality of the subject-\\nmatter. Logic has directly nothing to do for since the\\nlogical form of a proposition is A is B, it is taken\\nfor granted, as we have already seen, that this state-", "height": "3187", "width": "1915", "jp2-path": "elementsoflogic00copp_0087.jp2"}, "88": {"fulltext": "82 LOGIC.\\nment is true, and that, from the very form it assumes.\\nWith the subtleties of statements Logic is not con-\\ncerned taking for granted the truth of a proposition,\\nit makes use of it properly whatever falsity lies in\\nit will pervade the argument, but this will not be the\\nfault of Logic. In Logic the Quality of the subject-\\nmatter is accidental and not essential.\\nThe essential quality of propositions in Logic is\\nthen the quality of the expression and this quality\\nis made, as before shown, to depend upon the copula.\\nIf the copula is affirmative, the proposition is called\\naffirmative; as\\nAll A is B.\\nSome A is B.\\nIf the copula is negative, the proposition is said to be\\nnegative as\\nNo A is B.\\nSome A is not B.\\nTo mark these divisions according to quantity and\\nquality, and to simplify the future operations in which\\nthey are used to frame arguments, we employ letters\\nas symbols. Since every proposition must be univer-\\nsal or particular, and at the same time affirmative or\\nnegative, there are four and only four classes of sim-\\nple categorical propositions, which we represent by\\nthe following symbols\\nUniversal affirmative as All JT is Z by A.\\nUniversal negative as iVb X is T, hj E,\\nParticular affirmative as Sovie X is iT, by\\nParticular negative as Some X is not Y, by O.", "height": "3222", "width": "2054", "jp2-path": "elementsoflogic00copp_0088.jp2"}, "89": {"fulltext": "PROPOSITIONS. 83\\nThe sign of a universal proposition is the same as\\nthat of a distributed term; i. e., the prefix All or\\nEvery for the universal affirmative^ and No for a uni-\\nversal negative\\nAnd here it must be particularly observed that the\\nuniversal negative is only correctly written when in\\nthe form JVb A is B. It might at first sight seem\\nthat this is equivalent to All A is not B but it is\\nnot so, although often meant to be so Thus all\\nsoldiers are not cruel, has a very difi erent meaning\\nfrom no soldiers are cruel. The first is not indeed a\\nuniversal proposition as it appears to be, but a parti-\\ncular, implying that some soldiers are cruel, while\\nsome are not.\\nThe translators of our English Bible have, in a few\\ninstances, made use of this form improperly to express\\na universal. Thus, the Hebrew text of the Psalms\\nexpresses with regard to the wicked All his\\nthoughts are there is no God while the translators\\nhave it God is not in all his thoughts the mean-\\ning of this is evidently God is not in any of his\\nthoughts.\\nThe sign of a particular proposition is the same as\\nthat of an undistributed term, i. e. the prefix some,\\nfew, several, many, and like words, indicating a part\\nonly of a wliole, for particular affirmative propositions\\nand the same prefix, with a negative copula, for \u00c2\u00abr-\\nticular negative.", "height": "3187", "width": "1931", "jp2-path": "elementsoflogic00copp_0089.jp2"}, "90": {"fulltext": "84 LOGIC.\\nBut it constantly happens that a proposition has no\\nprefix, and we are then thrown upon our knowledge\\nof the subject-matter of the proposition to determine\\nwhether it be universal or particular. Such propo-\\nsitions as have no prefix to denote their quantity are\\ncalled indefinite propositions, which Logic alone will\\nnot enable us to understand. We must then look to\\ntheir meaning, and thus find out what prefix is their\\ndue. For example, 3fen are artists.\\nBy examining the matter of this, we find that only\\nsome men are artists^ and then making the proper\\nprefix we declare the proposition to be particular.\\nBirds fly. This is true of birds universally, and\\nwe have the right to prefix the sign all^ which de-\\nnotes it a universal proposition.\\nA singular proposition is one which has for its sub-\\nject a singular term as\\nAlexander was a conqueror.\\nCsesar was ambitious.\\nIt would seem at a first consideration of the quan-\\ntity of these propositions, that they were particular^\\nbut this is erroneous they are evidently universal\\nsince when I assert that Alexander luas a conqueror^\\nI mean the tvhole of Alexander, or Alexander taken\\nill his. fullest extension.\\nAs a general rule, then, singular propositions are\\nuniversal. There are many other divisions of pro-\\npositions which are curious rather than useful dis-", "height": "3219", "width": "2052", "jp2-path": "elementsoflogic00copp_0090.jp2"}, "91": {"fulltext": "PROPOSITIONS. 85\\ntinctions. The above are all those necessary to a\\ncomprehension of the logical processes which follow.\\n(28.) Of the Distribution of Terms in Propo-\\nsitions-\\nHaving treated of the quantity and quality of pro-\\nsitions, and observing that, as we have already seen,\\nthese propositions are to be hereafter used in the\\nframing of syllogisms, we come to consider the dis-\\ntrihutio7i of terms in propositions, and to establish\\nrules for this distribution. If we examine the four\\ncategorical propositions, with their geometrical nota-\\ntions,\\nAffirm. 4- If X!?^-^ Neg. f/NoX^Y.\\nT Some X IS Y. 0.\\\\ Some X is not Y.\\nfirst with reference to their subjects, it will be evident\\nthat in A and E the ivhole of the subject being con-\\nsidered, the subject is distributed., as is also indicated\\nby the prefixes All and No. It will be equally evident\\nthat in J and the subject is undistributed, a portion\\nonly being taken, as is indicated by the prefix Some.\\nThe rule deduced then, as far as the subjects are\\nconcerned, is very simple it is, that\\nAll universal projyositwns distribute the subject.\\nNo particulars distribute the subject.\\n8", "height": "3195", "width": "1915", "jp2-path": "elementsoflogic00copp_0091.jp2"}, "92": {"fulltext": "86 LOGIC.\\nBut since the predicates in these propositions have\\nno such prefixes, how are we to determine whether\\nthey are distributed or undistributed By an exami-\\nnation of the relation existing between the subject\\nand predicate in each case, we shall see that the dis-\\ntribution of the subject by no means implies that of\\nthe predicate.\\nIf we assert, 1st that All X is Y we do not assert\\nthat other things likewise may not be contained in\\nY; for though all X is Y, All W may be Y, All Z\\nmay be Y, c. or, to illustrate by a geometrical\\nfigure, we have\\nand still space enough for other things to be contained\\nin Y. Hence, it is evident that the whole of Y is\\nnot considered in the proposition all X is F, or that\\nY, the predicate, is not distributed in a universal\\naffirmative proposition.\\nAgain, if we take the proposition some X is Y, the\\nsame reasoning will apply, since many other things\\nmay be Y, besides this some X as is illustrated in\\nthe figure", "height": "3201", "width": "2040", "jp2-path": "elementsoflogic00copp_0092.jp2"}, "93": {"fulltext": "PROPOSITIONS. 87\\nLikewise then we see that the whole of Y is not\\ntaken in this case, or that the predicate of a particu-\\nlar affirmative proposition is not distributed.\\nThus far, then, we have found it true of affirmative\\npropositions, whether they he universal or ^particular,\\nthat they do not distribute the predicate.\\nIf now, we consider the universal negative, no X\\nis Y, we shall find that we must consider the whole\\nof X and the whole of Y, before we can assert that\\nno part of one belongs to any part of the other\\nthus\\nWe have already seen that the subject X is distribu-\\nted, and it thus appears that in a universal negative\\nproposition the predicate also is distributed. The\\nwhole of the subject is brought in contact with the\\nwhole of the predicate, or we could not entirely deny\\ntheir agreement. It remains now to consider only\\nthe predicate of a particular negative, some X is not\\nY. The same reasoning applies here as in the last\\ncase or we must know and consider the whole of Y,\\nbefore we can assert that no part of it belongs to the\\nsome X in question.", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0093.jp2"}, "94": {"fulltext": "S\u00c2\u00bb LOGIC.\\nIt therefore apj^ears that the predicate of a particular\\nnegative proposition is distributed.\\nIf we collect together these four results, we shall\\nthus establish two rules\\n1st. The subjects of universal propositions, and\\nnot of particulars, are distributed.\\n2d. The predicates of negative propositions, and\\nnot of affirmatives, are distributed.\\nIt may be well, for the sake of convenient refer-\\nence, to arrange the quantity and quality of proposi-\\ntions, and the distribution of the terms, in a tabular\\nform, so that it may be referred to until it be fixed in\\nthe mind of the student.\\nFour classes of Categorical\\nPropositions.\\nSubject.\\nPredicate.\\nSimple Form.\\nA. Universal affirmative.\\nDistributed.\\nUndistributed.\\nAll X is Y.\\nE. Universal negative.\\nDistributed.\\nDistributed.\\nNo X is Y.\\nI. Particular affirmative.\\nUndistributed.\\nUndistributed.\\nSome X is Y.\\n0. Particular negative.\\nUndistributed.\\nDistributed.\\nSome X is not Y.\\nThere is a logical process which is passed upon pro-\\npositions and upon propositions only, and this process\\nhas in view the use which we make of propositions in\\nthe framing of arguments. It is called Conversion.\\nWe cannot convert a term, nor is it proper to speak\\ntechnically, as some writers have done, of the conver-\\nsion of arguments,\\n(29.) Conversion.\\nConversion consists in transposing the terms of a\\nproposition in such a manner as to place the subject", "height": "3222", "width": "2040", "jp2-path": "elementsoflogic00copp_0094.jp2"}, "95": {"fulltext": "CONVERSION. 89\\nfor tlie predicate, and the predicate for the subject.\\nThus, having the proposition A is B, we convert it\\ninto B is A. When no other change than this is\\nmade, the conversion is called simple conversion but\\nby an examination of the four forms of categorical\\npropositions, it will be evident that they cannot all be\\nsimply converted, and retain in the converted propo-\\nsition or converse the truth of the original proposition\\nor exposita. As a simple example of this having\\nthe proposition\\nAll men are mortal;\\nwe cannot write the converse,\\nAll mortals are men.\\nNo other conversion is allowed in Logic than that\\nwhich is called illative, or that in which we may infer\\nthe truth of the converse from the truth of the ex-\\nposita.\\nTo simplify this, let us convert each of these propo-\\nsitions in turn.\\n1st. (A.) All X is Y All men are mortals.\\nIt is evident, as we have already seen, that we\\ncannot convert this proposition simply, for we can-\\nnot read\\nAll T is X All mortals are men,\\nsince I^(or mortals) includes many other races besides\\nmen.\\nWe, therefore, limit the quantity of the proposi-\\niVi and 3ro, {latum).", "height": "3198", "width": "1854", "jp2-path": "elementsoflogic00copp_0095.jp2"}, "96": {"fulltext": "1)0 LOGIC.\\ntion from universal io ijarticular, so that F, which was\\nundistributed in the original proposition^ may remain\\nso in the converse. Expressing then this non-distribu-\\ntion of Y hj the prefix some, we shall have as the\\nconverse\\nSome Fis X Some mortals are men.\\nFrom the nature of the process, this form of illative\\nconversion is called coyiversion by limitation.\\nFrom this we see that the converse of a universal\\naffirmative is a particular affirmative, or A becomes,\\nwhen converted, I. If we examine the universal\\nnegative,\\n2. (E.) No X is Y No men are trees,\\nwe shall see that as X and Fare taken in their whole\\nextension, or are distributed, we may here convert\\nsimply, and read\\nNo Y is X No trees are men.\\nThe converse of a universal negative is a universal\\nnegative.\\nSo, likewise, in the particular affirmative\\n3. (I.) Some X is Y Some men are cruel,\\nwe shall find that neither subject nor predicate is taken\\nin its full extent or distributed, and that we may,\\ntherefore, convert simply\\nSome Y is X Some cruel [beings) are men.\\n\u00e2\u0096\u00a0^The Latin name employed by logicians, for this kind of con-\\nversion, is conversio per accidens.", "height": "3201", "width": "2045", "jp2-path": "elementsoflogic00copp_0096.jp2"}, "97": {"fulltext": "CONVERSION. 91\\nThe converse of a particular affirmative remaiyis a\\nfarticular affirmative. There remains only the parti-\\ncular negative to be considered.\\n4. (0.) Some X is not Y Some quadrupeds are not horses.\\nThis proposition presents a special difficulty. We\\ncannot convert it simply as in the cases of E and I\\nfor we should then have Y^ which is distributed in the\\nexposita, undistributed in the converse thus we would\\nhave the absurdity\\nSome Y is not X Some horses are not quadrupeds.\\nNor can we invert the process of conversion by limi-\\ntation as in the case of A (l.,\\\\ and pass back from\\nparticular to universal^ as\\nAll Y is not X All horses are not quadrupeds.\\nTo overcome this difficulty we detach the negative\\nparticle not in the original proposition from the copula,\\nand attach it to the predicate thus, instead of the\\nopen form some X is not Y^ we read.\\nSome X is (not Y) Some quadrupeds are (not horses).\\nand then it is evident that for all logical purposes,\\nthe proposition ceases to be or particular negative,\\nand becomes I or particular affirmative, since for {7iot\\nY) we might place any other symbol, as Z, and convert\\nby simple conversion. But without this trouble, if we\\nconvert we shall have\\nSome (not Y) is X Some (not horses) are quadrupeds,\\nor in our ordinary language, to complete the sense\\nSome (beings luhich are) not horses are quadrupeds.", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0097.jp2"}, "98": {"fulltext": "92 LOGIC.\\nThis is called conversion by contraposition or by nega-\\ntion.\\nWe arrive by this process at a rule for illative con-\\nversion which is, that No term must he distributed in\\nthe converse ivhich was undistributed in the exposita.\\nBy arranging the different kinds of illative conver-\\nsion in tabular form, we shall simplify them for refer-\\nence. Taking the letter p to indicate conversion by\\nlimitation or per accidens s, siniple conversion and\\nconversion by negation^ we shall have the following\\ntable.\\nILLATIVE CONVERSION.\\nOriginal Propositions. Methods of Convertinrj. Converted Propositions.\\n(A.) AJl X is Y. p. Some Y is X. (I.)\\n(E.) No X is Y. s. No Y is X. (E.)\\n(I.) Some X is Y. s. Some Y is X. (I.)\\n(0.) Some X is not Y. Tc. Some (not Y) is X. (I.)\\nThe above are the regular forms of conversion, but\\nthere are certain Additional conversions to be noticed.\\nIt must be remarked that the universal affirmative,\\nAll X is Y All men are mortals,\\nis sometimes converted in another manner, i. e. by\\nputting immediately before both subject and predicate\\nthe negative particle not^ and then converting, thus\\nAll [not) Y is [?iot) X All (not) mortals are (not) men.\\ni. e.j All [ivho are 7iot) mortals are not men; or in\\ncommon phrase. None but Y can be X none hut\\nmortals can be men.\\nAgain, (E), which is converted simply, may be like-", "height": "3201", "width": "2054", "jp2-path": "elementsoflogic00copp_0098.jp2"}, "99": {"fulltext": "CONVERSION. 93\\nwise converted hy limitation^ since, if having the uni-\\nversal form\\nNo A is B No men are trees,\\nwe can say\\nNo B is A No trees are men,\\nwe can also say, what is less than this.\\nSome B is not A Some trees are not men.\\nIt may happen that for some purpose of logical\\ntechnicality it will be better to use t]ie particular when\\nwe have a right to use the universal, but from the ex-\\nistence of the universal we infer that of the particu-\\nlar, which is only a part of it.\\nThere remains only one remark to be made upon\\nthe subject of conversion it is that there are a few\\npropositions which bear the form of A or universal\\naffirmative, which are capable of simple conversion.\\nThe terms of such a proposition are said to be con-\\nvertible terms, or the predicate and subject are either\\nexactly equivalent or exactly co-extensive for exam-\\nple in the proposition All common salt is chloride of\\nsodium, we have a right to assert that all cliloride of\\nsodium is common salt. From the proposition All the\\ngood are saved, we have a right to infer that All (loho\\nare) saved are good. Many just definitions come\\nunder this class. Besides such propositions as these,\\nthere are many mathematical propositions which seem\\nto be single propositions with convertible terms, when\\nin reality they contain two distinct propositions, each", "height": "3179", "width": "1854", "jp2-path": "elementsoflogic00copp_0099.jp2"}, "100": {"fulltext": "94 LOGIC.\\nof which requires distinct proof. Thus, All equila-\\nteral triangles are equi-angular. The apparent con-\\nverse tliat All equi-angular triangles are equilateral,\\nis indeed true, but tliis is not inferred from the origi-\\nnal proposition, it is proved separately by geometri-\\ncians so that instead of being the converse of the\\nproposition stated it is, in reality, a distinct propo-\\nsition.\\nThe processes of conversion have been applied\\nabove only to the forms of simple categorical propo-\\nsitions they may likewise be applied, however, to\\ncompound propositions, and when we come to con-\\nsider these, we shall show how they may be converted\\nbut it may be here observed, that as all compound\\npropositions may be readily reduced to the simple\\ncategorical form, having shown how to convert these,\\nwe have in reality shown how to convert them all.\\nThe next process of importance in considering pro-\\npositions, is the manner and character of their oppo-\\nsition to each other, and this, like the process of\\nconversion, becomes of special value when we are\\njoining propositions together to frame arguments.\\n(30-) Of O^iposition.\\nTwo propositions are said to be opposed to each\\nother, when, having the same subject and predicate,\\nthe one denies either entirely or in part ivhat the other", "height": "3197", "width": "2022", "jp2-path": "elementsoflogic00copp_0100.jp2"}, "101": {"fulltext": "OPPOSITION. 95\\naffirms, or affirms either entirely or in part what the\\nother denies; as, for instance, the proposition\\n(A.) AU are 1, opposed b, both S\u00e2\u0080\u009er,^T SL*L (o:]\\nand (E.) NO are w\u00c2\u00bb, i\u00c2\u00ab opposed by both f ..^f** f4\\nAgain, two propositions are said to be opposed\\nwhen, having the same subject and predicate, the one\\naffirms in tvhole what the other affirms in part, or de-\\nnies in whole what the other denies in part, Thus\\n(A.) All men are mortal, {0pp.) Some men are mortal. (I.)\\n(E.) No men are trees, {0pp.) Some men are not trees. (0.)\\nIt will appear, then, that the opposition in propo-\\nsitions is both in quantity and in quality, and as there\\nare four forms of categorical propositions, and any\\ntwo may be thus opposed, we shall have four kinds\\nof opposition, which will best be illustrated by the\\nfollowing figure\\nA contraries E\\nOr.\\n.J:^\\nm\\nI sub-contraries O\\nIn which the two universal propositions A and E are\\ncalled contraries and differ only in quality, being re-\\nspectively affirmative and negative the two particu-\\nlars I and are called sub-contraries, differing\\nlikewise in quality only the two affirmatives and the\\ntwo negatives are called respectively subalterns, differ-", "height": "3195", "width": "1854", "jp2-path": "elementsoflogic00copp_0101.jp2"}, "102": {"fulltext": "96 LOGIC.\\ning ill quantity only the universal affirmative and\\nparticular negative, and the universal negative and\\njyartieular affirmative, are respectively called contra-\\ndictories, and differ both in quantity and quality.\\nIf we desire, as in applying Logic we may do, to\\ndetermine the relative truth and falsity of these re-\\nspective propositions, we must look for a moment at\\nthe matter which they may contain.\\n(31.) Of the Matter of Propositions.\\nThe matter of a proposition is the nature of the\\nunion betiveen the terms of the proposition, or in ordi-\\nnary language, the exact meayiing of the proposition.\\nBy considering the nature of this connexion be-\\ntween the terms, we shall see that it can be of only\\nthree kindg necessary, which is expressed by an\\naffirmative proposition impossible, expressed by a\\nnegative proposition, and contingent, which is ex-\\npressed by a particular proposition.\\nTo illustrate if we have given to us the two terms,\\nmen and mortal, and are told to connect them by a\\ncopula, we ask ourselves, what is the nature of the\\nconnexion between these two. The answer is, it is\\nnecessary, and we express that necessity by using an\\naffirmative copula, and prefixing the sign All\\nAll men are mortal.\\nAgain if we have given to us the two terms men and", "height": "3201", "width": "2034", "jp2-path": "elementsoflogic00copp_0102.jp2"}, "103": {"fulltext": "OPPOSITION. 97\\nt7 ees, to perform an analogous operation, we shall\\nassert the nature of the connexion between them to\\nbe impossible, and express that impossibility by the\\nuse of the prefix no\\nNo men are trees.\\nIf again, we have the terms me7i and handsome, we\\nassert the nature of the connexion to be contingent,\\nas some men are and some are not handsome, and thus\\nto express contingent matter we write the proposition\\nwith the prefix some\\nSome men are handsome.\\nSome men are not handsome.\\nIf, now, we examine the matter of these propositions\\nwe shall see that\\nIn necessary matter all affirmatives are true, and\\nnegatives false.\\nNecessary Matter.\\nTrue. False.\\n(A) All men are mortal. (E) No men are mortal.\\n(I) Some men are mortal. (0) Some men are not mortal.\\nIn impossible matter all negatives are true and affirma-\\ntives false.\\nImpossible Matter.\\nTrue. False.\\n(E) No men are trees. (A) All men are trees.\\n(0) Some men are not trees. (I) Some men are trees.\\nIn contingent matter all particulars are true and\\nuniversals false.\\n9 G", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0103.jp2"}, "104": {"fulltext": "9S LOGIC.\\nConimgent Matter.\\nTrue. False.\\n(I) Some men are handsome. (A) All men are handsome.\\n(0) Some men are not handsome. (E) No men are handsome.\\nFrom this examination we perceive that if one con-\\ntrary is true the other must be false, but if one is\\nfalse the other may he false also if one sub-contrary\\nis false the other must be true, but if one is true the\\nother r)iay he true also. But in the case of contra-\\ndictories, if one is either true or false, the other must\\nbe just the oi^posite, i. e., false or true.\\nIt remains to consider the suhalterns, which dififer\\nin quantity. If the universal (A or E) be true, the\\nparticular I or will be true also as\\n(A) All men are mortal, (E) No men are trees,\\nimplies implies\\n(1) Some men are mortal. (0) Some men are not trees.\\nIf the particular I or be true, the universal A\\nor E is not necessa7 ily true.\\n(I) Some islands are fertile, does not permit us to\\ninfer (A), All islands are fertile.\\n(0) Some islands are not fertile, does not permit us\\nto imply (E) No islands are fertile.\\nBut if the particular be false, the universal must\\nof necessity be false also. Thus the false particular\\nSome men are trees, would give us also All men are\\ntrees as a false universal.\\nBy summing up these inferences we may state the", "height": "3195", "width": "2035", "jp2-path": "elementsoflogic00copp_0104.jp2"}, "105": {"fulltext": "COMPOUXD PROPOSITIONS. 99\\nfollowing rules, which must be kept in the memory as\\nwe approach the subject of Reduction.\\nI. Contraries may both be false, but never both be\\ntrue.\\nII. Suh- contraries may both be true, but never\\nhoth false.\\nIII. Of Contradictories, if one be false the other\\nmust be true, and vice versa.\\nIV. In Subalterns we reason from the affirmation\\nonly of the universal to the affirmation of the parti-\\ncular but from the denial of the ^particular to the\\ndenial of the universal.\\nWith the remark that opposition may be also illus-\\ntrated in compound propositions or those not directly\\nin the simple categorical form or that such proposi-\\ntions may be reduced to this simple form, by an easy\\nprocess still to be explained; we pass to the subject\\nof compound propositions.\\n(32.) Of Compound Propositions.\\nA compound proposition consists of two or more\\nsimple propositions, united together either by a simple\\ncopulate, expressed or understood, or by a conjunc-\\ntion denoting an hypothesis.\\nCompound propositions are consequently divided\\ninto two classes, categorical and hypothetical.\\nCompound categorical propositions are of two kinds,\\ncopulative and discretive.", "height": "3170", "width": "1854", "jp2-path": "elementsoflogic00copp_0105.jp2"}, "106": {"fulltext": "100 LOGIC.\\nA copulative proposition consists of two or more\\nsubjects united with the same predicate, or with two\\nor more predicates, by the use of the copulative con-\\njunction, as\\nMen, horses, and birds are animals.\\nA discretive proposition consists of two simple pro-\\npositions, which are contrasted on account of an appa-\\nrent inconsistency, as\\nFox, though dissolute, was a patriot.\\nMany compound propositions are tacit or implied^\\nand thus have the form of simple propositions.\\nA hypotlietical proposition consists of two or more\\nsimple propositions united by a conjunction which\\nexpresses hypothesis. This conjunction is usually\\nplaced at the beginning of the proposition.\\nHypothetieals are divided into conditional, disjunc-\\ntive and causal, and take these names from the con-\\njunctions which express the condition of the hypo-\\nthesis.\\nA conditional proposition expresses the condition\\nby the conjunction if as\\nK A is B, C is D If John return, Harry will go.\\nA disjunctive proposition is formed with the con-\\njunctions either and or as\\nEither A is B, or C is D Either the day will be fine or cloudy,\\nA causal proposition unites its parts by the con-\\njunction because as\\nA is B, because C is D.\\nJohn is well because he is prudent.", "height": "3187", "width": "2026", "jp2-path": "elementsoflogic00copp_0106.jp2"}, "107": {"fulltext": "COMPOUND PROPOSITIONS. 101\\nIt is evident in the case of categorical propositions,\\nthat they may be at once resolved into the simple\\npropositions of which they are composed thus we\\nmay divide the copulative proposition given into three\\ndistinct propositions viz.,\\nMen are animals,\\nHorses are animals,\\nBirds are animals,\\nand the discretive may be divided into two thus\\nFox was dissolute.\\nFox was a patriot.\\nUnlike the compound categorical propositions, the\\nliy pathetic als contain within themselves the germ of an\\nargument, and only require that the hypothesis shall\\nhe established or fail of establishment, to arrive at\\na conclusion. Thus, having the proposition.\\nIf A is B, C is D,\\nwe need only know whether A is B, in order to\\nstate the argument and arrive at the conclusion that\\nC is D.\\nConditional propositions, however, may be, in every\\ncase, reduced to a categorical form, by regarding them\\nas universal affirmative categorical propositions, of\\nwhich the antecedent is the subject^ and the consequent\\nthe predicate. We then rid ourselves of the condition,\\nby the use of the words, the case of; thus, instead\\nof the form, If A is B, C is D, we shall have\\n[The case of) A being B, is {the case of) C being D,\\nwhich is purely categorical in form.", "height": "3189", "width": "1854", "jp2-path": "elementsoflogic00copp_0107.jp2"}, "108": {"fulltext": "102 LOGIC.\\nDisjunctive propositions may be reduced to con-\\nditionals thus\\nEither A is B, or C is D, is equivalent to If A is not B, C is D,\\nor we may place it at once in a categorical form with-\\nout this double process, by reading it thus\\nTfie tioo possible cases in this matter are that A is B, and that C is D.\\nIt is more usual to reduce the disjunctive however\\nto a conditional form, into which it very naturally\\nfalls.\\nThe causal proposition,\\nBecause A is B, C is D,\\nbecomes either at once categorical, when we establish\\nthe truth of because^ and thus we have\\nA is B, therefore C is D,\\nas an enthymeme, to which, having the subject-matter,\\nwe might supply the wanting premiss or the causal\\nproposition becomes simply conditional^ if the cause\\nexpressed by the first proposition A is B be doubt-\\nful, and then we read.\\nIf A is B, C is I),\\nwhich must be treated like the conditional above.\\nAs it seems, then, that all these are reducible to\\nthe conditional form, we need only show how the pro-\\ncess or conversion is applied to conditionals, in order\\nvirtually to apply it to them all. From what has\\nbeen said, it will appear that conditionals are con-", "height": "3201", "width": "2052", "jp2-path": "elementsoflogic00copp_0108.jp2"}, "109": {"fulltext": "THE NEW ANALYTIC. 103\\nverted hy negation onlj thus, to convert the propo-\\nsition,\\nIf John has the smallpox he is sick\\nwe may read\\nIf John is 7iot sick he has not the smallpox,\\nor, the conversion rests upon the fact that the denial\\nof the consequent leads to the denial of the antecedent.\\nWe cannot convert without this negation, for we\\ncould not reason from the affirmation of the conse-\\nquent to the affirmation of the antecedent thus,\\nIf John is sick he has the smallpox,\\nsince that consequent [sickness), may have sprung from\\nsome other antecedent than the smallpox.\\n(33.) The New Analytic.\\nAnd here it becomes necessary, before closing the\\nsubject of propositions, to refer briefly to the effort\\nof certain late writers to quantify the predicate that\\nis, to place prefixes before it similar to those placed\\nbefore the subjects of propositions to determine at a\\nglance its distribution or non-distribution, and to form\\nthus a new set or class of categorical propositions.\\nThus, instead of the form all men are animals, they\\nwould write all men are some animals, and claim\\nthereby not only a greater precision in the logical\\nstatement, but in some instances the establishment\\nof a distinct proposition as, for example.\\nAll A is (all) B.\\nIt may be admitted that sometimes a new idea is\\nsuggested by such a quantification of the predicate,", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0109.jp2"}, "110": {"fulltext": "104 LOGIC.\\nbut it is only suggested^ not contained in the proposi-\\ntion thus rendered. Thus if we say\\nAll men are sinners,\\nwe mean, by our rule, some sinners now the question\\nas to the comprehension of this word sinners may\\narise, when we place such a prefix whether angels\\nand devils may or may not be included in it and\\nwhether the ill-conduct of brutes is excluded from it.\\nWhereas, if we could write.\\nAll men are (all) sinners,\\nwe should exclude at once all other beings from the\\ncategory. Hence, the quantification of the predicate,\\nwhich in the old system is implied, does when expressed,\\nsuggest new thoughts or judgments, but those new judg-\\nments rest upon their own basis, and have really\\nnothing to do with the original proposition. There\\nseems really, therefore, nothing gained in the exten-\\nsion of the proposition by this attempt to quantify the\\npredicate, but rather a confusion of judgment and a\\ncomplication of logical forms.\\nIt is not intended to give, in detail, the applications\\nof the new analytic, nor to deny that results,\\ntotally out of the province of Logic, are attained by\\nit. It is evident that if we quantify the predicate, in\\ncategorical propositions, we shall have four additional\\nforms, viz.\\nEstablished Forms.\\nNeio Forms.\\nA.\\nAll A is B.\\nAll A is all B.\\nX.\\nE.\\nNo A is B.\\nNo A is some B.\\nY.\\nI.\\nSome A is B\\nSome A is all B.\\nU.\\nSome A is not B.\\nSome A is not some B.\\nZ.", "height": "3201", "width": "2058", "jp2-path": "elementsoflogic00copp_0110.jp2"}, "111": {"fulltext": "THE NEW ANALYTIC. 105\\nNow of these new forms we have already considered\\nX, as in the case\\nAll equilateral triangles are {all) equi-angular,\\nand in the cases of exact definitions, as\\nAll common salt is [all) chloride of sodium,\\nIn the first we have seen that there are two distinct\\npropositions, and in the second that there are but two\\nnames for the same object.\\nAs for Y, U, and Z, they are so clearly contained\\nin the old forms that they need but little elucidation.\\nY. Some trees are all oaks,\\nwhen converted gives us\\nAll oaks are trees. or A.\\nU. No heroes are some men,\\nConv. Some men are not heroes. 0.\\nZ. Some quadrupeds are not some horses,\\nby which we determine that the quadrupeds referred\\nto may belong to other species, or may be included in\\nthe species horse, apart from the some horses men-\\ntioned.\\n^eerOsepc\\nIt was attempted, in the new analytic, to simplify the\\nsubject of conversion, but, it seems, w^ith inadequate\\nresults.\\nAnd here we leave the subject of quantifying the\\npredicate so far as it relates to propositions alone.\\nIf carried out in the syllogism, it would much enlarge\\nthe domain of Figure, and give much fruitless labour\\nto the logician.", "height": "3187", "width": "1854", "jp2-path": "elementsoflogic00copp_0111.jp2"}, "112": {"fulltext": "106 LOGIC.\\nCHAPTER VII.\\n(34.) Of Arguments,\\nAn argument is an act of reasoning or ratiocina-\\ntion. It consists of two parts that to be proven,\\nand that by which it is proven.\\nThe part to be proven is embodied in the conclusion,\\nand that by w^hich it is proven is embodied in the\\npremisses. When these are inverted from the usual\\nlogical order, so that the conclusion is stated first, it\\nis called the question and the premisses which are\\njoined to it by the word because, are then called the\\nreason thus,\\n(Question) Why are all Americans mortal?\\nor All Americans are mortal.