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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: Jun 2, 2013 10:20 AM
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On 6/2/2013 7:49 AM, Herman Rubin wrote:
> On 2013-06-01, Julio Di Egidio <julio@diegidio.name> wrote:
>> "fom" <fomJUNK@nyms.net> wrote in message
>> news:9bWdnVL04P_k_DTMnZ2dnUVZ_t6dnZ2d@giganews.com...

>>> On 5/31/2013 10:36 AM, Julio Di Egidio wrote:
>
>>>> Isn't indeed self-referentiality
>>>> (circularity) the essential character of the (any) purely logical
>>>> system?

>
>>> My answer to that is yes.
>
>>> I have done a great deal of work to understand how modern mathematical
>>> logic has reached the point where its foundations are almost
>>> exclusively focused on non-circularity. So, while you see this
>>> condition as a matter of fact, such a claim in the mathematics
>>> community may get you some metaphorical version of tar and feathers.

>
>> My point was that mathematical logic is not logic, it's mathematics: it's an
>> abuse of language. Then I don't see why the mathematician should flame the
>> logician for a claim on logic, all the more so when the logician in question
>> is saying that mathematics cannot be reduced to logic in any meaningful
>> sense (and vice versa). In simpler terms, what I can see in the logistic
>> approach is, firstly reduce all endeavours to mechanics, then call
>> mathematics logic, finally assert that all derives from logic.

>
> Mathematical logic is not all of logic, but it is logic, not
> mathematics. There is more to the logic which is used by
> mathematicians, such as in metamathematics, than is in the
> first order predicate calculus, which is what is used in
> mathematical proofs. There are metamathematical proofs of
> mathematical theorems which do not have mathematical proofs.
>

Out of curiosity, could you give an example of
such a theorem?

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

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