Combining Philosophers

Ideas for Panaetius, Thales and Penelope Maddy

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7 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

18190

Completed infinities resulted from giving foundations to calculus [Maddy]

18171

Cantor and Dedekind brought completed infinities into mathematics [Maddy]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis

17615

Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

18196

An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]

18172

Infinity has degrees, and large cardinals are the heart of set theory [Maddy]

18175

For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18187

Theorems about limits could only be proved once the real numbers were understood [Maddy]