\\nBecause They are men.\\nBut in logical form and order the premisses are stated\\nfirst, and the conclusion is connected with them by\\nthe illative conjunction therefore thus\\nPremisses AH men are mortal,\\nt All Americans are men,\\nTherefore All Americans are mortal.", "height": "3201", "width": "2060", "jp2-path": "elementsoflogic00copp_0112.jp2"}, "113": {"fulltext": "ARGUMENTS. 107\\nThese two forms must be distinguished from what is\\nexpressed by the words inference and proofs which\\nhave not to do with the order of the parts in an argu-\\nment, but with the special design of the person who\\nuses the argument, i. 6., whether from known facts or\\npremisses, he seeks to establish a conclusion or has\\nadopted a conclusion, and is simply seeking for pre-\\nmisses by which to substantiate it.\\nLogic teaches us to draw from known proofs only\\na just inference, or to maintain a given inference only\\nby just proofs. We may more clearly illustrate by\\nobserving how, in the various professions, these\\ndifferent methods are used thus, a naturalist gets\\ntogether many observations and makes many experi-\\nments, forming a strong store of proofs, before he\\nmay justly infer a conclusion; while an advocate at\\nlaw, assumes the innocence of his client or the guilt\\nof the prisoner, as a foregone conclusion, and then\\nuses every means for obtaining proofs and thus estah-\\nlishing premisses by which to substantiate his con-\\nclusion.\\nIt has been observed that the logical form of an\\nargument is a syllogism, which consists of three pro-\\npositions, i. e. two ^premisses and a conclusion.\\nAfter fully explaining the syllogism, we shall con-\\nsider all forms of irregular and abridged arguments,\\nand show, as has been asserted, that they may all be", "height": "3184", "width": "1911", "jp2-path": "elementsoflogic00copp_0113.jp2"}, "114": {"fulltext": "108 LOGIC.\\nreduced to tliis simple form, so that the logical tests\\nmay be at once applied to them.\\n(35.) Of tlue SijUogism.\\nIn the analysis of Logic, the dictum of Aristotle\\nwas distinctly laid down and illustrated. Its form\\nwas\\nNo. 1. No. 2.\\nAll A is B. No A is B.\\nAll or some C is A. All or some C is A.\\nAll or some C is B. No C is B, or some C is not B.\\nThe principle of the dictum is, that whatever (B)\\nwe predicate {in the major premiss), of the whole class\\n(All A) under which class we assert [in the major\\npremiss), certain individuals (All or some C) to be\\nranged we may also predicate (in the conclusion) of\\nthose individuals.\\nThus, B is predicated of (All A), C is an individual\\nof the class A, therefore we have a right to predicate\\nBof C.\\nBut, as few arguments, in the ordinary uses of lan-\\nguage, are placed in this exact form (although all\\nvalid arguments may be), there have been laid down\\ntwo logical axioms and several important rules for\\ndetermining the validity of syllogisms, without the\\nlabour of bringing them to this form.\\nIt must be constantly remembered that it is a con-\\ndition of every syllogism that it contains three and\\nonly tliree terms the major term, the minor term, and", "height": "3201", "width": "2051", "jp2-path": "elementsoflogic00copp_0114.jp2"}, "115": {"fulltext": "THE SYLLOGISM. 109\\nthe middle term. The first two of these terms must\\nnot be confounded with the premisses which bear the\\nsame name, and which are propositions. Thus in the\\nexample.\\nMaj. prem.\\nmid.\\nA\\nis\\nr\\nmid. maj.\\nz=z All men are mortal.\\nMm. prem.\\nmin.\\nc\\nis\\nmid.\\nA\\nminor. mid.\\nAll Americans are men.\\nConcl.\\nrmn.\\nis\\nm^.\\nB\\nminor. Tnajor.\\nAll Americans are mortal,\\nB is the major term, and it is in the major premiss\\nC is the minor term, and it is found in the minor pre-\\nmiss A is the middle term, because it is the medium\\nof comparison between the other two. In the major\\npremiss, the middle term is compared with the major\\nin the minor premiss it is compared with the minor,\\nand in the conclusion, the minor and major terms,\\nhaving been thus found to agree with the same middle\\nterm, are asserted to agree with each other.\\nThe minor term is always the subject of the con-\\nelusion, and the major term the predicate.\\nThis simple process of comparison leads us to the\\nstatement of those axioms which determine the con-\\nditions of agreement and disagreement between the\\nmajor and minor terms, and to note some important\\nconsequences following from them.\\n(36.) Logical Axioms.\\n1st. If two terms agree with one and the same third\\nterm, they will agree with each other.\\n10", "height": "3195", "width": "1911", "jp2-path": "elementsoflogic00copp_0115.jp2"}, "116": {"fulltext": "110 LOGIC.\\n2(1. If of two terms, the one agree and the other\\ndisagree with one and the same third term, thej will\\ndisagree with each other.\\nRules.\\nL From the first of these axioms we observe that\\nif both premisses of a syllogism are affirmative, thus\\nexpressing the agreement of the major and minor\\nterms with the middle, the conclusion must likewise\\nbe affirmative, or express the agreement between these\\ntwo terms thus, B being the major term, C the minor,\\nand A the middle, we have\\nA is (or agrees with) B,\\nC is (or agrees with) A,\\nand we must consequently state the\\nconclusion\\nC is (or agrees with) B.\\nII. Again, from the second axiom, we see that if\\none of the premisses (as the major) be affirmative, and\\nthus express the agreement between the major term\\nand the middle, and the other be negati^^e and thus\\nexpress a disagreement between the minor term and\\nthe middle, w^e must have a negative conclusion to\\nexpress the disagreement between the major and the\\nminor, which we have thus shown, the one to agree\\nand the other to disagree in the premisses with one\\nand the same third (the middle).\\nThus if, A is not (or disagrees with) B,", "height": "3222", "width": "2059", "jp2-path": "elementsoflogic00copp_0116.jp2"}, "117": {"fulltext": "THE SYLLOGISM. Ill\\nAnd if, C is (or agrees with) A,\\nwe must have, C is not (or disagrees with) B.\\nIII. It is further evident that if both premisses he\\nnegative, we can draw no conclusion because in these\\npremisses the middle term, simply disagreeing with\\nboth the major and minor terms, is no longer a\\nmedium of comparison between them. For example,\\nstate the premisses,\\nNo A is B No men are trees,\\nNo C is A No horses are men;\u00e2\u0080\u0094\\nwe have established no relation whatever between\\nand B, or between horses and trees, so that, although\\nwe might truthfully write\\nNo horses are trees,\\nit would be an accidental statement, and not spring\\nfrom the premisses stated.\\nIn the conclusion is stated the relation between the\\nmajor and minor term, which was established in the\\npremisses by the medium of the middle term. The\\nminor term is the true subject of the conclusion, and\\nthe major term the true predicate. Sometimes in an\\ninverted or elliptical conclusion these terms may\\nappear transposed, but when properly written out\\nthey will take the places indicated.\\nThe middle term, which occurs twice in the pre-\\nmisses, is the medium of comparison between the two", "height": "3195", "width": "1791", "jp2-path": "elementsoflogic00copp_0117.jp2"}, "118": {"fulltext": "112 LOGIC.\\nOther terms, and is generally the name of a class, of\\nwhich in one premiss something is predicated, or to\\nwhich some quality is attributed, as\\n1. Man is a rational animal,\\nin which man is the name of a class, and rationality\\na predicate or attribute under which in the other\\npremiss we range an individual or individuals belong-\\ning to the class, as\\n2, John is a man,\\nand by means of which we have a right to predicate\\nor attribute this same thing rationality to the indivi-\\ndual thus,\\n3. John is a rational animal,\\nIV. Ambiguous middle.\\nIt is scarcely necessary to state that the middle\\nterm must be univocal, i, e., must have the same\\nmeaning in both premisses. If it be ambiguous, or\\npossess one meaning in the major premiss and a differ-\\nent one in the minor, we shall violate the first princi-\\nple in the construction of a syllogism, and hsiYe four\\nterms instead of the three, and only three, required.\\nMost languages have many such ambiguous words,\\nand the English particularly is full of them thus\\n1. A hank is a financial institution,\\n2. The margin of a stream is a bank,\\n3. The margin of a stream is a financial institution.", "height": "3199", "width": "2121", "jp2-path": "elementsoflogic00copp_0118.jp2"}, "119": {"fulltext": "THE SYLLOGISM. 113\\nMany such glaring examples will occur at once to the\\nstudent but it must be remembered that the sophist\\nwho would construct his artful fallacies to deceive,\\ndoes not employ such manifestly ambiguous words,\\nbut those whose double meanings are much more\\nnearly the same.\\nThus, in their philosophic meanings, the words\\nchurch and faith have given rise to sharp controversy\\nand violent partisanships. As ambiguous terms play\\na very prominent part in the subject of Fallacies, we\\nshall recur to them under that hea.d.\\nWhen the argument is written out in symbols, the\\nambiguity either disappears entirely, that is, when we\\nrepresent the term in both premisses by the same\\nletter, thus\\nis B,\\nC is A,\\nC is B,\\nor it becomes at once manifest, when we represent the\\nterm in the major premiss, by one symbol, as J., and\\nthat in the minor, having a different meaning, by ano-\\nther, as i thus\\nA is B,\\nC is D,\\nin which premisses there are four terms, and the error\\ndistinctly appears.\\nV. Undistributed middle.\\nThe middle term must be distributed, i. e., taken in\\n10* H", "height": "3195", "width": "1911", "jp2-path": "elementsoflogic00copp_0119.jp2"}, "120": {"fulltext": "114 LOGTC.\\nits whole comprehension, at least in one of the pre-\\nmisses^ for it will otherwise occur that we may com-\\npare the 7najor term with one part of the middle, and\\nthe minor with another imrt^ and thus it would fail to\\nbe a just medium of comparison. It might happen,\\nby chance, that these two parts should be the same,\\nbut it would be only by chance in the general case\\nthey would be different parts, and if we choose to\\nregard each part as a distinct term, we should again\\nrun into the error of having four terms instead of\\nthree; thus\\nSome quadrupeds are cows,\\nSome quadrupeds are sheep,\\nTherefore Some sheep are cows.\\nWhite is a colour,\\nBlack is a colour,\\nTherefore Black is white.\\nBut if one of the extremes be compared with the\\nwhole of the middle term, and the other be compared\\nonly loith a part, which part is necessarily contained\\nin the whole, they may then be compared with each\\nother.\\nVI. Illicit process.\\nAgain, in order to distribute either the major or\\nminor term in the conclusion it must have been pre-\\nviously distributed in the premiss in which it occurs\\nbecause, we only have a right to compare that part\\nof the term with the other, in the conclusion, which", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0120.jp2"}, "121": {"fulltext": "THE SYLLOGISM. 115\\nwe have already compared with the middle in the\\npremiss, thus\\nAll men are animals,\\nNo dogs are men,\\nTherefore No dogs are animals.\\nThe technical name for this logical fallacy is the illicit\\nprocess. In the example, the major term, animals^\\nwhich is not distributed in the premiss (as it is\\nthe predicate of an affirmative proposition) is distri-\\nbuted in the conclusion (as the predicate of a nega-\\ntive proposition) this is called an illicit process of the\\nmajor term if it be the minor term thus treated^ it\\nis called an illicit process of the minor term.\\nThe following is an example of illicit process of\\nthe minor.\\n1. All men are rational beings,\\n2. All men are animals,\\n3. All animals are rational beings.\\nIn this example the minor term animals^ which is un-\\ndistributed in the minor premiss as the predicate of\\nan affirmative proposition, is distributed in the con-\\nclusion, being there the subject of a universal.\\nLet it be remembered that this is called an illicit\\nprocess of the major or minor term^ not of the major\\nor minor premiss.\\nYII. If both premisses in a syllogism be particular\\npropositions, we can draw no conclusion thus\\n1. Some men are wise,\\n2. Some men are foolish.", "height": "3190", "width": "1773", "jp2-path": "elementsoflogic00copp_0121.jp2"}, "122": {"fulltext": "116 LO(UC.\\nleads us to no copclusion. Nor are we benefited if\\nwe make one of the premisses particular negative;\\nthus\\n1. Some men are wise,\\n2. Some men are not brave,\\nwe are as before without any medium of comparison.\\nThe fact is as stated the causes are various, and\\nwill be fully explained in the chapter on Figure.\\nIt is sufficient, now, for the student to know that\\nthe cause is in every case, either an undistributed\\nmiddle, or an illicit process of one of the other terms.\\nBy the foregoing axioms and rules, we extend the\\nrange of syllogistic forms, and are able to see the\\nvalidity or invalidity of an argument without reducing\\nit to the invariable formula of Aristotle s dictum.\\nWe proceed now to show how many of these forms\\nthere may be, and the relation they sustain to the\\ndictum itself; and this brings us to the subject of\\nFigure and Moods.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0122.jp2"}, "123": {"fulltext": "FIGURE AND MOODS. 117\\nCHAPTER yill.\\nOF FIGURE AND MOODS.\\n(37.) Figure.\\nFigure is the teclinical name employed to designate\\nthe classification of syllogisms according to the posi-\\ntion of the middle term with reference to the two ex-\\ntremes in the premises. Now, it is evident that the\\nmiddle term can have only four variations of position,\\nand hence we say there duVQ four figures.\\n1st. The middle term may be the subject of the\\nmajor premiss, and the predicate of the minor, and\\nthis designates the 1st figure.\\n2d. It may be the predicate of both premisses, and\\nthus the 2d figure is designated.\\n3d. In the Sd figure it is the subject of both pre-\\nmisses and\\n4th. In the 4:th figure (which is the reverse of the\\n1st), it is the pjredicate of the major premiss and the\\nsubject of the minor.\\nIf we designate the major term by P (as it is\\nalways the predicate of the conclusion), the minor", "height": "3195", "width": "1911", "jp2-path": "elementsoflogic00copp_0123.jp2"}, "124": {"fulltext": "118 LOGIC.\\nterm by S (being the subject of the conclusion)^ and\\nthe middle term by M, and merely state these various\\npositions of the middle term, without considering or\\ndenoting the quantity or quality of the propositions in\\nthe syllogism, we shall have the abstract syllogisms,\\nI.\\nII.\\nIII.\\nIV.\\nM is P.\\nP is M.\\nM is P.\\nP is M.\\nS is M.\\nS is M.\\nM is S.\\nM is S.\\nS is P.\\nS is P.\\nS is P.\\nS is P.\\nThese are called the four figures and to the syllo-\\ngisms which occur in them, the axioms and rules\\nalready laid down directly apply.\\nIf now we proceed to examine these figures in order,\\nwe shall find that the first figure is but the symbolical\\nrepresentation of Aristotle s dictum, the simplest form\\nof the syllogism. There will be four variations of\\nit viz.\\n1. 2. 3. 4.\\nAll M is P. All M is P. No M is P. No M is P.\\nAll S is M. Some S is M. All S is M. Some S is M.\\nAll S is P. Some S is P, No M is P. Some S is not P.\\nWe have simply supplied the quantity and quality\\nrequired.\\nSince, in the major premiss, then, of Aristotle s\\ndictum, we assert or deny the loredicate of the ^vliole\\nclass ivhich is the subject (All M), it is evident that in\\nthe first figure, the major premiss is ahvays universal.\\nIf, then, with this relative position of the middle term,\\ni. e. in the first figure, we find a syllogism, the major", "height": "3196", "width": "2121", "jp2-path": "elementsoflogic00copp_0124.jp2"}, "125": {"fulltext": "FIGURE. 119\\npremiss of wMcli is particular, we may at once declare\\nit to be invalid.\\nAgain, since the province of the minor premiss in\\nthe dictum is always to assert that certain individuals\\nbelong to the given class (and in no case to deny it),\\nit appears that in the first figure the minor premiss\\nmust always be affirmative, so that if we find a syllo-\\ngism in this figure with a negative minor premiss, we\\nmay at once declare it invalid.\\nThus, in stating the four forms of the dictum, we\\nhave stated the only four forms which the first figure\\ncan cover.\\nBut the other figures, which are not directly in the\\nform which the dictum assumes, instead of being ex-\\nplained by it, are to be considered in the light of the\\naxioms and rules for determining the validity of syllo-\\ngisms when the dictum does not directly apply. By\\nexamining the second figure,\\nP is M,\\nS is M,\\nSis P,\\nwe shall find that there are several forms which it\\nwill assume when we supply the quantity and quality\\nto the propositions. We observe at once that the\\nconclusion must, in every case, be negative, because\\n1st. The middle term is the predicate of both pre-\\nmisses\\n2d. The middle term must he distributed at least\\nonce in the syllogism", "height": "3195", "width": "1911", "jp2-path": "elementsoflogic00copp_0125.jp2"}, "126": {"fulltext": "120 LOGIC.\\n3d. In order that the j^ ^^dicate of a proposition\\nshall be distributed, the proposition must be negative\\n4th. This will give us one negative J9re77i2 8, and by\\nthe second axiom, if we have a negative premiss the\\nconclusion must be negative [universal or particular).\\nThird Figure,\\nM is P,\\nM is S,\\nSis P.\\nBy the supplying of quantity and quality this\\nfigure assumes a greater variety of forms than any\\nother.\\nBy considering the position of the terms here, it\\nwill appear that we can only draw particular conclu-\\nsions. For if both premisses be affirmative, and we\\ndraw a universal conclusion, or All S is P, then S\\n(the minor term) which was undistributed in the minor\\npremiss (being the predicate of an affirmative propo-\\nsition), will be distributed in the conclusion, as the\\nsubject of a universal or we shall have an illicit pro-\\ncess of the minor.\\nIf the major premiss be negative, and we draw a\\nuniversal conclusion, it is easily shown that the same\\nerror an illicit process of the minor obtains ar\\nif the minor premiss be negative, we shall have an\\nilUrit process of the major.", "height": "3194", "width": "2121", "jp2-path": "elementsoflogic00copp_0126.jp2"}, "127": {"fulltext": "MOOD. 121\\nfourth Figure.\\np is M,\\nM is S,\\nS is P.\\nThe fourth figure, which was not proposed by Aris-\\ntotle with the other three, and only recently adopted\\nby logicians, is an inversion of the first, and an un-\\nnatural and unnecessary form of the syllogism. By\\na similar examination of all the terms we shall find,\\nthat we may draw, as conclusions, in this figure all the\\ncategorical propositions except A^ which, as has been\\nshown, can only be drawn in the first figure. It is\\nthe prerogative of Aristotle s dictum alone, to dravf\\nfrom certain premisses a universal affirmative con-\\nclusion.\\nThe various forms of the syllogism due to the dif-\\nferent quantity and quality of the propositions compos-\\ning them, are arranged, in the different figures, in\\nwhat are called moods^ or a concise manner of ex-\\npressing a syllogism by symbols.\\n(38.) Of Mood.\\nIf, having any syllogisms, as the following\\nf All A is B, (A.) r No A is B. (E.)\\n1. All C is A, (A.) 2. Some C is A. (I.)\\n(AllCisB, (A.) Some C is not B. (0.)\\nwe write together the symbols characterizing each\\nproposition which composes them, we are said to deter-\\n11", "height": "3187", "width": "1773", "jp2-path": "elementsoflogic00copp_0127.jp2"}, "128": {"fulltext": "122 LOGIC.\\nmine the mood of the syllogism thus the symbol of\\nthe major premiss in the first syllogism is\\nA, or universal affirmative\\nthat of the minor,\\nA, or universal affirmative\\nand that of the conclusion likewise\\nA, or universal affirmative.\\nHence we say that A A Ah the mood of the syllogism.\\nIn the second syllogism we shall find by a similar\\nprocess that the mood is JE I 0,\\nNow, it is evident that the number of moods we\\ncan have will depend upon, 1st, the number of propo-\\nsitions in the syllogism, viz., three and 2d, upon the\\nnumber of categorical propositions which we can enu-\\nmerate, viz., four, A, E, I, it becomes then a\\nsimple algebraic arrangement of four letters A, E, I,\\n0, in three columns in every possible combination. The\\nnumber of these possible combinations will be sixty-\\nfour. For each of the propositions A, E, I, and 0,\\nmay be a major premiss and each of these may have\\neach in turn as a minor premiss thus,\\nMaj. prem. Maj. prem. Maj. prem. Maj. prem.\\nA E I\\nt\\nmay have as mi- 1\\nnor premisses,\\nAgain, each of these sets (sixteen in all) may have\\nfour difi erent conclusions, i. e. each of the categori-", "height": "3221", "width": "2121", "jp2-path": "elementsoflogic00copp_0128.jp2"}, "129": {"fulltext": "MOOD. 123\\ncals as a conclusion. Taking the first set, for example,\\nand supposing the operation performed for the rest,\\nFIRST SET.\\nMaj. prem. A.\\nI i I\\nMin. prem. A E I\\nill! i I I I I I I I I I I I\\nCond. AEIO AEIO AEIO AEIO\\nThis same process maybe performed for E, I, and 0.\\nThere will evidently be sixty-four moods, of which,\\nhowever, it is at once evident that very many will\\nviolate the axioms and rules already laid down, and\\nmust be for this reason discarded.\\nThus, all the combinations of affirmative premisses\\nhaving negative conclusions, as A A E, A I 0, c.,\\nc., must be thrown aside, because they violate the\\nfirst axiom.\\nAll the sets of negative premisses, with whatever\\nconclusions, are useless, as E E, 0, E 0, E, c.\\nAll the sets of particular premisses, with whatever\\nconclusions, must be neglected, such as 1 1, 0, I,\\nI 0, c.\\nIf all these eliminations be performed, and simple\\nas they are, the student is advised to go carefully\\nthrough them once for himself, we shall find twenty-\\neight moods excluded on account of negative and par-\\nticular premisses eighteen by the condition that the\\nconclusion follows the inferior part, and we shall see", "height": "3198", "width": "1911", "jp2-path": "elementsoflogic00copp_0129.jp2"}, "130": {"fulltext": "124 LOGIC.\\nthat one I E is rejected for an illicit process of\\nthe major term, in every figure, and finally that of\\nthe sixty-four arrangements which we call moods, only\\neleven represent valid arguments, or\\nFOUR AFFIRMATIVES and SEVEN NEGATIVES.\\nAAA\\nE A E\\nA I I\\nA E E\\nA A I\\nE A\\nI A I\\nA\\nA\\nE I\\nA E\\nIf now we apply these moods to each figure, in\\ndetail, it would seem, since there are four figures, that\\nwe should have 4 X 11 44 moods in all the figures,\\nbut in this application we find that many moods which\\nare valid in one figure, are not in others as, for ex-\\nample, the mood I A I, which is allowable in the third\\nfio;ure, would be in the first ficrure a case of undis-\\ntrihuted middle, and would further violate the prin-\\nciple of Aristotle s dictum, which requires that the\\nmajor premiss should be a U7iiversal proposition.\\nA E E is a valid mood in the second figure, while, in\\nthe first, it would have an illicit process of the major\\nterm, and would further violate that principle of the\\ndictum which requires the minor premiss to be always\\naffii mative.\\nBy applying these eleven moods to the four figures,\\nwe find that there would be six in each figure, or", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0130.jp2"}, "131": {"fulltext": "MOOD. 125\\ntwenty-four in all but even of these, five are omitted\\nas useless for example, the mood A A I, in the first\\nfigure, because it is implied and contained in the\\nmood AAA. Since, if the universal conclusion A\\nbe true, the particular I is necessarily true. By an\\napplication of each of these moods to every figure,\\nwe shall have left, finally, nineteen moods in all or,\\nFOUR in the first figure^ I OUR in the secondy Six in the\\nthird, and five in the fourth.\\nThe moods of the first figure are called perfect\\nmoods those in the other figures, imperfect moods.\\nAs it has been asserted that all arguments may be\\nput in the form of Aristotle s dictum, that is, that\\nall the imperfect moods may be made perfect, we pro-\\nceed to fulfil this assertion, by the process o? reduction,\\ni. e. the reducing of moods in the 2d, 3d, and 4th\\nfigures to the 1st figure, which is the form of the\\ndictum.\\nIn order to facilitate this process, as well as to re-\\ntain easily in the memory the different moods and\\ntheir value, the following verses, Latin in sound and\\nscansion, but without intrinsic meaning in the words,\\nhas been formed\\nFig. I.\u00e2\u0080\u0094 BArbArA, CElArEat, DArll, FErlO, dato primce.\\nFig. II.\u00e2\u0080\u0094 CEsArE, CAmEstrEs, FEstIno, FAkOrO, secundce.\\nFig III DArAptI, dIsAmIs, dAtlsI, FElAptOa,\\nL DOkAmO, fErlso, habet; quarta insuper addit\\nFig. IV.\u00e2\u0080\u0094 BrAmAntIP, cAmEnEs, dImArls, fEsApO, frEsIsOn.\\n11*", "height": "3195", "width": "1911", "jp2-path": "elementsoflogic00copp_0131.jp2"}, "132": {"fulltext": "12G LOGIC.\\nThere are variations in these lines, made by various\\nwriters we have adopted the above as the form which\\nwill indicate to us in the simplest manner the pro-\\ncesses of Reduction.\\nBefore explaining these lines, which the student\\nmust memorize in order to make them useful, that he\\nmay have the moods, and their places in the figures,\\nat his tongue s end, it will be observed that there are\\na few words used in these verses which are of no use\\nexcept to make out the hexameter lities of these are\\nclato frimcB in the first, secundoe in the second, tertia\\nhabet in the third, and quarta insuper addit, which\\nstates moreover the fourth adds, c. Leaving these\\nout of the consideration, in the lines themselves the\\nvotvels in each word represent the moods thus, har-\\nhara is the mood AAA; Cesare, the mood U A U,\\nc., c.\\nThe following consonants indicate what changes\\nare to be made in the given imperfect mood to reduce\\nit to a 2^e fe(^t mood of the first figure, s, that the pro-\\nposition indicated by the vowel immediately preced-\\ning it is to be converted simply thus in Oamestres, the\\nfirst 8 indicates the simple conversion of the first JE,\\nor the minor premiss, and the last s the simple con-\\nversion of the second jE^, or the conclusion. In simi-\\nlar relations p and Jc stand respectively for conver-\\nsion by limitation and conversion by negation; m,", "height": "3197", "width": "2121", "jp2-path": "elementsoflogic00copp_0132.jp2"}, "133": {"fulltext": "MOOD. 127\\nwherever it occurs, expresses that the premisses must\\nbe transposed the other consonants have no mean-\\ning, and are only employed to frame the words. P,\\nin the mood Biximantip of the fourth figure, denotes\\nthat the transposed premisses, indicated by M, will\\nwarrant a universal conclusion instead of a particular.\\nThe initial letters B, C, D, F, of the words which\\ncontain the moods, are so arranged throughout the\\nfigures as to indicate the mood in the first figure to\\nwhich any imperfect mood will he reduced; thus\\nDarapti of the third figure will, when reduced,\\nbecome Darii of the first, Camestres will become\\nCelarent^ c.\\nIt must be observed that this arrangement is only\\nfor the sake of convenience, as the process of reduc-\\ntion is invariable, and the mood Darapti would become\\nwhen reduced the mood A 1 1 of the first figure, whether\\nit were called Darii or by some other name. Stu-\\ndents are apt to be misled with reference to these ini-\\ntial letters, and to suppose that they will aid them in\\nthe process of reduction it is on this account that\\nthey are cautioned that this is only a convenient and\\nnot an auxiliary arrangement. Before proceeding to\\nexplain the system of reduction, let us give an ex-\\nample of each mood, in all the figures putting the\\nlogical frame-work to its legitimate use, and showing\\nevery form which the syllogism can assume. We shall", "height": "3193", "width": "1782", "jp2-path": "elementsoflogic00copp_0133.jp2"}, "134": {"fulltext": "128 LOGIC.\\nmake the examples very simple, leaving it to tlie stu-\\ndent, with these before him, to frame longer and more\\ncomplex ones for himself; a practical exercise which\\nwill be found very useful. The middle term is placed\\nin italics in each example.\\nExamjjles.\\nFIGURE I.\\nBarhara.\\nA. Every desi7^e to gain hy another s loss is cove-\\ntousness.\\nA. All gaming is a desire to gain hy another s loss.\\nA. All gaming is covetousness.\\nCelarent.\\nE. No one who is enslaved hy his appetites is free.\\nA. Every sensualist is one tvho is enslaved hy his\\nappetites.\\nE. No sensualist is free.\\nDarii.\\nA. All pure patriots deserve the rewards of their\\ncountry.\\nI. Some warriors are pure patriots.\\nI. Some warriors deserve the rewards of their\\ncountry.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0134.jp2"}, "135": {"fulltext": "EXAMPLES IN THE FOUR FIGURES. 129\\nFerio.\\nE. Nothing wMch impedes commerce is beneficial\\nto the revenue.\\nI. Some taxes impede commerce (or are things which\\nimpede commerce).\\n0. Some taxes are not beneficial to tbe revenue.\\nFIGURE II.\\nOesare.\\nE. No vicious conduct is praiseworthy,\\nA. All truly heroic conduct is praiseworthy.\\nE. No truly heroic conduct is (or can be) vicious.\\nQamestres.\\nA. Every true philosopher accounts virtue a good\\nin itself.\\nE. No advocate of pleasure accounts virtue a good\\nin itself.\\nE. No advocate of pleasure is a true philosopher.\\nThe true middle term here would be {one who)\\naccounts virtue a good in itself.\\nFestino.\\nE. No righteous acts will produce ultimate evil to\\nthe actor.\\n1. Some kinds of association will produce ulti-\\nmate evil to the actor.\\nI", "height": "3195", "width": "1911", "jp2-path": "elementsoflogic00copp_0135.jp2"}, "136": {"fulltext": "130 LOGIC.\\n0. Some kinds of association are not righteous\\nacts.\\nFahoro.\\nA. All true patriots d^vQ friends to religion.\\n0. Some great statesmen are noi friends to religion.\\n0. Some great statesmen are not true patriots.\\nFIGURE III.\\nDarapti.\\nA. All ivits are dreaded.\\nA. All wits are admired.\\n1. Some admired (persons) are dreaded.\\nBisamis.\\nI. Some laivful things are inexpedient.\\nA. All lawful things are wliat we have a right\\nto do.\\nI. Some things which we have a right to do are\\ninexpedient.\\nDatisi.\\nA. All tJiat wisdom dictates is right.\\nI. Something that wisdom dictates is amusement.\\nI. Some amusement is right.\\nFelapton.\\nE. No science is capable of perfection.\\nA. All science is worthy of culture.", "height": "3198", "width": "2121", "jp2-path": "elementsoflogic00copp_0136.jp2"}, "137": {"fulltext": "EXAMPLES. 131\\n0. Something worthy of culture is not capable of\\nperfection.\\nDohamo.\\n0. Some nohle characters are not philosophers.\\nA. All nohle characters are worthy of admiration.\\n0. Some (who are )worthy of admiration are not\\nphilosophers\\nFeriso.\\nE. No false theories exist in a perfect state of\\nbeing.\\n1. Some false theories are harmless things.\\n0. Some harmless things do not exist in a perfect\\nstate of being,\\nriauRE IV.\\nBramofntip.\\nA. All oaks are trees.\\nA. All trees are vegetables.\\n1. Some vegetables are oaks.\\nCamenes.\\nA. All miracles are things of rare occurrence,\\nE. No things of rare occurrence make a slight im-\\npression on the mind.\\nE. No (things which) make a slight impression on\\nthe mind are miracles.", "height": "3184", "width": "1777", "jp2-path": "elementsoflogic00copp_0137.jp2"}, "138": {"fulltext": "132 LOGIC.\\nDimaris,\\nI. Some taxes are oppressive.\\nA. All [that is) oppressive should be repealed.\\nI. Some things which should be repealed are taxes.\\nFesapo.\\nE. No immoral acts are proper amusements.\\nA. All proper amusements are designed to give\\npleasure.\\n0. Some (things) designed to give pleasure are not\\nimmoral acts.\\nFresison.\\nE. No acts of injustice are proper means of self-\\nadvancement.\\n1. Some proper means of self-advancement are un-\\nsuccessful.\\n0. Some unsuccessful (efforts) are not acts of in-\\njustice.\\nIt will be observed that the conclusions in the foui th\\nfigure are indirectly stated, and that it would seem as\\nif in tracing the major term back from its place as\\npredicate of the conclusion, it is in reality predicated\\nby means of the other terms of itself; thus in the\\nconclusion it is predicated of the minor, which in the\\nminor premiss is predicated of the middle, which in\\nthe major premiss is predicated of the major. The\\nfourth figure, therefore, is not often used, and is", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0138.jp2"}, "139": {"fulltext": "MOOD. 133\\nrather accidentally stumbled into than employed in-\\ntentionally.\\nThe exact accordancy of the first figure with the\\ndictum of Aristotle has been already stated. Of the\\nsecond figure, it may be remarked that it is commonly\\nused to disprove something that has been maintained,\\nor is likely to be believed, although not true. As an\\nillustration, suppose it had been asserted that\\nAll great statesmen are true patriots.\\nThen our example just given of Fahoro would be a\\nrefutation of this, and the argument would naturally\\ntake that form.\\nOf the third figure, it will appear that it will be\\nuseful where we have singular terms, which can only\\nbe subjects of propositions, e. tiqyqv p redicates and\\nalso where our purpose is to offer and sustain an ob-\\njection to our opponent s premiss, which is particular\\nwhen the argument requires it to be universal.\\nThere are very many inverted and curious forms\\nof arguments growing out of the elliptical and in-\\nverted forms of propositions, which we have already\\nconsidered. Two common examples of these are\\nadded by way of illustration.