Combining Philosophers
Ideas for Penelope Maddy, H.L.A. Hart and Thomas Hobbes
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16 ideas
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
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18182
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The extension of concepts is not important to me [Maddy]
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18177
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In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
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18164
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Frege solves the Caesar problem by explicitly defining each number [Maddy]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
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17825
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Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy]
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17826
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Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy]
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17828
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Numbers are properties of sets, just as lengths are properties of physical objects [Maddy]
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10718
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A natural number is a property of sets [Maddy, by Oliver]
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18184
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Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
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18185
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Unified set theory gives a final court of appeal for mathematics [Maddy]
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18183
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Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
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18163
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Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
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18186
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Identifying geometric points with real numbers revealed the power of set theory [Maddy]
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18188
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The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
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17618
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Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
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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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17830
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Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy]
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17827
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Sets exist where their elements are, but numbers are more like universals [Maddy]
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