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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.
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] |
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] |
13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [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] |