\\n1.\\nNone but ^vhites are civilized.\\nThe Hindoos are not whites.\\nThe Hindoos are not civilized.\\nThe phrase 7ione hut tvhites, may be rendered, other\\n12", "height": "3187", "width": "1852", "jp2-path": "elementsoflogic00copp_0139.jp2"}, "140": {"fulltext": "134 LOGIC.\\nthan whites and this being the true middle term, we\\nshall have\\nNo other than tohites are civilized.\\nAll Hindoos are other than whites.\\nNo Hindoos are civilized.\\nWhich is evidently a syllogism in Celarent, of the first\\nfigure.\\nNo one is rich who has not enough.\\nNo miser has enough.\\nNo miser is rich.\\nThe major and minor premisses must be put in the\\nform of categorical propositions, and we shall have\\nNo one who has not enough is rich.\\nEvery miser is one who has not enough.\\nNo miser is rich.\\nWhich is likewise in the mood Celarent. In both these\\nexamples the minor premiss, which appears to be a\\nnegative proposition, is in reality affirmative.\\n(39.) Of Reduction,\\nIf we have any imperfect mood, i. e., a mood in\\nthe second, third, or fourth figure, and we desire to\\nprove the same conclusion in the first figure, so that\\nthe dictum of Aristotle may immediately be applied\\nto it the process by which this is done is called\\nHeduction.\\nReduction is of two kinds, direct and indirect.\\nDirect reduction consists in proving in a perfect mood\\neither the same conclusion, or one which, being illa-\\ntively converted, will give us the same conclusion which", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0140.jp2"}, "141": {"fulltext": "REDUCTION. 135\\nwe had in the i7nperfect mood. Indiy ect reduction con-\\nsists in proving, not that the original conclusion is\\ntrue, but that its contradictor^/ is false, from which\\nby the scheme of opposition (30) we know that the\\noriginal conclusion must be true.\\nOf direct reduction.\\nIt has been shown that we have a right to coytvert\\nany of the propositions of the syllogism illatively\\nand it is also evident that we may transpose the pre-\\nmisses without aifecting the truth of the propositions\\nor the validity of the argument. If, then, we apply\\nthe processes indicated by the letters in the mnemonic\\nlines, we shall see that they will give us the forms of\\ndirect reduction.\\nTaking for example Cesare, the mood EAE in\\nthe second figure to write it out we remember in the\\nfirst place that the position of the middle term in the\\nsecond figure is predicate of both premisses, and we\\nobserve that the major premiss is E, universal negative,\\nthe minor premiss A, universal affirmative, and the\\nconclusion E, universal negative we have, then, X\\nbeing the major, 7i the minor, and Y the middle term,\\nCesare. Fig. II.\\nE. No X is Y No men are trees.\\nA. All Z is Y All oaks are trees.\\nE. No Z is X No oaks are men.\\nThe only consonant in the word CEsArE which in-\\ndicates a process of reduction is s, which tells us that", "height": "3183", "width": "1870", "jp2-path": "elementsoflogic00copp_0141.jp2"}, "142": {"fulltext": "136 LOGIC.\\nthe major premiss, expressed by the first E, is to be\\nsimply converted performing this operation we shall\\nhave\\nCelarent. Fig. I.\\nE. No Y is X No trees are men.\\nA. All Z is Y All oaks are trees.\\nE. No Z is X No oaks are men.\\nThis syllogism is in the first figure, since the mid-\\ndle term Y or trees, has become the subject of the\\nmajor and the predicate of the minor premiss again,\\nFakoro. Fig. II.\\nA. All X is Y All good men are virtuous.\\n0. Some Z is not Y Some clergymen are not virtuous.\\n0. Some Z is not X Some clergymen are not good men.\\nThe k expresses that the major premiss (A) is to be\\nconverted by negation performing this operation,\\n(there is no other indicated), we shall have\\nFerio. Fig. I.\\nE. All (not Y) is not X All (not virtuous) are not good men.\\nI. Some Z is (not Y) Some clergymen are (not virtuous).\\n0. Some Z is not X Some clergymen are not good men.\\nThis process, in efi*ect, changes our middle term\\nfrom Y ov virtuous to (not Y) or (not virtuous)^ while\\nwe have the same conclusion as before in the mood\\nFerio y of the first figure.\\nThe reduction of the other moods of the second\\nfigure will be analogous to those already performed,\\nand the student will find no difficulty in reducing\\nthem for himself. Passing then to the third figure^", "height": "3217", "width": "2121", "jp2-path": "elementsoflogic00copp_0142.jp2"}, "143": {"fulltext": "DIRECT EEDUCTION. 137\\nand remembering that in this figure the middle\\nterm is the subject of both premisses^ let us reduce\\nthe mood\\nDisamis. Fig. III.\\nI. Some Y is X Some men are heroes.\\nA. All Y is Z All men are mortal.\\nI. Some Z is X Some mortals are heroes.\\nThe two letters which indicate changes in the pro-\\ncess of reducing this mood are s (twice employed) and\\n7/1:8 indicates the simple conversion of the major\\npremiss and the conclusion, and m, the transposition\\nof the premisses performing these operations, we have\\nDarii. Fig. I.\\nA. All Y is Z All men are mortal.\\nI. Some X is Y Some heroes are men.\\nI. Some X is Z Some heroes are mortal.\\nwhich conclusion is the simple converse of the original\\nconclusion, as was indicated by the final s.\\nFesapo. Fig. IV.\\nE. No X is Y No quadrupeds are men.\\nA. All Y is Z All men are animals.\\n0. Some Z is not X Some animals are not quadrupeds.\\nConverting the major premiss simple/, and the minor\\npremiss by limitation, as indicated by the s and jp, we\\nshall have\\nFerio. Fig. I.\\nE. No Y is X No men are quadrupeds.\\n1. Some Z is Y Some animals are men.\\n0. Some Z is not X Some animals are not quadrupeds.\\nIt will be well for the student to reduce ever^ im-\\n12*", "height": "3195", "width": "1915", "jp2-path": "elementsoflogic00copp_0143.jp2"}, "144": {"fulltext": "138\\nLOGIC.\\nperfect mood, forming for himself particular ex-\\namples under each.\\nAlthough we have made the subject of Reduction\\nplain by the examples already given, we append a\\ntable of the manner of reducing each mood for refer-\\nence, until the student is familiar with them. It is\\nbut a recapitulation in tabular form of what has been\\nalready explained.\\nMood to he. reduced.\\nTf?H re-\\nduce to.\\nProcess of reduction.\\nCesare.\\nCamestres.\\nFig. I. -j\\nFestino.\\nI Fakoro.\\nf Darapti.\\nI Disainis.\\nFig. III. ^Datisi.\\nFelapton.\\nDokamo.\\nFeriso.\\nBramantip.\\nCamenes.\\nDimaris.\\nFig. IV.\\nFesapo.\\nFresison.\\nCelarent.\\nCelarent.\\nFerio.\\nFerio.\\nDarii.\\nDarii.\\nDarii.\\nFerio.\\nDarii.\\nFerio.\\nBarbara.\\nCelarent.\\nDarii.\\nFerio.\\nFerio.\\n(s) Convert major premiss simply.\\n(m) Transpose the premisses, (s s)\\nConvert the minor premiss and con-\\nclusion simply.\\n(s) Convert the major premiss simply.\\n(k) Convert the major premiss by ue-\\ngation.\\n(p) Convert the minor premiss by\\nlimitation.\\n(m) Transpose the premisses, (s s)\\nConvert the minor premiss and con-\\nclusion simply.\\n(s) Convert the minor premiss simply.\\n(p) Convert the minor premiss by\\nlimitation.\\n(k) Convert the major premiss by ne-\\ngation, (m) Transpose the premisses.\\n(s) Convert the minor premiss simply.\\n(m) Transpose the premisses, (p) Con-\\nvert the conclusion by limitation.\\n(m) Transpose the premises, (s) Con-\\nvert the conclusion simply.\\n(m) Transpose the premisses, (s) Con-\\nvert the conclusion simply.\\n(s) Convert the major premiss simply,\\n(p) Convert the minor premiss by\\nlimitation.\\n(s s) Convert the major and minor\\npremisses simply.", "height": "3189", "width": "2121", "jp2-path": "elementsoflogic00copp_0144.jp2"}, "145": {"fulltext": "INDIRECT REDUCTION. 139\\n(40.) Indirect Reduction,\\nThis process, called by the old logicians Beductio\\nad impossihile, is analogous to the reductio ad ahsur-\\ndum of geometry. It consists in proving that the\\ngiven conclusion cannot he false, by proving, in the\\nfirst figure y that its contradictory is false.\\nThe symbols used to indicate the processes of\\ndirect reduction, do not guide us in the indirect re-\\nduction, but we must deduce rules for this apart from\\nthe other.\\nTo illustrate, let us take the mood\\nFakoro. Fig. II.\\nA. All X is Y All good men are virtuous.\\n0. Some Z is not Y Some clergymen are not virtuous.\\n0. Some Z is not X Some clergymen are not good.\\nIf this conclusion he not true, its contradictory All Z\\nis X All clergymen are good, must he true. Assum-\\ning this as true, and taking it in the place of the\\nminor premiss in the syllogism, we shall have a new\\nsyllogism, as follows\\nA, All X is Y All good men are virtuous.\\nA. All Z is X All clergymen are good men.\\nfrom which premisses by our rules we draw the con-\\nclusion\\nA. All Z is Y All clergymen are virtuous.\\nBut this conclusion must be false, because it is the\\ncontradictory of the original minor premiss, and the", "height": "3193", "width": "1783", "jp2-path": "elementsoflogic00copp_0145.jp2"}, "146": {"fulltext": "140 LOGIC.\\npremisses were assumed to be true, lience one of\\nthese last premisses from \u00e2\u0080\u00a2which this conclusion is\\nderived must be false but it is not the major for\\nthat was one of the originally assumed premisses it\\nmust, therefore, be the mijior, which we know to be\\nthe contradictory of our original conclusion and the\\noriginal conclusion must therefore be true this, it\\nAvill be observed, is proven in the first figure, in the\\nmood Barbara. To take another example, let us re-\\nduce the mood\\nDarapti. Fig. III.\\nA. All Y is X All gold is precious.\\nA. All Y is Z All gold is a mineral.\\nI. Some Z is X Some mineral is precious.\\nIf this conclusion be not true, then must its contra-\\ndictory\\nNo Z is X No mineral is precious,\\nbe so. Substituting this as the major premiss in the\\nsyllogism, we have\\nNo Z is X =3 No mineral is precious.\\nAll Y is Z All gold is a mineral.\\nFrom which we draw the new conclusion\\nNo Y is X No gold is precious.\\nBut this conclusion is false, because it is the contrary\\nof the original major premiss, which we assume to be\\ntrue one of the premisses from which it was derived\\nmust be therefore false it cannot be the minor which\\nwas also assumed to be true it must, therefore, be", "height": "3216", "width": "2121", "jp2-path": "elementsoflogic00copp_0146.jp2"}, "147": {"fulltext": "INDIRECT REDUCTION. 141\\nthe major, whicli is the contradictory of the original\\nconclusion; hence, the original conclusion must be\\ntrue.\\nIt will occur, in reducing many of the moods by\\nthis process, as in the last example, that we shall find\\nthe conclusion false because it is the contrary and not\\nthe contradictory of one of the original premisses.\\nBy referring to the subject of Opposition (30), we see\\nthat if one contrary is true the other must be false.\\nWithout presenting a greater number of examples\\nof this kind of reduction, which the student may\\nmultiply for himself, we lay down the following rules\\nfor reducing the various inperfect moods.\\nRules for Indirect Reduction.\\n1st. In the second figure, substitute the contradic-\\ntory of the conclusion for the minor premiss, and pro-\\nceed as above in the mood Fahoro.\\n2d. In the third figure, substitute the contradictory\\nof the conclusion for the major premiss, and proceed\\nas with the mood Darapti.\\n3d. In the fourth figure, substitute the contradictory\\nof the conclusion for the minor premiss, and proceed\\nas before.\\nAs reference is always easier to a tabular form, we\\nannex one showing in what perfect mood the indirect\\nreduction of each imperfect mood will take place", "height": "3195", "width": "1915", "jp2-path": "elementsoflogic00copp_0147.jp2"}, "148": {"fulltext": "142\\nLOGIC.\\nFig. II.\\nFig. III.\\nFig. IV.\\nCesare to Ferio.\\nDarapti to Celarent.\\nBramantip to Celarent.\\nCamestres to Darii.\\nDisamis to Celarent.\\nCamenes to Darii.\\nFestino to Barbara.\\nFelapton to Barbara.\\nDimares to Celarent.\\nDatisi to Ferio.\\nFesapo to Celarent,\\nDokamo to Barbara.\\nFresison to Celarent.\\nFeriso to Darii.\\nBefore proceeding to consider the irregular, infor-\\nmal, and compound syllogisms, we pause to show the\\nmethod of geometrical notation, already referred to,\\nby which the pure syllogism may be expressed.\\n(41.) Notation of the Syllogism,\\nAs there subsists in the mathematics such a rela-\\ntion of analysis to geometry, as that most analysis\\nis capable of geometrical construction, and every form\\nof geometry may be stated analytically in terms of\\nits equation so mathematical logicians have attempted\\nto make for the analysis or symbolic form of the syl-\\nlogism such a geometrical notation as shall at a glance\\nrepresent to the eye, in areas of limited space, what\\nthe symbols do to the mind. Indeed, the idea is so\\nsimple that we have already illustrated the dictum of\\nAristotle through its agency. Many writers, however,\\nhave been inclined to go too far in its use.\\nThe schemes of notation best known are those of\\nEuler, Ploucquet and Lambert, and the more com-\\nplete one of Sir William Hamilton. This latter, how-\\never, passing beyond our needs, is suited to such", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0148.jp2"}, "149": {"fulltext": "NOTATION. 143\\nchanges as would result from the introduction of the\\nneiu analytic, and, as we have advisedly declined to\\nplace that system in our text-book, it is sufficient to\\nmention Sir W. Hamilton s scheme without explain-\\ning it. In a more extended historical treatise it\\nwould demand a special consideration. We can here\\nonly explain what we mean to use.\\nEuler s scheme of notation is altogether the one\\nbest suited to our purpose, and we shall limit our-\\nselves to the explanation of that. It is essentially an\\narrangement of three circles, to represent the three\\nterms of a syllogism, and, by their combination, the\\nthree propositions. Thus if we have the judgment\\nAll men arc mortal,\\nwe know that under this class, all men, are included\\nmany species and individuals as, for example, all\\nAmericans. Representing then the sphere of the\\nconception mortal, by a circle placing within this\\ncircle a smaller one, wholly contained in it, as the\\nsphere of all men, and yet a smaller one wholly con-\\ntained in this latter, as the sphere of all Americans,\\nwe shall have", "height": "3198", "width": "1915", "jp2-path": "elementsoflogic00copp_0149.jp2"}, "150": {"fulltext": "144\\nLOGIC.\\nwhich iy the notation of a syllogism in BArbArA.\\nBy similarity of process, we shall represent the syllo-\\ngism in CElArEnt\\nNo A is B,\\nAll C is A,\\nNo C is B.\\nDArll, will be thus expressed\\nAll A is B,\\nSome C is A,\\nSome C is B.\\nHere it is evident that it is only that some C which is\\ncontained in A that we have a right to assert is also\\ncontained in B, although other portions of C may by\\nchance be also contained in B.\\nFErlO\\nNo A is B,\\nSome C is A,\\nSome C is not B.\\n(2)\\nA", "height": "3201", "width": "2057", "jp2-path": "elementsoflogic00copp_0150.jp2"}, "151": {"fulltext": "NOTATION. 145\\nHere two cases are presented where no C is B, and\\n-where some C is B neither of which affects the truth\\nof the conclusion that some Q is not B. We have\\nonly applied this scheme to the first figure, but by\\nthis simple notation of Euler every syllogism in the\\nother figures may be represented to the eye, and made\\nclear to those who are much quicker at geometry than\\nat analytical work. Take for example Darajpti of\\nthe third figure\\nAU A is B,\\nAJl A is C,\\nSome C is B.\\nBut besides this representation of valid syllogisms,\\nthis system exposes at once fallacious arguments and\\nacts as a test upon a test of their unsoundness. Take\\nfor example the case of illicit process of the major\\nterm\\nAll quadrupeds are animals,\\nA bird is not a quadruped,\\nA bird is not an animal.\\nIn which the figure denies the conclusion by allowing\\nthe premisses, and yet showing that birds are contained\\n13", "height": "3185", "width": "1915", "jp2-path": "elementsoflogic00copp_0151.jp2"}, "152": {"fulltext": "146 LOGIC.\\nunder the genus animal. Or if we take the case of\\nDegative premisses\\nNo A is B,\\nNo C is A,\\nthe figure shows us that there is no relation whatever\\nestablished between or among the terms which would\\nentitle us to a conclusion.\\nThe student will find it easy and pleasant to write\\nout all the moods and the logical fallacies by this cir-\\ncular method of notation and, as two modes of coming\\nat facts make the memory more tenacious of them,\\nthis practice will fix clearly in his mind the moods\\nand figures of the syllogism.\\nThis system also illustrates the categorical proposi-\\ntions as to the distribution of their terms, very satis-\\nfactorily\\nAU A is B,\\nNo A. is B,\\nSome A is not B", "height": "3195", "width": "2121", "jp2-path": "elementsoflogic00copp_0152.jp2"}, "153": {"fulltext": "ABRIDGED SYLLOaiSMS. 147\\nCHAPTER IX.\\nOF IRREGULAR, INFORMAL, AND COMPOUND ARGU-\\nMENTS.\\n(42.) Of Abridged Syllogisms,\\nWe have thus far considered only those arguments\\nwhich appear directly and without analysis in the\\nform of a simple syllogism and have explained those\\nprocesses which we perform upon known and acknow-\\nledged facts, stated as premisses and conclusion but\\nthe mind of man sometimes passes intuitively over\\ncertain steps of these processes without stopping to\\nexpress them, which gives rise to abridged arguments\\nor it halts in doubt and uncertainty, being not sure\\nof its facts, but frequently balancing between two,\\none of which must be true, because of the truth or\\nfalsity of the other. This produces hypothetical\\nsyllogisms.\\nAW these in the present chapter will be treated of\\nas informal syllogisms, or arguments which are not", "height": "3195", "width": "1915", "jp2-path": "elementsoflogic00copp_0153.jp2"}, "154": {"fulltext": "148 LOGIC.\\nsyllogisms in form^ but which, if they be valid, must\\nbe capable of being put into the syllogistic form.\\nThe first of the abridged arguments to be con-\\nsidered, because the one in most common use, is\\nThe Entity meme.\\nThe enthymeme is a syllogism with one premiss sup-\\npressed it matters not which thus, having the syl-\\nlogism,\\nAll men are mortal,\\nCassar is a man,\\nCeesar is mortal,\\nwe may suppress the major premiss and write the\\nenthymeme,\\nCaesar is a man.\\nTherefore Caesar is mortal.\\nOr suppressing the minor premiss,, we have,\\nAll men are mortal.\\nTherefore Caesar is mortal,\\neither of which is a satisfactory expression, because\\nall three terms of the syllogism are expressed in either\\nform of the enthymeme, and we can at once recon-\\nstruct the syllogism thus, taking the latter form,\\nwith the minor premiss suppressed, we see by examin-\\ning the conclusion, in which the major and minor\\nterms are always contained, that Ccesar is the minor,\\nbeing the subject of the conclusion, and mortal the\\nmajor, being the predicate. 3Ien, then, must be the\\nevdvficonai, to conceivc in the mind.", "height": "3197", "width": "2121", "jp2-path": "elementsoflogic00copp_0154.jp2"}, "155": {"fulltext": "THE ENTHYMEME. 149\\nmiddle term, and we at once compare it witli tlie\\nminor term to form the suppressed premiss thus\\nCaesar is a man.\\nBy a similar process we may reconstruct the syllo-\\ngism when the major premiss is suppressed.\\nIt is worthy of observation that in ordinary dis-\\ncourse men suppress the major premiss habitually, as\\nthat to which the mind most readily yields assent,\\nalthough if the proof of its truth be required, the\\ntask would be more difficult than to establish the truth\\nof the minor. Thus, in the example given above, we\\nwould take for granted as a fact that\\nAll men are mortal\\nwhereas, without the declarations of the Bible and\\nLogic, as a science, moves independently of any ex-\\ntraordinary or supernatural dicta this proposition is\\nincapable of proof; for, although all men have died\\nthus far in the world s history, the process of induc-\\ntion cannot be finished until the end of man as a race.\\nBut this seems like a cavil. The major premiss,\\nalthough thus incapable of mathematical proof, is the\\none which most surely demands belief; and so, when\\nin the enthymeme we speak of the suppressed pre-\\nmiss, we mean the major premiss, unless it be other-\\nwise explained.\\nAs a simple rule for reconstructing the syllogism\\nfrom the enthymeme, we observe that,\\n13", "height": "3189", "width": "1810", "jp2-path": "elementsoflogic00copp_0155.jp2"}, "156": {"fulltext": "150 LOGIC.\\nIf the subject of the conclusion be found in the\\nexpressed premiss, that premiss is the minor. If the\\npredicate of the conclusion be found in the expressed\\npremiss, it is the major.\\nSometimes it becomes necessary to put the enthy-\\nmeme into logical form before proceeding to recon-\\nstruct it. Thus, the example given above might be,\\nand most commonly is, thus spoken or written\\nCsesar is mortal,\\nBecause Csesar is a man.\\nwhich is evidently a transposed form of the enthy-\\nmeme. Whenever the causal conjunction because\\nunites the propositions of an enthymeme, we may in-\\nvert the propositions and unite them with the illative\\nconjunction therefore, and then proceed to reconstruct\\nthe syllogism, thus\\nCsesar is a man,\\nTherefore He is mortal.\\nMany abridged arguments which appear in a hypo-\\nthetical form, are in reality simple enthymemes, thus\\nIf murder is a crime,\\nThe murderer should suffer.\\nIn which there is really no hypothesis or condition in\\nthe premiss, because all allow that murder is a crime\\nand are consequently ready to declare that\\nThe murderer should suffer.\\nWhen the enthymeme has been reconstructed into a", "height": "3196", "width": "2059", "jp2-path": "elementsoflogic00copp_0156.jp2"}, "157": {"fulltext": "THE SORITES. 151\\nsyllogism in any one of the figures, we shall be able\\nto put it directly into the first figure, and can then\\napply to it the test of Aristotle s dictum.\\n(43.) The jSarites,^ or Chain ATgument.-\\\\\\nThe Sorites is an abridged argument consisting of\\na series of propositions in which the predicate of the\\nfirst is the subject of the second the predicate of\\nthe second the subject of the third, and so on until\\nwe combine the subject of the first and the predicate\\nof the last to form a conclusion. Thus\\nA is B The mind is a thinking substance.\\nB is G A thinking substance is a spirit.\\nC is D A spirit has no composition of parts.\\nD is E (That which has) no composition of parts is indissoluble.\\nE is P (That which is) indissoluble is immortal.\\nConcl. A is F The mind is immortal.\\nNow, if we try to put this collection of abridged\\narguments into the syllogistic form, in order to apply\\nthe dictum of Aristotle to them, we shall see that the\\nSorites is an abridgment of a series of syllogisms in\\nthe first figure that the terms B, C, D, and E, which\\nare used twice, are middle terms, and that we may\\nconstruct as many syllogisms as we have middle terms.\\nTaking then the second proposition of the sorites, B\\nis (7, as the major premiss of the first syllogism and\\n(rapsiTTis a heap, or collection.\\nf Called by the Germans, more significantly, Kettenschluss, or chain\\nargument.\\nX This example is borrowed from Hedge s Logic, as it is one of the\\nbest for illustration.", "height": "3195", "width": "1867", "jp2-path": "elementsoflogic00copp_0157.jp2"}, "158": {"fulltext": "152 LOGIC.\\nthe first A is B, as the minor, we shall have as a con-\\nclusion A is 0, which we use as the minor premiss of\\na second syllogism, using the third proposition of\\nthe sorites as a major premiss and so on, as long as\\nthe middle terms last, thus\\nIst.\\n2d.\\n3d.\\n4th.\\nBisC,\\nCisD,\\nDisE,\\nEis F,\\nAisB,\\nAisC,\\nAisD,\\nA is E,\\nAisC.\\nA is D.\\nAisE.\\nAisF.\\nA thinking substance is a spirit.\\n1st. The mind is a thinking substance.\\nThe mind is a spirit,\\nA spirit has no composition of parts.\\n2d. The mind is a spirit.\\nThe mind has no composition of parts.\\nThat which has no composition of parts is indissoluble.\\n3d, The mind has no composition of parts.\\nThe mind is indissoluble.\\nThat which is indissoluble is immortal.\\n4th. The mind is indissoluble.\\nThe mind is immortal.\\nThese are all in the first figure, and consequently are\\nforms to which the dictum will directly apply.\\nIt must be observed that in the sorites the first pro-\\nposition, A is B, is the only one which may be particu-\\nlar, because it is the only minor premiss expressed,\\nevery other being used as a major, and we have\\nalready seen that in the first figure the major premiss\\nmust be universal.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0158.jp2"}, "159": {"fulltext": "THE SOEITES. 153\\nSo, again, the last proposition, E is F^ is tlie only\\none that may be negative, for, if any other be nega-\\ntive, we should have in one of the syllogisms a nega-\\ntive conclusion which is to be in turn the minor pre-\\nmiss of the succeeding syllogism, and we have already\\nshown that in the first figure the minor premiss must\\nbe affirmative. But the conclusion deduced from the\\nlast syllogism does not become a minor premiss, and\\nso the last conclusion may be negative it would then\\nread thus\\nNo E is F.\\nAll A is E.\\nNo A is F.\\nOr the chain of the sorites would be broken in what-\\never place the negative proposition should occur.\\nThe sorites is a very simple and conclusive abridged\\nform of argument for the mind, taking the only ex-\\npressed minor term A, which is expressed in the\\nchain, links it by jumping from middle term to middle\\nterm, B, C, D, E, to the final major term or F, as\\nsurely and more easily, than in the syllogisms into\\nwhich it is elaborated.\\nBy its aid we easily establish the points in any\\ngreat argument, either as recapitulating the process\\nof the argument, or as stating them preparatory to a\\ncomprehensive discussion. Thus, to establish the\\nefi ect of a republican government, we shall have,", "height": "3187", "width": "1901", "jp2-path": "elementsoflogic00copp_0159.jp2"}, "160": {"fulltext": "154 LOGIC.\\nThe Americans make their own laws.\\nThose who make their own laws are free.\\nThose who are free are contented.\\nThose who are contented are happy.\\nTherefore The Americans are happy.\\nIt is evident that the sorites may be properly stated\\nin the inverse order thus\\nD is E, C is D, B is C, A is B,\\nTherefore A is E.\\nHere the sorites starts from its widest terms, D\\nand E, to include the narrower and more limited\\nterms, C, B, and finally, A.\\nThis form is called the Goclenian Sorites^ from the\\nname of its originator. It serves, perhaps, better to\\nillustrate the fact stated that only the most extensive\\nproposition, which in the ordinary form is the last^ and\\nin this, the first, may be negative which, as we have\\nseen, will give us a negative conclusion thus\\nD is not E, C is D, B is C, A is B,\\nTherefore A is not E.\\nHypotJietical Sorites.\\nIf we have a string of conditional propositions,\\nsuch that the consequent of each becomes the ante-\\ncedent of the succeeding one, the argument is called\\na hypothetical sorites, and the conclusion is obtained\\neither by affirming the first antecedent with the last", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0160.jp2"}, "161": {"fulltext": "THE EPICHIREMA. 155\\nconsequent, or by denying the last consequent with\\nthe first antecedent thus\\n1. If A is B, C is D If C is D, E is F\\nBut Ais B, Therefore E is F.\\n2. If A is B, C is D If C is D, E is F\\nBut JS/ is not F, Therefore A is not B.\\nExamplss.\\n1.\\nIf the Bible is from God it should be taught\\nIf it should be taught, men should be set apart to teach\\nIf men should be set apart to teach, they should be supported\\nBut the Bible is from God, therefore its teachers should be supported,\\n2.\\nIf the Bible is false, it deceives the world\\nIf it deceives the world .it should be destroyed\\nBut it should not be destroyed, therefore it is not false.\\nTo the hypothetical sorites it is evident that the\\nGoclenian form will also apply. Indeed this is illus-\\ntrated in the last case mentioned, where we reason\\nback from the denial of the last consequent to the\\ndenial of the^rs^ antecedent.\\n(44.) Of the EpicliiremaJ^\\nMost arguments employed in ordinary conversation\\nand writing consist of simple syllogisms, abridged\\ninto enthymemes, linked together in a compound form\\nThe Greeks seem to have considered this a great logical weapon,\\nas the name they gave it signifies a violent onset, or laying of hands\\nupon, em, and x^^p-", "height": "3191", "width": "1852", "jp2-path": "elementsoflogic00copp_0161.jp2"}, "162": {"fulltext": "156 LOGIC.\\nbut in many cases the form of the syllogism is ob-\\nserved, where the premisses are arguments in them-\\nselves. When the premisses are thus separately\\nestablished, before the conclusion is deduced, the\\nargument is called an Epichii ema thus\\nThe victors are injured by war because it hardens their hearts\\nThe French were victors al Marengo, for they retained the field\\nThe French were injured by their victory.\\nThe major premiss is an enthymeme, which may be\\nexpanded into a syllogism the same is true of the\\nminor hence we have two distinct arguments within\\nthe one which originally appeared. To apply the\\ntests to their validity, they need only be written out\\nin syllogistic form. In most apparently simple syllo-\\ngisms, there is in reality implied the epichirema. As\\nfor example, in the one given to illustrate the mood\\nFakoro, of the second figure,\\nAll true patriots are friends to religion,\\nSome great statesmen are not friends to religion,\\nSome great statesmen are not true patriots,\\nthe major premiss demands in itself a reason.\\nThus:\\nAll true patriots are friends to religion, because religion is the basis\\nof national prosperity and advancement.\\nSo also does the minor.\\nSome great statesmen are not friends to religion, because their own\\nlives are not in accordance with its precepts.\\nEach of the premisses given is an enthymeme of", "height": "3188", "width": "2121", "jp2-path": "elementsoflogic00copp_0162.jp2"}, "163": {"fulltext": "HYPOTHETICAL SYLLOGISMS. 157\\nwhich the clause because, ^c, is the premiss, and the\\nfirst statement, all true patriots, ^c, is the conclusion.\\nNow, this premiss to the premiss is called the pro-\\nsyllogism.\\nSometimes the establishment of the final conclu-\\nsion will warrant us in drawing other conclusions\\nalso thus\\nA is B,\\nC is A,\\nTherefore C is B.\\nTherefore X is Y, c.\\nThis conclusion from a conclusion (X is Y) is called\\nthe epi-syllogism.\\nTo take the example before quoted, we shall have\\nAll true patriots are friends to religion.\\nSome great statesmen are not friends to religion.\\nSome great statesmen are not true patriots.\\nTherefore They deceive their countrymen,\\nand Deserve no rewards from their country, ^c.\\n(45.) Of Hypothetical Syllogisms.\\nCorresponding to the various forms of hypothetical\\npropositions, viz., conditional, causal, disjunctive, c.,\\nwe have conditional, disjunctive and causal syllogisms.\\nThey are all of so simple a nature that the mind\\nfinds no difficulty in the ratiocination which they ex-\\npress but as we have asserted that, if valid, they\\nmay be reduced to the form of a categorical syllogism\\n14", "height": "3169", "width": "1877", "jp2-path": "elementsoflogic00copp_0163.jp2"}, "164": {"fulltext": "158 LOGIC.\\nill the first figure, we proceed to show how this may\\nbe done.\\nConditional Syllogisms.\\nIf we examine a conditional proposition we shall\\nsee at once that the affirmation of the consequent will\\nfollow from the affirrtiation of the antecedent thus\\nIf A is B, G is D If he has a fever, he is sick.\\nBut if we de7iy the antecedent, we may not therefore\\ndeny the consequent, since this consequent might\\nspring from some other antecedent as well as from\\nthe one given. Thus\\nIf A is not B, if he has not a fever,\\nwe cannot say,\\nC is not i) he is not sick.\\nsince\\nC might he D he might be sick,\\nfrom some other cause than\\nA being B, or his not hav-ing a fever.\\nFor similar reasons we may pass from the denial of\\nthe consequent to the denial of the antecedent, but\\nnot from the affirmatioii of the consequent to the\\naffirmation of the antecedent. When we pass from\\nthe affirmation of the antecedent to the affirmation\\nof the consequent, the reasoning is called constructive\\nand when we pass from the denial of the consequent\\nto the denial of th antecedent, it is called destructive.\\nWe may form, then, tivo, and only tivo, forms of\\nconditional syllogisms, constructive and destructive.\\nTo form the first we take the whole conditional pro-", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0164.jp2"}, "165": {"fulltext": "CONDITIONAL SYLLOGISMS. 159\\nposition as the major 2^ ^emiss the affirmation of the\\nantecedent for the minor, from -which premisses we\\nshall draw the affirmation of the consequent as the\\nconclusion; thus\\n3IoJ. prem. If A is B, C is D If Le has a fever, he is sick.\\nMin. prem. A is B He has a fever.\\nConclusion. C is D He is sick.\\nTo frame the destructive conditional syllogism, we\\ntake the whole proposition as before for a major pre-\\nmiss the denial of the consequent for a minor, and\\nwe deduce as a conclusion the denial of the antece-\\ndent; thus\\nJfff/. prem. If A is B, C is D If he has a fever, he is sick.\\n3Iin. prem. C is not D He is not sick.\\nConclusion. A is not B He has not a fever.\\nAs these are the only possible forms of conditional\\nsyllogisms, and as we have shown that all other forms\\nof hypothetical propositions, disjunctive, causal, c.,\\nmay be easily reduced to conditional propositions we\\nhave only to show how these conditional syllogisms\\nmay be reduced to the form of simple categorical syl-\\nlogisms, and we shall, in effect, have shown it for all.