### Ideas from 'Review of Tait 'Provenance of Pure Reason'' by Charles Parsons [2009], by Theme Structure

#### [found in 'Philosophia Mathematica' (ed/tr -) [- ,]].

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###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
 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.
###### 6. Mathematics / C. Sources of Mathematics / 8. Finitism
 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?
###### 7. Existence / D. Theories of Reality / 10. Ontological Commitment / e. Ontological commitment problems
 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.