What Rests On What? The Proof-Theoretic Analysis Of Mathematics (1992)
| Venue: | Proc. 15 th International Wittgenstein Symposium |
| Citations: | 9 - 1 self |
BibTeX
@INPROCEEDINGS{Feferman92whatrests,
author = {Solomon Feferman},
title = {What Rests On What? The Proof-Theoretic Analysis Of Mathematics},
booktitle = {Proc. 15 th International Wittgenstein Symposium},
year = {1992}
}
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Abstract
analysis goes beyond concrete analysis by its use of arbitrary spaces of various kinds, e.g. metric spaces, Banach spaces, Hilbert spaces, etc. Moreover, for functional analysis, applications often involve spaces of functions such as the L p spaces, and, more abstractly, spaces of functions between give spaces. Thus the mathematics prima-facie requires variable types X;Y; : : : to represent talk about arbitrary spaces (of the kinds indicated) and highertype constructions such as of the type X ! Y of all functions from X to Y , from which function spaces are constructed. It happens that for most of the applications of abstract analysis one deals with separable spaces, i.e. those X for which there is a countable dense subset X 0 whose completion (under a suitable metric or norm) is X. Talk about such X may informally be recast by talk about X 0 , and the latter, being countable, may be coded as a subset of the natural numbers. It is in this way that parts of abstract analysis are indir...
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