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'Commentary on 'De Anima'', 'The Possibility of Metaphysics' and 'Mathematics without Foundations'
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5 ideas
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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I do not believe mathematics either has or needs 'foundations' [Putnam]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
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Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
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Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe]
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