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Ideas for
'Frege's Concept of Numbers as Objects', 'Hat-Tricks and Heaps' and 'What Required for Foundation for Maths?'
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19 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
17441
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Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck]
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13862
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There are five Peano axioms, which can be expressed informally [Wright,C]
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17853
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Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C]
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17854
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What facts underpin the truths of the Peano axioms? [Wright,C]
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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 / 5. Definitions of Number / c. Fregean numbers
13894
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Sameness of number is fundamental, not counting, despite children learning that first [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10140
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We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K]
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8692
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Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend]
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17440
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Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck]
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13893
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It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
13888
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If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C]
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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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