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2 ideas
| 8466 | For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein] |
| Full Idea: Quine feels that the intuitionist's ontology of abstract objects is too slight to serve the needs of classical mathematics. | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: Quine, who devoted his life to the application of Ockham's Razor, decided that sets were an essential part of the ontological baggage (which made him, according to Orenstein, a 'reluctant Platonist'). Dummett defends intuitionism. |
| 8467 | Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein] |
| Full Idea: Intuitionists will not admit any numbers which are not properly constructed out of rational numbers, ...but classical mathematics appeals to the real numbers (a non-denumerable totality) in notions such as that of a limit | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: (See Idea 8454 for the categories of numbers). This is a problem for Dummett. |