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Full Idea
The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle.
Gist of Idea
The old problems with the axiom of choice are probably better ascribed to the law of excluded middle
Source
Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2)
Book Ref
-: 'Philosophia Mathematica' [-], p.225
A Reaction
The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction.
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |