I have already spoken of the Immediate Inferences based on the rules of Contradictory and Contrary Opposition ([see p. 145])
Another process was observed by Thomson, and named Immediate Inference by Added Determinants. If it is granted that "A negro is a fellow-creature," it follows that "A negro in suffering is a fellow-creature in suffering". But that this does not follow for every attribute[7] is manifest if you take another case:—"A tortoise is an animal: therefore, a fast tortoise is a fast animal". The form, indeed, holds in cases not worth specifying: and is a mere handle for quibbling. It could not be erected into a general rule unless it were true that whatever distinguishes a species within a class, will equally distinguish it in every class in which the first is included.
Modal Consequence has also been named among the forms of Immediate Inference. By this is meant the inference of the lower degrees of certainty from the higher. Thus must be is said to imply may be; and None can be to imply None is.
Dr. Bain includes also Material Obversion, the analogue of Formal Obversion applied to a Subject. Thus Peace is beneficial to commerce, implies that War is injurious to commerce. Dr. Bain calls this Material Obversion because it cannot be practised safely without reference to the matter of the proposition. We shall recur to the subject in another chapter.
[Footnote 1:] I purposely chose disputable propositions to emphasise the fact that Formal Logic has no concern with the truth, but only with the interdependence of its propositions.
[Footnote 2:] Mark Duncan, Inst. Log., ii. 5, 1612.
[Footnote 3:] There can be no doubt that in their doctrine of Æquipollents, 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 versâ.
| 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. |