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

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 Charlie-Boo Posts: 1,609 Registered: 2/27/06
Re: LOGIC & MATHEMATICS
Posted: May 28, 2013 3:33 PM

On May 28, 8:33 am, Zuhair <zaljo...@gmail.com> wrote:
> 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.

"reduce" is a verb so to "reduce mathematics to logic" means to do
some action,

You are making a statement that at best is true or false. That
statement is not doing something.

And how is "logical discourse" quantified? Is the statement, "For all
mathematical discourses, there is a logical discourse in which it can
be interpreted."?

What have you done that constitutes the action of "reducing"?

C-B

> Logic is responsible for laying down a set of rules that results in
> generation of non contradictory statements in the most general manner.
>
> This mean that for a system to be logical it must be PRODUCTIVE, i.e.
> have a methodology by which one can produce a lot of string of symbols
> (statements), and it must have a truth labeling of those statements in
> such a manner that no statement and its negation are both labeled as
> True. And above all the system must do that in the most general
> manner, so its rules must not be limited to a special sector of
> concepts, in other word it must be topic free.
>
> Mathematics do not have the same 'general' motivation logic has, so
> arguably logic is more general than mathematics. Mathematics mainly
> pivots around strong concepts of structure, construction, succession,
> etc.. many of which are not so general as logical concepts are, the
> later involve itself with general concepts of Truth labeling,
> Predication, Identity, Proof, etc.. Frege added also to those the
> concept of "extending predicates". Those are very general concepts
> that can work virtually in any field of knowledge. The above system is
> also motivated along the same general lines logic has and it use the
> same tools and styles. Seeing that a particularly motivated system
> like second order arithmetic is interpenetrate in such a general kind
> of discourse about logical concepts really reduces mathematics to
> logic, we no longer need those particular motivations about
> constructions and structures nor about space and time that customarily
> mathematics are easily seen to negotiate, those are proved to be so
> STRONG, we don't need them to have mathematical systems, actually very
> weak motivations about general kinds of consistent discourse (i.e.
> logic) are just enough to produce mathematical systems. This reduce
> mathematics down to the level of general analytic machinery, rather
> than it being about a particular high content realm.
>
> In other words mathematics is just an offshoot of symbolic logic.
>
> 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