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.
pg013
§ 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."
pg014
(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
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