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Ideas for 'On What Grounds What', 'Reference and Definite Descriptions' and 'A Subject with No Object'

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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

13741	If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J]
	Full Idea: We can automatically infer 'there are roses' from 'there are red roses' (with no shift in the meaning of 'roses'). Likewise one can automatically infer 'there are numbers' from 'there are prime numbers'.
	From: Jonathan Schaffer (On What Grounds What [2009], 2.1)
	A reaction: He similarly observes that the atheist's 'God is a fictional character' implies 'there are fictional characters'. Schaffer is not committing to a strong platonism with his claim - merely that the existence of numbers is hardly worth disputing.

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

9934	Number words became nouns around the time of Plato [Burgess/Rosen]
	Full Idea: The transition from using number words purely as adjectives to using them extensively as nouns has been traced to 'around the time of Plato'.
	From: JP Burgess / G Rosen (A Subject with No Object [1997], III.C.2.a)
	A reaction: [The cite Kneale and Kneale VI,§2 for this] It is just too tempting to think that in fact Plato (and early Platonists) were totally responsible for this shift, since the whole reification of numbers seems to be inherently platonist.