[Logic by Carveth Read]@TWC D-Link bookLogic CHAPTER V 6/24
An Affirmative Proposition is, formally, one whose copula is affirmative (or, has no negative sign), as _S--is--P, All men--are--partial to themselves_.
A Negative Proposition is one whose copula is negative (or, has a negative sign), as _S--is not--P, Some men--are not--proof against flattery_.
When, indeed, a Negative Proposition is of Universal Quantity, it is stated thus: _No S is P, No men are proof against flattery_; but, in this case, the detachment of the negative sign from the copula and its association with the subject is merely an accident of our idiom; the proposition is the same as _All men--are not--proof against flattery_.
It must be distinguished, therefore, from such an expression as _Not every man is proof against flattery_; for here the negative sign really restricts the subject; so that the meaning is--_Some men at most_ (it may be _none) are proof against flattery_; and thus the proposition is Particular, and is rendered--_Some men--are not--proof against flattery_. When the negative sign is associated with the predicate, so as to make this an Infinite Term (chap.iv.Sec.
8), the proposition is called an Infinite Proposition, as _S is not-P_ (or _p), All men are--incapable of resisting flattery_, or _are--not-proof against flattery_. Infinite propositions, when the copula is affirmative, are formally, themselves affirmative, although their force is chiefly negative; for, as the last example shows, the difference between an infinite and a negative proposition may depend upon a hyphen.
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