The Project Gutenberg eBook ofSymbolic LogicThis ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.Title: Symbolic LogicAuthor: Lewis CarrollRelease date: May 5, 2009 [eBook #28696]Most recently updated: January 5, 2021Language: EnglishCredits: Produced by Tony Browne, Geetu Melwani, Greg Weeks, L.Lynn Smith and the Online Distributed Proofreading Teamat https://www.pgdp.net*** START OF THE PROJECT GUTENBERG EBOOK SYMBOLIC LOGIC ***
This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.
Title: Symbolic LogicAuthor: Lewis CarrollRelease date: May 5, 2009 [eBook #28696]Most recently updated: January 5, 2021Language: EnglishCredits: Produced by Tony Browne, Geetu Melwani, Greg Weeks, L.Lynn Smith and the Online Distributed Proofreading Teamat https://www.pgdp.net
Title: Symbolic Logic
Author: Lewis Carroll
Author: Lewis Carroll
Release date: May 5, 2009 [eBook #28696]Most recently updated: January 5, 2021
Language: English
Credits: Produced by Tony Browne, Geetu Melwani, Greg Weeks, L.Lynn Smith and the Online Distributed Proofreading Teamat https://www.pgdp.net
*** START OF THE PROJECT GUTENBERG EBOOK SYMBOLIC LOGIC ***
pg_iipg_iiipg_iv
A Syllogism worked out.That story of yours, about your once meeting the sea-serpent, always sets me off yawning;I never yawn, unless when I’m listening to something totally devoid of interest.The Premisses, separately.Diagram representing AllDiagram representing NeverThe Premisses, combined.Diagram representing the combinationThe Conclusion.Diagram representing the conclusionThat story of yours, about your once meeting the sea-serpent, is totally devoid of interest.
An envelope, containing two blank Diagrams (Biliteral and Triliteral) and 9 counters (4 Red and 5 Grey), may be had, from Messrs. Macmillan, for 3d., by post 4d.
I shall be grateful to any Reader of this book who will point out any mistakes or misprints he may happen to notice in it, or any passage which he thinks is not clearly expressed.
I have a quantity of MS. in hand for Parts II and III, and hope to be able——should life, and health, and opportunity, be granted to me, to publish them in the course of the next few years. Their contents will be as follows:—
Further investigations in the subjects of Part I. Propositions of other forms (such as “Not-allxarey”). Triliteral and Multiliteral Propositions (such as “Allabcarede”). Hypotheticals. Dilemmas. &c. &c.
Analysis of a Proposition into its Elements. Numerical and Geometrical Problems. The Theory of Inference. The Construction of Problems. And many otherCuriosa Logica.
The chief alterations, since the First Edition, have been made in the Chapter on ‘Classification’ (pp. 2,3) and the Book on ‘Propositions’ (pp. 10to19). The chief additions have been the questions on words and phrases, added to the Examination-Papers atp. 94, and the Notes inserted atpp. 164,194.
In Book I, Chapter II, I have adopted a new definition of ‘Classification’, which enables me to regard the whole Universe as a ‘Class,’ and thus to dispense with the very awkward phrase ‘a Set of Things.’
In the Chapter on ‘Propositions of Existence’ I have adopted a new ‘normal form,’ in which the Class, whose existence is affirmed or denied, is regarded as thePredicate, instead of theSubject, of the Proposition, thus evading a very subtle difficulty which besets the other form. These subtle difficulties seem to lie at the root of every Tree of Knowledge, and they arefarmore hopeless to grapple with than any that occur in its higher branches. For example, the difficulties of the Forty-Seventh Proposition of Euclid are mere child’s play compared with the mental torture endured in the effort to think out the essential nature of a straight Line. And, in the present work, the difficulties of the “5 Liars” Problem, atp.192, are “trifles, light as air,” compared with the bewildering question “What is a Thing?”
