iagram was to
bring this out, as is done in every exposition of it. Hence
it was called the Square of Opposition. But as a descriptive
title this is a misnomer: it should have been the Square of
Differences in Quantity or Quality. This misnomer has been
perpetuated by appropriating Opposition as a common name for
difference in Quantity or Quality when the terms are the same
and in the same order, and distinguishing it in this sense
from Repugnance or Incompatibility (Tataretus in Summulas,
_De Oppositionibus_ [1501], Keynes, _The Opposition of
Propositions_ [1887]). Seeing that there never is occasion to
speak of Opposition in the limited sense except in connexion
with the Square, there is no real risk of confusion. A common
name is certainly wanted in that connexion, if only to say
that Opposition (in the limited or diagrammatic sense) does
not mean incompatibility.]

[Footnote 2: Cp. Keynes, pt. ii. ch. ii. s. 57. Aristotle laid
down the distinction between Contrary and Contradictory to
meet another quibble in contradiction, based on taking
the Universal as a whole and indivisible subject like an
Individual, of which a given predicate must be either affirmed
or denied.]

[Footnote 3: I have said that there is little risk of
confusion in using the word Opposition in its technical or
limited sense. There is, however, a little. When it is
said that these Inferences are based on Opposition, or
that Opposition is a mode of Immediate Inference, there is
confusion of ideas unless it is pointed out that when this is
said, it is Opposition in the ordinary sense that is meant.
The inferences are really based on the rules of Contrary and
Contradictory Opposition; Contraries cannot both be true, and
of Contradictories one or other must be.]

CHAPTER III.

THE IMPLICATION OF PROPOSITIONS.--IMMEDIATE FORMAL INFERENCE.
--EDUCATION.

The meaning of Inference generally is a subject of dispute, and
to avoid entering upon debatable ground at this stage, instead of
attempting to define Inference generally, I will confine myself
to defining what is called Formal Inference, about which there is
comparatively little difference of opinion.

FORMAL INFERENCE then is the apprehension of what is implied in a
certain datum or admission: the derivation of one proposition,
called the CONCLUSION, from one or m