(3) If a "not" is placed before as well as after, the resulting forms are obviously equivalent (under Rule 1) to the assertion of the contradictories of the forms on the right (in the illustration of Rule 2).
| Not Not Not Not | All S is "not" P No S is "not" P Some S is "not" P Some S is "not" not P | = No S is P = All S is P = Some S is not P = Some S is P | = Some S is P. = Some S is not P. = All S is P. = No S is P. |
[Footnote 4:] Formal to distinguish it from what he called the Material Obverse, about which more presently.
[Footnote 5:] The mediæval word for the opposite of a term, the word Contradictory being confined to the propositional form.
[Footnote 6:] It is to be regretted that a practice has recently crept in of calling this form, for shortness, the Contrapositive simply. By long-established usage, dating from Boethius, the word Contrapositive is a technical name for a terminal form, not-A, and it is still wanted for this use. There is no reason why the propositional form should not be called the Converse by Contraposition, or the Contrapositive Converse, in accordance with traditional usage.
[Footnote 7:] Cf. Stock, part iii. c. vii.; Bain, Deduction, p. 109.
Chapter IV.
THE COUNTER-IMPLICATION OF PROPOSITIONS.
In discussing the Axioms of Dialectic, I indicated that the propositions of common speech have a certain negative implication, though this does not depend upon any of the so-called Laws of Thought, Identity, Contradiction, and Excluded Middle. Since, however, the counter-implicate is an important guide in the interpretation of propositions, it is desirable to recognise it among the modes of Immediate Inference.