onversion'; 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. Sec. 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. Sec. 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.

The predicate is treated as particular, when taking it for the new
subject, according to the rule not to go beyond the evidence. To infer
that _All things grey in the dark are cats_ would be palpably absurd;
yet no error of reasoning is commoner than the simple conversion of A.
The validity of conversion by limitation may be shown thus: if, _All S
is P_, then, by subalternation, _Some S is P_, and therefore, by simple
conversion, _Some P is S_.

O. cannot be truly converted. If we take the proposition: _Some S is
not P_, to convert this into _No P is S_, or _Some P is not S_, would
break the rule in chap. vi. Sec.