\\nConsidering first, the constructive form, and remem-\\nbering that the form of condition may be removed by\\nthe phrases ^^the case of, and -^the present case;\\nand that the proposition assumes the form of a cate-\\ngorical proposition, of which the antecedent hecomes\\nthe subject, and the consequent hecomes a predicate, we\\nshall have for the constructive form,", "height": "3219", "width": "1960", "jp2-path": "elementsoflogic00copp_0165.jp2"}, "166": {"fulltext": "160 LOGIC.\\nX\\nMaj. prem. The case of A being B is the case of C being D.\\nZ X\\nMin. prem. The present case is the case of A being B.\\nZ Y\\nConcl. The present case is the case of C being D.\\nor, All X is Y. (A.)\\nAll Z is X. (A.)\\nAll Z is Y. (A.)\\nwhich, X being the middle term, is evidently in the\\nfirst figure, and the dictum may be at once applied.\\nUsing the same phraseology, and thus translating the\\ndestructive form, we have,\\nX Y\\nThe case of A being B is the case of C being D.\\nZ Y\\nThe present case is not the case of C being D.\\nZ X\\nThe present case\\nis not\\nthe case of A being B,\\nor,\\nAll X is Y.\\n(A.)\\nNo Z is Y.\\n(E.)\\nNo Z is X.\\n(E.J\\nwhich, Y being the middle term, is in the second\\nfigure, and in the mood Camesfres, which must be re-\\nduced to the first figure, or the form of the dictum.\\nIf, now, we perform the operations indicated to re-\\nduce this mood {771, s, s), we simply convert the minor", "height": "3220", "width": "2121", "jp2-path": "elementsoflogic00copp_0166.jp2"}, "167": {"fulltext": "CONDITIONAL SYLLOGISMS. 161\\npremiss, and then transpose the premisses, and simply\\nconvert the conclusion we shall have,\\nY z\\nThe case of C being D is not the present case.\\nX Y\\nThe case of A being B is the case of C being D.\\nX Z\\nThe case of A being B is not the present case.\\nor simply converting the conclusion,\\nZ X\\nThe present case is not the case of A being B.\\nNo Y is Z. (E.)\\nAllXisY. (A.)\\nNoXisZ. (E.)\\nor, No Z is X.\\nwhich is the form of Oelarent in the first figure.\\nThe logical form of the conditional does not depend\\nupon the suhject-matter of the propositions composing\\nit. There may be, for example, two apparently inde-\\npendent propositions, that is, propositions in which\\nthe terms are entirely distinct, thus conjoined, or there\\nmay be a term the same in each which will cause no\\ndifference in the logical form thus we may have\\nIf A is B, C is D If John remain, James will go; or,\\nIf A is B, A is C If the Bible is true, it (the Bible) deserves our\\nattention.\\n14* ^L", "height": "3179", "width": "1908", "jp2-path": "elementsoflogic00copp_0167.jp2"}, "168": {"fulltext": "162 LOGIC.\\nTo explain this apparent difference, it will be re-\\nmembered that A, B, C, c., although terms in the\\nproposition, are not the terms of the syllogism when\\nit is put in a categorical form but that the antece-\\ndent and consequent become the true terms, and there-\\nfore it matters not whether there be three or four\\nindependent terms in the conditional proposition\\nbefore its change of form.\\nA few examples of conditional syllogisms are given\\nto accustom the student to the form, and to guard\\nhim against the improper use of it.\\nExamples.\\n1.\\nIf the fourth commandment is obligatory upon us, we are bound\\nto set apart one day in seven.\\nBut the fourth commandment is obligatory upon us.\\nTherefore we are bound to set apart, c.\\n2,\\nIf any theory could be framed to explain the establishment of\\nChristianity, by human causes, such a theory would have been\\nproposed before now.\\nBut none has been proposed.\\nTherefore, no such can be framed.\\n3.\\nIf the eclipses of Jupiter s moons occur sixteen minutes later,\\nwhen the earth is farthest from Jupiter than when she is neare8.t\\nto Jupiter, light must travel ninety-five millions of miles in eiglit\\nminutes.\\nBut these eclipses do occur so much later in the given position.\\nTherefore light travels at the rate stated or, two hundred\\nthousand miles in a second.\\n4.\\nIf taste is uniform, all men will admire the same objects.", "height": "3192", "width": "2121", "jp2-path": "elementsoflogic00copp_0168.jp2"}, "169": {"fulltext": "DISJUNCTIVE SYLLOGISMS. 163\\nBut all men do not admire the same objects (one sees beauty\\nwhere another only finds deformity).\\nTherefore, taste is not uniform.\\nDisjunctive Syllogisms.\\nA disjunctive syllogism is one, the major premiss\\nof which is a disjunctive propositio7i (26), and the\\nminor a categorical.\\nBrutus was either a parricide or a patriot Either A is B, or it is C.\\nHe was not a parricide A is not B.\\nHe was a patriot A is C.\\nHere, when the major premiss consists of two\\nmembers only, the minor asserts the one and the con-\\nclusion denies the other or the minor denies the one\\nand the conclusion asserts the other. Or we may\\nhave, instead of two alternatives, three or more\\nthus\\nThe angle A must be equal to, or greater or less than the angle B.\\nBut it is neither equal to or less than it.\\nTherefore it is equal to it.\\nIt is evident that the disjunctive syllogism may be at\\nonce stated in a categorical form by any simple phrase-\\nology which will rid us of the disjunctive form thus\\nBrutus could not be at the same time a parricide and a patriot\\n(but must be one of the two).\\nHe was a patriot.\\nTherefore he was not a parricide,\\nor, He was not a parricide,\\nTherefore he was a patriot.", "height": "3185", "width": "1898", "jp2-path": "elementsoflogic00copp_0169.jp2"}, "170": {"fulltext": "164 LOGIC.\\nExamples of Disjunctive Syllogisms.\\n1.\\nIt is either true that knowledge is useful, or that ignorance is so.\\nBut it is not true that ignorance is useful.\\nTherefore knowledge is so.\\n2.\\nMahomet was either an enthusiast or an impostor.\\nHe was an enthusiast.\\nTherefore he was not an impostor.\\nThis is Gibbon s argument, but it is faulty in point\\nof fact, for a man may be both enthusiast and im-\\npostor, and some men have a great enthusiasm for\\nimposture.\\n3.\\nA government either licenses a free press, or it is oppressive.\\nThe French government does not license a free press.\\nTherefore it is oppressive.\\n4.\\nA wise lawgiver must either recognise future rewards and pun-\\nishments, or must appeal to an extraordinary Providence.\\nMoses did not do the former.\\nTherefore he must have done the latter.\\nOf the Dilemma^ Trilemma, ^c.\\nA dilemma is a compound argument composed of\\nconditional propositions, upon which we reason dis-\\njunctively. When two conditional syllogisms are com-\\nbined with a disjunctive minor premiss, the argument\\nis called a dilemma. When three, four, c., are so com-\\nbined, they constitute a trilemma, tessaralemma, c.\\nThe generic name Dilemma, however, is technically\\ngiven to them all. Dilemmas are divided into four", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0170.jp2"}, "171": {"fulltext": "THE DILEMMA.\\n165\\nkinds, according to their being simple or complex,\\nconstructive or destructive.\\nA simple dilemma is one in wMcIl we have as a\\nmajor premiss, several antecedents, with a single con-\\nsequent, thus:\\nprem.\\nCo7iclusion. Therefore X is Y.\\nA complex dilemma is one in which we have several\\nantecedents, and each has its own consequent, thus\\nBut either\\nIf A is B,\\nIfCisD,\\nthen X is Y.\\n3Iin. prem.\\nAisB\\nor\\nCisD\\nor\\nIf E is F,\\nEisF\\nr\\nMaj. prem.\\nIf A is B, G is H.\\nIf C is D, I is K.\\nIf E is F, L is M.\\nConclusion. Therefore\\nMm. prem.\\nEither\\nGisH\\nor\\nlisK\\nor\\nLis M\\nEither\\nAis B\\nor\\nCis D\\nor\\nEisF\\nNow, if in the simple dilemma, instead of reasoning\\nas we have done constructively from the disjunctive\\naffirmation of the antecedents to the disjunctive affirma-\\ntion of the consequent, we reason destructively^ that\\nis, deny the single consequent; then all the antecedents\\nfall to the ground there is no longer the condition\\nof the dilemma for we have a simple conditional", "height": "3185", "width": "1887", "jp2-path": "elementsoflogic00copp_0171.jp2"}, "172": {"fulltext": "166 LOGIC.\\nsyllogism. Or if wc have one antecedent and several\\nconsequents^ aud reason destructively it is as though\\nwe had but 07ie co7isequent, since the denial of any\\none requires the denial of the one antecedent thus, in\\nthe argument,\\nr C is D,\\nIf A is B, G is H,\\nL is M,\\nit matters not whether we deny one or all the conse-\\nquents, the denial of the antecedent follows. Hence,\\nproperly speaking, there is no such thing as a simjjle\\ndestructive dilemma. It differs in no wise from a\\nsimple destructive conditional syllogism.\\nThe destructive dilemma proper, then, consists of\\nseveral antecedents, each with its own consequent, in\\nwhich we disjunctively deny the consequents, that is,\\ndeny any one of them or all in turn, and we may\\ndisjunctively deny the antecedents.\\nIf A is B, CisD. But either C is not D,\\nMaj.prem. 3hn. prem.\\nIfGisH, LisM. or Lis not M.\\nc.\\nc.\\nConclusion.\\nTherefore either A is not B,\\nor G is not H.\\nTo apply this abstract form to a particular example\\nlet us take the argument of Antisthenes\\n_, If we conduct the affairs of state well, we offend men.\\nIf we conduct them ill, we offend the gods.\\nIf now we reason constructively we shall add,\\nBut, we must either conduct them well,\\nMin. prem. i ^i -n\\nor conduct them ill.\\nConclusion. Therefore we must either offend men,\\nor offend the gods.", "height": "3216", "width": "2121", "jp2-path": "elementsoflogic00copp_0172.jp2"}, "173": {"fulltext": "THE DILEMxMA. 167\\nIf we reason destructively, we add as a minor\\nBut we must either not offend men, or not offend the gods.\\nand as a conclusion^\\nTherefore, we must either not conduct them well, or not conduct\\nthem ill.\\nTo rid themselves of the perplexities of the dilemma,\\nthe old logicians always established from their pre-\\nmisses an undue, because not a logical conclusion, but\\na moral and material one, a passage of the mind to a\\npurpose which had been suggested by the matter of\\nthe argument; thus, the conclusion of Antisthenes\\nfrom the perplexity of the dilemma was, that we had\\nbetter not meddle with the affairs of state at all. Take\\nanother illustration\\nIf a wife is beautiful, she excites jealousy\\nIf she is ugly, she gives disgust\\nand the illogical, but common conclusion is.\\nIt is best not to marry.\\nMost logicians have erred at the very outset, by\\nsupposing that, because there is an alternative ex-\\npressed in the dilemma, it is a disjunctive instead of\\na conditional syllogism, and thus have rendered it a\\nvehicle of fallacy which it would be impossible foi\\nLogic to arrest thus, they would read the last ex-\\nample.\\nEither a wife excites jealousy by her beauty.\\nOr disgust by her ugliness\\nHence it is better not to marry.", "height": "3178", "width": "1898", "jp2-path": "elementsoflogic00copp_0173.jp2"}, "174": {"fulltext": "168 LOGIC.\\nIn any such case, if we first put the dilemma in its\\ntrue conditional form, and then {leaving the province\\nof Logic which presumes all given propositions to be\\ntrue) examine the subject-matter of the propositions\\nthemselves, we shall find the falsity which causes per-\\nplexity thus, it is not true universally^ nor commonly^\\nas is implied in the example, that if a wife is beauti-\\nful, she excites jealousy. It is even less true, that is\\nin a fewer number of cases, that if she be ugly, she\\ncauses disgust hence the conclusion, that it is best\\nnot to marry is less true, i. e., applies to a fewer num-\\nber of cases than either of the foregoing assertions,\\ni. e. the falsehood is increased by the number of false\\nstatements preceding the conclusion.\\nIt is evident that the dilemma may be resolved into\\nas many conditional syllogisms as the greatest num-\\nber of antecedents or consequents and that these\\nmay be reduced according to the rules for the reduc-\\ntion of conditional syllogisms.\\nAny dilemma may also be stated in a categorical\\nform. Thus,\\nThe case of A being B, is the case of G being H.\\nThe case of C being D, is the case of E being F.\\nand we may then proceed as in conditional syllogisms.\\nExamples of the Dilemma.\\n1.\\nIf Eschines joined in the public rejoicings, he was inconsistent.\\nIf he did not, he was unpatriotic.\\nBut either he did join, or he did not:\\nTherefore, he was either inconsistent, or unpatriotic.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0174.jp2"}, "175": {"fulltext": "THE DILEMMA. 169\\nThe following dilemma was formed to confute the\\ndoctrine of Pyrrho, the sceptic, which was, that be-\\ncause everything has its contradictory, everything is\\nfalse or, that no one could know anything cer-\\ntainly.\\n2.\\nIf what you say is true, then there is something which is not\\nfalse [i. e..your system is wrong).\\nIf what you say is false, then it has no value as an argument (i. e.\\nyour system is wrong).\\nBut what you say must be either true or false.\\nTherefore, in either case your system is wrong.\\n3.\\nThere are two kinds of things which we ought not to fret about:\\nwhat we can help, and what we cannot.\\n(The student will put this in the form of a dilemma.)\\nHaving explained the various forms of argument,\\nsimple and compound, our next subject of investiga-\\ntion is of the erroneous use of these forms to this\\nhas been given the generic title of Fallacies.\\n15", "height": "3179", "width": "1896", "jp2-path": "elementsoflogic00copp_0175.jp2"}, "176": {"fulltext": "170 LOGIC.\\nCHAPTER X.\\nFALLACIES.\\n(46.) The Meaning and Comjprehension of a\\nFallacy.\\nDifferent terms are used to express the errors\\nwhich are found in terms, propositions, or arguments,\\nin Logic. Thus, we say of a term, when it is not uni-\\nvocal, i. e. when it has not one meaning, and only om,\\nthat it is equivocal or ambiguous, i. e. has more than one\\nmeaning of a proposition, if it be not true, that it is\\nfalse, which expresses in other words, that the predi-\\ncate and subject have no proper connexion of an\\nargument we say, when it violates the dictum of Aris-\\ntotle or any of the rules given, that it is invalid, and\\nsometimes of an invalid argument, we say that it is\\nfallacious.\\nA fallacy, then, is an invalid argument, which ap-\\npears at first sight to he valid. If it be used with the\\nintejition to deceive, the fallacy is called a sophism. An", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0176.jp2"}, "177": {"fulltext": "FALLACIES. 171\\nargument manifestly and foolishly invalid, would tlien\\nbe neither a sophism nor a fallacy.\\nThe subject of fallacies is one of the most import-\\nant in the study of Logic, for not only is Logic de-\\nsigned to teach us to reason correctly, but also it\\nshould teach us to perceive and detect all errors in\\nreasoning hence we find the earliest writers on Logic\\ngiving rules and cautions for avoiding and detecting\\nfallacies.\\nThe first division of fallacies which they have made\\nis into fallacies in dictions, and extra dictionem. As\\ndictio means the form of words and not the meaning\\nof the words, or what is expressed in our word\\ndiction, the class in dictione, or fallacies in form,\\nwill evidently come within the province of Logic,\\nwhile those extra dictionem, not being in the form,\\nbut in the subject-matter, with which Logic is only in-\\ndirectly concerned, will really not fall within the\\nscope of our study.\\nBut since the line between the two, although easy\\nto be drawn, is continually mistaken in practical argu-\\nment or controversy unless it be thus drawn, it be-\\ncomes necessary to explain both classes with care,\\nthat we may always distinguish between the truly\\nLogical and the non-Logical or material fallacies.\\nOne class of these material fallacies, which arises\\nfrom the ambiguity in words, and is therefore called", "height": "3178", "width": "1906", "jp2-path": "elementsoflogic00copp_0177.jp2"}, "178": {"fulltext": "172 LOGIC.\\nverbal fallacies, needs but a slight change, as we shall\\nsee, to become formal or logical fallacies.\\n(47.) Of Fallacies in dictio7ie, or Formal\\nFallacies.\\nThese are the fallacies, about which Logic is par-\\nticularly concerned.\\nUnder this class are included all violations of the\\ndictum of Aristotle, and of the axioms and rules\\nlaid down for determining the validity of an argu-\\nment. The fallacy in all cases under this head is\\napparent in the form of the expression hence the\\nname, formal fallacies. Of this kind are\\n1. Undistributed middle terms.\\n2. Illicit process of either term.\\n3. Negative premisses.\\n4. Affirmative conclusion from a negative premiss,\\nand vice versa.\\n5. More than three terms in the argument.\\nOf these, repeated examples have been already\\ngiven, in syllogistic form it is only by putting them\\nin this form that the fallacy is at once and easily\\ndetected.\\nBut it should be borne in mind that in practice,\\nsuch fallacies are not stated in the syllogistic form,\\nin which they are thus easily to be detected, but are\\nstated in the form of an enthymeme, or other abridged", "height": "3217", "width": "2121", "jp2-path": "elementsoflogic00copp_0178.jp2"}, "179": {"fulltext": "FALLACIES. 173\\nargument, and so covered with words that the effect\\nis produced without the mind being convinced the\\nconclusion allowed, because the mind cannot see\\nthe false steps which have been used, although it has\\nnot certified itself that the true have been taken.\\nLet the student then take the trouble, in each such\\ncase, to write out the argument in syllogistic form,\\nand, for greater clearness, to use symhols, and the in-\\nvalidity will be apparent.\\nThus, Ave are told that a certain man was a good\\nfather, because he attended to the physical necessities\\nof his children food and elotJiing, and shelter,\\nbeing the criterion of a good father. Let us apply\\nthe test of Logic to such an argument\\nX Y\\nAll good fathers provide for the physical wants of\\nMaj. mem.\\ntheir children.\\nMin. prem. A B did thus provide.\\nZ X\\nTherefore A B was a good father.\\nOr, using symbols,\\nAll X is Y,\\nZ is Y,\\nZ isX.\\nThat is, Y, which is the middle term, is undistributed,\\nbeing the predicate in two affirmative premisses.\\nAgain, it is asserted that brutes are not responsible\\n15-", "height": "3190", "width": "1916", "jp2-path": "elementsoflogic00copp_0179.jp2"}, "180": {"fulltext": "174 LOGIC.\\nbeings, because they arc not accountable wbich in-\\nvolves a fallacy of illicit process. Thus,\\nX Y\\nMaj. prcm. All responsible beings are accountable.\\nZ X\\nMill. prem. Brutes are not responsible beings.\\nZ Y\\nTherefore Brutes are not accountable.\\nAll X is Y,\\nNo Z is X, A^\\nNo Z is Y.\\nIn which Y^ which is distributed in the conclusion^\\nbeing the predicate of a negative proposition, is un-\\ndistributed in the major premiss an illicit process of\\nthe major term.\\nIt will be observed in this latter instance, that the\\nconclusion is, we believe, a true one, but it is not\\nreached by such premisses and thus indeed it con-\\nstantly happens, that men adopt a conclusion on inter-\\nnal grounds which they cannot explain, and then seek\\nin every direction for premisses by which to substan-\\ntiate it and so, on the other hand, many a just\\nstatement loses credence, from the fact that weak and\\nempirical men undertake to prove it by false premisses\\nor fallacious reasoning.\\nIt is further to be remarked, that men who are\\nguilty of fallacy in argument, either through design", "height": "3221", "width": "2121", "jp2-path": "elementsoflogic00copp_0180.jp2"}, "181": {"fulltext": "MATERIAL FALLACIES. 175\\nto deceive, or weakness of reasoning power, are apt\\nto combine many single arguments into a compound\\nargument. If, then, one of these be faulty in its\\nratiocination, every ulterior conclusion is endangered,\\nand the whole chain of argument is fallacious. To\\ndetect the error, therefore, requires that the whole\\nchain be exposed link by link, and that the proper\\ntests be applied to each argument. We have given\\nexamples of the fallacy of undistributed middle^ and\\nillicit process the student will not need illustrations\\nof the other formal fallacies mentioned.\\n(48.) Material^ or Informal Fallacies.\\nIt will be allowed that in every fallacious argument\\nthe conclusion does or does not follow from the pre-\\nmisses. If it do not follow from the premisses, then\\nwhen written out by symbols the fallacy is apparent,\\ncoming under one of the heads of formal fallacies\\nwhich we have just enumerated. The fault here is\\nevidently in the reasoning but when the conclusion\\ndoes folloiv from the premisses when, written out by\\nsymbols, the fallacy is not apparent, the fault will\\nnot lie in the reasoning, but either in the premisses or\\nin the conclusion, i. e, as to their truth or falsity, or\\nas to the amhiguous meaning of words used in both.\\nSuch fallacies, with which Logic is not directly con-\\ncerned, are called Material Fallacies.\\nIt has been remarked before, that Logic indeed", "height": "3188", "width": "1936", "jp2-path": "elementsoflogic00copp_0181.jp2"}, "182": {"fulltext": "176 LOGIC.\\ntakes for granted that the propositions composing its\\nsyllogisms are true and that when we write the\\ngeneral proposition A is B, no meanings shall be\\ngiven to A and B which shall violate the truth of the\\nproposition. If then we put for A, Learning and\\nfor B, useless^ and thus write,\\nLearning is useless,\\nor, by a change of words, the doctrine of the Stoics,\\nFain is (a lesser sort of) pleasure,\\nwe shall reason to false conclusions, the matter of\\nthe propositions forming the syllogism being false,\\nwhile the logic of the argument may be correct. It must\\nbe allowed that material fallacies are more numerous,\\nand more fruitful causes of error, than the logical, and\\nas such deserve a special consideration, although in-\\ndirectly allied to our subject.\\nWe shall, therefore, endeavour briefly to give the\\nprincipal forms or titles of material fallacies, and to\\nillustrate them by examples, observing at the outset,\\nthat they assume many and varied forms under these\\ntitles, all of which we cannot take the time to consider.\\nThe simplest division of them is one which grows\\nout of the consideration of\\n1. Errors in the premisses.\\n2. Errors in the conclusion.\\nOf Errors in the Premisses.\\nLogicians have adopted technical names for the", "height": "3222", "width": "2121", "jp2-path": "elementsoflogic00copp_0182.jp2"}, "183": {"fulltext": "MATERIAL FALLACIES. 177\\nfallacies of this kind; viz.: the petitio principii, or\\nbegging the question Arguing in a circle Non causa\\npro causa^ or the assignment of a false or undue\\ncause. These branch out into various minor divisions.\\nAs all these grow out of a false or undue assump-\\ntion of p)remisses, they are akin to each other, and\\nin many cases are not easily to be distinguished.\\nEspecially is this true of the first two.\\nI. Petitio principii. This consists in using as a\\npremiss to support an adopted conclusion or assertion,\\nthe same fact in other words. Thus we are told that\\nif the heart be touched death ensues, because it is\\na vital part, or that morphia produces sleep because\\nit is an anodyne.\\nNow what is it to say, but that death ensues, when\\nthe heart is touched, because death does ensue; or\\nthat morphia produces sleep, because it produces sleep.\\nOur language, which has so many synonyms from\\nthe Anglo-Saxon and the iiatin, gives full play to\\nthis sort of fallacy, and many a wordy man is guilty\\nof it without knowing his own error. And besides,\\nthis fallacy is the just recompense of those who en-\\ndeavour to prove axioms, or who seek to penetrate into\\nthe ultimate facts for which God assigns no cause but\\nthe fiat of his own will.\\nII. Arguing in a circle. This fallacy depends\\nupon finding a premiss to prove an asserted conclusion,\\nand then, when asked for the proof of the truth of\\nM", "height": "3186", "width": "1916", "jp2-path": "elementsoflogic00copp_0183.jp2"}, "184": {"fulltext": "178 LOGIC.\\nthat premiss, endeavoring to make the conclusion\\nprove the premiss or, as this would be easy of de-\\ntection, to make the circle still larger, i. e., proving\\nthe truth of the premiss by a third proposition which\\ndepends upon the conclusion, and then playing upon\\nthese three, like the juggler s balls of which one is\\nalways in the air, but which it is very difficult\\nto tell. In case of the simplest form, writing out\\nthe syllogism will detect it and in the latter and\\nmore complex case, the sorites, or its syllogisms.\\nwritten out, will find it out.\\nThus many men, not content with the everywhere\\nshining proof within and without that there is a God,\\nand mistaking the relations which the Holy Scrip-\\ntures bear to him, would prove the existence of a\\nG-od from the truth of the Scriptures, and then prove\\nthe inspiration of the Scriptures from the fact that\\nthey ca7)ie from Q-od.\\nAs the Scriptures are the word of God, what they declare must he true.\\nThe Scriptures declare that God exists.\\nTherefore That God exists is true.\\nOr again\\nThe word of God must he true.\\nThe Scriptures are the word of God.\\nThe Scriptures are true.\\nIII. Non Qausa pro causa. This fallacy, which\\nindeed may stand for the general title of unduly as-\\nsumed premisses, consists technically in assigning as a\\nreason or cause in the premisses, one which has nothing", "height": "3221", "width": "2121", "jp2-path": "elementsoflogic00copp_0184.jp2"}, "185": {"fulltext": "MATERIAL FALLACIES. 179\\nto do with the conclusion, or one which is not itself\\nproven, and is not therefore a sufficient cause. The\\nfirst of these errors is called the fallacy of a non tali\\ncausa fro tali^ or the assignment of a cause as though\\nit were a cause, when it is not and the second is the\\na non vera pro vera, in which the assumed premiss\\ncannot be proven to be true as a cause, and may\\ntherefore be considered false.\\nOf the latter of these, the a non vera, we find a\\nstriking example, and an excellent logical retort, in\\nthe reported dialogue between Charles II. and Milton,\\nafter the poet had become blind. Think you not,\\nsaid the king, that the crime which you committed\\nagainst my father must have been very great, seeing\\nthat Heaven has seen fit to punish it by such a severe\\nloss as that w^hich you have sustained -i Nay, sire,\\nMilton replied, if my crime on that account be ad-\\njudged great, how much greater must have been the\\ncriminality of your father, seeing that I have only\\nlost my eyes, but he his head. Another and com-\\nmon example of this is the following\\nThe natives of barbarous countries regard an eclipse\\nas portentous of war and famine, and should they come\\ntogether, they would assign it as the cause of their\\ntrouble. We know that it is not but they only note\\nto the conjunction of the two as satisfactory proof that\\nit is. Either of these may be easily written out in\\nthe syllogistic form, in which the propositions can be", "height": "3189", "width": "1930", "jp2-path": "elementsoflogic00copp_0185.jp2"}, "186": {"fulltext": "ISO LOGIC.\\nscrutinized as to their subject-matter, and the falsity\\ndetected. Of the a non tali, the following example\\n\u00e2\u0096\u00a0svill serve as an illustration viz.\\nAll poisons should be avoided.\\nBrandy and wine are poisons.\\nTherefore They should be avoided.\\nThat is, they are poisons only when taken in certain\\namounts and under certain circumstances. This is an\\ninvalid argument used by many good persons. The\\ntrue reason for avoiding brandy and wine being the\\ndanger of acquiring a habit of using them to such an\\nextent that they will be poisons.\\nErrors in the Conclusion.\\nWe come now to the second division of material\\nfallacies, those in which tlie error lies in the conclusion;\\nthey are all included under the general head of Igno-\\nratio elenchi, or irrelevant conclusion.\\nThe word elenchus, as used in the early writers,\\nmeant the contradictory of your opponent s assertion,\\nand thus implies, what indeed was a feature in earlier\\nLogic, the existence of an opponent. Dialectics were\\nalmost always in the form of dialogue, and the\\nSocratic mode of questions and answers was adopted\\nas the acutest method of argument.\\nThe disputatious spirit of the Greeks was as much\\nconcerned about the victory in logomachy or word-\\nwar, as about the discovery of truth, and hence arose\\nmany of their errors and paradoxes. This spirit of", "height": "3197", "width": "2121", "jp2-path": "elementsoflogic00copp_0186.jp2"}, "187": {"fulltext": "MATERIAL FALLACIES. 181\\ncontroversy, and the constant keeping in sight of the\\nelenchus has pervaded the methods of Logic to a very\\nlate period.\\nThe ignoratio elenchi is the ignorance of the contra-\\ndictory of our opponent s assertion, which we display\\nwhen, instead of establishing the elenchus, i. e, proving\\nthe contradictory, and thus proving his conclusion or\\nassertion false, we attempt to establish something re-\\nsembling the contradictory.\\nAs it is not our purpose to reproduce the Grecian\\ntechnicalities and method, let us get rid of this name\\nand form, and call the fallacy, as it has been called\\nby modern writers, the fallacy of irrelevant con-\\nclusion.\\nThose who employ it, and this, it may be remarked,\\nis the most common and practical of all the material\\nfallacies, generally state the conclusion as a fact, and\\nwhen asked for the premisses or proof, are compelled\\nto present such as display the irrelevancy of the con-\\nclusion. Thus, one asserts the fact that Alfred the\\ngreat w*as a scholar, and when asked for proof, says,\\n^because he founded the University of Oxford.\\nNow, there may be distinct proofs that he was a\\nscholar, but this certainly is not conclusive. Let us\\nstate the syllogism\\nThose who found universities are patrons of learning\\nAlfred the great founded the University of Oxford\\nTherefore, he tvas a scholar.\\n16", "height": "3195", "width": "1918", "jp2-path": "elementsoflogic00copp_0187.jp2"}, "188": {"fulltext": "182 LOGIC.\\nThe conclusion is irrelevant the true conclusion\\nbeing, from these premisses, that\\nlie was a patron of learning.\\nIf polemical writings, and especially those which\\npartake of the nature of popular and heated contro-\\nversy, be analyzed, this will be found to be the stand-\\ning fallacy, as often self-deceiving as deceiving others,\\nand responsible for much of the wide-spread error in\\nspeculative science.\\nSo varied is its nature, that it has been from the\\nearly times known under various names, and presents\\nits insidious temptations to all kinds of persons.\\nPerhaps that form which is of most universal appli-\\ncation is the argumentum ad hominem, the unfair\\nappeal to personal ojnnions, or to ones vanity or pre-\\njudice. After exhausting all the arts to prove a\\nthing wrong which is not so, the argument closes with\\nWell, you would not do so! Even in matters of\\nreligion we are triumphed over by the adversary by\\na reference to ourselves and our own imperfect\\nactions, when the question concerns the abstract\\ntruths of God s holy law. This form of the fallacy\\nneeds, then, a special watch as the most insidious.\\nNext in enumeration is the argumentum ad popu-\\nlum; which is the former fallacy extended from one\\nindividual to many, from personal opinion to popular\\nprejudice", "height": "3225", "width": "2121", "jp2-path": "elementsoflogic00copp_0188.jp2"}, "189": {"fulltext": "MATERIAL FALLACIES. 183\\nUnprincipled demagogues use this fallacy con-\\ntinually and vfliere the sophistry would be apparent\\nto any single mind gifted with common sense, the\\nenthusiasm and thoughtless spirit of a mob, moved\\nby a fiery harangue, is blind to its unreasonableness.\\nThis may be called the logic of revolutions.\\nA third kind of irrelevant conclusion is the argu-\\nmentum ad verecundiam, or appeal to the modest?/ of\\nour opponent, hoping that he will not presume to\\nattack respected authorities and time-honoured cus-\\ntoms. Although healthful progress may have de-\\nmonstrated their errors, and provided us with better\\nmethods, the cry is of recreancy to our fathers memo-\\nries, to old associations, to History and thus the\\nworld has been trammelled and clogged by what pro-\\nfesses to be the genius of conservatism, but what is\\nin reality the genius of obstinate error.\\nBesides these forms of irrelevant conclusion, there\\nare many which have been proposed in pleasantry,\\nsuch as the argu7nentum ad haculinum, and others\\nwhich Sterne humorously refers to in Tristram\\nShandy.\\nThere are, however, it must be particularly observed,\\nmany cases in which these very arguments are not fal-\\nlacies in which, indeed, they may with great propriety\\nbe used, clothed with all the graces of rhetoric and\\nimbued with all the fire of enthusiasm.\\nThe argumentum ad hominem is not a fallacy when", "height": "3187", "width": "1929", "jp2-path": "elementsoflogic00copp_0189.jp2"}, "190": {"fulltext": "184 LOGIC.\\nthe design is to teach pure truth, and when no unholy\\npassion or emotion of man is appealed to. In this\\napplication it was used by our Saviour himself to the\\nJews on many occasions, with great force and beauty.\\nHis touching, and yet searching, appeal to them for\\nthe woman taken in adultery, sent them out one hy\\none before its power. Each one felt the argument\\nand admitted the conclusion.\\nHis arguments in favour of healing on the Sahhath,\\nand searching the Scriptures, that they might find\\nevery page luminous with Him w^hom they denied,\\nwere examples of the unfallacious and powerful use\\nof this form of reasoning.\\nSo, too, an appeal {ad populum), not to the preju-\\ndices, but to the conscientious scruples and feelings of\\na multitude, is without fallacy, and is productive of\\nthe best results.