Combining Texts
Ideas for
'Thinking About Mathematics', 'Three Dialogues of Hylas and Philonous' and 'The Principles of Mathematics'
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11 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
14162
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Mathematics doesn't care whether its entities exist [Russell]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
14103
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Pure mathematics is the class of propositions of the form 'p implies q' [Russell]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21555
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For 'x is a u' to be meaningful, u must be one range of individuals (or 'type') higher than x [Russell]
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18003
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In 'x is a u', x and u must be of different types, so 'x is an x' is generally meaningless [Russell, by Magidor]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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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6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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
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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