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 the _Predicate_, instead of the _Subject_, 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 are _far_ more 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, at p. 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 a _Double_ Proposition (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 actual _existence_ of its Subject). This proof was given, in the earlier editions, incidentally, in the course of the discussion of the Biliteral Diagram: but its _proper_ place, in this treatise, is where I have now introduced it. pg-ix In 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 its _other_ portion. 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 are _not_ Specieses 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 the _other_ portion of the Class "ducks," viz. "Mrs. Bond has no gray ducks _out of_ this 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 of _substance_ in all this shadowy host----that, as the procession of phantoms glides before us, there is not _one_ that we can pounce upon, and say "_Here_ is a Proposition that _must_ be 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 "taking _both_ of 2 condiments (salt and mustard)," "telling 2 Lies" into "taking _neither_ of them" and "telling a Truth and a Lie (order not specified)" into "taking only _one_ condiment (it is not specified _which_)," I have escaped all those metaphysical puzzles, and have produced a Problem which, when translated into a Set of symbolized Premisses, furnishes the very same _Data_ as were furnished by the Problem of the "Five Liars." pg-x 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 have _three_ singular nouns, in English, of plural _form_, "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 its 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 study _Formal_ Logic, with a view to being able to answer Examination-Papers in that subject, will find the study of _Symbolic_ Logic 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 of _testing_ the 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 to _popularise_ this fascinating subject. It has cost me _years_ of hard work: but if it should prove, as I hope it may, to be of _real_ service 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._

pg-xi

INTRODUCTION.

_TO LEARNERS._

[N.B. Some remarks, addressed to _Teachers_, will be found in the Appendix, at p. 165.]

The Learner, who wishes to try the question _fairly_, whether this little book does, or does not, supply the materials for a most interesting mental recreation, is _earnestly_ advised to adopt the following Rules:--

(1) Begin at the _beginning_, 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 is _much_ too hard for me!", and thus losing the chance of adding a very _large_ item to your stock of mental delights. This Rule (of not _dipping_) is very _desirable_ with _other_ kinds 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 it _is_ as well just to know that all ends _happily_----that the much-persecuted lovers _do_ marry 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 in _India_? _Ans._ Because, somehow, uncles never _can_ get rich anywhere else) dies at exactly the right moment----before taking the trouble to read Vol. I. This, I say, is _just_ permissible with a _novel_, where Vol. III has a _meaning_, even for those who have not read the earlier part of the story; but, with a _scientific_ book, it is sheer insanity: you will find the latter part _hopelessly_ unintelligible, if you read it before reaching it in regular course. pg-xii (2) Don't begin any fresh Chapter, or Section, until you are certain that you _thoroughly_ understand the whole book _up 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 absolutely _conquered_, and that you are leaving no unsolved difficulties _behind_ you, 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 you _still_ don't understand it, _read it again_: if you fail, even after _three_ readings, 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 is _quite_ easy.

(4) If possible, find some genial friend, who will read the book along with you, and will talk over the difficulties with you. _Talking_ is a wonderful smoother-over of difficulties. When _I_ come 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 so _clearly_ to one's self! And then, you know, one is so _patient_ with one's self: one _never_ gets irritated at one's own stupidity!

If, dear Reader, you will faithfully observe these Rules, and so give my little book a really _fair_ trial, I promise you, most confidently, that you will find Symbolic Logic to be one of the most, if not _the_ most, 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_, to _many_ children, and have found 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, some _tolerably_ hard nuts to crack----nuts that will require all the nut-crackers they happen to possess! pg-xiii 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 to _show_ for it, as a _result!_ You enjoyed the Game, and the victory, no doubt, _at the time_: but you have no _result_ that you can treasure up and get real _good_ out of. And, all the while, you have been leaving unexplored a perfect _mine_ of 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 real _use_ to you in _any_ subject you may take up. It will give you clearness of thought----the ability to _see your way_ through a puzzle----the habit of arranging your ideas in an orderly and get-at-able form----and, more valuable than all, the power to detect _fallacies_, 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._

pg-xiv pg-xv

CONTENTS.

=BOOK I.=

=THINGS AND THEIR ATTRIBUTES.=

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