ar V 13072 r;M, m\K Cornell University Library arV13072 Questions on logic- 3 1924 031 306 610 olin,anx (fituxmW Hmretjsitg ptotig THE GIFT OF >Jt:d(k£jj%AjLieSUi^j^^ .h-'.C?-Ls:05r..- MM%±. Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31 924031 30661 QUESTIONS ON LOGIC. PART I. LATIN COMPOSITION AND SYNTAX. With copioas Exercises. By A. H. ^^^^cbopt M.A Oson and J. H. Haydon, M.A. Camb. and Lond. 2s. 6d. Key, 2s. 6d. net. " This is one of the best manuals on the ahove subject that we have met with sometime." — The Schoolmaster. "The clearness and concise accuracy of this book throughout are truly remark able. " — Education, CO-OEDINATE GEOMETEY: The Right Line and Circle. By William Briggs, LL.B., B.A., F.CS., and G. H. Bryan. M.A. 2s. Key, 4s. ed. net. ''Thoroughly sound throughout." — Education. " An admirable attempt on the jjart of its authors to realise the position of the average learner." — Educational Times. " We can warmly recommend the volume." — The Schoolmaster. ELEMENTARY MATHEMATICAL ASTEONOMY. By C. W. C. Barlow, M.A. Lond., Camb., and Edin., and G. H. Brtax, M.A. Camb., Fellow of St. Peter's College. 68. Bd. [/n th£ press. A MANUAL OF LOGIC. By J. Welton, M.A. Lond. 2 vols. Vol. I. lOs. Od. . IVol. II. in preparation. This work embraces the entire B. A. andB.Sc. Syllabus, and renders unnecessary the purchase of the large books hitherto used. The relative importance of the sections IS denoted by variety of type, and a minimum course of reading is thus indicated. ELEMENTABY TEXT-BOOK OF HEAT AND LIGHT. By R. W. Stewart, B.Sc.Lond. 3s. 6d. This book embraces the entire London Matriculation Syllabus, and contains over 150 Diagrams. ' ' A student of ordinary ability who worka carefully through this book need not fear the examination." — The Schoolmaster. " It will be found an admirable text-book," — Educational Netes. TEXT-BOOK OF HEAT. Covering the entire London Int. So. and Prel. Sci, Syllabus, with numerous Diagrams and Calculations. By R. W. Stewart, B.Sc. Lond. 3s. Gd. ' ' Clear, concise, well arranged, well illustrated, and, as far as we hare t^ted, accurate." — Journal qf Education, TEXT-BOOK OF LIGHT. (Uniform with the "Text-Book of Heat."} By R. W. Stewvrt B.Sc.Lond. 3s. 6d. " Clear and precise."— Prac(tcai Teacher. " Well adapted for general use." — School Quardian, ANALYSIS OF A SIMPLE SALT, With a Selection of Model Analyses. By William Briggs. LL B B^ F.C.S., and R. W.Stewart, B.Sc. Lond. 2au ' "* " Likely to prove of trustworthy assistance." — Nature, " Every help that can be given." — Education, lantv. Corr. Coll. tutorial Seriee. QUESTIONS ON LOGIC. PART I. BY H. BOLMAN, B.A., LATE SCHOLAR OF aONVILLE AKD CAIUS OOLLEOE, OAMBEIDSB, TUTOR OF UNIVERSITY OOREESPONDENCB COLLBaB. London: W. B. OLIVE & CO., UNIVEBSITY COEBBSPONDENCE COLLEGE PKBSS. •WAKBHOUSB : 13 BOOKSBLLBKS KOW, STKAND, W.C, I* PEE FACE. This book is primarily intended as a companion to Mr. Welton's Manual of Logic; though, of course, the working of the exercises may accompany the reading of any other text-book on Logic. It is an endeavour to supply the material for that exercise Lq the practical application of logical principles which is almost indis- pensable to a thorough mastery of the science, and most helpful as an aid to, and test of, clear apprehension. It is hoped that the Hints and Examples will supply such guidance as experience has shown to be useful to beginners. The questions have been selected from a wide range of University examination papers, but chiefly from those set at the University of London, since the book is mainly designed for students preparing for the examinations of that University. More than one question has, in some few cases, been given on the same subject, either on the ground of the suggestiveness of the questions themselves, or as examples of the different styles of question adopted at different Universities. 4 PBEFACE. A Key to the Questions is also published, in order that students may be able to test their answers — which is especially necessary in the case of problems in the more purely formal parts of the subject — and discover where, if at all, they have fallen into error. I wish to express my indebtedness to my friend, Mr. Welton, for much invaluable advice and assistance, with regard to both the Questions and the Key. H. H. University Correspondence College, November 1891. CONTENTS, Genekal Suggestions . Suggestions on Wkiting Answers Introduction, (a) Hints (V) Examples . ... Questions on Thought and Language . Questions on Definition and Scope- op Logic Questions on Relation op Logic to Other Sciences Questions on Laws of Thought Teems, (a) Hints .... (V) Examples . ... Questions on Terms ... . . Thb Predicables and Categories, (a) Hints . (V) Examples . Questions on The Predicables Questions on The Categories Definition, Division, and Classification, (a) Hints Questions on Definition Questions on Division . Questions on Classification 12 17 17 19 20- 21 22 24 24 25 29 29 30 32 33 (J) Examples 34 37 39 41 Eeduotion to Pbopositional Form, (a) Hints . . 42 (V) Examples . . 43 Questions on Eeduction to Prepositional Form ... 45 Propositions, (a) Hints. ... . . 48 (i) Examples .... . 48 Questions on Propositions 60 CONTENTS. Immediate Inpeeences. (a) Hints .... 57 (S) Examples .... 57 Questions on Immediate Inierenees . ... 60 Stllooisms. (a) Hints . 65 (5) Examples ....... 