Ideas from 'Vagaries of Definition' by Willard Quine [1972], by Theme Structure

[found in 'Ways of Paradox and other essays' by Quine,Willard [Harvard 1976,0-674-94837-8]].

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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
All the arithmetical entities can be reduced to classes of integers, and hence to sets
                        Full Idea: The arithmetic of ratios and irrational and imaginary numbers can all be reduced by definition to the theory of classes of positive integers, and this can in turn be reduced to pure set theory.
                        From: Willard Quine (Vagaries of Definition [1972], p.53)
                        A reaction: This summarises Quine's ontology of mathematics, which tries to eliminate virtually everything, but has to affirm the existence of sets. Can you count sets and their members, if the sets are used to define the numbers?
19. Language / A. Nature of Meaning / 10. Denial of Meanings
Meaning is essence divorced from things and wedded to words
                        Full Idea: Meaning is essence divorced from the thing and wedded to the word.
                        From: Willard Quine (Vagaries of Definition [1972], p.51)
                        A reaction: Quine's strategy is that a demolition of essences will be a definition of meaning. Personally I would like to defend essences, though I admit to finding meaning tricky. That is because essences are external, but meanings are in minds.
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
The distinction between meaning and further information is as vague as the essence/accident distinction
                        Full Idea: The distinction between what belongs to the meaning of a word and what counts as further information is scarcely clearer than the distinction between the essence of a thing and its accidents.
                        From: Willard Quine (Vagaries of Definition [1972], p.51)
                        A reaction: In lots of cases the distinction between essence and accident strikes me as totally clear. Tricky borderline cases don't destroy a distinction. That bachelors are married is clearly not 'further information'.