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.
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. § 6]; since S, undistributed in the convertend, would be distributed in the converse. If we are told that Some men are not cooks, we cannot infer that Some cooks are not men. This would be to assume that 'Some men' are identical with 'All men.'
By quantifying the predicate, indeed, we may convert O. simply, thus: