Combining Texts
Ideas for
'Thinking About Mathematics', 'Psychology from an empirical standpoint' and 'The Possibility of Metaphysics'
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10 ideas
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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8298
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Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe]
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8311
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If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
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8310
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Does the existence of numbers matter, in the way space, time and persons do? [Lowe]
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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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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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