Combining Philosophers
Ideas for Melvin Fitting, George Boolos and Oliver,A/Smiley,T
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6 ideas
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246
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If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491
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Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483
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Mathematics and science do not require very high orders of infinity [Boolos]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833
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Many concepts can only be expressed by second-order logic [Boolos]
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6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247
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Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490
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Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
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