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Ideas for 'On What Grounds What', 'On Certainty' and 'Topics'

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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units

12273	Unit is the starting point of number [Aristotle]
	Full Idea: They say that the unit [monada] is the starting point of number (and the point the starting-point of a line).
	From: Aristotle (Topics [c.331 BCE], 108b30)
	A reaction: Yes, despite Frege's objections in the early part of the 'Grundlagen' (1884). I take arithmetic to be rooted in counting, despite all abstract definitions of number by Frege and Dedekind. Identity gives the unit, which is countable. See also Topics 141b9

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.