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 ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: LOGIC & MATHEMATICS
Posted: May 26, 2013 9:49 AM

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.

> similarly here
> although recursion is used yet still we are speaking about logic,
> formation of formulas in the above manner is purely logically
> motivated.

"Purely logically motivated" isn't the same as "purely logical".

--
----------------------------------------------------
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