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'Thinking About Mathematics', 'On Signs (damaged)' and 'Philosophy of Mathematics'
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16 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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9606
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The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
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9612
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There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
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9610
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Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
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9620
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Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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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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9629
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For nomalists there are no numbers, only numerals [Brown,JR]
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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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9639
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Does some mathematics depend entirely on notation? [Brown,JR]
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9630
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The most brilliant formalist was Hilbert [Brown,JR]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
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9608
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There are no constructions for many highly desirable results in mathematics [Brown,JR]
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9645
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Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
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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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