Combining Philosophers
Ideas for B Hale / C Wright, Jackson/Pargetter/Prior and Crispin Wright
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13 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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13869
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Number platonism says that natural number is a sortal concept [Wright,C]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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13870
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We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
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13873
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Treating numbers adjectivally is treating them as quantifiers [Wright,C]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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8788
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Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
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10622
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The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
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13899
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The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C]
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13896
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The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C]
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8783
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Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
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12225
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Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
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7804
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Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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13863
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Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C]
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13895
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The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C]
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12224
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Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]
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