ABSTRACT
Among the most unfortunate ambiguities of language only, unaccompanied by any confusion of thought, are those expressions which we so frequently qualify by the words exclusive and inclusive. Whether the termini or extreme cases are to be both taken in, both left out, or one taken in and one left out, is a matter which often requires an additional sentence. In mathematics, no ambiguity is more common than a statement about greater or less, which leaves it uncertain whether the extreme case, namely equality, is or is not included. In logic, the same thing occurs in the propositional forms. ‘Every X is Y’ would be commonly understood as meaning that X is not coextensive with Y, though the extreme case, that in which there are no more Ys than A’s, would not be held formally excluded. The distinction of these two cases led Aristotle to what have since been called the predicables. Returning to the master himself, and not attending to his followers, we find the distinction of genus, of definition or property (words the distinction of which is extra-logical), and of accident. When all the A’s are some (only) of the Ys, Yis the genus of X; when all the A’s, and no other things, are Ys, Y is the definition or property of X (Thomson: Outlines of the Laws of Thought, p. 146).
