Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Zaljohar@gmail.com Posts: 2,665 Registered: 6/29/07
Re: LOGIC & MATHEMATICS
Posted: May 26, 2013 3:41 PM

On May 26, 4:49 pm, Nam Nguyen <namducngu...@shaw.ca> wrote:
> On 26/05/2013 3:52 AM, Zuhair wrote:
>
>
>
>
>
>
>
>
>

> > On May 26, 11:03 am, Nam Nguyen <namducngu...@shaw.ca> wrote:
> >> On 26/05/2013 12:52 AM, Zuhair wrote:
>
> >>> Frege wanted to reduce mathematics to Logic by extending predicates by
> >>> objects in a general manner (i.e. every predicate has an object
> >>> extending it).

>
> >> [...]
>
> >>> Now the above process will recursively form typed formulas, and typed
> >>> predicates.

>
> >> Note your "process" and "recursively".
>
> >>> As if we are playing MUSIC with formulas.
>
> >>> Now we stipulate the extensional formation rule:
>
> >>> If Pi is a typed predicate symbol then ePi is a term.
>
> >>> The idea behind extensions is to code formulas into objects and thus
> >>> reduce the predicate hierarchy into an almost dichotomous one, that of
> >>> objects and predicates holding of objects, thus enabling Rule 6.

>
> >>> What makes matters enjoying is that the above is a purely logically
> >>> motivated theory, I don't see any clear mathematical concepts involved
> >>> here, we are simply forming formulas in a stepwise manner and even the
> >>> extensional motivation is to ease handling of those formulas.
> >>> A purely logical talk.

>
> >> Not so. "Recursive process" is a non-logical concept.
>
> >> Certainly far from being "a purely logical talk".
>
> > Recursion is applied in first order logic formation of formulas,
>
> Such application isn't purely logical. Finiteness might be a purely
> logical concept but recursion isn't: it requires a _non-logical_
> concept (that of the natural numbers).
>

> > and all agrees that first order logic is about logic,
>
> That doesn't mean much and is an obscured way to differentiate between
> what is of "purely logical" to what isn't.
>

Recursion utilized in first order logic is to me a part of logic, so
is that utilized here.

Zuhair

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