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'works', 'Frege on Apriority (with ps)' and 'What Required for Foundation for Maths?'
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10 ideas
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17775
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If proof and definition are central, then mathematics needs and possesses foundations [Mayberry]
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17776
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The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry]
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17777
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Foundations need concepts, definition rules, premises, and proof rules [Mayberry]
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17804
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Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902
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Peano arithmetic requires grasping 0 as a primitive number [Burge]
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17792
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1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17793
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It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17794
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Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry]
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17802
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We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry]
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17805
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Set theory is not just another axiomatised part of mathematics [Mayberry]
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