66 Questions on Syllogisms 68 Questions on Canons of Pure Syllogism .... 69 Questions on Figure and Mood 72 Eeddction. (a) Hints . . . 75 (>) Examples ... 75 Questions on Reduction . . 76 Mixed Syllogisms, (a) Hints 78 (i) Examples 78 Questions on Mixed Syllogisms .... .80 Abeidsbd aud Conjoined Syllogisms, (a) Hints . . 83 (*) Examples . 83 Questions on Abridged and Conjoined Syllogisms . . 85 Questions on Functions of the Syllogism . . 86 Questions on Modifications of Syllogistic Docteine . SS Miscellaneous Questions .... . 90 INDEX TO SOUECES OF QUESTIONS. B. C. C.G.H. D. DUE. E. G. L. M. MEL. MCG. 0. — MODS O.C.M. E.tJ.I. ST. A. ST, A. — LL, Log. q. . Bombay Pniveesitt. Cambeidge Univeesitt Moeal Sciences Special. . Cambeidge Univeesitt Moeal Sciences Teipos. . Cape of Good Hope Univeesitt. . Dublin Univeesitt. . Dueham Univeesitt. . Edinbuegh Univeesitt. . Glasgow Univeesitt. . London University. . Madeas University. . Mblbouene Univeesitt. . McGiLL College and Univeesitt, Montreal. . Oxford University Moderations. . Owens College, Manchester. . RoTAL Univeesitt of Ieeland. . St. Andrews Univeesitt. St. Andrews Univeesitt Licentiate in Aets. 1 QUESTIONS ON LOGIC. GENERAL SUGGESTIONS. This book being specially designed as a companion to Mr. Welton's Manual of Logic, it is suggested that the following method of using it -will be likely to render it most helpful : — (1) That portion of the text-book which corresponds to the heading of the section of Questions should be thoroughly studied. The student is especially cautioned against any- thing like a superficial and unintelligent skimming of the author ; this will only lead to the formation of inaccurate or inadequate conceptions of the subject in hand. The attempt to answer questions upon work so done will cause still further mischief, in that the act of committing ideas so gained to paper serves to impress them more deeply upon the mind, and the subsequent correction, if any, of them will be very unlikely to completely undeceive the student or to remove his false ideas. The following suggestions as to reading may prove of service to the inexperienced learner : — (a) Read slowly ; and, if necessary, re-read several times, till you are convinced 'that you have thoroughly grasped the author's meaning. Wherever possible, supplement the examples given in the text-book by some of your own, and analyse them so as to be quite sure of their relevancy. Where appeal is made to mental processes or experiences, always refer to your own for corroboration and illustration. Such endeavours will afford a good test of intelHgent reading. 10 QUESTIONS ON LOGIC. (4) Memorize thoroughly. In every science there is a certain amount of technical detail which has to be com- mitted to memory; but the learner will find that he has, at first, to memorize a good deal more than this. Although one who has made an intelligent study of a subject has already done much of the memorizing, and so made much more easy and certain what remains to be done, yet this will never wholly obviate the necessity of further efibrt. The marginal summaries in Mr. Welton's book supply just the matter which should be memorized. By memorizing is meant, not the obtaining of the mere ability to repeat sentences in a given order, but the securing of such a vivid mental impression of the order and logical sequence of the parts of a subject that they can be repro- duced in memory with facility, certainty, and accuracy. The repetition necessary to accomplish this will be found to involve much more than a mere mechanical reiteration ; for the endeavour to secure a vivid impression of the arguments used, and the conclusions reached, will be likely to suggest new thoughts upon the subject, and to clear up any vagueness or uncertainty. Nothing is more unsatis- factory and disappointing to a learner than to find that, after reading carefully through a certain amount of book- work, he has, a few days after, entirely forgotten what he fondly imagined he had learnt. This can only be obviated by recognizing the need of, and taking means to secure, a sufficient amount of accurate memorizing. (c) Recapitulate. This can be best done by closing the text-book and reproducing mentally, or in writing, a brief abstract of the arguments, or facts, or both, just studied. It may, with advantage, be done both immediately after having studied a portion of the author, and immediately before commencing the next portion. Then test — and correct, if necessary — this recapitulation by reference to the table of contents, or to the marginal summaries. If these three points are conscientiously attended to, the student need have but little fear of not attaining a really satisfactory knowledge of the subject. (2) The questions given on the subject-matter just studied should then be answered. It is important that the whole GENERAL SUGGESTIONS. 