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4 ideas
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
From: Plato (Parmenides [c.364 BCE], 144a) | |
A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
Full Idea: Crudely, the scientist posits only those entities without which she cannot account for observations, while the set theorist posits as many entities as she can, short of inconsistency. | |
From: Penelope Maddy (Naturalism in Mathematics [1997], II.5) |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
Full Idea: It could turn out that all applications of continuum mathematics in natural sciences are actually instances of idealisation. | |
From: Penelope Maddy (Naturalism in Mathematics [1997], II.6) |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
Full Idea: Recent commentators have noted that Frege's versions of the basic propositions of arithmetic can be derived from Hume's Principle alone, that the fatal Law V is only needed to derive Hume's Principle itself from the definition of number. | |
From: Penelope Maddy (Naturalism in Mathematics [1997], I.1) | |
A reaction: Crispin Wright is the famous exponent of this modern view. Apparently Charles Parsons (1965) first floated the idea. |