Complete Works of Lewis Carroll (140 page)

CHAPTER II.

PROPOSITIONS OF EXISTENCE.

A ‘
Proposition of Existence
’, when in normal form, has, for its
Subject
, the Class “existing Things”.

Its Sign of Quantity is “Some” or “No”.

[Note that, though its Sign of Quantity tells us
how many
existing Things are Members of its Predicate, it does
not
tell us the
exact
number: in fact, it only deals with
two
numbers, which are, in ascending order, “0” and “1 or more.”]

It is called “a Proposition of Existence” because its effect is to assert the
Reality
(i.e.
the real
existence
), or else the
Imaginariness
, of its Predicate.

[Thus, the Proposition “Some existing Things are honest men” asserts that the Class “honest men” is
Real
.

This is the
normal
form; but it may also be expressed in any one of the following forms:—

(1) “Honest men exist”;

(2) “Some honest men exist”;

(3) “The Class ‘honest men’ exists”;

(4) “There are honest men”;

(5) “There are some honest men”.

Similarly, the Proposition “No existing Things are men fifty feet high” asserts that the Class “men 50 feet high” is
Imaginary
.

This is the
normal
form; but it may also be expressed in any one of the following forms:—

(1) “Men 50 feet high do not exist”;

(2) “No men 50 feet high exist”;

(3) “The Class ‘men 50 feet high’ does not exist”;

(4) “There are not any men 50 feet high”;

(5) “There are no men 50 feet high.”]

CHAPTER III.

PROPOSITIONS OF RELATION.

§ 1.

Introductory.

A
Proposition of Relation
, of the kind to be here discussed, has, for its Terms, two Specieses of the same Genus, such that each of the two Names conveys the idea of some Attribute
not
conveyed by the other.

[Thus, the Proposition “Some merchants are misers” is of the right kind, since “merchants” and “misers” are Specieses of the same Genus “men”; and since the Name “merchants” conveys the idea of the Attribute “mercantile”, and the name “misers” the idea of the Attribute “miserly”, each of which ideas is
not
conveyed by the other Name.

But the Proposition “Some dogs are setters” is
not
of the right kind, since, although it is true that “dogs” and “setters” are Specieses of the same Genus “animals”, it is
not
true that the Name “dogs” conveys the idea of any Attribute not conveyed by the Name “setters”.
Such Propositions will be discussed in Part II.]

The Genus, of which the two Terms are Specieses, is called the ‘
Universe of Discourse
,’ or (more briefly) the ‘
Univ.
’

The Sign of Quantity is “Some” or “No” or “All”.

[Note that, though its Sign of Quantity tells us
how many
Members of its Subject are
also
Members of its Predicate, it does not tell us the
exact
number: in fact, it only deals with
three
numbers, which are, in ascending order, “0”, “1 or more”, “the total number of Members of the Subject”.]

It is called “a Proposition of Relation” because its effect is to assert that a certain
relationship
exists between its Terms.

§ 2.

Reduction of a Proposition of Relation to Normal form.

The Rules, for doing this, are as follows:—

(1) Ascertain what is the
Subject
(i.e., ascertain what Class we are
talking about
);

(2) If the verb, governed by the Subject, is
not
the verb “are” (or “is”), substitute for it a phrase beginning with “are” (or “is”);

(3) Ascertain what is the
Predicate
(i.e., ascertain what Class it is, which is asserted to contain
some
, or
none
, or
all
, of the Members of the Subject);

(4) If the Name of each Term is
completely expressed
(i.e.
if it contains a Substantive), there is no need to determine the ‘Univ.’; but, if either Name is
incompletely expressed
, and contains
Attributes
only, it is then necessary to determine a ‘Univ.’, in order to insert its Name as the Substantive.

(5) Ascertain the
Sign of Quantity
;

(6) Arrange in the following order:—

Sign of Quantity,

Subject,

Copula,

Predicate.

[Let us work a few Examples, to illustrate these Rules.

(1)

“Some apples are not ripe.”

(1) The Subject is “apples.”

(2) The Verb is “are.”

(3) The Predicate is “not-ripe * * *.”
(As no Substantive is expressed, and we have not yet settled what the Univ.
is to be, we are forced to leave a blank.)

(4) Let Univ.
be “fruit.”

(5) The Sign of Quantity is “some.”

(6) The Proposition now becomes

“Some | apples | are | not-ripe fruit.”

(2)

“None of my speculations have brought me as much as 5 per cent.”

(1) The Subject is “my speculations.”

(2) The Verb is “have brought,” for which we substitute the phrase “are * * * that have brought”.

(3) The Predicate is “* * * that have brought &c.”

(4) Let Univ.
be “transactions.”

(5) The Sign of Quantity is “none of.”

(6) The Proposition now becomes

“None of | my speculations | are | transactions that have brought me as much as 5 per cent.”

(3)

“None but the brave deserve the fair.”

To begin with, we note that the phrase “none but the brave” is equivalent to “no
not
-brave.”

(1) The Subject has for its
Attribute
“not-brave.”
But no
Substantive
is supplied.
So we express the Subject as “not-brave * * *.”

(2) The Verb is “deserve,” for which we substitute the phrase “are deserving of”.

(3) The Predicate is “* * * deserving of the fair.”

(4) Let Univ.
be “persons.”

(5) The Sign of Quantity is “no.”