11 of the portion studied should be reproduced, in answers to questions, before beginning to study a fresh subject. Two points should be observed in regard to the answers — (a) They should be as full as possible, whilst rigorously avoiding all that is irrelevant, or mere verbiage. (b) On no account should any reference to the text-book (or to the I^ey) be made, whilst writing them. This second point should be insisted upon, or the student will delude himself into the idea that he is making progress, when, as a matter of fact, he is doing nothing of the kind. (3) The answers should be corrected by an appeal to the solutions given in the Key. These solutions should Tiot be " looked up " before the answer is written : such a method would fail to obtain any of the advantages of practice for examinations, or of a test of the knowledge and intelligence really acquired by previous study. Neither, therefore, should the questions be attempted immediately after study- ing a subject — the best discipline for such occasions has already been indicated (see Recapitulation). This point, of " looking up " the answers to questions before attempting to answer them, is an important one, and the learner will do well to allow himself no indulgence, under any circumstances whatsoever. The almost certain result of doing so, would be to make the exercise a mere mechanical eifort of memory. There would be little, if any, obligation to make that serious study, and thorough intellectual assimilation, of the subject, which alone is either helpful or permanent. The object of writing answers to questions is to ascertain how far the student has " read, marked, learned, and inwardly digested " the subject-matter. The judgment required in selecting those parts of the work done which relate to a given question, and in synthesizing them into a logical answer, is the best test of intelligent study, and a really good mental discipline. A good general rule, as to the time for answer- ing questions, would be to study a given subject one week, and answer questions on it during the next week, whilst also studying a fresh subject, — the two exercises would react upon, and assist, each other, ]^2 QUESTIONS ON LOGIC. SUGGESTIONS ON WRITING ANSWERS. It is -well known, at least to those who have had any considei*able experience in tuition, how unequal are the merits of written answers, as such, i.e. without regard to the amount of knowledge they express. Some are able to write an effective answer with a minimum of knowledge ; others, with far greater knowledge, write very poor answers ; whilst those who combine knowledge with the power of good ex- pression are the brilliant exceptions. Though it is not possible to impart the secret of a brilliant Hterary style, if one is so fortunate as to possess it, yet it is possible to give such hints as shall guide a person in making the best and most effective use of his knowledge in answering questions in a written examination. The following points should be carefully attended to. (1) Read the question very carefully, and endeavour to make quite sure that you have apprehended the real point of it. It wiU not, as a rule, take long to decide as to what the real point is ; and even if it does take a minute or two to make sure of this, the answer will probably gain much by this delay, and will almost certainly lose by the contrary method. For example, in regard to the question, " Compare the following terms with respect to their definabihty, . . ." it is not a sufficient or satisfactory answer simply to say all that is known about their logical characteristics, or merely to point out which are connotative and which are non-connotative ; and yet scores of such answers have actually been written in reply to such a question. The whole point of the question is : Indicate those terms which are more easily and fully definable than the others. This depends upon the relative predominance of connotation or denotation, in each case, and should be shown by arranging them in groups, if there are several of the same kind, of an increasing or decreasing degree of definability, and giving reasons for this order. The whole question of relevancy or ii-relevancy turns upon this preliminary consideration. The writing of a lot of miscellaneous matter, so as to fill up space is woi-se than useless, — it is sure to create a bad impression on the GENERAL SUGGESTIONS. 13 examiner's mind. The student may easily deceive himself by doing this, but he is not likely to impose upon the examiner, who may generally be credited with knowing something about the subject, and a good deal about the little plans for imposing upon his supposed credulity and complacency. As an example of irrelevancy the following may be given : — In answer to the question '' Show how Mediate and Immediate Inference depend upon the Laws of Thought," many commence their answer by a statement, and full discussion of the Laws of Identity, Contradiction, and Excluded Middle. Now the statement of the Laws is perfectly relevant, but the detailed discussion of them is wholly out of place, — the mere statement of the Laws should, at least for present purposes, be taken as implying their acceptance after full discussion. The point of the answer should be to show the dependence of Inference upon these Laws. Examples of such errors of judgment might easily be multiplied. (2) Endeavour to make your answer cogent, and exhaustive, without being verbose. This will be best secured by per- forming — (a) An act of analysis, i.