Timeline for Brouwer vs. Cantor
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2015 at 0:05 | comment | added | Frode Alfson Bjørdal | I am puzzled for the same reason. | |
| Jan 11, 2015 at 23:52 | comment | added | Todd Trimble | What's a little puzzling to me about this discussion is that, to the best of my knowledge, contemporary mathematicians accept Cantor's argument that a set cannot map onto its power set as completely consistent with intuitionistic principles (I am not considering objections coming from predicative mathematics, where power sets are rejected). | |
| Jan 11, 2015 at 23:48 | comment | added | Todd Trimble | Yes, I think the story must be complicated (and unfortunately I'm no scholar here). The second reference touches on Brouwer's notion of choice sequences which were apparently crucial to his conception of the continuum. Thus (and I think this gets closer to your concerns), my rough reading is that Brouwer could not accept the idea of the continuum as a "bag of points" which could be considered in isolation, but considered that the continuum had to be given as a whole (and so he rejected the classical constructions of the continuum). | |
| Jan 11, 2015 at 23:11 | comment | added | Frode Alfson Bjørdal | Thanks for these. I have been aware of Troelstra and others as famous exponents of intuitionism. But your reference here does not to me seem to locate something that vindicates that Brouwer had ideas which somehow successfully (justifies by its own philosophy, as it were) evaded Cantor's idea that there are uncountable sets. | |
| Jan 11, 2015 at 15:17 | history | edited | Todd Trimble | CC BY-SA 3.0 |
added 175 characters in body
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| S Jan 11, 2015 at 15:00 | history | answered | Todd Trimble | CC BY-SA 3.0 | |
| S Jan 11, 2015 at 15:00 | history | made wiki | Post Made Community Wiki by Todd Trimble |