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.

We may, then, state the following rule for the conversion of
propositions in which the whole relation explicitly stated is taken as
the copula: Transpose the terms, and for the given relation substitute
its reciprocal. Thus--

_A is the