«., pulling the question to pieces, so to speak, and seeing what, and how many, are the points to be stated, demonstrated, attacked, or substantiated ; then, (6) An act of synthesis, i.e., building up the answer in logical order and sequence, — each step or argument naturally following from the preceding one — so that the total effect is cumulative and convincing. Thus, in dealing with such a question as " Has Logic any practical utihty ? " some such method as the following should be used : — (1) What is Logic? It is the science of the principles which regulate valid thought. [This should be explained in detail, so that we may know exactly what we are discussing.] (2) Does Thought need such regulative principles ? Undoubtedly ; the experiences of everyday life show us how liable we are to jump at conclusions, to draw false conclusions from true data : e.g., a boy is accused of theft, he is embarrassed and evasive, therefore he is the thief — as a matter of fact, timidity, the mere thought that he is suspected, desire to shield another, etc., may be the cause of his confusion ; 14 QUESTIONS ON LOGIC. again, the superstitions, intolerance, cruelty, etc., of past times, considered in the light of present knowledge, are seen to be very largely the results of ignorance and preju- dice, i.e., of invalid reasoning. Many errors, dissensions, and strifes, are caused by the want of a clear apprehension of the meaning of a word, and a consistent logical use of such a meaning in argument — of. such words as church, capital, faith, etc. [Such examples should be worked out in detail, so as to show clearly their bearing upon the point under discussion.] (3) Does Logic fulfil such a function ? Certainly ; it investigates and states the legitimate con- clusions that may be drawn from given data ; it demands clear and precise meanings of terms ; and it supplies rules for testing and secui-ing valid conditions for valid thought. Wherever, therefore, exact thought is desii-able. Logic is of paramount importance; and it will hardly be contended that exact thought is ever superfluous or unnecessary. (4) The specific uses of Logic. [For a full discussion of these, see Manual, pp. 19, 31.] In such questions as are most concerned with the repro- duction of book-woi'k, e.g. a description or summary of some part of logical doctrine, the points to be aimed at are : — (1) clear and orderly arrangement ; (2) full but concise treatment {cf. Example 2 of the Introduction, in this book). To avoid verbosity is, practically, to avoid all para- phrase and repetition. Whatever can be said, clearly, in a sentence, should not occupy a paragraph. For example, if it were desired to express the judgment " Logic is a science, in that it systematizes our knowledge of the regulative principles of Thought," it would be pure verbosity to para- phrase this into " We have every right, in accordance with the general rules of thought and the usual practice in regard to the application of the conventional meaning of the term, to apply the name 'science' to that department of systematized knowledge {i.e., of our acquaintance with facts and the antecedents which precede and produce them, reduced to series governed by a general law), which is generally kno-svTi under the appellation of I.iOgic, and is so called from the fact that this word ' Logic,' in its original form, signifiesthe thought which words express." The use of elaborate sj-non-snns and GENERAL SUGGESTIONS. 15 equivalent phrases should be avoided ; e.g., say " affirmation or denial," not " the assertion of congruence, agreement, or compatibility, or the assertion of incongruence, disagree- ment or incompatibility " ; say " these things agree," not "these things may be said to be in agreement, i.e., they are congruent one with another, or are not incompatible with each other." In brief, so long as neither clearness nor cogency are sacrificed, say what you have to say in as few words as possible. (3) An example, or illustration, should be given wherever relevant. Thus, after making such an assertion as " Words with no definitely fixed meanings are unsuited for use as scientific terms," it will be well to exemplify by taking a word, such as " Labour," which may at diiFerent times and for distinct purposes, mean (1) manual labour, (2) wage- paid labour, and (3) any exertion, whether physical or mental ; and so long as the word is not definitely limited to one or other of these meanings, a discussion concerning " Labour " wUl be true or false according as the reader supplies one or other of them. It will be obvious how much more is con- veyed by such an example, given in support of the statement, than by the mere statement itself. There is also the fact that such a treatment is a pretty sure indication that the student has an intelligent grasp of the subject, and is not merely writing down remembered sentences and dicta. Probably the best rule for the general mental attitude to be assumed, in regard to the manner of answering a question, is to write as though demonstrating a fact or'principle to a fairly intelligent reader who has Uttle, if any, previous knowledge about the subject. Nothing should be assumed, as to the immediate point of the question, which is not definitely implied, or stated, in the question itself. Of course, the examiner will know all about such matters, but the object of the question is to find out all the examinee knows about it. In such a question as " Are the Laws of Thought all equally funda- mental 1 " the ordinary statement of them should be taken for granted; but, in answering the question "What difierent statements have been given of the Law of Excluded Middle ? " reasons should be given for accepting one of them as being the preferable form of statement. 