§ 286. As we cannot be sure which of these two relations of A to B is
meant, the predicate B has to be reckoned undistributed, since a term
is held to be distributed only when we know that it is used in its
whole extent.
§ 287. To say 'No A is B,' however, is to say that A falls wholly
outside of B, which involves the consequence that B falls wholly
outside of A.
[Illustration]
§ 288. Let us now apply the same mode of illustration to the
particular forms of proposition.
§ 289. If I be taken in the strictly particular sense, there are, from
the point of view of extension, two things which may be meant when we
say 'Some A is B'--
(1) That A and B are two classes which overlap one another, that is
to say, have some members in common, e.g. 'Some cats are black.'
[Illustration]
(2) That B is wholly contained in A, which is an inverted way of
saying that all B is A, e.g. 'Some animals are men.'
[Illustration]
§ 290. Since we cannot be sure which of these two is meant, the
predicate is again reckoned undistributed.
§ 291. If on the other hand 1 be taken in an indefinite sense, so as
to admit the possibility of the universal being true, then the two
diagrams which have already been used for A must be extended to 1, in
addition to its own, together with the remarks which we made in
connection with them (§§ 285-6).
§ 292. Again, when we say 'Some A is not B,' we mean that some, if not
the whole of A, is excluded from the possession of the attribute B. In
either case the things which possess the attribute B are wholly
excluded either from a particular part or from the whole of A. The
predicate therefore is distributed.
[Illustration]
From the above considerations we elicit the following--
§ 293. Four Rules for the Distribution of Terms.
(1) All universal propositions distribute their subject.
(2) No particular propositions distribute their subject,
(3) All negative propositions distribute their predicate.
(4) No affirmative propositions distribute their predicate.
§ 294. The question of the distribution or non-distribution of the
subject turns upon the quantity of the proposition, whether universal
or particular; the question of the distribution or non-distribution of
the predicate turns upon the quality of the proposition, whether
affirmative or negative.
CHAPTER V.
_Of the Quantification of the Predicate._
§ 295. The rules that have been given for the distribution of terms,
together with the fourfold division of propositions into A, E, 1, 0,
are based on the assumption that it is the distribution or
non-distribution of the subject only that needs to be taken into
account in estimating the quantity of a proposition.
§ 296. But some logicians have maintained that the predicate, though
seldom quantified in expression, must always be quantified in
thought--in other words, that when we say, for instance, 'All A is B,'
we must mean either that 'All A is all B' or only that 'All A is some
B.'
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