It is only when Opposition is taken to mean merely difference in Quantity and Quality that there can be said to be greater opposition between Contradictories than between Contraries. Contradictories differ both in Quantity and in Quality: Contraries, in Quality only.
There is another sense in which the Particular Contradictory may be said to be a stronger opposite than the Contrary. It is a stronger position to take up argumentatively. It is easier to defend than a Contrary. But this is because it offers a narrower and more limited opposition.
We deal with what is called Immediate Inference in the next chapter. Pending an exact definition of the process, it is obvious that two immediate inferences are open under the above doctrines, (1) Granted the truth of any proposition, you may immediately infer the falsehood of its Contradictory. (2) Granted the truth of any Contrary, you may immediately infer the truth of its Subaltern.[3]
[Footnote 1:] This is the traditional definition of Opposition from an early period, though the tradition does not start from Aristotle. With him opposition (ἀντικεῖσθαι) meant, as it still means in ordinary speech, incompatibility. The technical meaning of Opposition is based on the diagram (given afterwards in the text) known as the Square of Opposition, and probably originated in a confused apprehension of the reason why it received that name. It was called the Square of Opposition, because it was intended to illustrate the doctrine of Opposition in Aristotle's sense and the ordinary sense of repugnance or incompatibility. What the Square brings out is this. If the four forms A E I O are arranged symmetrically according as they differ in quantity, or quality, or both, it is seen that these differences do not correspond symmetrically to compatibility and incompatibility: that propositions may differ in quantity or in quality without being incompatible, and that they may differ in both (as Contradictories) and be less violently incompatible than when they differ in one only (as Contraries). The original purpose of the diagram 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.