LECTURE VIII NEGATION, AND OPPOSITION OF JUDGMENTS
Distinction between Contrary and Contradictory opposition [1]
1. The only important point in the traditional diagram of opposition of Judgments is the distinction between contrary and contradictory opposition, the opposition, that is, between A and E, and the opposition between A and O, or E and I.
[1] Read Bain, pp. 55-6, on “Negative Names and the Universe of the Proposition,” also on “Negative Propositions,” p. 83 ff.; Venn, Empirical Logic, pp. 214—217; Jevons, Elementary Logic, ix., on “Opposition of Propositions”; Mill, ch. iv. § 2.
In Contrary Opposition the one Judgment not only denies the other, but goes on to deny or assert something more besides. The mere grammatical shape “No man is mortal” conceals this, but we easily see that it says more than is necessary to deny the other, “All men are mortal.”
In Contradictory Opposition, the one Judgment does absolutely nothing more than is involved in destroying the other.
The Contrary Negation has the advantage in positive, or at least in definite import.
The Contradictory or pure Negation has the advantage in the exhaustive disjunction which it involves.
This is plain if we reflect that Contrary Negation only {127} rests on the Law of Contradiction, “X is not both A and not A.”
Ordinary Diagram of Opposition of Judgments.