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. 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: 

    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., Sec. 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).

Now, any relation between two terms may be viewed from either side—­A:  B or B:  A.  It is in both cases the same fact; but, with the altered point of view, it may present a different character.  For example, in the Immediate Inference—­A > B .’. B < A—­a diminishing turns into an increasing ratio, whilst the fact predicated remains the same.  Given, then, a relation between two terms as viewed from one to the other, the same relation viewed from the other to the one may be called the Reciprocal.  In the cases of Equality, Co-existence and Simultaneity, the given relation and its reciprocal are not only the same fact, but they also have the same character:  in the cases of Greater and Less and Sequence, the character alters.