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| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle |
| Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle. | |||
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |||
| A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction. |
| 13419 | If functions are transfinite objects, finitists can have no conception of them |
| Full Idea: The finitist may have no conception of function, because functions are transfinite objects. | |||
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4) | |||
| A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given? |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status |
| Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |||
| From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |||
| A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |