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

 Messages: [ Previous | Next ]
 fom Posts: 1,968 Registered: 12/4/12
Re: LOGIC & MATHEMATICS
Posted: May 27, 2013 12:43 PM

On 5/27/2013 10:51 AM, Charlie-Boo 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"?

Historically, mathematics had been seen as treating the science
of number and the science of form. Classes had been considered
the subject of logic. As mathematics developed in the 19th
century, issues associated with geometry motivated a general
arithmetization of mathematics. The Fregean program of
logicism involved establishing the foundations of mathematics
by defining arithmetic in terms of classes.

A more modern author who makes a simple statement of such
is Quine in "Methods of Logic" if I recall correctly.

> see after this first post seem to debate what that means, as well. If
> (since) you are going to give (giving) a formal answer, then what is
> the formal problem? Trigonometry is part of Mathematics. How would
> we "reduce trig to Logic"? Or start with a simple case: What is the
> criteria for something said to reduce number theory to logic?
>
> Computers process only zeros and ones. Anything you do on paper can
> be done with a computer. If 0 is replaced by FALSE and 1 is replaced
> by TRUE, does a computer reduce mathematics to logic?
>

in logic more mathematically. So, your example
notions of logic with the Boolean arithmetical
representation.

This is opposite to what you ask.

Sometimes one sees reference to Boole as being
associated with an algebraic approach to logic
(a Boolean algebra is a logical algebra, right?)
in contrast to the symbolic approach to logic
associated with philosophical treatments.

I would probably classify your reference to
what can be done "on paper" along the lines
of a symbolic approach, and, the Russian
school of constructive mathematics is explicit
in their treatment of number along such lines.

So, to decide the issue, what is a number?

chuckle

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