Combining Texts
Ideas for
'Thinking About Mathematics', 'On What There Is' and 'The Central Questions of Philosophy'
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11 ideas
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
1613
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Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine]
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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
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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1616
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Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine]
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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
1615
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Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine]
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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
1614
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Conceptualism holds that there are universals but they are mind-made [Quine]
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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
8730
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'Impredicative' definitions refer to the thing being described [Shapiro]
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