Some men are not cooks ∴ No cooks are some men.
And the same plan has some advantage in converting A.; for by the usual method per accidens, the converse of A. being I., if we convert this again it is still I., and therefore means less than our original convertend. Thus:
All S is P ∴ Some P is S ∴ Some S is P.
Such knowledge, as that All S (the whole of it) is P, is too precious a thing to be squandered in pure Logic; and it may be preserved by quantifying the predicate; for if we convert A. to Y., thus—
All S is P ∴ Some P is all S—
we may reconvert Y. to A. without any loss of meaning. It is the chief use of quantifying the predicate that, thereby, every proposition is capable of simple conversion.
The conversion of propositions in which the relation of terms is inadequately expressed (see [chap. ii., § 2]) by the ordinary copula (is or is not) needs a special rule. To argue thus—
A is followed by B ∴ Something followed by B is A—
would be clumsy formalism. We usually say, and we ought to say—
A is followed by B ∴ B follows A (or is preceded by A).