16 QUESTIONS ON LOGIC. (4) In the case of a written examination -with a time limit, it is important to apportion the time a's are S. . (A.) \ _ (i) / ~ (ii) \= « S s flstowe are not P j (ii) All non-S's are />. Ora?!/ some S's are P \ (i) Some S's are P. Some S's aloTie are P j ~ (ii) Some S's are not P. Only S's are not P \ (i) Some S's are not P J- (ii) Only some S's are not P\ (i) Some S's are not P. (I.) (0.) (0.) (A.) (0.) (I.) (I.) Some S's alone axe not PJ (ii) Some S's are P. (vii) All S's exc/!j)t one are P = (i) Some (most) S's are P. (ii) Some (one) S is not P. . (0.) No S's except one are P = (i) Some (most) S's are not P. (I.) (ii) Some (one) S is P. . . (0.) See Manual, vol. i., pp. 187-90, 193-4. 4. Complex and Compound sentences must be first resolved into their constituent parts (see Manual, vol. i., pp. 190-4). 5. Always endeavour to reduce to a proposition having an adjective, or adjective phrase, as predicate — to show the predicative force of the proposition (see Momual, vol. i., pp. 175, 216-7). N.B. — In this section the Copula is always italicized, so as to indicate (1) the Subject, — all that comes before the Copula, (2) the Copula, and (3) the Predicate, — all that follows the Copula. EXAMPLES. 1. All those present had not tickets. Here the obvious purpose of the sentence is to suggest the assertion 'some (at least) had not tickets.' The use of " all " is simply for emphasis. The strict logical form is : — Some (persons) present are not possessed of tickets. (0.) 2. Some only who praise virtue act virtuously. " Some only (do),'' clearly implies that there has been an observation of cases in which " some do not," or there would be no justification for limiting the assertion to ''some only." The logical force, therefore, is : — (i) Some who praise virtue are virtuous. (I.) (ii) Some who praise virtue are not virtuous. (0.) 3. None who were there failed to applaud. This in logical form is : — None present are non-applauders. (E.) Such propositions, having negative copulas (see Manual, p. 178) and predicates, are best expressed by 44 QUESTIONS ON LOGIC. omitting the negatives, which, counteract each other, e.g. All present are applauders (A.) [see Manual, vol. i., pp. 285-8, Obversion], which may be taken as the strictly logical form of the proposition. 4. Among the sights of London, the visitor should not miss St. Paul's Cathedral. This is best expressed, logically, by : — St. Paul's Cathedral is worthy to be seen by all visitors to London. (A.) 5. Only graduates have the right to be present. This sentence concerns 'those with the right to be present,' and says that only " graduates " are such. The logical form, therefore, is : — ■ (i) Some graduates are justified in being present. (I.) (ii) No non-graduates are justified in being present. (E.) Or — All with the right to be present are graduates. (A.) 6. The honest alone are respected. This is similar to (5) and is equivalent to : — (i) Some honest persons are respected. (I.) (ii) No dishonest persons are respected. (E.) Or — All respected persons are honest. (A.) 7. Milton is the only poet, except Dante, who has written religious poetry of the highest order. This may be resolved into : — • (i) Milton is a writer of religious poetry of the highest order. (A.) (ii) Dante is a writer of religious poetry of the highest order. (A.) (iii) No other poet is a writer of religious poetry of the highest order. (E.) 8. We cannot be right in saying either that the good are necessarily happy, or the happy necessarily good. This means that it is false to say : — (i) All good men are happy (A.), or (ii) All happy men are good. (A.) What is implied, therefore, is : — (i) Some good men are not happy. (0.) (ii) Some happy men are not good. (0.) 9. None know the brave are timid but the brave. This is best expressed by : — REDUCTION TO PROPOSITIONAL FOBM. 45 (i) Some brave are aware that the brave are timid. (I.) (ii) No non- brave are aware that the brave aie timid. (E.) Or — All who are aware that the brave are timid are brave. (A.) QUESTIONS. 144. Eeduce each of the following to its strict logical form, and indicate whether it is A, E, I, or : — {a) All birds have two wings. (6) We know what matter is by the evidence of one or more of our senses, (c) It cannot be said that a thief has any sense of honour, (rf) Not all ovir ideas deserve consideration, (e) Only a few men maintain consistent conduct. (/) Every one knows that a politician cannot be produced out of a mixture of a Republican and a Royalist. {g) Every one knows that no politician can combine the opinions of a Republican and a Royalist. ih) They never forgive who have done an injury, (i) All men are not honest who say that they are. (7) All his shots but two hit the mark. 145. Resolve the following into logical propositions, and indicate the quantity and quality of each : — (a) Cambridge is the only town in England, except Oxford, which contains an ancient university. (6) No man ever fails to remain poor who is both ignorant and lazy. (c) The great is not good, but the good is great. {d) No one can be learned who is not both studious and ambitious, and not always then. (e) Though it may be granted that old things are not there- fore the best, yet they deserve careful consideration. (/) The more, the merrier. {g) It is just as false to say that Englishmen alone are brave, as to say that they alone are not. 146. Indicate the logical Subject, Predicate, and Copula of the following : — {a) Nothing succeeds like success. (6) There are many such in the country. (c) He envies others' wealth who has none himself. 