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2 ideas
17783 | A number is not a multitude, but a unified ratio between quantities [Newton] |
Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity. | |
From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2 | |
A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern. |
3663 | How can you contemplate Platonic entities without causal transactions with them? [Putnam] |
Full Idea: Platonism has the attendant problem of how we can succeed in thinking about and referring to entities we can have no causal transactions with. | |
From: Hilary Putnam (Phil of Mathematics: why nothing works [1979], Modalism) |