§ 752. The special characteristic of the partly conjunctive syllogism
lies in the transition from hypothesis to fact. We might lay down as
the appropriate axiom of this form of argument, that 'What is true in
the abstract is true--in the concrete,' or 'What is true in theory is
also true in fact,' a proposition which is apt to be neglected or
denied. But this does not vitally distinguish it from the ordinary
syllogism. For though in the latter we think rather of the transition
from a general truth to a particular application of it, yet at bottom
a general truth is nothing but a hypothesis resting upon a slender
basis of observed fact. The proposition 'A is B' may be expressed in
the form 'If A is, B is.' To say that 'All men are mortal' may be
interpreted to mean that 'If we find in any subject the attributes of
humanity, the attributes of mortality are sure to accompany them.'
CHAPTER XXII.
_Of the Partly Conjunctive Syllogism regarded as an Immediate
Inference_.
§ 753. It is the assertion of fact in the minor premiss, where we have
the application of an abstract principle to a concrete instance, which
alone entitles the partly conjunctive syllogism to be regarded as a
syllogism at all. Apart from this the forms of semi-conjunctive
reasoning run at once into the moulds of immediate inference.
§ 754. The constructive mood will then be read in this way--
If A is B, C is D,
.'. A being B, C is D.
reducing itself to an instance of immediate inference by subaltern
opposition--
Every case of A being B, is a case of C being D.
.'. Some particular case of A being B is a case of C being D.
§ 755. Again, the destructive conjunctive will read as follows--
If A is B, C is D,
.'. C not being D, A is not B.
which is equivalent to
All cases of A being B are cases of C being D.
.'. Whatever is not a case of C being D is not a case of A being B.
.'. Some particular case of C not being D is not a case of A being
B.
But what is this but an immediate inference by contraposition, coming
under the formula
All A is B,
.'. All not-B is not-A,
and followed by Subalternation?
§ 756. The fallacy of affirming the consequent becomes by this mode of
treatment an instance of the vice of immediate inference known as the
simple conversion of an A proposition. 'If A is B, C is D' is not
convertible with 'If C is D, A is B' any more than 'All A is B' is
convertible with 'All B is A.'
§ 757. We may however argue in this way
If A is B, C is D,
C is D,
.'. A may be B,
which is equivalent to saying,
When A is B, C is always D,
.'. When C is D, A is sometimes B,
and falls under the legitimate form of conversion of A per accidens--
All cases of A being B are cases of C being D.
.'. Some cases of C being D are cases of A being B.
§ 758. The fallacy of denying the antecedent assumes the following
form--
If A is B, C is D,
.'. If A is not B, C is not D,
equivalent to--
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