Timeline for Is there any physical or computational justification for non-constructive axioms such as AC or excluded middle?
Current License: CC BY-SA 4.0
9 events
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| Mar 24, 2019 at 11:18 | comment | added | Franka Waaldijk | yes, this is what i meant. intuitionistic math has raised awareness of different views and approaches, and i believe that almost all of Brouwer's 'revolutionary' (or even 'mystic') views have already found their place within classical math, albeit mostly under a very different name and with little acknowledgment. Brouwer was unpopular in foundations' circles, and to this day people are reluctant to associate themselves with intuitionistic math... To me, what counts in the long run is that the ideas are picked up nonetheless. | |
| Mar 23, 2019 at 22:11 | comment | added | user44143 | Seeing reals as potential infinities and without equivalence classes seems like a sensible physical heuristic. Is this connected to the historical claim in your comment, that intuitionist math has already had a pervasive influence on classical physics? | |
| Mar 23, 2019 at 19:51 | comment | added | Franka Waaldijk | @MattF. i updated to reflect your questions... cheers, frank | |
| Mar 23, 2019 at 19:50 | history | edited | Franka Waaldijk | CC BY-SA 4.0 |
added an update to refglect the questions in the comments
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| Mar 14, 2019 at 15:25 | comment | added | Franka Waaldijk | your second comment does not exude a great confidence in my answer however... but such a position is not uncommon, especially of course in people with little knowledge of constructive mathematics. (on the other hand i know you to be well enough versed in Bishop-style mathematics, so perhaps i'll elaborate the following short response also in the answer above.). the short of it is that intuitionistic mathematics has already had a pervasive and irreversible influence on classical mathematics and physics, even if no one cares to explicitly credit intuitionistic math for this. | |
| Mar 14, 2019 at 15:16 | comment | added | Franka Waaldijk | @MattF. thank you for your questions! please give me some time to write a response, i'm quite swamped at the moment. i think i will add my response to the answer above, since it needs some more words and formatting than the comments' formatting provides. | |
| Mar 9, 2019 at 20:42 | comment | added | user44143 | An alternative point of view is: 100 years after the work of Brouwer and Weyl, 85 years after Heyting, 65 years after Markov, 50 years after Bishop, 40 years after the synthetic differential geometers....if we don't have any noteworthy physical insights yet from intuitionist and constructive mathematics, maybe it is not such a fruitful framework for looking at the physical world. | |
| Mar 9, 2019 at 18:23 | comment | added | user44143 | Will you say give examples of b and c? For what area of physics is the intuitionist perspective most promising? In what area of physics is the mathematical machinery more complicated than necessary? | |
| Feb 20, 2019 at 11:32 | history | answered | Franka Waaldijk | CC BY-SA 4.0 |