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3 ideas
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) |
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) |
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. |