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

 Messages: [ Previous | Next ]
 LudovicoVan Posts: 4,165 From: London Registered: 2/8/08
Re: LOGIC & MATHEMATICS
Posted: May 28, 2013 11:05 AM

"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote in message
> On May 28, 6:17 am, "Julio Di Egidio" <ju...@diegidio.name> wrote:
>> "Zuhair" <zaljo...@gmail.com> wrote in message

>> > On May 27, 6:51 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>> >> On May 26, 2:52 am, Zuhair <zaljo...@gmail.com> wrote:
>>
>> >> > Frege wanted to reduce mathematics to Logic
>>
>> >> What does it mean to "reduce mathematics to Logic"?
>>
>> > It means that any mathematical discourse can be interpreted within a
>> > logical discourse.

>>
>> > Logic is responsible for laying down a set of rules that results in
>> > generation of non contradictory statements in the most general manner.

>>
>> Logic is not just mathematical logic: case in point, you can make of
>> identity an axiom, but the notion of identity itself presupposes an
>> existential stance, so it is not a purely logical notion (in the sense
>> you
>> have just stated). My take is that mathematics uses logic (as the
>> language
>> of mathematics is as well logical) and logic uses mathematics (as the
>> logical calculus is mathematical), but neither can be reduced to the
>> other.
>> Mathematics is the study and applications of "numbers", which is not a
>> purely logical endeavour, while logic is the study and applications of
>> "rational discourse", which is not an essentially mathematical endeavour.
>>
>> 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.
>>
>> Just my 2c, feedback welcome.

>
> Or, both as of objects of plain reason (then with as well geometry):
> the philosophical, logical roots are of the nature of the objects of a
> system with truth.

But logic is not bothered by matters of true, logic is all and only about
validity, i.e. non self-contradiction on logical forms. In particular,
logic is that which abstracts from the specific nature of objects or any
other contingencies. As you may expect, on the other hand, I do not see how
geometry is not just a mathematics.

Then one might retort that the logical true of abstract form constitutes the
object of logic, but that's just a paralogism: logic is purely
self-referential, not just purely abstract as mathematics is.

Julio

> That the or a same fundamental principle can be
> see to bestow upon the objects of logic, numbers, and geometry their
> nature is rather compelling where the same criterion applies to each
> object.
>
> Basically seeing points, numbers, and collections or distinctions as
> primary (in geometry, number theory for mathematics, and set theory
> for proper "logic"), then, how does an axiomless system of natural
> deduction see the inference and deduction of and about them?
>
> Points and their properties of being any different than another point
> can see built a geometry with less axioms than Euclid's, here courtesy
> their being objects, ditto numbers and Peano/Dedekind, ditto sets and
> Zermelo.

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