On 5/29/2013 7:13 AM, Julio Di Egidio wrote: > "fom" <fomJUNK@nyms.net> wrote in message > news:kOadnWJJuKCozzjMnZ2dnUVZ_qCdnZ2d@giganews.com... >> On 5/28/2013 8:17 AM, Julio Di Egidio wrote: > <snipped> > >> Although generally ignored, Kant invoked a strict demarcation >> between logic and mathematics. Frege's logicism is essentially >> the idea that one can have "logical objects" and this had been >> one of the things that Kant had rejected. > > Of course Kant rejected it: "logical object" is an oxymoron, what is > rather defended is just the original meaning of logic on a side and of > mathematics on the other. -- Then some would ask for definitions, > which would make an interesting aside, on definitions... Anyway, as a > great book on the matter of what logic is, I'd suggest P. F. Strawson, > "Introduction to Logical Theory" (along the lines of the analytic > school, with great attention to foundations and demarcations).
I am a huge fan of Strawson. His paper "On referring" had been an opening salvo in criticism of Russellian description theory. And, I have read his book on "Individuals" where his discussion of identity distinguishes between qualitative and quantitative. His example of the difference invokes geometric relations in contrast with the assertions of logicism and logical atomism. This particular idea is important to me.
However, I have not had the opportunity to read the book you mention. Well, maybe I can visit amazon in about two weeks...
> >>> I'd think the only way to operate the "unification" you have in mind is >>> by reducing *everything* to just its operational side, the calculus: >>> then there is not even any difference left between logic and >>> mathematics, indeed you'd have destroyed the very nature of both. >> >> This is exactly how I feel when I run into views >> that reject model theory. I am at a loss of how >> a "syntax only" view of mathematics is coherent. > > Reductionism and scepticism, de-spiritualisation and weak thinking, etc. > etc.: since the advent of Hume, coherent with a systematic politics of > the demolition of western, then global rationality and culture. On > this, here is a very nice excerpt from D. C. Williams, "The Ground of > Induction": <http://web.maths.unsw.edu.au/~jim/williams.html> >
Interesting response. It is a difficult problem to mount a successful academic defense against Humean skepticism.
Opinions demeaning Kant almost always seem misplaced because they rarely reflect an understanding that Kant had been motivated by finding a response to Hume.
> (By the way, your news: links do not work, at least not for me.) >
Thanks. In the future I will have to take the time to find http links. I just did not realize there was a problem for others.