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'General Draft', 'Identity' and 'Philosophy of Mathematics'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10201
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Virtually all of mathematics can be modeled in set theory [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10213
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Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro]
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18243
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Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18245
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Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro]
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
16014
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It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]
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