(6) The Proposition now becomes

“No | not-brave persons | are | persons deserving of the fair.”

(4)

“A lame puppy would not say “thank you” if you offered to lend it a skipping-rope.”

(1) The Subject is evidently “lame puppies,” and all the rest of the sentence must somehow be packed into the Predicate.

(2) The Verb is “would not say,” &c., for which we may substitute the phrase “are not grateful for.”

(3) The Predicate may be expressed as “* * * not grateful for the loan of a skipping-rope.”

(4) Let Univ.
be “puppies.”

(5) The Sign of Quantity is “all.”

(6) The Proposition now becomes

“All | lame puppies | are | puppies not grateful for the loan of a skipping-rope.”

(5)

“No one takes in the
Times
, unless he is well-educated.”

(1) The Subject is evidently persons who are not well-educated (“no
one
” evidently means “no
person
”).

(2) The Verb is “takes in,” for which we may substitute the phrase “are persons taking in.”

(3) The Predicate is “persons taking in the
Times
.”

(4) Let Univ.
be “persons.”

(5) The Sign of Quantity is “no.”

(6) The Proposition now becomes

“No | persons who are not well-educated | are | persons taking in the
Times
.”

(6)

“My carriage will meet you at the station.”

(1) The Subject is “my carriage.”
This, being an ‘Individual,’ is equivalent to the Class “my carriages.”
(Note that this Class contains only
one
Member.)

(2) The Verb is “will meet”, for which we may substitute the phrase “are * * * that will meet.”

(3) The Predicate is “* * * that will meet you at the station.”

(4) Let Univ.
be “things.”

(5) The Sign of Quantity is “all.”

(6) The Proposition now becomes

“All | my carriages | are | things that will meet you at the station.”

(7)

“Happy is the man who does not know what ‘toothache’ means!”

(1) The Subject is evidently “the man &c.”
(Note that in this sentence, the
Predicate
comes first.) At first sight, the Subject seems to be an ‘
Individual
’; but on further consideration, we see that the article “the” does
not
imply that there is only
one
such man.
Hence the phrase “the man who” is equivalent to “all men who”.

(2) The Verb is “are.”

(3) The Predicate is “happy * * *.”

(4) Let Univ.
be “men.”

(5) The Sign of Quantity is “all.”

(6) The Proposition now becomes

“All | men who do not know what ‘toothache’ means | are | happy men.”

(8)

“Some farmers always grumble at the weather, whatever it may be.”

(1) The Subject is “farmers.”

(2) The Verb is “grumble,” for which we substitute the phrase “are * * * who grumble.”

(3) The Predicate is “* * * who always grumble &c.”

(4) Let Univ.
be “persons.”

(5) The Sign of Quantity is “some.”

(6) The Proposition now becomes

“Some | farmers | are | persons who always grumble at the weather, whatever it may be.”

(9)

“No lambs are accustomed to smoke cigars.”

(1) The Subject is “lambs.”

(2) The Verb is “are.”

(3) The Predicate is “* * * accustomed &c.”

(4) Let Univ.
be “animals.”

(5) The Sign of Quantity is “no.”

(6) The Proposition now becomes

“No | lambs | are | animals accustomed to smoke cigars.”

(10)

“I ca’n’t understand examples that are not arranged in regular order, like those I am used to.”

(1) The Subject is “examples that,” &c.

(2) The Verb is “I ca’n’t understand,” which we must alter, so as to have “examples,” instead of “I,” as the nominative case.
It may be expressed as “are not understood by me.”

(3) The Predicate is “* * * not understood by me.”

(4) Let Univ.
be “examples.”

(5) The Sign of Quantity is “all.”

(6) The Proposition now becomes

“All | examples that are not arranged in regular order like those I am used to | are | examples not understood by me.”]

§ 3.

A Proposition of Relation, beginning with “All”, is a Double Proposition.

A Proposition of Relation, beginning with “All”, asserts (as we already know) that “
All
Members of the Subject are Members of the Predicate”.
This evidently contains, as a
part
of what it tells us, the smaller Proposition “
Some
Members of the Subject are Members of the Predicate”.

[Thus, the Proposition “
All
bankers are rich men” evidently contains the smaller Proposition “
Some
bankers are rich men”.]

The question now arises “What is the
rest
of the information which this Proposition gives us?”

In order to answer this question, let us begin with the smaller Proposition, “
Some
Members of the Subject are Members of the Predicate,” and suppose that this is
all
we have been told; and let us proceed to inquire what
else
we need to be told, in order to know that “
All
Members of the Subject are Members of the Predicate”.

[Thus, we may suppose that the Proposition “
Some
bankers are rich men” is all the information we possess; and we may proceed to inquire what
other
Proposition needs to be added to it, in order to make up the entire Proposition “
All
bankers are rich men”.]

Let us also suppose that the ‘Univ.’
(i.e.
the Genus, of which both the Subject and the Predicate are Specieses) has been divided (by the Process of
Dichotomy
) into two smaller Classes, viz.

(1) the Predicate;

(2) the Class whose Differentia is
contradictory
to that of the Predicate.

[Thus, we may suppose that the Genus “men,” (of which both “bankers” and “rich men” are Specieses) has been divided into the two smaller Classes, “rich men”, “poor men”.]

Now we know that
every
Member of the Subject is (as shown at p.
6) a Member of the Univ.
Hence
every
Member of the Subject is either in Class (1) or else in Class (2).