46 QUESTIONS ON LOGIC. (d) It is cowardly to kick a man when he is down. («) Only experts can judge scientific matters. (_/) Great are the glories which surround a throne. 147. State in logical form ; indicate the Subject and Predicate ; and give the quantity and quality of the following : — (a) There's not a joy the world can give like that it takes away. He jests at scars who never felt a wound. Axioms are self-evident. Natives alone can stand the climate of Africa. Not one of the Greeks at Thermopylae escaped. f) All that glitters is not gold. 148. Express in Logical form: — (a) Not all his answers were wrong. (6) Not all your endeavours will accomplish it. (c) There is no wit like bought wit. (d) Girton and Newnham are the only colleges for ladies at Cambridge. (e) Visitors to Cambridge should make a point of seeing King's College Chapel. {/) There is nothing that disgusts a man so much as failure after boasting. (g) All that act honourably shall not be forgotten. ih) All Greeks are not dishonest. (i) Fine feathers do not make fine birds. (j) Amongst Englishmen many great generals are found. (k) Amongst graduates are a few scholars. (l) All ilowering plants have beauty. 149. Point out any possible ambiguities in — (a) Some of the men have behaved disgracefully. (6) All are not wise who read much. (c) All the books cost a sovereign. 150. Give six examples of Indesignate propositions, and say what you take to be, from material considerations, the quantity of each. 151. Give, in each case, two propositions fulfilling the following conditions — (a) General terms for subject and predicate. REDUCTION TO PROPOSITIONAL FOEM. 47 (b) Abstract terms for subject and predicate. (c) Collective term for subject. (d) Singular terms for subject and predicate. (e) Singular abstract term as subject. (/) Negative terms for subject and predicate. (g) Relative terms for subject and predicate. 152. What would you take to be implied if it be asserted that the following propositions are false — (a) Some horse-dealers are honest. (b) Englishmen, as a race, are brave. (c) Some Volunteers did not deserve discredit. (d) None but the prejudiced were unconviilced. (e) All men are liars. (/) Honesty is the best policy. 153. Resolve the following passage into logical propo- sitions, and indicate their kind : — " The material upon which thought is exercised is sup- plied by the world of objects which surrounds us, and from which we receive, through our senses, impressions of various kinds, which act as stimuli to the mind and so give rise to ideas" (Welton). 154. Express in a single proposition of the simplest logical form the sense of each of the following sentences : — (1) If the sky were to fall, we should catch larks. (2) It never rains but it pours. (3) Many are called, but few are chosen. (4) Unless help arrives, we are beaten. (5) You cannot have your cake and eat it. (6) Use every man after his desert, and who should 'scape whipping ? [o. — mods.] 155. Express as adequately as you can in a single pro- position of the simplest logical form the sense of each of the following sentences : — (1) A man may smile and smile and be a villain. (2) Few men think, but all have opinions. (3) When clouds appear, wise men put on their cloaks. (4) Oblige her, and she'll hate you while you live. (5) Angels are bright still, though the brightest fell. [O. — MODS.] PROPOSITIONS. HINTS. 1. Give special attention to Mr. Welton's scheme of diagrams (see Manual, vol. i., pp. 253-4), as they can be used very largely in illustrating formal processes. 2. Notice that in a Conditional Proposition, the Conse- quent is subordinate in force to the Antecedent, whilst in a Hypothetical it is co-ordinate in force with the Antecedent. 3. Ordinarily either of the terms Conditional and Hypothetical is understood to include both. The differ- ence between this and Mr. "V\'elton's division of propositions must be carefully borne in mind when answering examina- tion questions (ihid. pp. 171, 197-9). 4. Always reduce propositions to a strictly logical form, if not so given. 5. The distinction between Divisional and Contingent Disjunctives is important, and follows from the distinction between Conditional and HypotheticaL 6. In a Disjunctive proposition the implication is: — If it is not one (or more), then it tsthe other (or remainder) ; but it Is not implied that — If it is one (or more) then it is not the other (or remainder), since this would exclude the possibility of being both (or all), i.e. it would accept the eiccZustwe view, which the Manual gives reasons for rejecting (see vol. L, pp. 209-11). EXAMPLES. 1. Say whether the following are Hypothetical or Con- ditional propositions, and why : — (a) If knowledge is power, then ignorance is weakness. (6) If a man is moral, he leads a rational life, (c) If Z is Y, then Z is W. PROPOSITIONS. 