In the Chapter on ‘Propositions of Relation’ I have inserted a new Section, containing the proof that a Proposition, beginning with “All,” is aDoubleProposition (a fact that is quite independent of the arbitrary rule, laid down in the next Section, that such a Proposition is to be understood as implying the actualexistenceof its Subject). This proof was given, in the earlier editions, incidentally, in the course of the discussion of the Biliteral Diagram: but itsproperplace, in this treatise, is where I have now introduced it.
pg_ixIn the Sorites-Examples, I have made a good many verbal alterations, in order to evade a difficulty, which I fear will have perplexed some of the Readers of the first three Editions. Some of the Premisses were so worded that their Terms were not Specieses of the Univ. named in the Dictionary, but of a larger Class, of which the Univ. was only a portion. In all such cases, it was intended that the Reader should perceive that what was asserted of the larger Class was thereby asserted of the Univ., and should ignore, as superfluous, all that it asserted of itsotherportion. Thus, in Ex. 15, the Univ. was stated to be “ducks in this village,” and the third Premiss was “Mrs. Bond has no gray ducks,” i.e. “No gray ducks are ducks belonging to Mrs. Bond.” Here the Terms arenotSpecieses of the Univ., but of the larger Class “ducks,” of which the Univ. is only a portion: and it was intended that the Reader should perceive that what is here asserted of “ ducks” is thereby asserted of “ ducks in this village.” and should treat this Premiss as if it were “Mrs. Bond has no gray ducks in this village,” and should ignore, as superfluous, what it asserts as to theotherportion of the Class “ducks,” viz. “ Mrs. Bond has no gray ducksout ofthis village”.
In the Appendix I have given a new version of the Problem of the “Five Liars.” My object, in doing so, is to escape the subtle and mysterious difficulties which beset all attempts at regarding a Proposition as being its own Subject, or a Set of Propositions as being Subjects for one another. It is certainly, a most bewildering and unsatisfactory theory: one cannot help feeling that there is a great lack ofsubstancein all this shadowy host——that, as the procession of phantoms glides before us, there is notonethat we can pounce upon, and say “Hereis a Proposition thatmustbe either true or false!”——that it is but a Barmecide Feast, to which we have been bidden——and that its prototype is to be found in that mythical island, whose inhabitants “earned a precarious living by taking in each others’ washing”! By simply translating “telling 2 Truths” into “takingbothof 2 condiments (salt and mustard),” “telling 2 Lies” into “takingneitherof them” and “telling a Truth and a Lie (order not specified)” into “taking onlyonecondiment (it is not specifiedpg_xwhich),” I have escaped all those metaphysical puzzles, and have produced a Problem which, when translated into a Set of symbolized Premisses, furnishes the very sameDataas were furnished by the Problem of the “Five Liars.”
The coined words, introduced in previous editions, such as “Eliminands” and “Retinends”, perhaps hardly need any apology: they were indispensable to my system: but the new plural, here used for the first time, viz. “Soriteses”, will, I fear, be condemned as “bad English”, unless I say a word in its defence. We havethreesingular nouns, in English, of pluralform, “series”, “species”, and “Sorites”: in all three, the awkwardness, of using the same word for both singular and plural, must often have been felt: this has been remedied, in the case of “series” by coining the plural “serieses”, which has already found it way into the dictionaries: so I am no rash innovator, but am merely “following suit”, in using the new plural “Soriteses”.
In conclusion, let me point out that even those, who are obliged to studyFormalLogic, with a view to being able to answer Examination-Papers in that subject, will find the study ofSymbolicLogic most helpful for this purpose, in throwing light upon many of the obscurities with which Formal Logic abounds, and in furnishing a delightfully easy method oftestingthe results arrived at by the cumbrous processes which Formal Logic enforces upon its votaries.
This is, I believe, the very first attempt (with the exception of my own little book,The Game of Logic, published in 1886, a very incomplete performance) that has been made topopularisethis fascinating subject. It has cost meyearsof hard work: but if it should prove, as I hope it may, to be ofrealservice to the young, and to be taken up, in High Schools and in private families, as a valuable addition to their stock of healthful mental recreations, such a result would more than repay ten times the labour that I have expended on it.
L. C.
29, Bedford Street, Strand.Christmas, 1896.
[N.B. Some remarks, addressed toTeachers, will be found in the Appendix, atp. 165.]
[N.B. Some remarks, addressed toTeachers, will be found in the Appendix, atp. 165.]
