Combining Texts

Ideas for 'Science and Method', 'Word and Object' and 'Academica'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
10245 One geometry cannot be more true than another [Poincaré]
     Full Idea: One geometry cannot be more true than another; it can only be more convenient.
     From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
     A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17905 Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine]
     Full Idea: The condition on an explication of number can be put succinctly: any progression will do nicely. Russell once held that one must also be able to measure multiplicity, but this was a mistake; any progression can be fitted to that further condition.
     From: Willard Quine (Word and Object [1960], §54)
     A reaction: [compressed] This is the strongest possible statement that the numbers are the ordinals, and the Peano Axioms will define them. The Fregean view that cardinality comes first is redundant.