4i (a) A Hypothetical proposition. Tliere are two quiti independent, co-ordinate, propositions, but the second cannoi be categorically asserted as true unless the first is grante( as true, i.e. there is a dependence of inference. We cannot from the data given, assert that ' he who is ignorant is weak, since this begs the question as to whether ' knowledge is power . (6) A Conditional proposition. The second proposition her( is subordinate, since " he " (i.e. that man) has a relative force The whole can be expressed by, ' If the life of a man is moral it is also rational ' ; by which we see that the possession o one attribute (rationality) follows from that of anothe: (morality), i.e. there is a dependence of phenomena. (c) Is only an empty form. It may be filled in bj (1) If I visit London, I will come and see you (Hypothetical) or (2) If any boy is impertinent, he deserves punishmen (Conditional). 2. Reduce, if possible, the following to categorica propositions — (as) If the weather remains fine, I shall go to town. (6) If candidates are numerous, choice is difficult. (c) Every man is either a politician or a poor patriot. (d) This man is either guUty or innocent. (a) Is a Hypothetical, and cannot, therefore, be reduce( to a Categorical. (6) Is logically : ' If any choice must be made amongs many candidates, that choice is difficult.' This is a Con ditional, and reduces to the Categorical : < Every case o choosing from many candidates is difficult.' (c) Is a Divisional Disjunctive, and reduces to : — (1) If any man is not a pohtician, he is a poor patrio (Conditional). (2) If any man is not a poor patriot, he is a politiciai (Conditional). These reduce to the following Categoricals : — (1) Every non-politician is a poor patriot. (2) Every not-poor-patriot is a politician. (d) This is a Contingent Disjunctive, and reduces to : — (1) If this man is not guilty, he is innocent (Hypo thetical). 50 QUESTIONS ON LOGIC. (2) If this man is not innocent, he is guilty (Hypo- thetical). These cannot be reduced to Oategoricals. QUESTIONS. 156. Define a Proposition ; and enumerate, with examples, the various kinds of Propositions. 157. What do you understand by Categorical Propo- sition ? What other forms of judgment can be expanded into Categorical Propositions 1 158*. Give a full discussion, with examples, of the Logical Copula. 159*. What do you consider to be the essential distinc- tion between the Subject and Predicate of a proposition ? Apply your answer to the following : — From hence thy warrant is thy sword. That is exactly what I wanted. [c. — hons.] 160. Explain fuUy what is meant by the Quality and Quantity of propositions. 161. Give a full discussion of Universal, Particular, and Indesignate propositions. 162. What are the signs of Quantity recognized in Logic, and to what scheme of propositions do they lead ? How do these signs of quantity affect the terms to which they belong 1 1 63*. State, and discuss, the signs of Quantity, other than the strictly logical, used in ordinary speech. 164. Explain the effects of complex terms in Propositions. 165*. Give a full discussion . of Compound Categorical Propositions. 166. How does the Quality of a proposition affeet its Quantity ? Is the relation a necessary one 1 [l. — B.A.] 167*. Define ' Modality of Propositions ' ; and say what you know about the subject. 1 68*. What position should be assigned to the Modality of Propositions in a complete system of Logic 1 If excluded from Logic, where and how would you ti-eat it 1 [l. — M.A.] PROPOSITIONS. 51 169*. What was meant by the 'contingent' and the ' possible ' in Modal propositions ? How should you define these terms now ? [l. — b.a. hons.] 1-70. Explain clearly, with examples, the essential differ- ence between a Conditional and a Hypothetical Proposition. Under what kind of proposition do they both come ? 171. Do distinctions of Quality and Quantity apply to Conditional and Hypothetical Propositions 1 Give examples. 172. Indicate which of the following are Conditional, and which Hypothetical, propositions, and why : — (1) If any man is a thief, he deserves to be punished. (2) If the report is true, what you say is untrue. (3^ If any A is B, that A is C. (4) If study is well done, the student will gain. .(5) If the whole is greater than its part, a church is greater than its nave. (6) If this work requires three hours a day, it is more than I can do. 173. Discuss, with examples, the question whether Inferential Propositions can be reduced to Categorical Propositions. 174. Eeduce, if possible, the following to Categorical Propositions : — (1) If a boy is encouraged, he will study diligently. (2) Often when there is a shower, we see a rainbow. (3) If any S is M, that S is P. (4) If he gains 50 per cent, of the marks, he will pass. (5) Every inhabitant of London is either British or alien. (5) This hat is either yours or mine. 175. "What is a Disjunctive Proposition? Discuss the question how such a proposition should be interpreted. 176. Have Disjunctive Propositions any distinctions of Quality and Quantity? Can they be reduced to Categorical Propositions ? 177. What do you take to be the exact significance of a Negative Judgment? Apply your answer to the follow- ing :— If S is P, it is not Q ; S is neither P nor Q ; S is' either P or Q ; No S is both P and Q. [l.— b.a. hons.] 52 QUESTIONS ©N LOGIC. 