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Ideas for 'fragments/reports', 'Word and Object' and 'Knowledge and the State of Nature'

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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.