Timeline for Consistency strength needed for applied mathematics
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| Feb 10, 2011 at 10:59 | comment | added | Marcos Cramer | Nice one. However you then need an even larger cardinal to show that it is consistent to assume the existence of an inaccessible cardinal... This is where my original concern comes back, and with it the possibility to found mathematics empirically. If HOL Light does not have a larger consistency strength then that needed for applied mathematics (now refraining to include a consistency proof of HOL Light into applied mathematics), then HOL Light can be justified on empirical grounds, and you don't need a proof of its consistency. Hence the inaccessible cardinal is not needed in applied math. | |
| Feb 9, 2011 at 19:33 | history | answered | none | CC BY-SA 2.5 |