178. Discuss the relation of the Disjunctive Proposition to (a) the Hjrpothetical, (b) the Categorical. [l. — B.A. HONS.] 179*. Distinguish between Ampliative and Exphcative Propositions, and give several examples of each Mnd. [l. — M.A.] 180*. In a Negative Proposition, does the negative par- ticle belong to the copula or to the predicate ? [l. — m.a.] 181. Distinguish between a Judgment, a Proposition, a Sentence, and a Truth. With which is Formal Logic con- cerned ? [c] 182*. What do you understand by Modality, and by Modal Propositions ? What notice, if any, do they receive in Modem Logic ? [c. — hons.I 1 83. What are the points involved in the question of the Import of Categorical Propositions ; and what is the prac- tical importance of the question ? 184. Discuss the meaning, and the value, of the Predica- tive View of the Import of Propositions. 185. State, and criticize, the Class-inclusion View of Propositions. To what scheme of propositions does it lead? 186*. Examine the case for expressing Propositions in the form of Equations, (a) from the theoretic, (6) from the practical point of view. [l. — b.sc] 187. State and discuss the different theories as to the import of a Proposition. [o. — mods., l. — b.a. hons.] 188*. What different views of the nature and aims of Logic are involved in the question of the Quantification of the Predicate ? [l.— b.a. eons.] 189.* Give the new prepositional forms developed by the Quantification of the Rrecficate ; and state how far different logicians admit them into the scheme of the Syllogism. [l. — B.A. HONS.] 190*. Explain the meaning and practical explanation of the doctrine that " Logic postulates to be allowed to state explicitly in language aU that is implicitly contained in thought." [L.— B.A. HONS.] PEOPOSITIONS. 53 191*. Estimate critically the value of Hamilton's scheme of the Quantification of the Predicate. 192*. What different meanings have been given to 'some' in Hamilton's'scheme, and with what effect upon the pro- positional forms 1 193*. Explain the precise meaning of the proposition " some X's are not some Y's " (the proposition w of Thom- son). What is its Contradictory ? Give your opinion of its importance. [l.— b.a. hons.] 194*. What is the nature of Predication? Discuss Hamilton's doctrine that every judgment pronounces that of two notions one does or does not constitute a part of the other. • [l. — bsc] 195*. State the chief theories of the Import of Pro- positions. On what theory does the adoption of A, E, I and O, as the fundamental forms rest ? Criticise the additional forms which arise when the Quantification of the Predicate is adopted. [c] 196. State clearly MUl's view of the Import of Pro- positions, and say what objections can be urged against it. 197*. Examine the Existential or Compartmental View of the Import of Propositions. What special utility has this view 1 198*. State your opinion on the question whether every proposition implies or asserts the existence of Resemblance between the things or classes of things denoted by the terms. [l. — B.A. hons.] 199*. What are the Nominalist views of the meaning of Propositions? Distinguish carefully between the several phases of Nominalism. [l. — b.sc] 200*. What is an Essential Proposition? and in what cases is it difficult, to draw the line between Essential and Eeal Propositions ? [l. — b.a. hons.] 201*. Examine the doctrine that a Proposition is the expression of a relation between two ideas. [l. — m.a.] 202*. Examine the following statement : — " The supposed meaning in extension of a proposition has no meaning at aU, until interpreted by the meaning in comprehension. All 54 QUESTIONS ON LOGIC. concepts require to be construed in comprehension, and their comprehension is the whole of their meaning." [l. — B.A. HONS.] 203. Explain and discuss briefly the following : — (a) In a judgment the subject is naturally interpreted in denotation and the predicate in connotation. (6) Every proposition is an assertion that' two names are or are not applicable to one and the same subject. [l. — B.A.] 204*. State explicitly which of the following meanings must be assigned to the mark of quantity " some " in the Aristotehan system: — some only; some, perJiaps none; some, it may be all or none ; some certainly, and it may he all ; point out the difficulties which arise from an eironeous interpretation of this little word. [l. — m.a.] 205*. In what difierent ways is the Import of Propositions regarded from the point of view of Formal or Conceptual and of Material Logic. [l, — b.a. hons.] 206*. Can all kinds of propositions be exhibited in the intensive as well as the extensive form ? Give reasons in support of your answer, and in the event of its being in the negative, draw up a list distinguishing between those kinds of propositions which can and those which cannot he so exhibited. [l.- — b.a. hons.] 207. Examine fully the question : — " Does the assertion of a categorical proposition necessarily imply that its terms are the names of really existing things ? " 208*. Discuss, fully and critically, the view that "universal propositions do not, but particulars do, imply the existence of their subjects." 209*. State and discuss any views that you know of, other than the Predicative view and that held by Dr. Keynes, as to the Implication of Existence in propositions. 210*. Are the following examples of Hamilton's eight- fold scheme of propositions ? Give reasons for your answer. (1) All trains stop at all stations. (U) (2^ AU trains stop at some stations. (A) (3) Some trains do not stop at some stations. (OTO in jn«e and arrangement of Parts.) 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