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Topic: LOGIC & MATHEMATICS
Replies: 96   Last Post: Jun 6, 2013 5:19 AM

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 fom Posts: 1,968 Registered: 12/4/12
Re: LOGIC & MATHEMATICS
Posted: May 29, 2013 8:55 PM

On 5/29/2013 7:13 AM, Julio Di Egidio wrote:
> "fom" <fomJUNK@nyms.net> wrote in message

>> 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.

Date Subject Author
5/26/13 Zaljohar@gmail.com
5/26/13 namducnguyen
5/26/13 Zaljohar@gmail.com
5/26/13 namducnguyen
5/26/13 Peter Percival
5/26/13 namducnguyen
5/26/13 Peter Percival
5/26/13 namducnguyen
5/26/13 Zaljohar@gmail.com
5/28/13 Charlie-Boo
5/28/13 Charlie-Boo
5/26/13 Zaljohar@gmail.com
5/27/13 zuhair
5/27/13 fom
5/27/13 Zaljohar@gmail.com
5/27/13 fom
5/28/13 namducnguyen
5/28/13 Zaljohar@gmail.com
5/28/13 namducnguyen
5/29/13 Peter Percival
5/30/13 namducnguyen
5/30/13 Peter Percival
5/30/13 Peter Percival
5/30/13 namducnguyen
5/31/13 Peter Percival
5/30/13 Bill Taylor
5/30/13 Peter Percival
5/30/13 Zaljohar@gmail.com
5/30/13 Zaljohar@gmail.com
5/30/13 namducnguyen
5/31/13 Peter Percival
5/31/13 Zaljohar@gmail.com
5/31/13 LudovicoVan
5/31/13 fom
5/28/13 Peter Percival
5/28/13 namducnguyen
5/27/13 Charlie-Boo
5/27/13 fom
5/28/13 Charlie-Boo
5/28/13 fom
6/4/13 Charlie-Boo
6/4/13 fom
6/5/13 Zaljohar@gmail.com
5/28/13 Zaljohar@gmail.com
5/28/13 LudovicoVan
5/28/13 ross.finlayson@gmail.com
5/28/13 LudovicoVan
5/28/13 LudovicoVan
5/28/13 fom
5/29/13 LudovicoVan
5/29/13 fom
5/30/13 LudovicoVan
5/29/13 fom
5/30/13 LudovicoVan
5/30/13 fom
5/31/13 LudovicoVan
5/31/13 Zaljohar@gmail.com
5/31/13 LudovicoVan
5/31/13 ross.finlayson@gmail.com
6/1/13 LudovicoVan
6/1/13 namducnguyen
6/1/13 ross.finlayson@gmail.com
6/2/13 LudovicoVan
6/2/13 ross.finlayson@gmail.com
6/3/13 Shmuel (Seymour J.) Metz
6/3/13 ross.finlayson@gmail.com
6/4/13 LudovicoVan
6/4/13 namducnguyen
6/4/13 Peter Percival
6/5/13 Shmuel (Seymour J.) Metz
6/5/13 fom
6/6/13 Peter Percival
5/31/13 fom
6/1/13 LudovicoVan
6/1/13 fom
6/2/13 ross.finlayson@gmail.com
6/2/13 fom
6/2/13 Herman Rubin
6/2/13 fom
6/2/13 LudovicoVan
6/3/13 Herman Rubin
6/3/13 Peter Percival
6/4/13 Herman Rubin
6/4/13 Peter Percival
6/4/13 Peter Percival
6/1/13 fom
6/1/13 LudovicoVan
6/1/13 namducnguyen
6/5/13 Peter Percival
6/1/13 fom
6/2/13 LudovicoVan
6/2/13 fom
5/28/13 Zaljohar@gmail.com
5/28/13 Charlie-Boo
5/27/13 Zaljohar@gmail.com
5/28/13 Charlie-Boo
5/30/13 Zaljohar@gmail.com