l.

The manipulation of formulae, indeed, has its own special snare. We are
apt to look for the counterparts of them in the grammatical forms of
common speech. Thus, it might seem to be a fair application of our law
to infer from the sentence, "Wheat is dear," that the speaker had in
his mind that Oats or Sugar or Shirting or some other commodity is
cheap. But this would be a rash conclusion. The speaker may mean this,
but he _may_ also mean that wheat is dear now as compared with some
other time: that is, the Positive subject in his mind may be "Wheat as
now," and the Contrapositive "Wheat as then". So a man may say, "All
men are mortal," meaning that the angels never taste death, "angels"
being the contrapositive of his subject "men". Or he may mean merely
that mortality is a sad thing, his positive subject being men as
they are, and his contrapositive men as he desires them to be. Or his
emphasis may be upon the _all_, and he may mean only to deny that some
one man in his mind (Mr. Gladstone, for example) is immortal. It would
be misleading, therefore, to prescribe propositions as exercises in
Material Obversion, if we give that name to the explicit expression
of the Contrapositive Subject: it is only from the context that we can
tell what this is. The man who wishes to be clearly understood gives
us this information, as when the epigrammatist said: "We are all
fallible--even the youngest of us".

But the chief practical value of the law is as a guide in studying the
development of opinions. Every doctrine ever put forward has been
put forward in opposition to a previous doctrine on the same subject.
Until we know what the opposed doctrine is, we cannot be certain of
the meaning. We cannot gather it with precision from a mere study of
the grammatical or even (in the narrow sense of the word) the logical
content of the words used. This is because the framers of doctrines
have not always been careful to put them in a clear form of subject
and predicate, while their impugners have not moulded their denial
exactly on the language of the original. No doubt it would have been
more conducive to clearness if they had done so. But they have not,
and we must take them as they are. Thus we have seen that the Hegelian
doctrine of Relativity is directed against certain other doctrines
in Logic and in Ethics; that Ultra-Nominalism is a contradiction of
a certain form of Ultra-Realism; and that various theories of
Predication eac