\\nMany customs, long honoured, and dear to every\\nheart customs national, civic, professional, domestic,\\nunmingled with error, unopposed to progress, make\\nthe argumentum ad verecundiam a most proper and\\neffective appeal.\\nBut such is the wayw^ardness of man that the temp-\\ntation to fallacy in their use is exceedingly strong,\\nand must be carefully guarded.\\nArgumentum ad rem and ad judicium.\\nOpposed to all these, when used as fallacies, are two\\nforms of valid argument the first expresses a con-", "height": "3217", "width": "2121", "jp2-path": "elementsoflogic00copp_0190.jp2"}, "191": {"fulltext": "FALLACY OF OBJECTIONS. 185\\ncentration solely upon the reason of the tiling itself j\\nand is therefore called the argumentum ad rem the\\nsecond is when the appeal is made to the unbiassed\\nexercise of the individual judgment: this argument\\nis called argumentum ad judicium. Many writers\\nhave increased the number of these fallacious argu-\\nraenta to a much greater extent but those given are\\nthe principal ones, and will sufficiently indicate the\\nprocess by which they are coined when needed.\\nChanging the j^oint in disunite.\\nAnother form of the irrelevant conclusion is the\\nfallacy of changing the point in disjnite, in which one\\nof the parties in a long and difficult controversy, after\\nhaving tried in vain to establish his irrelevant conclu-\\nsion, dexterously shifts his ground from the point in\\ndispute to some other, and pertinaciously claims that\\nto be true wdiich has not been disputed, while the true\\nmatter of contention is left, vfithout an honest confes-\\nsion of his inability to prove his assertion. Eor ex-\\nample, a person undertakes to prove that the people in\\ngeneral are not educated i. e., he first denies that they\\nare but failing of this, he really proves, what no one\\ndenies, viz. that all the people shouM he educated.\\nFallacy of Objections.\\nIt has been remarked, that Ignorance may state in\\na few words objections against Science, which wise men\\ncould not refute in whole volumes. The truth of this\\n16-", "height": "3187", "width": "1918", "jp2-path": "elementsoflogic00copp_0191.jp2"}, "192": {"fulltext": "186 LOGIC.\\nis manifest. The error of reasoning from the state-\\nment or existence of these objections, to the falsity\\nof the science, is one of the forms of irrelevant con-\\nclusion which has been called the Fallacy of Ohjec-\\ntiofis. It consists in asserting that, since there are\\nobjections against a Science, that Science is false;\\nwhereas the judgment demands that the claims of the\\nScience as well as the objections be duly stated and\\nthat the turning of the scale decide whether truth or\\nerror predominate.\\nIf it be a complicated system, it will be found to\\ncontain portions of both if an abstract theory, it will\\nstand or fall by such a test. This fallacy has been indus-\\ntriously aimed by sceptics against the mysteries of the\\nChristian faith, but it soon loses its point in such an\\nencounter. From the consideration of the various spe-\\ncies of the fallacy of irrelevant conclusion which have\\nbeen mentioned, and the examples given, it will be seen\\nthat it is in all its forms the standing sophism in houses\\nof legislative convocation that it is the demon of de-\\nbate. Few subjects of debate are so abstract and unit-\\nlike but what dull minds will find room to wander about,\\none losing the very point in question, another con-\\ncerned about a crowd of details which have little or\\nno bearing upon it, a third mistaking the fine and\\ndelicate points of the logical argument some, becom-\\ning heated in the controversy, will lose their temper\\nand reasoning powers together, and overpowered by", "height": "3196", "width": "2121", "jp2-path": "elementsoflogic00copp_0192.jp2"}, "193": {"fulltext": "FALLACY OF OBJECTIONS. 187\\nthe truth and Logic of their opponents, will have re-\\ncourse to appeals to the prejudices and interests of\\ntheir audience and others, more shrewd than just, will\\nseek to bring by similar means the cause and persons\\nof their adversaries into disrepute, by the light arrows\\nof ridicule, or the more ponderous weapons of insult.\\nIt is amidst such scenes, and under such circumstan-\\nces, that the master mind shows itself as it rises over\\nthe storm of the debate, and brings them back first\\nto the consideration of the subject in dispute, in its\\ntrue and abstract form. Perhaps the most striking\\nillustration of this is found in our own Congressional\\nhistory. After Mr. Webster s first speech on Foote s\\nresolution, many senators had delivered their views,\\nand much sectional excitement was aroused. Mr.\\nWebster began his famous second speech, with just\\nsuch a master-effort to come back to the true merits\\nof the controversy\\nMr. President, When the mariner has been tossed for many,\\ndays in thick weather and on an unknown sea, he naturally avails\\nhimself of the first pause in the storm, the earliest glance of the\\nsun, to take his latitude, and ascertain how far the elements have\\ndriven him from his true course. Let us imitate this prudence, and\\nbefore we float farther on the waves of this debate, refer to the\\npoint from which we departed, that we may at least be able to con-\\njecture where we now are. I ask for the reading of the resolution\\nbefore the Senate.\\nThe resolution was read the Senate found their\\ntrue position, and Mr. Webster s speech is as mas-\\nterly for its logic as for its oratory.", "height": "3187", "width": "1912", "jp2-path": "elementsoflogic00copp_0193.jp2"}, "194": {"fulltext": "188 LOGIC.\\n(4 Verbal Fallacies.\\nThere is still a most important class of invalid\\narguments to be considered it is that growing out\\nof the amhiguoiis or equivocal meanings of words\\nmany words being identically the same, and yet bear-\\ning widely different meanings. Thus, the simple word\\nline, when U5ed in different connexions, means many\\ndistinct things for example a cord used in fishing\\na feio ivords in a letter an arrangement of troops or\\nships in battle arrofy and when we see the word\\nporter, we are in doubt which of three meanings is\\nintended, a gate or door-keeper, a man who hears\\nburdens, or a kind of malt drink.\\nIn most such cases, however, there is a single root\\nto which we may trace all these secondary meanings\\nthus all the meanings of a line refer to the mathema-\\ntical definition that it is length, ivithout breadth or\\nthickness, and all the uses of j^orter refer to the Latin\\nword which signifies to hear.\\nIt is true that there are examples of words spelt\\nalike which have different etymologies but these are\\nfew host, from hostis, and host from hostia in the\\nsacrifice of the mass, are examples of this so also\\nleague from ligare to bind, and league from the Latin\\nlocus or distance between places, contracted in French\\nto lieue, as the word /be^/s is into/ gu; are examples\\nof such words. AY.ith these few illustrations of am-", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0194.jp2"}, "195": {"fulltext": "VEEBAL FALLACIES. 189\\nbiguous terms, let us see how they are used in argu-\\nment.\\nThe ambiguous word is sometimes the middle term,\\nand sometimes it is the major or minor in most cases,\\nhowever, it assumes the former place, so that the\\ngeneral name given to this form of verbal fallacy, is\\nthe Ambiguous middle.\\nY\\nis the company of faithful people.\\nZ\\nThis stone building is the church.\\nTherefore This stone building is the company, c.\\nNow, if this glaring and absurd fallacy be stated\\nby symbols, we shall have\\nXisY,\\nZisX,\\nZ is Y,\\nwhich is the form of a valid argument in the first\\nfigure so that the fault lies in the matter of the\\npropositions which compose the argument, and not in\\nthe form, which is correct the fallacy then must be\\nclassed, with such an investigation, among the mate-\\nrial, and not among the formal fallacies. But let us\\ngo a step farther; since the church in the major\\npremiss means something entirely different from the\\nchurch in the minor, they are in reality different\\nterms let us symbolize them by different letters, and", "height": "3195", "width": "1921", "jp2-path": "elementsoflogic00copp_0195.jp2"}, "196": {"fulltext": "190 LOGIC.\\ncalling tlie first X, let us call the second P; we shall\\nhave, writing by symbols, as before,\\nX is Y,\\nZ is P,\\nZ is Y,\\na formal fallacy, in which there are, contrary to the\\nrules laid down, four terms instead of three; and\\nthis comes within the province of Logic. The fallacy\\nof Ambiguous middle has very justly, then, been called\\nby logicians, a semi-logical fallacy before we dis-\\ncern the ambiguity it is a material fallacy, with which\\nLogic is not concerned but as soon as ive discover\\nthe ambiguity^ it discloses /owr terms, which make it a\\nformal or logical fallacy. It is because of this pecu-\\nliarity, and because it is so very much used in com-\\nmon life, that we treat of it under the distinct head\\nof ve7^bal fallacies. But we have said that it is not\\nonly in the middle term that this ambiguity occurs\\nit also happens in the major and minor terms and is\\nquite as sophistic when it lurks there as in the middle\\nterm. We have therefore discarded the title Ambi-\\nguous middle, as applied to the general class, pre-\\nferring Verbal fallacies, as more truly illustrative\\nof the error in any of the terms.\\nThere are many ways in which words are used\\nambiguously, and we shall give a few of them with\\nillustrations and first, we place the influence of\\nEtymology.", "height": "3223", "width": "2121", "jp2-path": "elementsoflogic00copp_0196.jp2"}, "197": {"fulltext": "ETYMOLOGY. 191\\nEtymology,\\nA word which origmallj meant one thing, now means\\nquite another, and the fallacy consists in using it in\\nthe two senses, in two propositions of the syllogism.\\nThus, taking the first meaning oi i^agan to be a villa-\\nger (paganus*), and its present meaning to be a be-\\nliever in some other religion than that of Christ, we\\nhave,\\nA pagan is a disbeliever in Christ\\nvery villager is ii pagan;\\nEvery villager is a disbeliever in Christ.\\nAkin to this, and indeed ranging under the general\\nsubject of etymology, is the use of paronyms, or jpa-\\nronymous words.\\nParonymous words, are the noun substantive, ad-\\njective, verb, c., belonging to each other and spring-\\ning from the same root. To project, prdject, pro-\\njection, projector, kc, are paronyms, springing from\\nthe Latin compound of pro and jaceo. So presume\\n(in its two senses), presumption, presumptive, pre-\\nsumptuous, c., are paronyms growing from the root\\npresumo.\\nTake the following example, in which the ambi-\\nguity will lie in the middle term\\nPresumption is impertinence\\nThat the sun shines, I presume (or, is my presumption)\\nTherefore I am impertinent.\\nFrom pagus, a village.", "height": "3187", "width": "1937", "jp2-path": "elementsoflogic00copp_0197.jp2"}, "198": {"fulltext": "192\\nLOGIC.\\nIt will be reincmbered that the true logical form of\\nthe minor premiss, which is usually written, I pre-\\nsume that the sun shines, is\\nsubj. pi-ed.\\nThat the sun shines is presumed by me.\\nAgain\\nTo propose a railroad is a, project (or n projector s work.)\\nThis man proposed a railroad.\\nTherefore He is a projector.\\nin which the ambiguity lies in the major term. Now,\\nno one can Avork advisedly, without making projects,\\nwhereas one of the m.eanings of j^ ^ojector, is a schem-\\ning and visionary man, who ought not to be relied\\nupon.\\nFallacy of Interrogations.\\nThis is a use of tw^o or more terms in a question,\\nmaking thus in reality two questions, requiring tw^o\\ndistinct answers, and the ambiguity lies in the single\\nanswer given to both. It is common for those who\\nuse this fallacy to express but one question, while the\\nother is implied. Thus, if a man who has always\\nbeen temperate is asked, when he gave up drinhing V\\nthe implied question is, did he ever drinlcV and\\nthen, if so, when did he cease or, in the celebrated\\ninquiry of King Charles II., why a dead fish does\\nnot add to the loeight of a vessel of ivaterf the im-\\nplied question being does a dead fish add, c. and", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0198.jp2"}, "199": {"fulltext": "FALLACY OF INTERROGATIONS. 193\\nif SO, why, c. This fallacy, which is called by\\nthe writers, Fallacia plurimum inter rogationunij is\\nmade more subtle by the number, and closeness of\\n\u00e2\u0080\u00a2esemblance, of the points included in the questions.\\nAmjyhibolou^ Sentences.\\nSometimes the ambiguity, instead of residing in the\\nwords which compose the argument, lies in the con-\\nstruction, and thus, by different punctuations, we\\nhave double and opposite meanings. This passes\\nfrom the ambiguous words to amphibolous sentences.\\nAmong the most celebrated of these is the response\\nof the Delphic oracle to Pyrrhus when he went to\\nencounter the Komans\\nAio te (Eacida Romanos vincere posse,\\nIbis redibis nunquam in bello peribis.\\nIn the first line, either accusative may be taken\\nwith the infinitive, thus making either Pyrrhus, or\\nthe Romans, able to conquer and in the second,\\nnunquam may qualify either redibis or peribis.\\nSo also in the Nicene Creed, we have, in reference\\nto our Saviour, the words being of one substance\\nwith the Father, by whom all things were made.\\nThe latter clause, so manifestly introduced by the\\nCouncil, to declare the creative power and Godhead\\nof Christ, in reality by strict rhetoric applies to\\n^he Father.\\nThe name given to this fallacy is the fallacy of\\n17 N", "height": "3187", "width": "1927", "jp2-path": "elementsoflogic00copp_0199.jp2"}, "200": {"fulltext": "194 LOGIC.\\namphibolous sentences, i. e., tossed from one to\\nanother, with a doubtful meaning.\\nCauses of Ambiguity.\\nHaving mentioned the various kinds of ambiguity\\nin words, we come to consider why words have two or\\nmore meanings.\\nWe have already seen that many words expressing\\nsimple primitive ideas grow by usage to have other\\nmeanings, in which, however, the primitive idea is to\\nsome extent retained thus, line, in all its meanings,\\nadheres to the mathematical notion of extension in\\nlength.\\nNow, without being able to trace the exact process\\nin all cases, by which a word is thus gradually changed,\\nwe find that it ranges itself under one of these heads\\n1. Resemblance; 2. Analogy; Z. Association 4. El-\\nlipsis 5. Accident.\\n1. Resemblance. Many things bear the same name,\\nfrom their actual similarity in appearance. Thus, in\\ncarpentry, a dove-tailed joint is so called from its\\nsimilarity to a dove s tail, or a spear of grass from\\nits resemblance to the military weapon, a spear. So\\nin the military art, a priest-cap, or swallow-tail\\nis a redoubt so named from its actual resemblance to\\nthese two things, and a crow s foot takes its name\\nfrom the form of a bird s talons.\\nayi pL and ^aWw.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0200.jp2"}, "201": {"fulltext": "ASSOCIATION. 195\\n2. Analogy. Our ordinary speech is full of the use\\nof this figure of speech, and this fact has contributed\\nto the ambiguity in many words. As resemblance is\\na similarity in appearance, analogy is a similarity in\\nuse, i^urpose, or relation. Thus, we speak of the arm\\nof a chair, because it holds the relation to the chair\\nwiiich the arm does to the human body and thus an\\narm-chair is a chair which has arms.\\nWe speak equally of a sweet food, or a sweet sound,\\nbecause there is a similarity between the relations of\\nthe food to the palate, and the sound to the ear. So\\na sour lemon and a sour indiyidual, create relatively\\nsimilar effects upon the taste and upon the mind.\\nAmbiguity of resemblance and of analogy are both\\nproduced and perpetuated by the use of metaphor\\nand comparison, in our ordinary discourse, and a way-\\nward fancy, expressing itself in the social exaggera-\\ntions of the day, is robbing some of our best words\\nof their true shades of meaning for example, sweet,\\nlovely, liorrid, agony, wretch, are deflected from their\\noriginal neanings entirely.\\n3. Association. By this we mean the connexion\\nof pans in the same structure or institution, or to pro-\\nduce a single result. Thus, a door is the opening in\\nthe wall, or the swinging shutter that closes it. Faitli\\nis belief, and ^^tlie Faith is the system of Christi-\\nanity. Shot is the leaden pellet a good shot is\\neither the person who shoots, or the effect of the shot.", "height": "3179", "width": "1929", "jp2-path": "elementsoflogic00copp_0201.jp2"}, "202": {"fulltext": "196 LOGIC.\\nIt is by the association of ideas, which, unlike our\\nexamples, are subtle and difficult to fix and determine,\\nthat fallacies have grown out of this ambiguity; and\\nsuch is the want of correctness in the language of\\nthe great number of people, that the tendency to this\\nfallacy of words, expressing associated ideas, is par-\\nticularly strong and dangerous.\\n4. Ellipsis. Another habit into which men natu-\\nrally fall, in trying to avoid the use of many words,\\nand words conveying thoughts which the mind will\\nreadily supply without their being expressed, is the\\nuse of elliptical language. While in most cases this\\nis harmless and even profitable, in some it leads to\\nerror. Thus, we speak constantly of Scott, Byron,\\nc., when we mean their works or their persons. We\\nuse the form to my father s, at Mrs. Smith s, when\\nwe mean the houses or parties of these persons, and\\nsuch ellipsis is always understood but many persons\\nare deceived in their business relations by such\\nellipsis as the statement of another s wealth at so\\nmany thousands of dollars, when in reality, although\\nit may produce the interest on such a sum, it cannot\\nbe made available for anything like the amount of\\nthe principal sum mentioned.\\n5. Accident. It seems in certain cases as though a\\nword had assumed two meanings in a manner inex-\\nplicable and accidental. Such, for example, is the\\nword light, which is equally opposed to heavy and", "height": "3216", "width": "2121", "jp2-path": "elementsoflogic00copp_0202.jp2"}, "203": {"fulltext": "ACCIDENT. 197\\ndm h and which in conduct means the opposite of\\nserious or dignified. But even in such a case we\\nshall find one idea, however subtle, pervading them\\nall, and that is the removal of a covering of some\\nsort thus, light removes the pall or covering of\\ndarkness the incumbent weight of something heavy\\nthe just restraints of dignity and sobriety. In strict\\ntruth, then, there is no accidental ambiguity, for,\\nalthough there may be words in the double meanings\\nof which we can discover no relation to a single idea,\\nthat relation undoubtedly exists, and by a profound\\nresearch the number of such words would be very\\nmuch diminished.\\nMany words are forced into a double meaning by\\na popular or political use, which may be called acci-\\ndental, but which in reality is designed by one party\\nas an equivoque, or stratagem, in the way of retort\\nupon the other. It was thus with the use made of the\\nword Pretender, by the English Jacobites. When it\\nbecame treasonable in any way to maintain the claims\\nof James Stuart, the son of James II., who was called\\nthe Pretender, they toasted him in the well-known\\nverses\\nGod bless the king; God bless the Faith s Defender;\\nGod bless no harm in blessing the Pretender.\\nBut which is the Pretender; which the king?\\nGod bless us all, that s quite a different thing.\\nIt is evident that such a use of the word would de-\\nceive no one nor was it indeed so designed, but rather\\n17", "height": "3174", "width": "1864", "jp2-path": "elementsoflogic00copp_0203.jp2"}, "204": {"fulltext": "108 LOGIC.\\nto violate tlie spirit and yet adhere to the letter of\\nthe law. The true argument used by the adherents\\nof the new dynasty, was\\nThose who aid a pretender to the English throne, deserve pun-\\nishment.\\nJames Stuart is a pretender.\\nThose who aid James Stuart, deserve punishment.\\nIt must be understood that pretender in both pre-\\nmisses has the same meaning, i. e.^ false claimant.\\nBut there is still another form of ambiguity w^hich\\nleads to fallacious arguments it is where the ambi-\\nguity lies not in words but in the context or where\\nour assertion means one thing when taken in a general\\nsense, and quite another if considered in a special\\nsense. Of these fallacies, arising from ambiguity in\\nthe context, there are two kinds,\\n1. The fallacy of accidents.\\n2. TJie fallacy of division and composition.\\nUnder the first head are included the Fallacia acci-\\ndentis, and the Fallacia a dicto secundum quid ad\\ndictum simpliciter. These are the converse of each\\nother.\\nFallacia accidentis.\\nThis is where, in one premiss, we assert something\\nof a subject in a general sense, and, in the other, place\\nupon that subject some accidental peculiarity, which\\nwill lead us to error in the conclusion thus,\\nThings bought in market we eat.\\nRaw meat is a thing bought in market.\\nTherefore, Raw meat is what we eat.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0204.jp2"}, "205": {"fulltext": "FALLACY OF DIVISION AXD COMPOSITION. 199\\nHere the middle term is things bought in market, and\\nit is considered in the major premiss as to its essence\\nviz. that these things are in market for general use as\\nfood in the minor we lose sight of its essence, and only\\nregard some accident of it, viz. that the meat bought\\nin market is raw. Thus, in reality, the error is thrown\\nupon the middle term, which is shown to he not one,\\nbut ttvo distinct terms, and the fallacy is thus exposed.\\nThe other form of this, which for shortness is\\ncalled the Fallacy of Quid, may be translated reason-\\ning from the broad sense of a term (secundum quid),\\nto its special reference or application (ad dictum sim-\\npliciter). Thus\\nA horse drinks on all fours and out of a trough.\\nThis man drinks like a horse.\\nHe drinks on all fours, c.\\nFallacy of Division and Composition,\\nIn this fallacy the middle term is used in its collec-\\ntive or additive sense in one premiss, and in its dis-\\ntributive sense in the other. When the middle term\\nis used collectively in the major premiss, and distri-\\nbutively in the minor, the fallacy is of Division\\nwhen the reverse takes place, it is a fallacy of\\nComposition. The following are examples:\\nFallacy of Division.\\nThe Christians were persecuted at Rome.\\nConstantine was a Christian.\\nTherefore He was persecuted at Rome.", "height": "3187", "width": "1906", "jp2-path": "elementsoflogic00copp_0205.jp2"}, "206": {"fulltext": "200 LOGIC.\\nFallacy of Composition,\\nThree and two are two numbers (distribntively).\\nFive is three and two (additively).\\nFive is two numbers.\\nPositive and Negative Intention,\\nAkin to these fallacies are those absurd conclusions\\nreached by a play upon certain negative words, such\\nas nothing, and no, when used as an adjective; thus:\\nNothing is better than Heaven.\\nA shilling is better than nothing.\\nTherefore A shilling is better than Heaven.\\nNo cat has two tails.\\nEvery cat has one tail more than no cat.\\nEvery cat has three tails.\\nIn these examples the middle terms notTiing and\\nno cat, are taken in a positive sense in the major\\npremiss, as though they expressed living or existing\\nthings, while in reality they mean non-existence. In\\nthe minor premiss they are taken in their true nega-\\ntive sense.\\nThe best method of refuting them is to deny the\\nmajor premiss, or to demand that it be put in other\\nwords, thus\\nIt is not true of anything that it is better than Heaven:\\nwhich will foil the one who wishes to draw the absurd\\nconclusion. It should be observed that such argu-\\nments are really used only in sport, but it is well to\\ndetect and understand the error which they contain.", "height": "3220", "width": "2121", "jp2-path": "elementsoflogic00copp_0206.jp2"}, "207": {"fulltext": "REMOVING AMBIGUITY IN TERMS. 201\\n(50.) The Manner of removing Ambiguity in\\nTerms,\\nThe true method of riddmg ourselves of this ambi-\\nguity of terms in argument, is to demand a defini-\\ntion^ in each case, and to keep our terms distinct when\\nthus defined. It will not, in most cases, be neces-\\nsary to give a real definition, as a nominal one will\\nanswer every purpose. The ambiguity is usually\\nsuch that by giving the true, limited and exact name\\n(which is the province of a nominal definition), we\\nshall detect and remove it.\\nIn many cases where the fallacies consist of a num-\\nber of arguments and many ambiguous terms, the\\nfirst thino- to be done is to disentans-le the w^eb of\\nsophistry, by writing them out in full, and in due\\norder, and then after detecting the terms in which the\\nambiguity lies, to demand a definition in a few but\\nplain and conclusive words, in every case.\\nThe equivocal nature of the word becomes appa-\\nrent, if we change the language, as in the translation\\nof the familiar example, into Latin\\nLight is contrary to darkness.\\nFeathers are light.\\nTherefore, Feathers are contrary to darkness.\\nwe shall have,\\nLux est contraria tenehris,\\nPlumse sunt leves.\\nPlumse sunt contrarise tenebris.*\\nLatham s Logic, p. 221.", "height": "3176", "width": "1845", "jp2-path": "elementsoflogic00copp_0207.jp2"}, "208": {"fulltext": "202 LOGIC.\\nThis change of language, it will be seen, is of the\\nnature of a definition.\\n(51.) The Fallacy of Probabilities, or the Galdu-\\nlation of Chances.\\nThis consists in stating two probable premisses, and\\nthen drawing a certain conclusion, as though the\\nnumber of probabilities combined amount to cer-\\ntainty, whereas, in most cases, the conclusion will be\\nless probable than either thus\\nThose who have the plague jt?ro6a6Z?/ die\\nThis man jyrobably has the plague\\nTherefore He -will {certainly) die.\\nWhereas, suppose ten out of twelve of those who\\nhave the plague die, then, if we express certainty by\\nthe number 1, that probability is expressed by the\\nfraction jj or and if it is an even chance whether\\nor not he has the plague, that probability will be ex-\\npressed by J. The probability of the conclusion,\\ntherefore, will be X J 737, or as J is the expression\\nfor perfect doubt, i. e., an even chance of his living\\nor dying, he is less likely to die than to live, his chances\\nof dying being 5 out of 12, and of living, 7 out of 12.\\nThis fallacy is practically used in times of sickness\\nand mortality, when fear of evil, excited by nervous-\\nness, affection, c., place an anticipated conclusion\\nfor the true one.\\nWhen instead of one syllogism, or enthymeme.", "height": "3221", "width": "2121", "jp2-path": "elementsoflogic00copp_0208.jp2"}, "209": {"fulltext": "FALLACY OF PROBABILITIES. 203\\nmany are combined to make a compound argument,\\nand the errors of probability are thus multiplied, the\\nresult will be at once farther from the truth, and\\nmore difficult to detect.\\nLet us deduce then a simple rule for the calculation\\nof probabilities. The subject has been called the\\ndoctrine of chances.\\nWhen we speak of chance, we really mean prohahle\\nresults of Grod s latos, and in the use of either word,\\nwe express our ignorance of the connexion between\\nnatural causes and effects. Now, as that ignorance\\nmay be partial or entire, the probability ranges be-\\ntween the two extremes, cei^tainty and impossibility/.\\nWe do not pretend to assert by this that man may divine\\nthe results of God s doings in the future but that\\naccording to the action of natural laws, and the se-\\nquence of an established order, we may approximate\\nto the truth without assuring ourselves of it.\\nThus, in throwing dice, we cannot be sure that any\\nsingle face or combination of faces will appear but\\nif, in very many throws, some particular face has not\\nappeared, the chances of its coming up are stronger\\nand stronger, until they approach very near to cer-\\ntainty. It must come and as each throw is made\\nand it fails to appear, the certainty of its coming\\ndraws nearer and nearer.\\nThe probability of a single event depends upon the\\nnumber of chances, of which it is one thus, if A is", "height": "3187", "width": "1914", "jp2-path": "elementsoflogic00copp_0209.jp2"}, "210": {"fulltext": "204 LOGIC.\\nin a single action where 10 men are killed, his com-\\npany numbering 50, the chance which each man\\nstands of being killed, and consequently that of A,\\nis ij or i. If we subtract J from 1, or certainty^ we\\nshall have for his chance of being saved. The cal-\\nculation of probabilities becomes more complicated\\nwhere the events are combined. Thus, if in a second\\naction 10 men more are killed, his chance of being\\nkilled in this last action, is as 10 to 40, or J and that\\nof his being saved If now we would determine his\\nchance of being saved, after both actions, we must mul-\\ntiply the two chances together X 2\u00c2\u00a7 f\\nwhich is as it should be, since 20 men are lost of the\\noriginal 50, and 30 remain, his chance of being among\\nthe latter should be as 30 to 50, or\\nIt is upon this principle of calculating chances that\\ninsurance companies are founded and it finds a bene-\\nvolent issue and scope particularly in those Life-assu-\\nrance companies, which, demanding but a small per-\\ncentage, making a large aggregate, are thus enabled\\nto pay to widows and orphans an honourable support\\nsnatching out of the jaws of death the means of life\\nand social comfort.\\nIt is, however, upon a false study or rather in an igno-\\nrant and fatal reliance upon this principle, that those\\nwho frequent gaming-houses throw away their means,\\nreputation, and life for the true gainers are not the\\nfrequenters of the gaming-table, but the keepers, who", "height": "3230", "width": "2121", "jp2-path": "elementsoflogic00copp_0210.jp2"}, "211": {"fulltext": "POPULAR FALLACIES. 205\\nare acting upon this very doctrine of chances. By a\\ncalculation of chances it is found that in the long run,\\nthe keeper of a gaming house must win, in almost every\\nkind of game played while only an occasional player,\\nwith what is called a marvellous run of luck, chances\\nto win largely.\\nThe subject of probabilities, which in its right use\\nis not fallacious, but is reduced to arithmetical accu-\\nracy, has been placed under the general head of Fal-\\nlacies, because of its being so liable to fallacious use,\\nand so much employed thus. Mingling as it does with\\nthe superstition in our nature, we deem those things\\nmore probable than they are, which we desire or fear.\\nThe wish is father to the thought, for pleasant\\nhopes and presentiments of evil are taken for its\\nprobable coming, in our gloomy periods. We give a\\nrule by the use of which all this may be avoided.\\nRule.\\nThe probability of any event is expressed by a frac-\\ntion, of which the numerator is the number of chances\\nin its favour, and the denominator is the sum of all\\nthe chances.\\n(52.) Popular Fallacies.\\nIt will be well, before closing the chapter on Falla-\\ncies, to show their practical use, especially in a popu-\\nlar illustration. A community, a state, a nation, will\\n18", "height": "3187", "width": "1914", "jp2-path": "elementsoflogic00copp_0211.jp2"}, "212": {"fulltext": "206 LOGIC.\\nunite upon a fallacy, from which it will be a sort of\\nsocial treason to dissent an age will be tinctured by\\nerror, pervading all classes, which only the innova-\\ntion of a succeeding age can remove a false principle\\nwill cling to human nature, in the mass, during many\\ncenturies, which the philosophic mind can only de-\\nplore in secret.\\nIt will be our purpose then to put forth some of\\nthe simplest forms of popular fallacy, beginning with\\nthe most general. Some of these have been already\\nmentioned in their logical places, as the different\\nforms of irrelevant conclusion, c.\\nI. The fallacy which is expressed by the adage,\\nNil de mortuis nisi honum. There is a just meaning\\nto this indeed it is that the tongue of private enmity\\nshould be silenced that we should consider Death\\nas having adjusted all difficulties as between man and\\nman, and awed our mortal infirmities into a silence\\nand forgetfulness of the evil which existed in him\\nwho is now dead. So far the adage is good but,\\nwhen it becomes a principle in public morals when\\nit tinctures the historian and the historical biographer,\\nwho should deal with the dead as with living defend-\\nants, arraigned for trial, its evil nature is apparent.\\nWhen it eulogizes the dead at the expense of the\\nliving, and runs riot in obsequious praises and flatter-\\ning epitaphs, it assumes its most sophistic form.", "height": "3223", "width": "2121", "jp2-path": "elementsoflogic00copp_0212.jp2"}, "213": {"fulltext": "POPULAR FALLACIES. 207\\nThe same man, says Jeremy Bentham, who be-\\npraises you when dead, would have plagued you with-\\nout mercy when living. The reason of this is appa-\\nrent. A dead man cannot be a rival; he incurs\\nnobody s envy, and is removed from all the results of\\nmalice.\\nII. Not unlike the preceding is the fallacy con-\\nveyed in the trite saying De gustibus non est dispu-\\ntandum. This is used fallaciously to put a stop to\\ncontroversy the assertion implying that as God gave\\nman, each his own taste, one taste is as good as\\nanother. But all our systems of education teach us\\nthat this is not true that there is, on every subject\\nwhich comes under the dictum of taste, a true stan-\\ndard, which can and ought to be used. It certainly\\nis better to put an end to controversy by saying that\\nit is better to diifer than to become excited and\\nquarrel, than falsely to state that there can be no\\ndispute about tastes.\\nIII. There is a fallacy which particularly assails\\npatriotism it is the fallacy of asserting that any one\\nform or system of Crovernment is abstractly the best.