The Learner, who wishes to try the questionfairly, whether this little book does, or does not, supply the materials for a most interesting mental recreation, isearnestlyadvised to adopt the following Rules:—
(1) Begin at thebeginning, and do not allow yourself to gratify a mere idle curiosity by dipping into the book, here and there. This would very likely lead to your throwing it aside, with the remark “This ismuchtoo hard for me!”, and thus losing the chance of adding a verylargeitem to your stock of mental delights. This Rule (of notdipping) is verydesirablewithotherkinds of books——such as novels, for instance, where you may easily spoil much of the enjoyment you would otherwise get from the story, by dipping into it further on, so that what the author meant to be a pleasant surprise comes to you as a matter of course. Some people, I know, make a practice of looking into Vol. III first, just to see how the story ends: and perhaps itisas well just to know that all endshappily——that the much-persecuted loversdomarry after all, that he is proved to be quite innocent of the murder, that the wicked cousin is completely foiled in his plot and gets the punishment he deserves, and that the rich uncle in India (Qu.Why inIndia?Ans.Because, somehow, uncles nevercanget rich anywhere else) dies at exactly the right moment——before taking the trouble to read Vol. I.pg_xiiThis, I say, isjustpermissible with anovel, where Vol. III has ameaning, even for those who have not read the earlier part of the story; but, with ascientificbook, it is sheer insanity: you will find the latter parthopelesslyunintelligible, if you read it before reaching it in regular course.
(2) Don’t begin any fresh Chapter, or Section, until you are certain that youthoroughlyunderstand the whole bookup to that point, and that you have worked, correctly, most if not all of the examples which have been set. So long as you are conscious that all the land you have passed through is absolutelyconquered, and that you are leaving no unsolved difficultiesbehindyou, which will be sure to turn up again later on, your triumphal progress will be easy and delightful. Otherwise, you will find your state of puzzlement get worse and worse as you proceed, till you give up the whole thing in utter disgust.
(3) When you come to any passage you don’t understand,read it again: if youstilldon’t understand it,read it again: if you fail, even afterthreereadings, very likely your brain is getting a little tired. In that case, put the book away, and take to other occupations, and next day, when you come to it fresh, you will very likely find that it isquiteeasy.
(4) If possible, find some genial friend, who will read the book along with you, and will talk over the difficulties with you.Talkingis a wonderful smoother-over of difficulties. WhenIcome upon anything——in Logic or in any other hard subject——that entirely puzzles me, I find it a capital plan to talk it over,aloud, even when I am all alone. One can explain things soclearlyto one’s self! And then, you know, one is sopatientwith one’s self: onenevergets irritated at one’s own stupidity!
If, dear Reader, you will faithfully observe these Rules, and so give my little book a reallyfairtrial, I promise you, most confidently, that you will find Symbolic Logic to be one of the most, if notthemost, fascinating of mental recreations! In this First Part, I have carefully avoided all difficulties which seemed to me to be beyond the grasp of an intelligent child of (say) twelve or fourteen years of age. I have myself taught most of its contents,vivâ voce, tomanychildren, and havepg_xiiifound them take a real intelligent interest in the subject. For those, who succeed in mastering Part I, and who begin, like Oliver, “asking for more,” I hope to provide, in Part II, sometolerablyhard nuts to crack——nuts that will require all the nut-crackers they happen to possess!
Mental recreation is a thing that we all of us need for our mental health; and you may get much healthy enjoyment, no doubt, from Games, such as Back-gammon, Chess, and the new Game “Halma”. But, after all, when you have made yourself a first-rate player at any one of these Games, you have nothing real toshowfor it, as aresult!You enjoyed the Game, and the victory, no doubt,at the time: but you have noresultthat you can treasure up and get realgoodout of. And, all the while, you have been leaving unexplored a perfectmineof wealth. Once master the machinery of Symbolic Logic, and you have a mental occupation always at hand, of absorbing interest, and one that will be of realuseto you inanysubject you may take up. It will give you clearness of thought——the ability tosee your waythrough a puzzle——the habit of arranging your ideas in an orderly and get-at-able form——and, more valuable than all, the power to detectfallacies, and to tear to pieces the flimsy illogical arguments, which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art.Try it.That is all I ask of you!
L. C.
29, Bedford Street, Strand.February 21, 1896.