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2 ideas
| 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. |
| 5202 | Maths and logic are true universally because they are analytic or tautological [Ayer] |
| Full Idea: The principles of logic and mathematics are true universally simply because we never allow them to be anything else; …in other words, they are analytic propositions, or tautologies. | |
| From: A.J. Ayer (Language,Truth and Logic [1936], Ch.4) | |
| A reaction: This is obviously a very appealing idea, but it doesn's explain WHY we have invented these particular tautologies (which seem surprisingly useful). The 'science of patterns' can be empirical and a priori and useful (but not tautological). |