'Whatever is true in one form of words is true in every other form
of words which conveys the same meaning.'
§ 535. There is a sort of inference which goes under the title of
Immediate Inference by Added Determinants, in which from some
proposition already made another is inferred, in which the same
attribute is attached both to the subject and the predicate, e.g.,
A horse is a quadruped.
.'. A white horse is a white quadruped.
§ 536. Such inferences are very deceptive. The attributes added must
be definite qualities, like whiteness, and must in no way involve a
comparison. From 'A horse is a quadruped' it may seem at first sight
to follow that 'A swift horse is a swift quadruped.' But we need not
go far to discover how little formal validity there is about such an
inference. From 'A horse is a quadruped' it by no means follows that
'A slow horse is a slow quadruped'; for even a slow horse is swift
compared with most quadrupeds. All that really follows here is that
'A slow horse is a quadruped which is slow for a horse.' Similarly,
from 'A Bushman is a man' it does not follow that 'A tall Bushman is a
tall man,' but only that 'A tall Bushman is a man who is tall for a
Bushman'; and so on generally.
§ 537. Very similar to the preceding is the process known as Immediate
Inference by Complex Conception, e.g.
A horse is a quadruped.
.'. The head of a horse is the head of a quadruped.
§ 538. This inference, like that by added determinants, from which it
differs in name rather than in nature, may be explained on the
principle of Substitution. Starting from the identical proposition,
'The head of a quadruped is the head of a quadruped,' and being given
that 'A horse is a quadruped,' so that whatever is true of 'quadruped'
generally we know to be true of 'horse,' we are entitled to substitute
the narrower for the wider term, and in this manner we arrive at the
proposition,
The head of a horse is the head of a quadruped.
§ 539. Such an inference is valid enough, if the same caution be
observed as in the case of added determinants, that is, if no
difference be allowed to intervene in the relation of the fresh
conception to the generic and the specific terms.
CHAPTER VIII.
_Of Mediate Inferences or Syllogisms._
§ 540. A Mediate Inference, or Syllogism, consists of two
propositions, which are called the Premisses, and a third proposition
known as the Conclusion, which flows from the two conjointly.
§ 541. In every syllogism two terms are compared with one another by
means of a third, which is called the Middle Term. In the premisses
each of the two terms is compared separately with the middle term; and
in the conclusion they are compared with one another.
§ 542. Hence every syllogism consists of three terms, one of which
occurs twice in the premisses and does not appear at all in the
conclusion. This term is called the Middle Term. The predicate of the
conclusion is called the Major Term and its subject the Minor Term.
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