Combining Texts
Ideas for
'Unconscious Cerebral Initiative', 'Naturalism in Mathematics' and 'Introduction to the Philosophy of Mathematics'
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9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17928
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Ordinal numbers represent order relations [Colyvan]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17923
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Intuitionists only accept a few safe infinities [Colyvan]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
18190
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Completed infinities resulted from giving foundations to calculus [Maddy]
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18171
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Cantor and Dedekind brought completed infinities into mathematics [Maddy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
18172
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Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
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18175
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For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
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18196
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An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
17941
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Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18187
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Theorems about limits could only be proved once the real numbers were understood [Maddy]
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