Combining Philosophers
Ideas for H.Putnam/P.Oppenheim, John Richardson and Penelope Maddy
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7 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
18171
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Cantor and Dedekind brought completed infinities into mathematics [Maddy]
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18190
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Completed infinities resulted from giving foundations to calculus [Maddy]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615
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Every infinite set of reals is either countable or of the same size as the full set of reals [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 / 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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