Hume's principle

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one-to-one correspondence

Gottlob Frege (1848—1925) German philosopher and mathematician, founder of modern logic


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The principle that the number of things with the property F equal the number of things with the property G if and only if there is a one-to-one correspondence between those that are F and those that are G. The attribution to Hume derives from the discussion in Treatise, i. 3. 1: ‘When two numbers are so combined as that the one has always an unit answering to every unit of the other we pronounce them equal; and it is for want of such a standard of equality in extension that geometry can scarce be esteemed a perfect and infallible science.’ The principle was central to Frege, and the ‘neo-Fregean’ approach to the philosophy of mathematics hopes to define the idea of number on the foundation it provides.

Subjects: Philosophy.

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