The Mathematical Works of Lewis Carroll. Ð›ÑŒÑŽÐ¸Ñ ÐšÑрролл
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!
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.
BOOK I.
THINGS AND THEIR ATTRIBUTES.
CHAPTER I.
INTRODUCTORY.
The Universe contains ‘Things.’
[For example, “I,” “London,” “roses,” “redness,” “old English books,” “the letter which I received yesterday.”]
Things have ‘Attributes.’
[For example, “large,” “red,” “old,” “which I received yesterday.”]
One Thing may have many Attributes; and one Attribute may belong to many Things.
[Thus, the Thing “a rose” may have the Attributes “red,” “scented,” “full-blown,” &c.; and the Attribute “red” may belong to the Things “a rose,” “a brick,” “a ribbon,” &c.]
Any Attribute, or any Set of Attributes, may be called an ‘Adjunct.’
[This word is introduced in order to avoid the constant repetition of the phrase “Attribute or Set of Attributes.”
Thus, we may say that a rose has the Attribute “red” (or the Adjunct “red,” whichever we prefer); or we may say that it has the Adjunct “red, scented and full-blown.”]
CHAPTER II.
CLASSIFICATION.
‘Classification,’ or the formation of Classes, is a Mental Process, in which we imagine that we have put together, in a group, certain Things. Such a group is called a ‘Class.’
This Process may be performed in three different ways, as follows:—
(1) We may imagine that we have put together all Things. The Class so formed (i.e. the Class “Things”) contains the whole Universe.
(2) We may think of the Class “Things,” and may imagine that we have picked out from it all the Things which possess a certain Adjunct not possessed by the whole Class. This Adjunct is said to be ‘peculiar’ to the Class so formed. In this case, the Class “Things” is called a ‘Genus’ with regard to the Class so formed: the Class, so formed, is called a ‘Species’ of the Class “Things”: and its peculiar Adjunct is called its ‘Differentia’.
As this Process is entirely Mental, we can perform it whether there is, or is not, an existing Thing which possesses that Adjunct. If there is, the Class is said to be ‘Real’; if not, it is said to be ‘Unreal’, or ‘Imaginary.’
[For example, we may imagine that we have picked out, from the Class “Things,” all the Things which possess the Adjunct “material, artificial, consisting of houses and streets”; and we may thus form the Real Class “towns.” Here we may regard “Things” as a Genus, “Towns” as a Species of Things, and “material, artificial, consisting of houses and streets” as its Differentia.
Again, we may imagine that we have picked out all the Things which possess the Adjunct “weighing a ton, easily lifted by a baby”; and we may thus form the Imaginary Class “Things that weigh a ton and are easily lifted by a baby.”]
(3) We may think of a certain Class, not the Class “Things,” and may imagine that we have picked out from it all the Members of it which possess a certain Adjunct not possessed by the whole Class. This Adjunct is said to be ‘peculiar’ to the smaller Class so formed. In this case, the Class thought of is called a ‘Genus’ with regard to the smaller Class picked out from it: the smaller Class is called a ‘Species’ of the larger: and its peculiar Adjunct is called its ‘Differentia’.
[For example, we may think of the Class “towns,” and imagine that we have picked out from it all the towns which possess the Attribute “lit with gas”; and we may thus form the Real Class “towns lit with gas.” Here we may regard “Towns” as a Genus, “Towns lit with gas” as a Species of Towns, and “lit with gas” as its Differentia.
If, in the above example, we were to alter “lit with gas” into “paved with gold,” we should get the Imaginary Class “towns paved with gold.”]
A Class, containing only