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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 5:52 AM

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, and
all agrees that first order logic is about logic, similarly here
although recursion is used yet still we are speaking about logic,
formation of formulas in the above manner is purely logically
motivated.

>
>

> > The surprise is that Second order arithmetic is interpretable in the
> > above LOGICAL system.

>
> > Thus highly motivating Logicism!
>
> > So mathematics is formed in the womb of logic.
>
> > Frege was not far after all.
>
> --
> ----------------------------------------------------
> There is no remainder in the mathematics of infinity.
>
>                                        NYOGEN SENZAKI
> ----------------------------------------------------

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