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'works', 'Foundations without Foundationalism' and 'Logic in Mathematics'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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16869
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To create order in mathematics we need a full system, guided by patterns of inference [Frege]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
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13641
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Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
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13676
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Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
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13677
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Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
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13652
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The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro]
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