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Ideas for 'How the Laws of Physics Lie', 'The World as Will and Idea' and 'Universal Arithmetick'

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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic

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.