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Authors: Lewis Carroll
Complete Works of Lewis Carroll (138 page)
SYMBOLIC LOGIC
CONTENTS
REPRESENTATION OF PROPOSITIONS.
INTERPRETATION OF BILITERAL DIAGRAM WHEN MARKED WITH COUNTERS.
REPRESENTATION OF PROPOSITIONS IN TERMS OF x AND m, OR OF y AND m.
INTERPRETATION, IN TERMS OF x AND y, OF TRILITERAL DIAGRAM, WHEN MARKED WITH COUNTERS OR DIGITS.
REPRESENTATION OF PROPOSITIONS OF RELATION.
EXAMPLES, ANSWERS, AND SOLUTIONS.
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.
pg_xiiThis, 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.
(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 pg_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, 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
one
Member is called an ‘
Individual
.’
[For example, the Class “towns having four million inhabitants,” which Class contains only
one
Member, viz.
“London.”]
½Hence, any single Thing, which we can name so as to distinguish it from all other Things, may be regarded as a one-Member Class.
[Thus “London” may be regarded as the one-Member Class, picked out from the Class “towns,” which has, as its Differentia, “having four million inhabitants.”]
A Class, containing two or more Members, is sometimes regarded as
one single Thing
.
When so regarded, it may possess an Adjunct which is
not
possessed by any Member of it taken separately.
[Thus, the Class “The soldiers of the Tenth Regiment,” when regarded as
one single Thing
, may possess the Attribute “formed in square,” which is
not
possessed by any Member of it taken separately.]