8649 | Two numbers are equal if all of their units correspond to one another [Hume] |
9956 | 'The number of Fs' is the extension (a collection of first-level concepts) of the concept 'equinumerous with F' [Frege, by George/Velleman] |
17442 | Frege thinks number is fundamentally bound up with one-one correspondence [Frege, by Heck] |
14425 | A number is something which characterises collections of the same size [Russell] |
18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
18149 | There are many criteria for the identity of numbers [Bostock] |
10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
8266 | Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe] |
8302 | Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe] |
10133 | Frege's Theorem shows the Peano Postulates can be derived from Hume's Principle [George/Velleman] |
13527 | Frege's cardinals (equivalences of one-one correspondences) is not permissible in ZFC [Wolf,RS] |