\\nThe Russian deems that men cannot be controlled in\\nmasses, without single autocratic power the English-\\nman defies the world to pick a flaw in his limited\\nmonarchy and superb aristocracy; while the American\\nboldly declares that the best government is the de-\\nmocratic, representative form. Where such men as", "height": "3187", "width": "1919", "jp2-path": "elementsoflogic00copp_0213.jp2"}, "214": {"fulltext": "208 LOGIC.\\nMilton and Locke have astonished the world by\\nsignal absurdities in their models of government, we\\nmight be sure that its theory must be difficult but\\nthe truth is, there is no abstract theory of human\\ngovernment.\\nAsiatic barbarians, when they leave their patriarchal,\\nwandering life, as in Russia, and come into the first\\ncorruptions of a half^civilized life, must he governed\\nhy despotic poiver they cannot be republican: while\\non the other hand, it is only where education is gene-\\nral among the people that they may know their wants,\\nand how to supply them, and where individual honesty\\nand virtue are everywhere felt, that no undue means\\nmay be taken to bring about such an end, that a\\ndemocratic government is the right one. Then, in this\\nfreest form there is a reciprocal influence between the\\ngovernment and that upon which it is founded. A free\\ngovernment enlightens and purifies the people while\\nthe enlightenment and purity of the people strengthen\\nand insure the government under which they live.\\nly. There is a popular fallacy, which may be called\\nS weeping classifications. It consists in ascribing to\\nan individual something really belonging to another\\nindividual, only because the two happen to be of the\\nsame class thus, during the French Revolution, when\\nthe fate of Louis XVI. seemed to hang upon a thread,\\none pamphlet was issued with the title The Crimes\\nof Kings. Now, as there had been many bad kings", "height": "3241", "width": "2121", "jp2-path": "elementsoflogic00copp_0214.jp2"}, "215": {"fulltext": "POPULAR FALLACIES. 209\\nin Europe, and not a few in France, Louis XVI., the\\nbest of them, was put into the category of condemna-\\ntion, simply because he was a king.\\nIn times of religious revolution this has been very\\ncommon as, when we hear the cry, the cruelties of\\nthe Roman Catholics, uttered at a time when a bill\\nfor their relief was before Parliament. Former cru-\\nelties in far distant countries all being thrown upon\\nthe shoulders of the disabled and harmless Roman\\nCatholics of that day. Such, too, was the cry among\\nRoman Catholics themselves in the time of James II.,\\nand the after Jacobite struggles, of Protestant in-\\ntolerance. As a further example, we refer to the\\nstories circulated about the Jews, in the fourteenth\\nand fifteenth centuries that they crucified Christian\\nbabes, and were guilty of secret crimes of great\\nenormity.\\nV. Space would fail in which to enumerate the\\ncurrent and manifest popular fallacies, most of which\\nare used in legislatures and councils, and are consid-\\nered in the light of shrewd and dexterous diplomacy.\\nThere is the ?^o precedent argument. It is stated\\nthus The plan proposed is entirely new. This is\\ncertainly the first time such an idea has been broached\\nin this honourable house and therefore, the secret\\nhope is, that this house will not now entertain it.\\nNext, we have personalities introduced, laudatory\\n18*", "height": "3187", "width": "1821", "jp2-path": "elementsoflogic00copp_0215.jp2"}, "216": {"fulltext": "210 LOGIC.\\nor abusive, by which to turn the current of the argu-\\nment.\\nAnother form is the assertion with regard to any\\nmeasure, that as no complaint has ever been brought\\nagainst it before, it must be a good one.\\nBut perhaps the most insinuating form of popuhar\\nfallacy is that by which a man is required to join one\\nor the other party in every question thus causing the\\nyoung ignorantly and prematurely to commit them-\\nselves to views and measures which later experience\\nteaches them to be wrong if then they change they\\nare traitors or turncoats, if it be a national or political\\nquestion and fickle and unreliable, if it be of a less\\ngeneral nature. It is lamentable to see party guides\\nbringing those under their control forward to swell the\\nranks of their party; and those thus introduced,\\nglorying in their new distinction, when self-interest\\nand not truth has been the motive on both sides.", "height": "3226", "width": "2121", "jp2-path": "elementsoflogic00copp_0216.jp2"}, "217": {"fulltext": "APPLICATION OF LOGIC. 211\\nCHAPTER XL\\n(53.) Of certain modes in tvliich Logic is applied.\\nIt is not within the scope of this work to enter\\nupon the subject of applied Logic; this would re-\\nquire an investigation of all the sciences, or at least\\nof a very numerous classification. But it is designed\\nto explain the meanings of certain phrases which\\nrefer to the general applications of Logic.\\nWe have the phrase moral reasoning, and it is\\noften used as if conveying an opposite or contrary\\nmeaning to demonstrative reasoning.\\nThis has reference, not, as we have clearly shown,\\nto the kind of reasoning as there is but one but to\\nthe nature of the evidence employed the meaning\\nof evidence being, that testimony which sets forth the\\ntruth of a proposition. Then, moral reasoning is\\nthe use of evidence in moral subjects, and demonstra-\\ntive reasoning its us-e in mathematical subjects.\\nNow, evidence may be of three kinds, that is as to", "height": "3187", "width": "1889", "jp2-path": "elementsoflogic00copp_0217.jp2"}, "218": {"fulltext": "212 LOGIC.\\nthe manner in whicli we obtain it it may be intuitive,\\ninductive or deductive.\\nOf Intuition, Induction and Deduction.\\nWe come now to consider the means of discovering\\ntruth, which are most useful, but which have been\\nstrangely confounded with Logic. They are processes\\nas much bound by logical laws as all other movements\\nof the reason are.\\nIt is evident, that in order to the Logical process,\\nwe must have premisses now, these premisses are\\nobtained evidently by the three methods just men-\\ntioned Intuition, deduction, and induction or experi-\\nment.\\nBy intuition, we mean the absolute knowledge\\nwhich, without any apparent effort, we find implanted\\nin us. Such for example, is the aspiration of man s\\nsoul after a Deity, as exemplified in the religious\\nsystems of all people even the most barbarous, and\\nsuch as the existence of certain affections, and notions\\nof moral conduct.\\nThe truth of axioms is determined by intuitive\\nevidence or intuition and in brief, consciousness in\\nmost of its forms, and the testimony of our external\\nsenses, are said to be sources of intuition.\\nBut most of our knowledge is derived from what\\nwe possess already in another form, as where we\\ndeduce certain inferences from acknowledged pre-", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0218.jp2"}, "219": {"fulltext": "INTUITION, INDUCTION AND DEDUCTION. 213\\nmisses, or from observation and experiment, and\\ngenerally, many observations or experiments are\\nnecessary before we can determine a general law;\\ntlius, it required centuries of observation to determine\\nthe Copernican theory of our solar system and\\nalmost all the developments in natural science are\\nthe fruit of many observations and experiments\\naggregated in each case to form one general law.\\nIt is an effort of man by a close study of the\\nphenomena M aLvo^sva\\\\ or appearances of nature, to\\narrive at some degree of acquaintance with the\\nnoumena hoov/xsvaj or essences of its objects.\\nTo unite these was the aim even of the heathen\\nphilosophers, and with their obscure lights they worked\\nardently in the labour it remained for a doubter\\n(Sextus Empiricus), two centuries after the coming of\\nChristianity, to connect them for another purpose,\\nand that was to arrive at a suspension of all judg-\\nment on objects whose nature is obscure, and thus to\\nacquire a certain repose of mind (a-rapalta), and perfect\\nequanimity of disposition (^stpvoTtadsia). But the in-\\nductions of Sextus were never really performed he\\ntheorized to his scepticism, and his theories will not\\nbear the rude hand of physical practice.\\nIn order to illustrate the difference between in-\\nduction and deduction, let us suppose a law already\\ndetermined, which we state in the proposition A is B.\\nLet any number of particular examples, as x, y, z,", "height": "3187", "width": "1929", "jp2-path": "elementsoflogic00copp_0219.jp2"}, "220": {"fulltext": "214 LOGIC.\\nrange under this law, thus, x is A, y is A, z is A.,\\nand we can manifestly reach the conclusion that x,\\ny, and z, are all and severally B.\\nBut suppose the general law unknown, and that it\\nbe approximated to in proportion to the number of\\nparticular examples we shall thus have x is B, y is\\nB, z is B, c. but x, y, z, c., as we increase the\\nnumber of the examples, represent the class A hence\\nwe may state the law A is B the truth of which\\nwill depend upon the number and extent of the expe-\\nriments performed and particular instances observed.\\nOr, to recapitulate in syllogistic form\\nDeduction, Induction.\\n(Laio) A is B. (Part, examples) x, y, z, ifec, are B.\\n(Fart, examples) x, y, z, c., are A. A is the class to which x, y, z, c belong.\\n(Conclusion) x, y, z, c., are B. (Law) A is (likely to be) B.\\nNow there are certain sciences in which, from the\\nnature of things, we can never state more certain re-\\nsults from induction than this likelihood; but this\\nlikelihood, it must be observed, becomes greater and\\ngreater, and at length touches absolute certainty,\\nwhen we examine many particular instances and find\\nnone of them failing to range itself under the law\\nwhich we call likely. So that at the last we write it\\nto all intents and purposes as a categorical proposition,\\nA is B. In some sciences we may exhaust all the\\nparticular examples and finish our induction by a\\ncertain law. This induction has led, as the other\\ncould not, to certainty.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0220.jp2"}, "221": {"fulltext": "215\\nThere are two kinds of induction, material and\\nformal; and it is by a want of proper distinction be-\\ntween them that the error has arisen of comparing\\ninduction improperly with the syllogism, and asserting\\nthat while induction is one kind of reasoning, the syl-\\nlogism is another, i. e. deduction.\\nHence Lord Bacon and his followers, finding that\\ndeduction generally moved from what was contained in\\nknown premisses to lower classes or individuals con-\\ntained in them, threw aside the syllogism as useless,\\nand inaugurated induction as the new Logic of experi-\\nmental philosophy. A simple examination of material\\nand formal induction will set us right. Material in-\\nduction is the process of experiment and observation\\nthe laborious investigation of facts, as to their dis-\\ncovery and their combination but formal induction\\nis obtained by the use of the syllogism itself: not\\nconfined, as some writers have attempted to show, to\\nthe third figure, but in most examples capable of being\\nat once written out in the first figure, the form in\\nwhich they may be immediately tested by the dictum\\nof Aristotle as in the exiample\\nMn-i Whatever is true of the cow, goat, deer, c., is likely\\nto be true of all horned animals\\nMin. prem. Eumination is true of the cow, the deer, c.\\nConcl. (Law). Rumination is likely to he true of all horned animals.\\nThe naturalist receives this as the only just con-\\nclusion from the formal induction to which the syllo-\\ngism has helped him but, having as yet found no", "height": "3187", "width": "1924", "jp2-path": "elementsoflogic00copp_0221.jp2"}, "222": {"fulltext": "216 LOGIC.\\nexception to the rule, he writes it out boldly and\\nwithout fear of contradiction,\\nAll horned animals are ruminant.\\nOf certain modes of using Syllogisms,\\nArgument a priori. This is the mode of passing\\nfrom known antecedents, to necessary consequents\\nor, in the sciences, from cause to effect. Thus, if we\\nconsider the being of a God and of his attributes to\\nbe independently known, as by intuition, then we rea-\\nson a priori to the existence of his works, the univer-\\nsality of his providence, and the gracious designs of\\nhis redemption this reasoning is most plainly stated\\nin the form of the constructive conditional syllogism\\nthe affirmation of the antecedent or cause helping\\nus to the affirmation of the consequent or effect.\\nArgument a posteriori. This is reasoning from\\neffect to cause. If, by an inverse process, we first study\\nnatural religion, and experiment upon the wonders\\nof the human mind, and then pass back from these\\nworks around us to the establishment of the existence\\nof a first great cause, who must have made them all,\\nwe are said to reason a posteriori, or from results to\\ntheir causes.\\nOf the two modes of reasoning, both are useful\\nand effective, but the reasoning a prio7 i is the most\\ncertain, and analogous to deductive inference, while\\nthe reasoning a posteriori must always have some un-", "height": "3220", "width": "2121", "jp2-path": "elementsoflogic00copp_0222.jp2"}, "223": {"fulltext": "MODES OF USING SYLLOGISMS. 217\\ncertainty akin to the processes of induction. For if\\ntlie argument be placed in the conditional form, as\\nbefore, we have really no right to pass from the affirma-\\ntion of the consequent^ to the affirmation of the antece-\\ndent. It is usual, therefore, to limit the conditional in\\nreasoning a posteriori, so that the consequent in ques-\\ntion must be considered to spring from that antece-\\ndent, and no other.\\nHistory uses both forms, and combines them with\\ngreat success taking, for example, on the one hanc^\\nthe early elements of a nation s life its people, its\\ngeography, its tendencies of government history\\nseeks to trace these to their legitimate results among\\nthe changing scenes of national existence w^hile on\\nthe other, looking around at the present condition and\\nconduct of a nation, she takes these results, and tracing\\nthem back, in careful combination, with each step re-\\nmoved from the present, she seeks for their early and\\nprime causes, in the classic times of the country s\\norigin.\\nThere are, it must also be observed, certain results\\nof a spiritual kind, both in natural and revealed re-\\nligion, which may be justly reasoned upon a posteriori.,\\nto their certain causes and source. Such, if we mis-\\ntake not, is our Saviour s teaching, when he declares,\\ni by their fruits ye shall know them: asserting the\\nexact analogy between the fruits of the Spirit and the\\n19", "height": "3187", "width": "1918", "jp2-path": "elementsoflogic00copp_0223.jp2"}, "224": {"fulltext": "218 LOGIC.\\nfruits of vegetable life. Since certain events of which\\nwe are aware, while yet their causes are unknown to\\nus, may have sprung from any one of several causes,\\nwe must be careful upon what subjects and to what\\nextent we use the d posteriori mode of reasoning, for\\neven when it seems most applicable, it may fail us.\\nThus, if in time of yellow fever we should see a man\\nsuddenly sick, and should assert,\\nThis man is sick,\\nTherefore, He has the fever\\nit might prove an exceptional case he might be sick\\nof something else. This is a very open and familiar\\nillustration, but serves to indicate the dangers to which\\nit is liable. Almost all the processes of discovery in\\nnatural religion are by means of the reasoning d\\nposteriori.\\nArgument d fortiori. This is a method by which\\nwe establish a stronger conclusion even than ordinary\\npremisses need to warrant us. Thus,\\nA is greater than B.\\nB is greater than C.\\nA is greater than C.\\nThat this conclusion is just there can be no doubt\\nand that the form of it is not exactly that of the regular\\nsyllogism, is equally apparent.\\nHence, some writers have denied that it is a syllo-\\ngism, or can be put at once into syllogistic form.", "height": "3227", "width": "2121", "jp2-path": "elementsoflogic00copp_0224.jp2"}, "225": {"fulltext": "MODES OF USING SYLLOGISMS. 219\\nEasily to demonstrate the error of such, let us trans-\\npose the apparent premisses, thus\\nB is greater than C.\\nA is greater than B.\\nA is greater than C.\\nAnd replacing {greater than 0) hj X, we shall have\\nB is X.\\nA is B (because it is greater than B).\\nA is X.\\nThis conclusion is a comparative proposition which can\\nbe at once shown by replacing X, by its value, (greater\\nthan C).\\nThis reasoning a fortiori is very effective and\\nproper and was used by our Saviour in his invectives\\nupon Chorazin, Bethsaida and Capernaum, with\\nthrilling effect. So also is it forcibly used by the\\napostle, to the Hebrews (x. 28), in the words\\nii He who despised Moses law, died without mercy\\nunder two or three witnesses of how much sorer\\npunishment shall he be thought guilty, who hath\\ntrodden under foot the Son of God, c.", "height": "3195", "width": "1938", "jp2-path": "elementsoflogic00copp_0225.jp2"}, "226": {"fulltext": "220 LOGIC.\\nCHAPTER XII.\\nA HISTORICAL SKETCH OF LOGIC.\\n(5i.) Division of the Suhject.\\nHaving completed, in general outline, tlie study of\\nthe formal Logic, in its present condition of exactness\\nand practical use, we are ready to go back to its\\nfeeble beginnings, and trace it in its slow and tram-\\nmelled movements from the days of the early Greek\\nPhilosophy, through the applications of Roman\\nScience, the enlightening process of Christianity, the\\ndarkness of the scholastic subtleties, the dawn and\\nadvance of Experimental philosophy and the meta-\\nphysics of the eighteenth century, down to the con-\\ntroversies of our own day.\\nNor are we yet to regard the science of Logic as\\nestablished beyond dispute, and fairly stationed among\\nits sister sciences it is yet an arena of dispute, and\\nthe most distinguished philosophers disagree, as has\\nbeen seen, even as to what it is, and as to what is its\\nscope.", "height": "3232", "width": "2121", "jp2-path": "elementsoflogic00copp_0226.jp2"}, "227": {"fulltext": "HISTORY OF LOGIC. 221\\nIt would be of great interest and profit to take\\nsuch a historical view in detail but the limits of this\\nwork will not permit it, and, besides, for all practical\\npurposes, the periods of the history naturally divide\\nthemselves into four. These so much transcend all\\nothers in interest and value, and so absorb the events\\nwhich just precede or immediately follow them respec-\\ntively, that they form the plainest and most conve-\\nnient method in which to present the History of Logic.\\nThey may be marked by the titles\\n1. Aristotle.\\n2. Christianity and Logic.\\n3. Bacon, and the rise of Inductive Science.\\n4. The present system.\\n1. Under the first may be classed all the efforts of\\nthe human mind in the arrangement of a canon of\\nreasoning, in that early time when knowledge, preced-\\ning method, was only seeking in darkness and ob-\\nscurity that system of laws and principles by which\\nalone knowledge may be made available. Around\\nAristotle, too, cluster the great expansions of science\\nwhich were due to the conquests of Alexander, and\\nthe great kingdoms of his successors.\\n2. In the coming of Christianity, Logic found not\\na rival, but a guide, and in the early church it was\\nthe weapon of their spiritual warfare. To the church,\\nas the representative of Christiatiity, is due much of\\nthe error as well as the good of scholasticism.", "height": "3187", "width": "1937", "jp2-path": "elementsoflogic00copp_0227.jp2"}, "228": {"fulltext": "222 LOGIC.\\n3. Logic was the servant, the ill-used servant of\\nInductive philosophy, and owes much of its long bon-\\ndage and oppression to the illustrious founder of the\\nsystem of Experimental philosophy.\\nFrom these considerations, it has been assumed that\\nwe are better able to look into this history now that we\\nare acquainted with the scope of the science otherAvise\\nwe might fall into the same error, by reason of the\\nhonourable company in which we should find ourselves.\\n4. Since the time of Lord Bacon, and perhaps by\\nreason of his example in condemning the syllogism,\\nLogic has been degraded from its position as the con-\\ntroller of the reason on all subjects, and has been so\\nintermixed with Mental philosophy as quite to lose its\\nidentity, and be miscalled by its own name. This was\\nits condition during the eighteenth century. In the\\nnineteenth there have sprung up many champions of\\nAristotle and the syllogism, among whom first in dis-\\ntinction is Archbishop Whately. The universal prin-\\nciple of reasoning has been rescued by him from obli-\\nvion and degradation and Logical science, although\\nstill maligned and fiercely attacked, seems ready to\\ntake its permanent place among the great Elemen-\\ntary sciences of human investigation and instruction.\\n(55.) Aristotle.\\nIt must be considered that the progress of such a\\nscience as Logic was necessarily gradual and slow\\nthat from the beginning, men had been contemplating", "height": "3198", "width": "2121", "jp2-path": "elementsoflogic00copp_0228.jp2"}, "229": {"fulltext": "ARISTOTLE. 223\\ntoe operations of tlie reason, or were making vain but\\nprogressive efforts to distinguish tlie exact functions\\nof the reason, among the mazy elements of the human\\nintellect. Many men had collected much material,\\nwhich lay floating in a chaotic state upon the great\\ndeep of the human mind.\\nThe logical doctrines of conception as expressed\\nin terms, of judgments as formed in pro-positions, were\\nknown to Socrates and Plato. Indeed, Zeno the\\nEleatic, who is mentioned as the inventor of Dialectic,\\nhad invented logical puzzles which required an inves-\\ntigation of the laws of thought, and that caused a\\nrace of so-called teachers of Dialectic to spring up\\nin Greece.\\nSo the first movements in Logic were trammelled\\nby the ignorance and empiricism of those who called\\nthemselves teachers.\\nThe experience of our own age has taught us that\\ntrue science is more impeded and injured in this than\\nin any other way. A whole class of speculative logi-\\ncians in the early times went by the name of Sophists.\\nWe are accustomed to hear the Sophists spoken of\\nin terms of contempt, and sophistry has come to mean\\nFallacy. But we should err very greatly, as many\\nin all ages have erred, if we regarded them as wholly\\nevil. The most enlightened writers of modern times\\nhave demonstrated, that much of the odium which", "height": "3187", "width": "1934", "jp2-path": "elementsoflogic00copp_0229.jp2"}, "230": {"fulltext": "224 LOGIC.\\nattaches to the name, belongs really to the abuse of\\nthen- art they were paid teachers, among whom\\nare enumerated Protagoras and Gorgias, whose duty\\nwas to train up young men for the duties and pursuits\\nof public life. The character of the Greeks, who\\nwere fond of riddles and disputes, and the errors of\\nthe age, led to their real sophistry^ and their abuse of\\nthe rhetorical art to make the worse appear the\\nbetter reason; after that, their efforts were not for\\nthe purpose of widening the range of knowledge\\nand truth, but really served to check these, and thus\\ngive a free course to fallacious reasoning.\\nThe Logic of Euclid consisted in negative proofs\\nhis design was, in encountering an opponent in con-\\ntroversy, not to attack his premisses, but his conclu-\\nsion.\\nChief among the early logicians, as he is distin-\\nguished among the sages of the world, was Socrates.\\nMuch interest and sympathy attach to the virtuous\\nand heroic life, and the tragical fate, of this wise and\\ngood man but it is principally by his philosophy and\\nlogic that he has been useful to the world. Keeping\\nin view always before his numerous scholars, the\\ndignity of Logic as a science, and the loftiness of the\\nreasoning powers, he guided the logical processes by\\nwhat is now called common sense. This is implied\\nin Cicero s declaration, that Socrates brought philo-", "height": "3226", "width": "2121", "jp2-path": "elementsoflogic00copp_0230.jp2"}, "231": {"fulltext": "ARISTOTLE. 225\\nsophy from Heaven to earth, Xenophon, likewise, tells\\nus in his Memorabilia, that when he wished to\\nform a decision on any subject, his reasonings always\\nproceeded from propositions generally assented to or\\nunderstood. Condemning the errors into which the\\nSophists had been led, he claimed Truth as the real\\naim of reasoning, and established in all his arguments\\na high principle of moral responsibility. The analytic\\nprocess was that mainly employed by Socrates and\\nthus, when Plato appeared, he found the science of\\nLogic, and the art of Dialectics, presented by de-\\ntached and isolated views, as the result of previous\\ninvestigations. The analysis had only prepared for\\nthe synthesis.\\nThe plan adopted by Plato was the Synthetic\\nmethod^ and by this he worked out many great results.\\nPerhaps the best feature in the Logic of Plato was\\nthat on approaching the science, he tells us to keep\\nthe mind free from all preoccupations and preconcep-\\ntions he declared, as an axiom, that Ignorance is\\nthe true start point for Science. Disputing the asser-\\ntion of the earlier philosophers that sensation was the\\nfoundation of truth, he proved it to be one of the\\ninstruments by which truth is arrived at. Without\\nstopping to give a sketch of his system, we may state\\nthat his Logic and theology are so intimately con-\\nnected, that we may judge of the vigour of the one\\nBlakey s Historical Sketch of Logic, p. 24.\\nP", "height": "3187", "width": "1946", "jp2-path": "elementsoflogic00copp_0231.jp2"}, "232": {"fulltext": "2 2C LOGIC.\\nbj the developments of the other. He proved the\\nexistence of a Deity, who was the measure of all\\nknowledge, the centre of all truth and in mysterious\\nlanguage he declares that this centre is the begin-\\nning, middle, and end of all things. But Plato was\\nto be eclipsed by a greater mind in fact one of the\\ngreatest minds the world has ever seen.\\nWhen much material was thus collected, v/hen\\nmany vague theories had thus been started, and when\\ncrowds of ignorant pretenders had arisen to be con-\\nverted or silenced, Aristotle came to create a new\\nsystem to enlighten, to harmonize, and to sweep away\\nall the errors of the Dialecticians and the Sophists.\\nHe, who was to correct the characteristic errors of\\nthe Greek philosophy, was himself a Greek. The\\nGreek mind was eminently a curious one. All the\\nspeculations of philosophy, all the systems of Ethics,\\nwere directed apparently and nominally indeed to the\\ndiscovery of truth but if they reached, by specious\\narguments, a pleasant conclusion, it mattered little\\nfor pure truth. They contented themselves with the\\nfruits of their system, once that system was estab-\\nlished.\\nThe Athenians were characterized by the apostle\\nas spending their time in nothing else but the pur-\\nsuit of novelty and they were but the types and\\nrepresentatives of the other states and cities of\\nI", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0232.jp2"}, "233": {"fulltext": "ARISTOTLE. 227\\nGreece. There are in the early Greek authors many\\ncorroborations of the apostle s assertion.\\nAristotle, building upon the combined foundations\\nof Socrates and Plato, discovered many new princi-\\nples and established new rules, until he had elaborated\\nthe system of Logic which we have at this day.\\nHis Logical works, published in full under the title\\nof Aristotle s Organon, comprise the following\\nworks: 1. The Book of the Categories; 2. Of In-\\nterpretation; 3. The Prior Analytics 4. The Post\\nAnalytics 5. Topics 6. Of Sophisms.\\nOf these, the most important are The Book of the\\nCategories, and both Analytics. We shall pro-\\nceed directly to explain their meaning.\\nHe drew the true and somewhat nice distinction\\nbetween Logic and Ehetoric, and established the fact\\n(a fact not yet learned by many who call themselves\\nlogicians) that Logic is not concerned with the truth\\nof propositions, but only with the reasoning upon\\nsuch propositions as are given into its charge. If\\nthe premisses be true^ then Logic will give a time\\nconclusion but if the premisses he false, Logic gives\\na false conclusion but in this latter case the Logic\\nis as good, the argument as valid, as in the former.\\nIn establishing his dictum, which we have assumed\\nto be the universal principle of reasoning, he laid\\ndown the general law of Logic, a law which has been", "height": "3195", "width": "1907", "jp2-path": "elementsoflogic00copp_0233.jp2"}, "234": {"fulltext": "228 LOGIC.\\nmisunderstood and misinterpreted, for this dictum\\nwas not a model for common arguments, but simply a\\ntest for all.\\nAs the Greeks looked for truth and found that\\nLogic did not impart it that before Logic could be\\nused they must be possessed of premisses, which pre-\\nmisses were given them either by intuition or by\\nobservatmi, i. e., induction^ they either abused Logic\\nfor not doing what it could not propose to do, or else\\ninjured it much more than their abuse could do, by\\nusing it as a vehicle for false philosophy and mythic\\nreligion. They took, to save themselves the trouble\\nof laborious induction in search of premisses, the\\nvagaries of their own quick, joyous and disputatious\\nminds, and thus produced monstrous and absurd con-\\nclusions, which, since their Logic was valid, they felt\\nsatisfied to consider as true.\\nThe union of this Grecian spn it with the equally\\nvague and fantastic imagination of the Orientals, with\\nwhom by conquest they became acquainted, further\\ncorrupted their intellects, and robbed Logic of its\\ntrue character and mission leaving the whole domain\\nof Philosophy without the true guide of Reasoning.\\nLet us now look in turn at the logical works com-\\nprising the Organon.\\nThe Categories,\\nWe are in the habit of using the word category, for", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0234.jp2"}, "235": {"fulltext": "AEISTOTLE. 229\\nexample, we speak of a person or thing being but in\\nthis or that category the word and its use we owe to\\nAristotle. His categories are ten in number. They are\\nnot all now considered of importance in classification,\\nbut are still worth an explanation, as the original sys-\\ntem^ from which, by careful elimination, we have pro-\\nduced our own later classifications. The categories\\nwere supposed to imply answers to all possible ques-\\ntions concerning a term, expressing an act of appre-\\nhension i. e., all of which we can have any knowledge.\\n1st, Substance. 2d, Quantity. 3d, Quality. 4th,\\nRelation. 5th, Action. 6th, Passion. 7th, The\\nWhere. 8th, The When. 9th, Position, in space.\\n10th, Possession.\\nThe categories may be thus more fully ex-\\nplained\\n1. Substance may be defined that which is in itself,\\nwhich may be conceived as existing by itself. This\\nis divided into spiritual and temporal and subdivided\\naccording to classes, genera, sj^ecies, c.\\n2. Quantity may be translated how much, or\\nhow great, and by implication, as to time, how long.\\nThus, under the head of Quantity, we have the three\\nspecial considerations of Numher, Magnitude and\\nTime (as to duration). Number, we know, is either\\nabstract or concrete, as when we speak of a number\\ndisconnected with any objects, or, of a number of\\n20", "height": "3187", "width": "1956", "jp2-path": "elementsoflogic00copp_0235.jp2"}, "236": {"fulltext": "230 LOGIC.\\nobjects or things. Thus, quantity^ as a category, covers\\nthe science of arithmetic. Magnitude is either linear,\\nsuperficial or solid and thus its genus quantity cov-\\ners, likewise, the science of geometry. Time is either\\npermanent or successive, and is used to indicate the\\nmovements or conjunctions of Number and Magni-\\ntude.\\n3. Quality describes the kind or sort of which a\\nthing is and is subdivided into Habit, or a quality\\ninduced by frequent repetition of the same act, as\\nvirtue, vice, c. Inherent nature, as man s reason\\nFrom these grow the many subdivisions of colour,\\nsound, hardness and shape.\\n4. Relation is the consideration of two or more ideas\\nwith reference to each other. The first idea of tivo,\\nis called the relative, the second the correlative, as\\npnnce and subject master and servant.\\n5. Action has a double meaning it is at once the\\nexertion of power by one body on another, and the\\neffect produced by such an exertion.\\n6. Passion is the endurance of another s action.\\n7. The Where includes the three meanings which\\nwe express by the words where, whence and whither\\nas in Philadelphia, from Netv York, to London.\\n8. The When has reference to the exact period\\nof time, and not its deration, wdiich, as we have seen,\\nbelongs more properly to quantity. The When may", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0236.jp2"}, "237": {"fulltext": "ARISTOTLE. 231\\nbe expressed by the pbrases to-day^ to-morrow^ a hun-\\ndred years ago,\\n9. Position has reference, not to the place wliere^\\nbut to the ijosture in ivhich a body is found, as lying\\ndown, standing up, kneeling, c. The question then\\nis, how did you find it not where f\\n10. Possessio:n has reference to something belong-\\ning to the object, or placed upon and clothing it and\\nas a category, covers all questions concerning the\\nrights of property.\\nOf these categories, it will appear that substance\\nstands apart from the rest, in that it is sensibly exist-\\nent, and they are all attributes of such an existence\\nIt will further appear, upon examination, that Quan-\\ntity and Quality are essential attributes, i. e., belong\\nto the essence of the object necessarily while Rela-\\ntion, Action, Passion, The Where, The When, Posi-\\ntion, and Possession, are accidental circumstances\\nwhich may be dissociated from it.