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Ideas for 'fragments/reports', 'Causes and Counterfactuals' and 'Treatise of Human Nature'

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6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

8649	Two numbers are equal if all of their units correspond to one another [Hume]
	Full Idea: When two numbers are so combin'd, as that the one has always a unit answering to every unit of the other, we pronounce them equal.
	From: David Hume (Treatise of Human Nature [1739], I.III.1)
	A reaction: This became known as Hume's Principle after Frege made use of it for logicism (Foundations §63). It reduces equality to something fairly simple and visual (one-to-one correspondence). But we also say that two logicians or musicians are 'equal' in ability.