Rescuing Frege
By way of a link to a Lambda-the-Ultimate post from Nathan, here’s an interesting paper that attempts to avoid some paradox of Frege’s.
This paper claims that you can allow unrestricted impredicative quantification if you keep careful track of Frege’s sense-reference distinction, and distinguish between predicates and names of predicates. This (if it really works — I haven’t done more than skim the paper yet) would be a different method of using a predicative hierarchy to avoid the paradoxes.
Paul C. Gilmore’s An Intentional Type Theory: Motivation and Cut-Elimination
Disclaimer: I haven’t yet had the time to read the paper, so by “interesting”, I mean that I’m interested in looking at it myself :-P Mostly, this post was to serve as a later reminder for me to read it! And yes, I will indeed post comments & observations when I get around to it.
emma :: Mar.19.2007 :: misc, semantics, logic, philosophy :: 1 Comment »
Man, you’ve got to love the convention of writing, “Thing in strange esoteric symbols. Here, the strange esoteric symbol means something using another strange esoteric symbol. Here, that other strange esoteric symbol means…” Couldn’t you explain it *before* you use it? (It doesn’t help that [#] is used to indicate both semantic types and papers from the references section.)
Utlimately, though, I’m not really clear on what it is he’s trying to solve here, since the words “Frege” and “paradox” don’t occur between page 2 and the references, which makes it really hard to skim. Well, that, and the fact that I don’t speak fluent ITT. If you do read the paper, let us know what it means?