\\nTo render this clearer, for facility of reference, we\\nstate it in a tabular form. In this table we place all\\nthe explanatory parts as by the rules of division be-\\nfore given, but number the categories, that the eye\\nmay at once rest upon them.", "height": "3195", "width": "1948", "jp2-path": "elementsoflogic00copp_0237.jp2"}, "238": {"fulltext": "232 LOGIC.\\nThe object or existence expressed hy a term.\\nAttribufes belonging\\nto the substance.\\n1. Substan\\nce.\\nCircumstantial.\\nEssential.\\n4. Re\\nlation.\\n2. Quantity. 3. Quality.\\n1\\nNumber.\\n1 1\\nMagnitude. Time.\\nHabit.\\nluhereut nature. Shape, c.\\nIll III\\n5. Action. 6. Passion. 7. The Where. 8. The When. 9. Position. 10. Possession.\\nAristotle asserted, that everjtliing which could be\\nsaid of any subject is included in one, some, or all of\\nthese categories, and his own illustration of their use\\nis one of the simplest which can be found. It was as\\nfollows: Substance, man; Quantity, one; Qua-\\nlity, ivhite Relation, greater The Where, in the Fo-\\nrum The When, yesterday Position, sitting Ac-\\ntion, ivhatever he may he doing Passion, ivhatever\\nmay he heing done to him.\\nIt is under this first attempt at method, that the\\nsciences began to range themselves in classes, and by\\nthis all other systems of classification seem to have been\\nsuggested. Thus Substance is the foundation of all\\nPhysical and Historical investigation Quantity, the\\nsubject of Mathematics; Quality, of Medicine; Rela-\\ntion, of Ethics Action and Quantity, of Astronomy,\\nMusic and Mechanics Passion and Action, of Elec-", "height": "3201", "width": "2038", "jp2-path": "elementsoflogic00copp_0238.jp2"}, "239": {"fulltext": "AEISTOTLE. 238\\ntricitj the Where, of Geography the When, of\\nChronology Position and Quality, of Sculpture\\nSahit and JPosition, of Painting and so each art and\\nscience would be found to range under one of these\\nsingly, or more than one, when combined.\\nThe books of Prior and Post Analytics originate\\nand develop his system, of the doctrines and use of the\\nSyllogism. They have been the resort of all writers\\non formal Logic since his time, and there has been but\\nlittle alteration in his method. Aristotle established\\nbut three figures of the syllogism, the fourth being\\nafterwards added by Galen.\\nIn his book of Topics, he discusses the subject of\\nPi^edicahles, or Classes, and establishes the expression\\nof a predicable to be in four ways, i. e., by genus,\\ndifferentia, property, and accident: in these he im-\\nplies the species, since we have seen that if we add\\nthe differentia to the genus, we obtain the species.\\nIn his book of Sophisms he states thirteen Fallacies,\\nas including all those which can bear a syllogistic\\nform. Six of these refer to the tvords used, and are\\ncalled Fallacies in dictione, and seven consist in the\\nmatter of the propositions, and are called Fallacies\\nextra dictioyiem.\\nThe logical works of Aristotle seem to have been\\nprovidentially preserved. Transmitted by his dis-\\nciples from hand to hand, they were at length con-\\ncealed in a vault during one hundred and thirty years,\\n20*", "height": "3187", "width": "1964", "jp2-path": "elementsoflogic00copp_0239.jp2"}, "240": {"fulltext": "234 LOGIC.\\nuntil they had mouldered into an almost illegible con-\\ndition. Restored from this condition, they came by\\nthe fortune of war into the hands of a Roman gene-\\nral, and thus were given a second time to the world.\\nWe cannot pause to notice all the changes attempted\\nin Logic and Philosophy from this time until the Chris-\\ntian era. After the Peripatetics, came Pyrrho of Elis\\nand his Sceptics^ who seem to have employed Logic to\\ndeny the possible attainment of pure truth. They\\nembodied their system in Ten Tropes, or logical rules\\nfor the government of mind in the search of truth.\\nTheir doubt led to what they termed a suspension of\\njudgment, rather than a positive denial.\\nOf the Epicureans and Stoics, it may be said that\\nthey aimed at the establishment of no Logical system,\\nbut rather a few tenets in the shape of propositions\\nby these, as doctrines, they guided their course.\\nThe tenets of Epicurus may be comprised in the\\nassertion that whatever is useful, pleasant and de-\\nlightful, is true. This is to assert that man s senses\\nand bodily appetites are the only test of truth. These\\nhave been called his emotional criteria.\\nThe Stoics rejected the categories of Aristotle and\\nadopted four of their own and attained the conclusion\\nthat pain is no evil: a philosophic stretch of the\\nimagination which has given its. name to an unshrink-\\ning endurance of pain and evil.\\nVery little transpires concerning Roman systems", "height": "3198", "width": "2121", "jp2-path": "elementsoflogic00copp_0240.jp2"}, "241": {"fulltext": "AEISTOTLE. 285\\nof Logic. Altliougli Cicero, Maximus of Tyre, and\\nGalen lay claim to the title of logicians, the logical\\nsystem of Aristotle was adopted by them all\\nRhetoric became the more valued and important\\nstudy.\\nThe history of Logic, then, from the time of Aris-\\ntotle to the coming of Christ, is not a history of\\nchange but the logic however unchanged of Aristotle\\nhad been most unworthily used. No longer the guide\\nand test of just reasoning, it became the vehicle of\\ningenious falsehood, was made to support any theory,\\nand gave power to its possessor to argue on both\\nsides of any question. To satisfy curiosit}^ it estab-\\nlished any paradox, and one being made the premiss\\nto another, the error was multiplied in infinite pro-\\ngression undefined. It was not the logical system,\\nbut the mind of man, which needed purification not\\nabstract propositions, but the matter they contained,\\nwhich demanded scrutiny.\\nWe shall see also that the misconception of the\\nsphere of Logic was equally fruitful of error long\\nafter the establishment of Christianity, and that it\\nhas remained for the nineteenth century, notwith-\\nstanding the utmost resistance of many learned but\\ndogmatic philosophers, to give to Aristotle and his\\nsystem their true place in the domain of science an\\ninstauration, not by one man a new Organon, not\\nthe product of one teeming brain, but the tribute of", "height": "3187", "width": "1956", "jp2-path": "elementsoflogic00copp_0241.jp2"}, "242": {"fulltext": "286 LOGIC.\\nPhilosophy, inductive and deductive, to Aristotle,\\nthe great founder and framer of that system which\\nalone controls the unbridled reason, and sends pure\\ntruth into the channels of usefulness and practice.\\nBut, meanwhile, the coming of Christianity was to\\nproduce great marvels in the domains both of Logic\\nand Philosophy.\\n(56.) The Logic of Christianity.\\nThe Loo^ic of the Grecian schools had been the\\nguide of man s Reason, but now it was itself to be\\nbrought into companionship with a higher human\\nattribute. Faith. Premisses were no longer to be\\nsought by the ordinary means of evidence, but to be\\nsupplied in a new and marvellous manner. Chris-\\ntianity combined this new element w^ith Philosophy,\\nand takino- the art of Loo;ic as the vehicle of its\\ngreat truths, used it in a manner at once beneficial\\nand practical putting an end, as it seemed, to the\\ncontroversies and paradoxes which had beguiled and\\nengaged the Greek and Roman mind.\\nBy this new tutelage of human reason, Christianity\\nproduced an immediate and startling change in Philo-\\nsophy, by opening the Finite upon which man may\\nuse his reason, as well as indicating the Mysterious\\nand Infinite to his faith.\\nAs much as we may despise the Greek systems of", "height": "3226", "width": "2121", "jp2-path": "elementsoflogic00copp_0242.jp2"}, "243": {"fulltext": "LOGIC OF CHRISTIANITY. 23T\\nspeculative Ethics, upon wliich they employed their\\nnobler Logic, we must remember that they were the\\ngropings of men in the dark, pursuing a faint glimmer\\nof light in the hope that it would lead them into the\\nfull sunshine and free air of Truth. They had no\\nrevelation of intelligible fact or of mystery. The\\nefforts of Plato to attain to different degrees of know-\\nledge which he calls the absolute, the probable,\\nthe imperfect, the Politics and Ethics of Aristotle\\nthe bold dicta and quiet endurance of the Stoics\\nthe emotional criteria of Truth, propounded by\\nEpicurus, and so much abused by his disciples, were\\nall vain attempts to arrive at that knoAvledge which\\ncould come to man only by miraculous revelation.\\nGod vouchsafed no such revelation to them it is no\\ncause of wonder that they erred greatly without it.\\nThis, then, was the crowning glory of Christianity,\\nthat it gave to man pure Truth, and furnished him\\nwith a world of new facts upon which to reason, of\\nglorious propositions upon which to try the powers of\\nhis Logic. The language of God to man, was, first,\\nCome, now let us reason together, and thus the\\nwhole system is based upon reason and afterwards, as\\nif thus founded surely and safely, Believe, and ye\\nshall be saved.\\nUnlike the Greeks, the Jews had always possessed\\nthis revelation, in a ceremonial and progressive form.\\nTheir own Scriptures had disclosed to them not only", "height": "3187", "width": "1964", "jp2-path": "elementsoflogic00copp_0243.jp2"}, "244": {"fulltext": "238 LOGIC.\\ntlie true story of man s origin and fall, but of God s\\nsupremacy, and his gracious design of restoratix\u00c2\u00bbn,\\nand their prophets had told them with a heavenly\\nLogic of Type and Symbol premiss upon premiss in\\nglorious abundance, of that certain conclusion, the\\nadvent of the Messiah.\\nThe fulness of time came, and the event fulfilled\\nthe prophecies, the conclusion completed the pre-\\nmisses. Christianity brought philosophic as well as\\nreligious light.\\nBy a strange infatuation, they who had thus awaited\\nHis coming, refused Him when He came and since\\nHe could not be the glory of His earthly people\\nIsrael, He was, in a truly philosophic sense, a light\\nto lighten the Gentiles.\\nIn three centuries. He had been eagerly embraced\\nby Heathen Rome, and the Logic of Aristotle, freed\\nfrom its vile and improper uses, and used as the\\npropounder of a full and pure creed, was applied with\\ngreat power to the spread of the Christian religion.\\nWhere false premisses had been ignorantly used, lead-\\ning to a false conclusion, or where false conclusions\\nhad been improperly deduced from true premisses,\\neverything for a time was changed. Truth was every-\\nwhere triumphant, and its reign seemed to be eternal.\\nSuch was the first influence of Christianity upon\\nLogic. Containing in itself nothing repugnant to\\nreason, it gave a host of new and glorious truths,", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0244.jp2"}, "245": {"fulltext": "LOGIC OF CHRISTIANITY. 239\\nfresh from the mouth of God it simply threw away\\nthe vague speculations, the unsound paradoxes, which\\nhad been heretofore used as premisses, and took these\\nnew trutli8 to reason upon. In the teachings of our\\nSaviour and the apostles, it need scarcely be remarked,\\nnot only that every statement is true, but that every\\nargument is valid.\\nOn the other hand. Logic, turning gladly away\\nfrom the subtleties and absurdities of mythical phi-\\nlosophy, pressed forward with ardour in the task of\\nsystematizing and promulgating the new doctrines of\\nChristianity.\\nIn this manner arose the logical systems of the early\\nChristian ^vriters and apologists, known as the\\nfathers, There is, indeed, error to be found in their\\nuninspired writings, such as we should expect in all\\nhuman productions, but from Justin Martyr to St.\\nAugustine, one object of their writings seems to have\\nbeen the harmonizing of Christian doctrine with the\\nLogic of Aristotle, and thus while they preached the\\ntruth, to show at once the union and true relation of\\nReason and Faith. How well they succeeded as a\\nclass, may be seen at the present day from the grow-\\ning interest in their writings which is manifested by\\nall who are interested in Religion or Philosophy.\\nNever forgetting that they were surrounded by enemies\\nand error, one part of their works was fiercely contro-\\nversial, always keeping in view the elenchuSy and", "height": "3187", "width": "1960", "jp2-path": "elementsoflogic00copp_0245.jp2"}, "246": {"fulltext": "240 LOGIC.\\nwarily observing an opponent, or rather tlie many op-\\nponents who were scrutinizing their deeds and words.\\nWhere, in the old system of Philosophy, Sensation\\nwas the starting point, and man must evolve philoso-\\nphy from within himself they established Revelation\\nas the centre and starting point, and would draw, by\\nthe same logical formulae, all true philosophy from\\nGod. From this time, Logic was inseparably con-\\nnected with theology the Church ruled the world.\\nThe Christian Church had, in its union with the\\nRoman empire, a strength and stability from which\\ngreat philosophic results must have sprung; but just\\nw^hen they were framing this glorious system at once\\nof Religion and Philosophy, the Roman empire of th\u00c2\u00ab\\nwest fell under the ruthless attacks of the Northern\\nbarbarians, and the Church was temporarily paralyzed\\nby the shock. For centuries after, the great efforts\\nof the Church w^ere directed to the attainment of a\\nfirm social basis, and political power.\\nWe have already stated the connexion between\\nLogic and Philosophy. They may be dissociated, but\\nare both then useless. Thus, indirectly, Philosophy\\nhas exerted such an influence upon the uses of Logic\\nthat it is important to trace the systems with which\\nLogic was combined, and to promulgate which it was\\nused after the establishment of Christianity. Most\\nof the Christian writers investigated the subject of\\nthe human reason, and studied the Logic of Aristotle.", "height": "3220", "width": "2121", "jp2-path": "elementsoflogic00copp_0246.jp2"}, "247": {"fulltext": "LOGIC OF CHRISTIANITY. 241\\nAs might be expected, so magical a transformer as\\nChristianitj was not without fierce philosophic oppo-\\nsition. With equal steps Scepticism and Heresy ad-\\nvanced. Those who were doubters before where only\\nSoience was concerned, were doubly doubters when\\ntold of Christian mysteries.\\nThe representative of the new sceptics was Sextus\\nEmpiricus, who lived in the beginning of the third\\ncentury, and who was but a new incarnation of Pyrrho\\nof Elis. Unwilling to receive, on prima facie evi-\\ndence, the truth of the new revelation, they had\\nfallen back upon the old material, and had worked to\\nthe same results as the Greek philosophers they\\nturned their backs on the light, which admits of no\\nbetter proof than the physical light of day, and\\nwalked into the cave of darkness, of doubt, and, in a\\nreligious view, of despair.\\nThe scepticism of Pyrrho, three hundred years\\nbefore Christ, was consistent, and well deduced when\\ncompared with this, and yet the Greek academicians,\\nwe know, had convicted him of absurdity. Be-\\ncause everything is contradictory, everything is false.\\nNow, if this be true^ the axiom itself is false, and so\\nthe sceptic, thrown upon the horns of a dilemma, must\\ngrope again, in vain, for new proofs of falsehood, and\\nnew certainties of doubt.\\nOf the Neo-Platonic, Eclectic or Alexandrian\\n21 Q", "height": "3187", "width": "1980", "jp2-path": "elementsoflogic00copp_0247.jp2"}, "248": {"fulltext": "242 LOGIC.\\nschool, the object seems to have been to unite the\\nGreek philosophy and Oriental dogmatism into one\\nsystem; but it was a false and feeble combination,\\nfated to a speedy and ridiculous end.\\nIts metaphysics, as prepared by Plotinus, was the\\nattempt by the combination of heathen obscurities to\\nattain to Christian light; its theology, as reduced by\\nlamblichus, was a strange retrogradation from the\\nScriptures, which revealed the person and word of\\nGod, to the ridiculous deities of the Pantheon; and\\nits Logic, of which the great Porphyry was the ap-\\nplier, was an attempt, by the use of the Aristotelian\\nsystem, to establish all these errors, at the expense\\nof the fair fame and even of the existence of Logic.\\nNor in the singular applications of Christianit}^ to\\nLogic must the Gnostics be forgotten. Their name\\nindicated their creed; yj^cocjtj, knoivleclge^ as opposed to\\nfaith Naked Logic, stripped of its armour, was made\\nagain to do duty in the ranks of the Prince of Dark-\\nness. Gnosticism took such portions of the Gospel\\nas suited its views or struck its fancy; but these rays\\nof light they mingled with such a chaos of absurdity,\\nthat the apostles would hardly have recognised their\\nown doctrines.\\nThe greatest, perhaps, of the indirect evidences of\\nBurton s Heresies of the Apostolic Age, p. 15, quoted by\\nNeU.", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0248.jp2"}, "249": {"fulltext": "LOGIC OF CimiSTIAXITY. 248\\nthe truth of the Christian religion is, that in spite of\\nthe false systems which sprang up to oppose it, it has\\nsteadily and mightily prevailed in its progress it has\\npurified human philosophy, and unfettered Logic\\nhut it did not accomplish this without fierce contests\\nit was to come upon dark days, in which it was the\\nonly glimmer of light days in which the misuses of\\nLogic were no longer to he confined to profane sys-\\ntems or heretical creeds. Unfortunately, they are\\nconstantly found in the career of the Christian Church\\nherself. As an institution designed to convey Chris-\\ntian truth to all generations, it would he supposed\\nshe could have little to do with the conflicts of the\\nworld around her. Not so. As soon as the Church\\nwas struck with the ambition for power, the lust for\\nempire, she began to pervert facts and degrade Logic.\\nThe days of the truthful and zealous Fathers had\\ngiven way to that of ambitious prelates, and greedy\\necclesiastics of every degree. It was the dark age\\nof Logical Philosophy. As long as she was weak,\\nand feared lest the brute force of kings and barons\\nshould crush her power, and check her increasing\\ninfluence, she asserted the difi erence and distinction\\nbetween the secular and spiritual; and thus main-\\ntained herself as the spijntually strong but as soon\\nas she had acquired strength and control, in her spi-\\nritual capacity, she claimed a share in temporalities,", "height": "3187", "width": "1956", "jp2-path": "elementsoflogic00copp_0249.jp2"}, "250": {"fulltext": "244 LOGIC.\\nand put her strong band upon all the kingdoms of the\\nworld she usurped the power and province of her\\ndivine Master, and said, By me do kings reign, and\\nprinces decree justice.\\nClaiming infallibility at first, only in doctrine at\\nlength, in general opinion; she trammelled science,\\nexpurgated literature controlled, or attempted to\\ncontrol, the thoughts of men, and placed the gaunt-\\nleted hand of despotism upon philosophy, demanding\\nthat it should speak only at her will and by her\\ndictum. It was an evil day for the Logic of Aristotle,\\nwhen this corrupt Church claimed it as the frame-\\nwork of her ethical system, because she used it only\\nto draw from false premisses, false conclusions. It\\nwas a happy thing for the Church that Logic did not\\nlook beyond the form of the expression, or her ma-\\nchinations would have been more thoroughly exposed.\\nAssuming premisses slightly false, the Church rea-\\nsoned to conclusions monstrously false. From j)rohahle\\npremisses, it arrived at ce7^tain conclusions and not\\nunfrequently was it guilty of Logical fallacies, as\\nwell as Material. A slight and cursory examina-\\ntion of the sophistries of the Church in the Middle\\nAges, would show us hovr Logic was degraded and\\nmisused but we shall content ourselves with a few\\nwords upon the rise and progress of Scholasticism,\\nthe form which seems, in its changes, to present at\\nonce the Philosophy and the Logic of Christian", "height": "3181", "width": "2121", "jp2-path": "elementsoflogic00copp_0250.jp2"}, "251": {"fulltext": "LOGIC OF CHRISTIANITY. 245\\nEurope in the Middle Ages. That the Church should\\nhave espoused the formal Logic of Aristotle was not\\nentirely without good for as the Church espoused\\nit, it became a popular science in the new schools\\nwhich arose wherever the Church went. Thus arose\\nin the foundations of Charlemagne, the Schoolmen,\\nwhose object was to connect or harmonize the elements\\nof all truth which remained to man after the fearful\\nconvulsions in the Western Empire a restoration\\nin Philosophy similar to that of Charlemagne in do-\\nminion.\\nThe duty of the Schoolmen seems to have been to\\ndetermine what was Philoso phy^ and how much it had\\nto do with Religion. In such a question Philosophy\\nwould surely hide its diminished head. Distinguished\\nPopes, like Gregory the Great, were for proscribing\\nall secular studies, and making theology the only study\\nof the world in order to effect this purpose, we\\nknow that he destroyed valuable manuscripts. A host\\nof mad enthusiasts, called Saracens, had destroyed a\\nwealth of history and science in the library of\\nAlexandria but the very darkness of the times was\\nsignificant of the coming dawn.\\nThe first era of Scholasticism was the adoption\\nof Logic as the form and vehicle for Religion, and\\nthus far they were in the right path.\\nThe second phase was the attempt to unite Religion\\n21*", "height": "3187", "width": "1927", "jp2-path": "elementsoflogic00copp_0251.jp2"}, "252": {"fulltext": "246 LOGIC.\\nand Philosophy, and this produced new champions of\\nRealism.\\nThe third phase was an opposition Religion and\\nPhilosophy were rudely dissevered, and this produced\\nNominalism.\\nIf, now, we separately consider these three phases\\nof the Scholastic philosophy, we shall perceive that\\nthe first was the just and true one, and that the suc-\\nceeding ones were learning which had to be unlearned.\\nThat part of the Greek system which could be\\nmade th.Q form and vehicle of religion, as it is of all\\ncorrect reasoning, was only the Logic. To apply that\\nto the service of Faith, was just the first design of\\nChristianity towards Logic, and thus far the School-\\nmen were right indeed, it would seem ignorantly\\nright for while using the forms which constitute Lo-\\ngic, they still persisted in calling many other parts of\\nthe Greek philosophy by the name of Logic, and\\nthus making Logic bear the blame which truly be-\\nlonged to the errors, obscurities, and absurdities of\\nexploded systems of metaphysics, theology, and\\nmorals.\\nThis is apparent in the works of Alcuin, the con-\\ntemporary and friend of Charlemagne, and especially\\nin his dialogues on Grammar, Rhetoric, and Logic.\\nSo, too, Erigena lays down the logical rules of Divi-\\nsion, Definition, Analysis, and Demonstration, and\\nasserts, that by the use of these man may attain to", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0252.jp2"}, "253": {"fulltext": "LOGIC OF CHRISTIANITY. 247\\ntruth, manifestlj begging the question, and asserting\\nthat man attains to truth hy arriving at truth. There\\nmust have been a great superiority of intellect about\\nthis man, however, as we know that he was regarded\\nby the Church as dangerous, and his works afterwards\\nplaced in the Index Expurgatorius. More lofty\\nwas the simple distinction of St. Anselm, that there\\nare but two modes of Cognition Faith and Science\\nand grander yet the idea, that Science begins where\\nFaith ends, in the bosom of God\\nBut let us consider the second and third phases.\\nNominalism and Realism were but the reproduction\\nin the ninth century of the old Platonian controversy,\\nalready referred to. Nominal and real were the abstrac-\\ntions of what we call respectively universal and jjar-\\nticular.\\nWhen I speak of a single man, and point him out,\\nI designate a real existent individual when I speak\\nof man, as a common term, is there a real entity cor-\\nresponding to the vford The realists said Yes the\\nnominalists said No it is but a name to indicate num-\\nbers. This had been the origin of the controversy.\\nPlato, with his divine but vague philosophy, had\\nasserted that there was a real existence, an archetype\\nin the bosom of God corresponding to the name of a\\nclass, as man, angel Aristotle, that they were only\\ngeneralized names from many individual abstractions.\\nAnd thus these great parents of Logical Philosophy", "height": "3179", "width": "1943", "jp2-path": "elementsoflogic00copp_0253.jp2"}, "254": {"fulltext": "248 LOGIC.\\nset the example of wrangling to their myriad children\\nof the schools. It is curious to see how such a dis-\\npute first connected itself with religion. It was thus\\nthe question seemed to involve another and a more\\nimportant one, viz. what is the foundation of\\nhuman knowledge Roscellinus of Compeigne, who\\nlived in the eleventh century, was the originator of\\nthe new controversy in the Middle Ages between the\\nrealists and the nominalists. He was a fierce nomi-\\nnalist^ and as this led to supposed heresies, he was an\\nobject of persecution on this account. As warmly\\nwas the cause of realism espoused by William of\\nChampeaux and throughout the schools there was a\\nword-war of great fierceness on this subject.\\nPassing over the quarrels of the schoolmen until\\nwe reach the time of Roger Bacon, and thus neglect-\\ning many great names in the history of Logical Philo-\\nsophy, we are struck with the power of his experiments\\nand analysis, and the manifest fact that he deserves\\nthe name of the founder of Inductive Philosophy that\\nhis Opus Majus may justly be considered the\\nprecursor of the Novum Organum of his more\\nillustrious namesake, Francis Bacon.\\nDisgusted wdth the categories of Aristotle as tram-\\nmelling an ardent physical scholar, who must establish\\ncategories for himself by experience, he considers\\nexperiment, based upon constant observation, the only\\nrule for philosophy, and in his works in the labora-", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0254.jp2"}, "255": {"fulltext": "LOGIC OF CHRISTIANITY. 249\\ntory and with his pen we discern the first dawning of\\nthe day of Induction.\\nFor awhile, as was very natural, formal Logic fell\\ninto disrepute, and gave way to experiment in physics\\nand from that day down to our own times, there has\\nbeen but little appreciation or understanding of the\\nart of reasoning, although it has been constantly used,\\nand constantly ignored. Like savages, who breathe\\nthe invisible air around them and are not aware of\\nits existence, so minds of all kinds and calibres have\\nused the Logic which they found established as the\\nvehicle of thought, without knowing where to make\\ntheir acknowledgments.\\nAt length the Logic of Aristotle received a shock\\nruder than any which it had yet experienced.\\nLong used by the powerful Church, and long\\nsubtly applied to many sophistries by that Church\\nit had been accused also of becoming corrupt errors\\nand crimes, not its own, were imputed to it it was\\ncontaminated by the theology, stained by the prac-\\ntices, monopolized by the avarice of the Church and\\nwas conseqently to go through two distinct phases\\nfirst, to be punished with that Church and, secondly,\\nto be disenthralled and separated from it. The first\\ntook place at the Reformation, of which premonitory\\nsymptoms had been seen by Roger Bacon in England,\\nin the 13th century, and distinct signs by Wiclif in\\nthe 14th. In this, both Bacon and Wiclif were efii-", "height": "3187", "width": "1956", "jp2-path": "elementsoflogic00copp_0255.jp2"}, "256": {"fulltext": "250 LOGIC.\\nclent instruments. Still, the battle cries were, nomi-\\nnalism and realism. Realism suited the blind belief\\nof the Church, and nominalism the unmasking dog-\\nmatism of the reformers.\\nPeter Ramus, in the early part of the 16th cen-\\ntury, having published a thesis, controverting some\\nof the chief tenets of Aristotle, and disparaging his\\nentire system, which system it will be remembered\\nhad been adopted by the Church, the Pope condemned\\nhim and his book as rash, impudent and ignorant\\nwhereupon Boileau put forth a satire in the form of\\nan humble petition, craving an interdict against\\nReason and Experience, because they would not\\nsubmit to the laws of Aristotle. This satire and\\nridicule gained the day; and when the shock came\\nparalyzing the Church, there were weightier questions\\nof concernment than those of the schools. It is a\\nmost interesting inquiry to examine the logical views\\nof the Reformers. As a matter of course, they con-\\ndemned in the most sweeping manner, the logical\\nsystem of Aristotle, endorsed by the Church, and all\\nscholastic dialectics. Perhaps the views of Luther\\nare the fairest illustration of their system, if it may\\nso be called and Luther was not ignorant of Logic,\\nthat being one of his branches when a professor.\\nBut in a fervour of enthusiasm, he seems to ignore\\nrather than disprove the doctrines of Aristotle and\\nthe schoolmen asserting with a certain unanswerable", "height": "3222", "width": "2063", "jp2-path": "elementsoflogic00copp_0256.jp2"}, "257": {"fulltext": "LOGIC OF CHRISTIANITY. 251\\nair: In divine things, tlie Father is the Grammar^\\nfor he imparts words the Son is Logic^ and suggests\\norder, arrangement and sequence of ideas the Holy\\nGhost is Rhetoric^ who persuades and presses home.\\nAnd so charging the schoolmen with having given\\nup the substance for silly trifles, he goes on to say\\nthat, the Decalogue is the doctrine of doctrines the\\nCreed the history of histories the Lord s Prayer the\\nprayer of prayers and the Sacrament the ceremonies\\nof ceremonies. In short, his purpose, and that of the\\nother Reformers, seems to have been to find every-\\nthing in the Bible, and to seek for nothing out of it.\\nThis is not to be wondered at it was the period of\\nenlightenment first, the dark places must be illu-\\nminated, before the errors could be made manifest\\nand the Reformers were right in their views for the\\ntimes and to efi ect the purpose desired.\\nThe light which was thus produced, soon began to\\nshine with great power and brilliancy, and its effects\\nwere no less to be observed in philosophy than in\\nreligion and morals. The kingdom of Nature lay\\nexposed to its searching beams, and invited the\\nNaturalist to examine and comprehend her works\\nthe Mind, disenthralled and opened, was no less a\\nsubject of most interesting study the reformation in\\nreligion was but the precursor of the birth of Experi-\\nmental Philosophy, and the Reformers were heralds of\\nLord Bacon as its interpreter.", "height": "3187", "width": "1935", "jp2-path": "elementsoflogic00copp_0257.jp2"}, "258": {"fulltext": "252 LOGIC.\\n(57.) The Logic of Experiynental Philosophy\\nIn order clearly to understand the origin of Ex-\\nperimental Philosophy, we must remember that the\\nunion of Christianity and philosophy had been fairly\\ntried and had proved unsuccessful scholasticism,\\nfulfilling its true purpose, but not that designed by\\nits founders, in gradually emancipating man s reason\\nfrom the thraldom of the schools of theology, by\\nmanifesting its own imbecility, had failed in its first\\ndesign, that of intellectual progress. Now, an ele-\\nment seems to have been introduced into philosophy,\\nwhich till then had been considered unimportant\\nand that was observation and experiment or, to use\\nthe term by which we have expressed the methodical\\nand successive observations of such phenomena in\\nnature as will lead us to general laws, Induction.\\nAristotle himself had stated the value of induction\\nfor the discovery of new truth and men, in all ages,\\nhad used it as an exercise of common sense in their\\nordinary conduct so that it must not be supposed\\nthat in any sense, Bacon is its inventor. He only\\napplied it by system to natural science.\\nLogic, which is the vehicle of truth in its intellec-\\ntual passage from premiss to conclusion, had only\\nreasoned upon the hnoivn and conceded: mainly\\nfrom some general law to a 2^(^ ^ticular example now\\nits premisses were to be new truths aggregated by", "height": "3221", "width": "2121", "jp2-path": "elementsoflogic00copp_0258.jp2"}, "259": {"fulltext": "LOGIC OF EXPERIMENTAL PHILOSOPHY. 253\\nexperiment it was to reason from many particular\\nexamples to the establishment of a general law.\\nThis, then, let it be borne in mind, was the only new\\nduty which Logic was called upon to perform and\\nthis, had it been desired, she had always been ready\\nand able to do.\\nShe had been the fearful servant of ecclesiastical\\nauthority and theocratic reverence to argue without\\npermission of the Church, or otherwise than by\\npriestly dictation, was worse than vicious it was\\nheretical.\\nBut when the reformation in Europe had thrown\\ncontempt on the authority of the Church, the intel-\\nlectual bonds of Europe also were burst, and the\\nchildhood of experimental philosophy began. The\\nunchangeable principle of reasoning was simply\\napplied to new subjects and investigations.\\nThere were two great realms to be emancipated, or\\nrather released from prison and darkness the realms\\nof Nature and Thought, or as they are ordinarily\\ncalled, matter and mind. The founders of the new\\nsystem adopted the same method for both, A7ialysis\\nconstant experiment and observation upon the pheno-\\nmena of the outer world, and upon those of the con-\\nsciousness within.\\nBacon was the early interpreter of Nature Des-\\ncartes the analyzer of Thought. To each is due an\\nillustrious share of the developments in philosophy.\\n22", "height": "3187", "width": "1943", "jp2-path": "elementsoflogic00copp_0259.jp2"}, "260": {"fulltext": "2i i LOGIC.\\n13 Lit Bacon is the more distinguished, because his in-\\nvestigations were made in every domain of nature\\nand his system is at once more intelligible and popular\\non that account.