Combining Philosophers

Ideas for Panaetius, Thales and Penelope Maddy

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8 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17823 If mathematical objects exist, how can we know them, and which objects are they? [Maddy]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
8756 Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17733 We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
18204 Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
18207 Maybe applications of continuum mathematics are all idealisations [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
17829 Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
18167 We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]