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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. |