Combining Philosophers
Ideas for George Boolos, Bernard Linsky and Vittorio Hsle
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10 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 / 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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10833
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Many concepts can only be expressed by second-order logic [Boolos]
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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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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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21723
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The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
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21721
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Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
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21703
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Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
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21714
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The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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21713
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Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
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21715
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For those who abandon logicism, standard set theory is a rival option [Linsky,B]
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