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'On the Question of Absolute Undecidability', 'Quaestiones de Potentia Dei' and 'The Possibility of Metaphysics'
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5 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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17887
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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8297
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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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8266
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Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe]
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8302
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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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