Combining Texts
Ideas for
'Thinking About Mathematics', 'Frege's Concept of Numbers as Objects' and 'On Wisdom'
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15 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 / c. Neo-logicism
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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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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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8744
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Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
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8749
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Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
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8750
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Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
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8752
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Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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8753
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Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
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8731
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Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
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8730
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'Impredicative' definitions refer to the thing being described [Shapiro]
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