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Single Idea 13741

[filed under theme 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism ]

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'.

Gist of Idea

If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers'

Source

Jonathan Schaffer (On What Grounds What [2009], 2.1)

Book Ref

'Metametaphysics', ed/tr. Chalmers/Manley/Wasserman [OUP 2009], p.358

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.

The 12 ideas from 'On What Grounds What'

13734 Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J]
13739 Maybe categories are just the different ways that things depend on basic substances [Schaffer,J]
13743 We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J]
13741 If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J]
13744 The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J]
13740 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J]
13742 There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J]
13748 Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J]
13747 Supervenience is just modal correlation [Schaffer,J]
13751 If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J]
13749 Belief in impossible worlds may require dialetheism [Schaffer,J]
13752 The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J]