Closely connected with such cases as the above are those mentioned by
Archbishop Thomson as "Immediate Inferences by added Determinants"
(_Laws of Thought_, § 87). He takes the case: '_A negro is a
fellow-creature_: therefore, _A negro in suffering is a fellow-creature
in suffering_.' This rests upon the principle that to increase the
connotations of two terms by the same attribute or determinant does not
affect the relationship of their denotations, since it must equally
diminish (if at all) the denotations of both classes, by excluding the
same individuals, if any want the given attribute. But this principle is
true only when the added attribute is not merely the same verbally, but
has the same significance in qualifying both terms. We cannot argue _A
mouse is an animal_; therefore, _A large mouse is a large animal_; for
'large' is an attribute relative to the normal magnitude of the thing
described.
§ 4. Conversion is Immediate Inference by transposing the terms of a
given proposition without altering its quality. If the quantity is also
unaltered, the inference is called 'Simple Conversion'; but if the
quantity is changed from universal to particular, it is called
'Conversion by limitation' or '_per accidens._' The given proposition is
called the 'convertend'; that which is derived from it, the 'converse.'
Departing from the usual order of exposition, I have taken up Conversion
next to Subalternation, because it is generally thought to rest upon the
principle of Identity, and because it seems to be a good method to
exhaust the forms that come only under Identity before going on to those
that involve Contradiction and Excluded Middle. Some, indeed, dispute
the claims of Conversion to illustrate the principle of Identity; and
if the sufficient statement of that principle be 'A is A,' it may be a
question how Conversion or any other mode of inference can be referred
to it. But if we state it as above (chap. vi. § 3), that whatever is
true in one form of words is true in any other, there is no difficulty
in applying it to Conversion.
Thus, to take the simple conversion of I.,
_Some S is P; ∴ Some P is S._
_Some poets are business-like; ∴ Some business-like men are poets._
Here the convertend and the converse say the same thing, and this is
true if that is.
We have, then, two cases of simple conversion: of I. (as above) and of
E. For E.:
_No S is P; ∴ No P is S._
_No ruminants are carnivores; ∴ No carnivores are ruminants._
In converting I., the predicate (P) when taken as the new subject, being
preindesignate, is treated as particular; and in converting E., the
predicate (P), when taken as the new subject, is treated as universal,
according to the rule in chap. v. § 1.
A. is the one case of conversion by limitation:
All S is P;
∴ Some P is S.
All cats are grey in the dark;
∴ Some things grey in the dark are cats.
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