"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'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>
(By the way, your news: links do not work, at least not for me.)