Combining Texts

Ideas for 'On What Grounds What', 'Nature Without Essence' and 'Logic as Semiotic: Theory of Signs'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

17877	The number series is primitive, not the result of some set theoretic axioms [Almog]
	Full Idea: On Skolem's account, to 'get' the natural numbers - that primal structure - do not 'look for it' as the satisfier of some abstract (set-theoretic) axiomatic essence; start with that primitive structure.
	From: Joseph Almog (Nature Without Essence [2010], 12)
	A reaction: [Skolem 1922 and 1923] Almog says the numbers are just 0,1,2,3,4..., and not some underlying axioms. That makes it sound as if they have nothing in common, and that the successor relation is a coincidence.

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.