Combining Philosophers
Ideas for Hermarchus, George Boolos and Stephen Read
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8 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
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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 / d. Actual infinite
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11025
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Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
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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
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10979
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Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read]
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10980
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Second-order arithmetic covers all properties, ensuring categoricity [Read]
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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 / 5. Definitions of Number / g. Von Neumann numbers
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10997
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Von Neumann numbers are helpful, but don't correctly describe numbers [Read]
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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
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10490
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Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
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