Re: Does logic belong to philosophy or mathematics?



"G. Frege" wrote:
Conbra wrote:


Does logic belong to philosophy or mathematics? Who could tell me.

It used to belong to philosophy but beginning with Boole, Frege, etc.
it became part of mathematics (hence the name /mathematical logic/ for
the modern form of logic).

Actually, Frege wanted to show that mathematics could be reduced
to logic -- the logicist thesis.

Such an idea may have been "in the air" at the time: from Augustus
DeMorgan we have:

"It will hereafter be acknowledged that, though the geometer did
not think it necessary to throw his ever-recurring /principium
et exemplum/ into imitation of /Omnis homo est animal, Sortes
est homo,/ etc., yet the algebraist was living in the higher
atmosphere of syllogism, the unceasing composition of relation,
before it was admitted that such an atmosphere existed."

[Transactions of the Cambridge Philosophical Society, X, 358 (1860)]

I think of /mathematical logic/ as that study that seeks to
found mathematical concepts on a small conceptual basis.

In the hands of mathematicians, logic has become a much more
powerful instrument -- one that is particularly suitable for the
purposes of mathematicians.

No doubt, since mathematicians study logic, it is a part of
mathematics. But on the other hand, mathematicians cannot
take a step without the use of logic.

My own opinion is that logic is epistemologically prior to
and distinct from mathematics.

Still a philosopher can be a logician (if
he isn't afraid of mathematics). And of course there's a field called
_philosophical logic_ (besides the philosophy of logic).

http://en.wikipedia.org/wiki/Philosophical_logic
http://en.wikipedia.org/wiki/Mathematical_logic

You might enjoy

"The Road to Modern Logic -- An Interpretation"
by Jose Ferreiros at:

http://www.math.ucla.edu/~asl/bsl/0704/0704-001.ps

If you can't read Post-Script, Google it for a text-page.

--
hz

Mathematicians are like Frenchmen: whatever you say to them,
they translate it into their own language, and forthwith it
means something entirely different.

- Johann Wolfgang von Goethe -
(also attributed to Bertrand Russell)

--
Posted via a free Usenet account from http://www.teranews.com

.

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