\\nThe starting point of Bacon s philosophy was the\\nassertion that the unive7 se is a great store-house of\\nfacts; and that it is man s duty and interest, and it\\nought to be his pleasure, to explore, discover and\\nunderstand these facts, not only in their isolated cha-\\nracters, but in their relations to each other and to the\\nuniverse itself. His experiments and his use of the\\nexperiments of others, was to enable him to arrive at\\ngeneral laws of the universe. Now, corresponding\\nwith the world around us, that is, the world of Nature,\\nthere is a world within us, the world of Thought.\\nLet either be impaired or cease to exist, and in just\\nsuch a proportion is the other impaired or does it\\ncease to exist.\\nTo unite them we have sensation and perception,\\nand the union is lost if sensation and perception fail.\\nThe happy union, then, of Thought and Nature\\nwould lead man to Truth, and to attain to Truth is\\nhis highest aim. It will at once be seen that this\\nwas the establishment, not of a logical, but of a\\nphilosophical system. But to proceed the various\\nforms which truth assumes to inspire the faculties and\\nentice the pursuits of men, are called sciences, and\\nby an examination of multitudes of these phenomenal", "height": "3219", "width": "2046", "jp2-path": "elementsoflogic00copp_0260.jp2"}, "261": {"fulltext": "LOGIC OF EXPERIMENTAL PHILOSOPHY. 255\\nfacts, the true definitions of the sciences might be\\nmade, their true relation determined, and a plan of\\nclassification formed for practical purposes.\\nSuch then, very briefly, was the aim of the new\\nexperimental philosophy, a great restoration which was\\nproposed by Bacon in his Instauratio Magna. With\\nit directly, Logic had but little to do but that little\\nled men of science into errors, which remain to the\\npresent day.\\nWithout attempting to enter into the details of the\\nGreat Restoration, it will be well to consider some\\nof the steps proposed by Bacon, as preliminary to it.\\nFinding, in his inquiries about facts, or phenomena,\\nthat they greatly difi er in importance that some\\nare simple, others complex some are easy of inter-\\npretation, others very difficult he proposed a classi-\\ncation of the instances in which any phenomenon or\\nfact occurred, and this should be a sort of value scale\\nof the instances in which a special phenomenon\\noccurred. These he calls prerogative instances, or\\nthose cases of most importance to us in interpreting\\na fact or a series of facts. He has stated twenty-\\nseven of these, from which we shall choose four,\\nas better illustrating their own meaning than it can\\nbe done in other words. Our purpose is not to use\\nthese, but merely to indicate their nature and design,\\nI. Solitary instances, or those in which two or\\nmore objects agree or differ in all qualities save one.", "height": "3179", "width": "1923", "jp2-path": "elementsoflogic00copp_0261.jp2"}, "262": {"fulltext": "2^)G LOGIC.\\nII. Forth-shoiolng instances. Under this head,\\nrange those facts or instruments which show forth the\\nquality in question in the highest degree as a gal-\\nvanic battery, in electricity, and a barometer in pneu-\\nmatics.\\nIII. Analogous instances. Those in which are found\\nobjects bearing a resemblance of purpose or relation,\\nhowever unlike the objects themselves may be. Thus,\\na camera obscura is analogous to the eye, and a sys-\\ntem of waterworks to the heart.\\nIV. Crucial instances. There are two probable mean-\\nings to the word crucial^ as here used. It may be\\nthe putting nature to the torture crucifying her to\\nwring from her her secrets, or it may have reference\\nto the way-side crosses, which at the parting of the\\nroads indicate the true direction to the traveller.\\nFranklin s electric kite might be called a crucial in-\\nstance, in the first sense. Such also, in the second,\\nwas Newton s law of gravitation, a finger-board for\\never to point to the true direction of investigation\\nand belief, concerning our solar system.\\nThe other instances, which we cannot stop to men-\\ntion, are designed to exhaust the classification of\\nexperiments on facts, and to lead to induction and\\nhere began the danger and difificulty it was here,\\nalso, that the syllogism, which Bacon despised and\\nmisunderstood, was, and always is, the only safe guide\\nof Philosophy. For, suppose the facts ranging under", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0262.jp2"}, "263": {"fulltext": "LOGIC OF EXPERIMENTAL PHILOSOPHY. 257\\nthese instances to be established, how many of them\\nwill give us the right to the establishment of a general\\nlaw, or a distinct science We have seen that, in\\nmost sciences, we only attain to likelihood. On ac-\\ncount of human ignorance, the process has been this\\nwe first establish a few facts we then adopt a hypo-\\nthesis or theory based upon them, i. e., jump at the\\ngeneral law, simply in order to make a nidus for our\\naccumulating facts; and thus proceed to verify if\\nthe new facts will verify our proposed theory. The\\ntendency of man s mind is so great, however, to repose\\nupon a darling theory, even if it be unsound, and\\nrather to seek\u00e2\u0080\u0094 like an advocate for such facts and\\nstatements as will support it, than to look for just\\nproof, and in the absence of such to discard it, that\\ninduction has often led to grievous error. Many a\\nstudent has learned one theory of some part of Na-\\ntural Science, and when lie had just mastered it, has\\nbeen obliged to discard it for another.\\nIn the consideration of Judgment, Bacon has given\\nspecial attention, to the Fallacies which assail the\\nmind of man. These he calls idols of the intellect,\\nand in almost every case, since they are contained in\\nfalse judgments, they belong to the class of material\\nfallacies. But all these idols occasionally assume the\\ngarb of logical fallacies.\\nThese idols, or sidco-Ka, which Bacon calls the deepest\\nfallacies of the human mind, are the sources of error\\n22* R", "height": "3187", "width": "1935", "jp2-path": "elementsoflogic00copp_0263.jp2"}, "264": {"fulltext": "258 LOGIC.\\nwhich assail men in their investigations in Philosophy,\\nand which must be renounced, and the intellect\\nwholly freed and purified therefrom, before we can\\nhope for healthful progress. By the word idol,\\nBacon means the prejudice which stands in our way\\nof receiving truth, and the bias of the mind from\\nwhich such prejudices arise.\\nBut these idola will most clearly explain them-\\nselves they are of four classes. Idola Tribus, Idola\\nSpecus, Idola For iy Idola Theatri and with reference\\nto these, an author of his own time remarks The\\ntemple which he purified was not that of nature it-\\nself, but the temple of the Mind in its innermost\\nsanctuary were all the idols which he overthrew.\\n1. The idols of the Tribe are those which are im-\\nposed upon the understanding by the general nature\\nof mankind in other words, they belong to the human\\ntribe, in its universal comprehension. Thus, he asserts\\nthat men as men are quicker to be moved by affirm-\\native and active events than by negative and ^jrivative,\\nthough in justice they should be moved by both. To\\nillustrate this, he tells the story of the Greek, who\\nwas shown, in Neptune s temple, the votive pictures\\nof those who had escaped shipwreck, and when asked\\nif he did not now acknowledge his divinity, said,\\nshow me first where those are painted who paid their\\nvows and were then shipwi ecked.\\n2. The idols of the den or cave spring from the nature", "height": "3221", "width": "2121", "jp2-path": "elementsoflogic00copp_0264.jp2"}, "265": {"fulltext": "LOGIC OF EXPERIMENTAL PHILOSOPHY. 259\\nof eacli particular man, and grow out of his peculiar\\nnature both of mind and body these may also be\\nfostered or developed by education, custom or acci-\\ndent. The name is suggested by fancying the con-\\nfusion and error of a man being brought out of a\\ndark den or cave into the full light and glory of\\nNature. This finds its counterpart in the world of\\nphilosophy, where men only emerge from the den of\\ntheir minds to find confusion and disorder in the\\nbeautiful universe of God.\\n3. The idols of the marliet are errors which grow\\nout of words and communication^ such as are the\\npass-words and common coin of conversation and\\nintercourse in the market-place and they imply, like\\nthe idols of the tribe, a social organization, but on a\\nmuch more limited scale. Instead of being universal\\nwith men, they are errors which belong to a small\\ncircle, like a crowd in a market-place, moved at the\\nsound of an orator s words, by a common impulsion\\nof prejudice, passion or other emotion. These idols\\nare causes of the greatest disturbance, as they are\\nimmediately connected with the naming of things,\\nfor words are generally given according to vulgar\\nconception, and divide things by such differences as\\nthe common people are capable of; but when a more\\nacute understanding or a more careful observation\\nwould distinguish things, better words murmur\\nao-ainst it.", "height": "3187", "width": "1943", "jp2-path": "elementsoflogic00copp_0265.jp2"}, "266": {"fulltext": "260 LOGIC.\\nThus, many words in our every day use convey no\\ndefinite meaning to the mind but have, in their very\\nindefiniteness, so many shades of meaning that they\\nare a constant cause of verbal fallacy. As special\\nreference has been made to such words in the chapter\\non Fallacies (X.), it will only be necessary to mention\\na few such to illustrate the idols of the market-place:\\nsuch is the word republic, which we have been apt to\\nconfound with democracy Liberty means either free-\\ndom or license, as its champions wish and taste and\\nbeauty have as many forms as there are eyes to see\\nor imaginations to indulge.\\nThe last of the sources of error enumerated among\\nthe idols of Bacon, are the idols of the theatre.\\nThese he distinguishes from the others, as perhaps of\\nmore social power and influence. Of these, he says,\\nthey are superinduced by false theories or philoso-\\nphies, and the perverted laws of demonstration.\\nThey are comprehended under three heads Parti-\\nsanship, Fashion and Authority.\\nPartisanship is the generic name under which are\\nfound factions in politics and in. religion and under\\nwhose influence wars of creed and caste have so often\\ndesolated the world.\\nFashion is a kind of partisanship, which, however,\\nhas few opponents, and no great rivalries but which\\npervades society from high to low. We do not refer\\nto its simple sway in dress, equipage and social life", "height": "3228", "width": "2046", "jp2-path": "elementsoflogic00copp_0266.jp2"}, "267": {"fulltext": "LOGIC OF EXPERIMENTAL PHILOSOPHY. 261\\nbut to its more comprehensive dominion, over all tlie\\nworks and thoughts of man, over a.rt, science, reli-\\ngion. Grreat masses of men are herded like cattle,\\nand driven willingly in the train of this all-swaying\\nFashion resting their happiness here, and their hopes\\nin an eternal future, upon the dictum of Fashion.\\nAs Fashion partakes of the nature of Partisanship,\\nso is Authority strengthened by an alliance with\\nboth. This consists in blind obedience to an existing\\ncontrol, and reliance upon it, without the use of our\\nown judgment.\\nAs God, who has given man Reason, has made\\nsome things higher than that reason, but nothing\\nrepugnant to it, every theory of authority in Church,\\nin state, or in general philosophy is, of right, to be\\nexamined by our reason, before we can accord to it\\nour belief. Reliance upon authority, without a due\\nunderstanding of its claims, is to treat our own moral\\nconstitution with injustice, and to stop the wheels of\\nhealthful progress, both of individuals and societies.\\nIt was an increasing distrust of authority that\\nbrought about the Reformation in the Church that\\nexploded the scholastic philosophy and the supersti-\\ntious practices of the Middle Ages and that destroyed\\nthe divine rio-ht of kinars, with a host of evils which\\nappertained to it. To examine the claims of asserted\\nauthority is to investigate nature and mind and to", "height": "3187", "width": "1927", "jp2-path": "elementsoflogic00copp_0267.jp2"}, "268": {"fulltext": "262 LOGIC.\\ndo this, is to move forward to new and glorious vic-\\ntories in the domains of both.\\nIn reviewing these error-sources, it is scarcely\\nnecessary to remark that it is the abuse and not the\\nuse of our words and associations which lead to them.\\nThus, the idols of the tribe, would not be false and\\ndeceitful, if man should concur universally and every-\\nwhere in just and truthful opinions nor would the\\nden darken men s minds to the true light, if they\\nwere capable of carrying into their meditation the\\ntrue elements of combination and just views of the\\nobjects in the universe around them. Heraclitus has\\ntold us that men seek the sciences in their own\\nnarrow worlds, and not in the wide one. Such is\\nthe influence, but not the necessary consequence of\\nthe den.\\nSo it is easy to avoid the errors which grow out of\\nambiguous words, such as those which mark the idols\\nof the market by demanding just definitions, and\\nwhen such cannot be given, either agreeing /or argu-\\nment sake upon one which is not just; or, declining\\nto argue at all where the very question is involved in\\nobscurity.\\nWe may observe, concerning the idols of the\\ntheatre, that partisanship has its good as well as its\\nevil character and that to championize the right is\\nnoble and just it is, however, even in such a cause\\nthat its tendency is to extremes.", "height": "3222", "width": "2121", "jp2-path": "elementsoflogic00copp_0268.jp2"}, "269": {"fulltext": "LOGIC OF EXPERIMENTAL PHILOSOPHY. 263\\nBo fashion^ crowds of whose votaries are miserable\\nand self-tortured, is incident to man s social character,\\nand is productive to those who use it aright, of method\\nand comfort, and success. Although fashion has\\ndone much evil, it could not be spared in our social\\nor intellectual systems. Nor must Autliority, how-\\never formidable the name, be accounted of slight\\nimportance for under just authority are ranged\\nobedience^ order and wJiolesome discipline without it\\ngovernment would be anarchy, and education w^ould\\nbe a curse instead of a blessing. It is the time-\\nhonoured abuse of it, which demands our dislike and\\nresistance.\\nBeyond a few, and very erroneous allusions to the\\nLogic of Aristotle, Bacon and his immediate succes-\\nsors did very little for it as a science.\\nHobbes seems to have had just views of the syllo-\\ngism, as the instrument of demonstration, but\\ncarried his investigations his written ones at least\\nvery little beyond such a statement.\\nResting upon the basis of the Baconian philosophy,\\nthe thinkers of the seventeenth and eighteenth cen-\\nturies seem to have neglected the art of reasoning for\\nthe subject-matter about which we reason, and thus to\\nhave entirely confounded Logic with the art of think-\\ning. For this they had the authority of their great\\nmaster, Bacon, who, in his Advancement of Learn-\\ning, has divided the Art of Judgment into Induction", "height": "3179", "width": "1944", "jp2-path": "elementsoflogic00copp_0269.jp2"}, "270": {"fulltext": "264 LOGIC.\\nand the Syllogism and has classified as four kinds of\\ndemonstration 1. Tliat by immediate consent and\\ncommon notions 2. By Induction 3. By Syllogism\\nand 4. By Congruity. The error of this classification\\nis at once apparent to us.\\nIndeed it may justly be said, that in everything\\npertaining to Logic, in its proper meaning, Lord Bacon\\nis entirely at fault while in everything which bears\\nupon Experimental Philosophy, he is great beyond\\nany competitors he is the inventor of Induction,\\nand as a fcAV words have shown that all induction\\nmust be brought to the syllogism to verify and test\\nthe laws at Avhich we arrive, his philosophy can be\\neasily disconnected from his Logic, and the faults of\\nthe latter exert no evil influence over the excellencies\\nof the former.\\nMany logicians in England, France and Germany,\\nfollowed in the steps of Bacon in the seventeenth\\ncentury, attempting to unite Logic and Experimental\\nPhilosophy in a manner which was injurious to the\\nformer.\\nLocke, misunderstanding the syllogism as Lord\\nBacon had done, discards it from his system, and\\nbases his views of the understanding on two sources\\nby which ideas enter the mind, viz. Sensation and\\nBeflection. But to show how so great a thinker\\nerred, by his false notions of the syllogism, he states\\nreasoning to consist of four parts 1st. Finding", "height": "3225", "width": "2061", "jp2-path": "elementsoflogic00copp_0270.jp2"}, "271": {"fulltext": "LOGIC OF EXPERIMENTAL PHILOSOPHY. 205\\nproofs; 2d. Arranging them; 3d. Showing their con-\\nnexion and 4th. Employing them correctly.\\nNow, what is all this, but, 1st. Finding middle\\nterms by which to establish premisses 2d. Stating\\nsyllogisms; and 4th. Combining arguments. As for\\nthe 3d, that is included in the 2d, for they cannot be\\narranged without their connexion being manifest.\\nLeibnitz, in Germany, seems to have thrown light\\nupon the theories of Descartes, and to have elucidated\\nalso many things in Locke.\\nMilton has been called the most learned man of his\\nage he vindicated this opinion by writing upon\\nalmost every subject within the range of knowledge,\\nand in most cases, writing v/ell. We are not, there-\\nfore, astonished to find that he has written a work on\\nLogic. It is in Latin, and seems to be very little\\nknown. Li that he adheres to much of the Aristote-\\nlian doctrine, and specially championizes Peter\\nRamus, the logical Martyr. He divides Logic, which\\nhe calls the chief of Arts, into two kinds Natural,\\ni. e., the faculty of reason in the human mind and\\nA7-tificial, I. e., rules for directing the operations of\\nthat faculty. But even Milton erred in stating that\\nit belongs to Logic to lead us from universals to\\nparticulars, which would limit the Syllogism to\\nDeductive reasoning.\\nIn this state of confusion. Logic existed until the\\nnew rise of Philosophy in the 18th century, the", "height": "3187", "width": "1951", "jp2-path": "elementsoflogic00copp_0271.jp2"}, "272": {"fulltext": "266 LOGIC.\\nsource of which was the continent of Europe rather\\nthan E no-land.\\n(58.) Logic in the Elgliteenth and Nineteenth\\nCenturies.\\nBut little remains to be said, in order to complete\\nthis brief sketch of the History of Logic. Even to\\nmention the names of the principal writers who have\\nsprung up under the impulse of the Baconian philo-\\nsophy, from that time to the present, would occupy\\nmore space than we can give and to discuss their\\nmetaphysical works would in this connexion be diffi-\\ncult and improbable.\\nThe logicians of the eighteenth century seem to\\nhave bent their energies to the task of classifying the\\nscience of making such a logical arrangement as\\nwould make much labour unnecessary, and find for\\neach its true niche in the temple of Truth.\\nIn England, Doctor Isaac Watts published a trea-\\ntise on Logic, or Right Use of the Reason, which\\nis a compound of Logic and Philosophy alike injurious\\nto both. Selecting a few tenets from Aristotle, from\\nLord Bacon, and from the Schoolmen, he has endea-\\nvoured to harmonize them. In another of his volumes,\\nThe Improvement of the Mind, he has moved upon\\nsurer ground and with much better success.\\nBishop Berkeley wrote the Principles of Human", "height": "3230", "width": "2058", "jp2-path": "elementsoflogic00copp_0272.jp2"}, "273": {"fulltext": "EIGHTEENTH AND NINETEENTH CENTURIES. 267\\nKnowledge, a work of profound thought and excel-\\nlent reasoning and Bishop Butler has exemplified\\nthe correct use and application of Logic, in his famous\\ntreatise on the Analogy of Religion.\\nFrance has also produced in the eighteenth century\\nmany fine logical minds, who have devoted themselves\\nto science specially in attempts at classification\\namong these were D Alemhert, Diderot, and their\\ncoadjutors, known as the Encyclopaedists, who, in the\\neighteenth century, startled the world not less by\\ntheir methodical arrangement of the sciences, than\\nby the scepticism which their studies induced, and\\nthe atheism or denial of God s existence, which took\\nthe place of doubt.\\nIt would be improper in a treatise of this kind to\\ndo more than simply refer to the present writers on\\nLogic, and the present condition of the science.\\nArchbishop Whately has renewed the Logic of\\nAristotle in its pristine vigour and placed it in its\\ntrue position as the only sure guide or Art of Reason-\\ning. Many English writers have differed from him\\nsome, in his conception of the meaning and scope of\\nLogic itself, and others as to the extent to which the\\nAristotelian system may be carried.\\nOf the first, may be mentioned Mr. J. S. Mill,\\nwhose work, according to the view we have taken,\\nmay fitlier be called an encyclopasdia of philosophic", "height": "3179", "width": "1947", "jp2-path": "elementsoflogic00copp_0273.jp2"}, "274": {"fulltext": "268 LOGIC.\\ntenets connected with, or resulting from, the Science\\nof Logic.\\nOf the second, are Sir William Hamilton, and\\nMr. Augustus de Morgan, who would develop more\\nthan four categorical propositions, and establish what\\nw^e have called the New Analytic.\\nThe most important changes, however, in the ap-\\nplications of Logic to science are to be found, as has\\nbeen said, in the subject of Categories and Classifica-\\ntion and to this, in illustration of the later move-\\nments of the science, we shall now give a few words.\\nIt will be at once perceived, that the object is to\\nreach a summum genus under which all the sciences\\nmay range, and then by a logical tree of division^ to\\nplace all the lower classes and their co-ordinate\\nspecies, in their proper places. In any less general\\nclassification it is evident that the principle of classi-\\nfication will be changed for the different sciences.\\n(59.) Of Categories and Classification.\\nThis is a part of the duty of Method.\\nThe Categories of Aristotle which have already\\nbeen explained, may be considered the basis of the\\nclassification of the sciences. For although there\\nhas been, in former times, much dispute concerning\\nNeil s Art of Ileasoniug, p. 23-1.", "height": "3225", "width": "2044", "jp2-path": "elementsoflogic00copp_0274.jp2"}, "275": {"fulltext": "OF CATEGORIES AND CLASSIFICATION. 269\\ntheir true reference, that is, whether it be to words,\\nor things, or conceptions, it is now allowed that,\\nimperfect as thej are, they are designed to apply to\\nthe summa genera, under which all things which are\\nnamed may range themselves. This establishment of\\nproper summa genera, then, is the true start point of\\nclassification.\\nMany writers have simplified these categories mainly\\nby reducing the number. The schools of Pythagoras,\\nPlato, and Epictetus had each its corresponding list\\nor table Locke wrote three, viz. Physica, Praetica\\nand Semeiotica, or, as they have been translated,\\nSuh stance, Modes and Relations; Hume, two, viz.:\\nIdeas and Impressions. But these are manifestly\\nnone of them of that practical form and character\\nv/hich is desirable for useful reference, and hence it\\nhas been the aim of later writers, especially upon\\nMetaphysics and Logic, to write out tables of classi-\\nfication which should comprise and methodize all\\nforms of human science. To classify palpable, tan-\\ngible objects, is to arrange them in groups according\\nto a certain method, and that method will usually be\\nbased first upon the great division of kingdoms, and\\nafterwards upon the relation of species to genus.\\nIf we reflect for a moment upon the innumerable\\nforms of life and existence in the three great king-\\ndoms, Animal, Vegetable, and Mineral, we shall at\\nonce be struck with the difficulty and labour of a just\\n23*", "height": "3179", "width": "1935", "jp2-path": "elementsoflogic00copp_0275.jp2"}, "276": {"fulltext": "270 LOGIC.\\nand adequate classification; and yet, strange as it may\\nseem, true progress in any of these branches has but\\nkept pace with such a classification the naming and\\nplacing of a minute species in its proper place being\\nthe necessary way of fixing it there for ever.\\nIt has already been said that the basis of physical\\nclassification is the establishment of the summiim ge-\\nnus, and that the rules of Logical division must deter-\\nmine all the subaltern genera and species. This must\\nserve us for the classification of the known and deter-\\nmined but in the w^orld of Theory, another mode may\\nwith propriety be adopted it is the classification by\\nseries, investigated by Comte. It consists in select-\\ning some particular phenomenon, the laws of which are\\nto be investigated, and then ranging the various ob-\\njects which sustain a relation to it, in a nearness pro-\\nportional to that relation.\\nWith this subject of classification, scientific nomen-\\nclature is immediately connected, and it will appear\\nhow important this must be regarded, when we con^\\nsider that the value of the classification will depend\\nupon the names of the difi*erent classes, as to their\\n2Jrecision or total want of ambiguity, their comiylete-\\nness, or expressing the whole of the class specified, and\\ntheir expressiveness, in denoting the propei ties of the\\nobject, and the reason of its classification. Thus, in\\nchemistry, a law of nomenclature has been formed,\\nbased, indeed, upon some unfortunate beginnings,", "height": "3216", "width": "2121", "jp2-path": "elementsoflogic00copp_0276.jp2"}, "277": {"fulltext": "OF CATEGORIES AND CLASSIFICATION. 271\\nwliicli have been allowed to remain, but very system-\\natic, and universal in its reception.\\nBut the high aim of metaphysical philosophers, to\\nsmooth the paths of Logic, has been, not the classi-\\nfication of one science, but the analysis and classifi-\\ncation of universal Science, the establishment of a\\ncomplete table, in which all human investigation\\nshould find its place, and link itself to the great mind\\nof all ages in its study of all topics within its sensual\\nor intellectual range.\\nIt v/ill not be attempted to give a history of classi-\\nfication, nor to prepare or copy a complete table of\\nany previous author, but rather to indicate the manner\\nin which it has been done, with a general reflection\\nupon the results attained. Classification, to be logi-\\ncal and just, must be made after certain investigations,\\nwhich are necessary to determine the true class of\\nthe object in question. This will be done in Physics\\nby formal analysis, such as the organic analysis in\\nchemistry, and in the exact sciences by the applica-\\ntion of the principles of demonstrative proof.\\nPassing by, only because our limits do not permit\\ntheir consideration, the system of Bacon, which was\\nadopted by the French Encyclopedists of the last\\ncentury as the basis of their great work, L Ency-\\nclopedie Methodique, and the details of the system\\nof Locke, we come down to our own times before we\\nfind any definite attempt to supply the want. An", "height": "3187", "width": "1959", "jp2-path": "elementsoflogic00copp_0277.jp2"}, "278": {"fulltext": "272 Locrc.\\neminent Scotch writer, as he reviewed the efforts of\\nprevious philosophers to classify human knowledge,\\nasserted that it was an impossible task, and so, from\\nits magnitude, it would fairly seem.\\nNothing daunted by such an assertion, Coleridge\\nsuggested the plan of classification, which was adopted\\nin the arrangement of the English Encyclopaedia\\nMetropolitana, but which he found to require, after\\nhe had exhausted his categories, an additional cate-\\ngory of Miscellaneous species; the unfortunate\\nsubalterns which had no summum genus under which\\nto range themselves.\\nAmong the curious but highly philosophic remains\\nof Jeremy Bentham, is a proposed system of scientific\\nclassification but, like his other works, it is only a\\nstore-house of theory from which less gifted but more\\npractical men draw capital for constant use.\\nAll the more modern writers agree in considering\\nthe system of Am2:)ere the most correct and useful.\\nIt is based upon the two categories of mind and\\nmatter, and under these it expands into a very great\\nnumber of subordinate sciences, many of which, it\\nmust be said, are created, i. c, in name to fill up\\ngaps which would spoil the symmetry of his table.\\nIt is not our purpose to wTite out his table in full\\nit would be out of place in a text book, as it could\\nonly be examined, not studied but we will form a", "height": "3220", "width": "2064", "jp2-path": "elementsoflogic00copp_0278.jp2"}, "279": {"fulltext": "OF CATEGOEIES AND CLASSIFICATION. 273\\ntree of one or two of his subjects, to illustrate his\\nplan, and indicate its truthfulness and use.\\nHis First Table contains\\n[Kingdoms),\\nC Cosmological sciences, Noological sciences,\\nI i. e., pertaining to matter. J i e., pertaining to mind.\\nCosmologies proper. Physiologies. Noologics Soeial seienees.\\nI I proper.\\n1 I\\nMathematics. Physics. Nat. sciences. Med. sciences. Philosophies, c. Ethnology,\\nI I I I c.\\nGeometry, c. c. c. c. i\\nI c.\\nElementary geometry, c.\\nI\\nSynthetical and analytical geometry,\\nc.\\nOf these there are several tables and more than a\\nhundred branches. In thus indicating rather than\\nwriting out in full the tables of Ampere, w^e spare\\nthe student the reading, in place, of many names\\nunknown to our ordinary scientific studies, such as\\nDialegmatics JEleutherotechnics Technesthetics,\\nwhile we present to him what is alone our present\\npurpose, the theory and principle of classification.\\nThe chief merit of his tables, which he spent his\\nlife in constructing, seems to be that there are no\\ncross divisions that no subordinate science lies out\\nof its own class or laps over into another errors\\nwhich rendered Bacon s system worthless, and which\\ncaused Bentham to abandon his great idea and leave\\nit in its inchoate form.\\nAuguste Comte, who has given to the world, in his\\nS", "height": "3187", "width": "1935", "jp2-path": "elementsoflogic00copp_0279.jp2"}, "280": {"fulltext": "2T4 LOGIC.\\nCours de la Pliilosophie Positive, his views of philo-\\nsophy, did not attempt so much to classify science as\\nto determine the true relation between general science\\nand positive science to make positive science more\\ngeneral in its application, and general science more\\npractical and positive. This has been his life-work.\\nThere is much of his work which bears indirectly\\nbut dangerously upon religious belief, and there is\\nan elaborate description of the historical progress of\\npositive science through what he calls the mystical\\nand metaphysical eras, to the positive.\\nTo explain more clearly his view of this positive\\nera, it is that in which the mysticism or mytliology of\\nancient and early times, as well as the crude meta-\\nphysical notions of the Middle Ages, which found their\\nissue in astrology and magic, are swept away, by the\\nlight of modern free thought and investigation, and\\nin their place are substituted the laws of creation, laws\\nwhich regulate its origin, its progress and its destiny.\\nThere are six positive sciences, which include every\\nthing that can be known. These are Mathematics,\\nAstronomy, Physics, Chemistry, Biology, and Soci-\\nology.\\nBut it is not within our scope to explain his philo-\\nsophy we have only to do with its Logic, and this\\nis found in his classification.\\nThe subject of classification is yet open, and will\\nbecome, without doubt, clearer and more practical as", "height": "3197", "width": "2121", "jp2-path": "elementsoflogic00copp_0280.jp2"}, "281": {"fulltext": "OF CATEGORIES AND CLASSIFICATION. 275\\nscience advances to the discovery of the proximate\\nlaws of creation.\\n(60.) Conclusion.\\nFrom the foregoing investigation of the art of Rea-\\nsoning, we may pause a moment at the end to reflect\\nupon its real value and importance. If Logic is really\\nthe art which controls and guides the reason in its\\nworkings, and without which we can attain to no truth\\nupon which the reason is exercised, it is surely worthy\\nof a high place in the catalogue of elementary studies,\\nand the statement and adoption of its laws must be\\nconsidered of the first importance.\\nAnd, above all, should it be placed upon its own\\nfoundation, and dissociated from any other sciences\\nwhich either rob it of its own identity, or use it with-\\nout acknowledging its office.\\nTHE END.\\n3HEAES DUSEXBEKT, STEREOTTPERS, C. SHERMAN SON, PRINTERS.", "height": "3187", "width": "1943", "jp2-path": "elementsoflogic00copp_0281.jp2"}, "282": {"fulltext": "678\\n678", "height": "3201", "width": "2121", "jp2-path": "elementsoflogic00copp_0282.jp2"}, "283": {"fulltext": "", "height": "3171", "width": "1863", "jp2-path": "elementsoflogic00copp_0283.jp2"}, "284": {"fulltext": "", "height": "3201", "width": "2054", "jp2-path": "elementsoflogic00copp_0284.jp2"}, "285": {"fulltext": "", "height": "3179", "width": "1940", "jp2-path": "elementsoflogic00copp_0285.jp2"}, "286": {"fulltext": "\u00e2\u0096\u00a01^.\\n::vl\\n\u00e2\u0096\u00a0u^\\nnX^^\\n1^ s^\\n-^t.\\n\u00e2\u0096\u00a0y K.-y Deacidified using the Bookkeeper process.\\nt\\\\ ^O V 2 ^9 agent: Magnesium Oxide\\na\\\\ 1 Treatment Date: Sept. 2004\\nt v^ Preservationlechnologies\\np, ^V A WORLD LEADER IN PAPER PRESERVATION\\n\\\\r y 1 11 Thomson Park Drive\\nCranberry Township. PA 16066\\n,0- ^O ^A V^- (724)779-2111", "height": "3201", "width": "2230", "jp2-path": "elementsoflogic00copp_0286.jp2"}, "287": {"fulltext": "", "height": "3242", "width": "2013", "jp2-path": "elementsoflogic00copp_0287.jp2"}, "288": {"fulltext": "", "height": "3419", "width": "2263", "jp2-path": "elementsoflogic00copp_0288.jp2"}}