[Footnote 3: There can be no doubt that in their doctrine of AEquipollents, the Schoolmen were trying to make plain a real difficulty in interpretation, the interpretation of the force of negatives. Their results would have been more obviously useful if they had seen their way to generalising them. Perhaps too they wasted their strength in applying it to the artificial syllogistic forms, which men do not ordinarily encounter except in the manipulation of syllogisms. Their results might have been generalised as follows:-- (1) A "not" placed before the sign of Quantity contradicts the whole proposition. Not "All S is P," not "No S is P," not "Some S is P," not "Some S is not P," are equivalent respectively to contradictories of the propositions thus negatived. (2) A "not" placed after the sign of Quantity affects the copula, and amounts to inverting its Quality, thus denying the predicate term of the same quantity of the subject term of which it was originally affirmed, and _vice versa_. All S is "not" P = No S is P. No S is "not" P = All S is P. Some S is "not" P = Some S is not P. Some S is "not" not P = Some S is P. (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 | All S is "not" P = No S is P | = Some S is P. Not | No S is "not" P = All S is P | = Some S is not P. Not | Some S is "not" P = Some S is not P | = All S is P. Not | Some S is "not" not P = Some 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 mediaeval 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.