Combining Texts
Ideas for
'Thinking About Mathematics', 'Essays on Active Powers 3: Princs of action' and 'Sets, Aggregates and Numbers'
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7 ideas
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
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8764
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Categories are the best foundation for mathematics [Shapiro]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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17817
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Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
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8762
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Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
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17815
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We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
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17821
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You can ask all sorts of numerical questions about any one given set [Yourgrau]
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6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
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8760
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Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
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8761
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A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
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