Re: Does logic belong to philosophy or mathematics?

On 6 22 , 6 12 , G. Frege <nomail@invalid> wrote:
On Thu, 21 Jun 2007 17:48:10 -0400, herbzet <herb...@xxxxxxxxx> wrote:

Moreover, this form of logic would still be /mathematical logic/, even
if he succeeded.

No, what do you mean "this form"?

I meant /the modern form/ of logic. (The old form sometimes is refered
to as "traditional logic".)



You mean symbolic logic?

Yeah. Modern Logic, Formal Logic, Symbolic Logic, Mathematical Logic,
as you like it.



I knew Peirce's father Benjamin Peirce was a mathematician,
but Wikipedia says Charles Sanders Peirce got his training
in chemistry:

He went on to obtain the BA and MA from Harvard [doesn't say in
what], and in 1863 the Lawrence Scientific School awarded him
its first M.Sc. in chemistry.

Just found the following:

Who is the most original and the most versatile intellect that the
Americas have so far produced? The answer "Charles S. Peirce" is
uncontested, because any second would be so far behind as not to be
worth nominating. Mathematician, astronomer, chemist, geodesist,
surveyor, cartographer, metrologist, spectroscopist, engineer,
inventor; psychologist, philologist, lexicographer, historian of
science, mathematical economist, lifelong student of medicine; book
reviewer, dramatist, actor, short story writer; phenomenologist,
semiotician, logician, rhetorician and metaphysician. He was, for a
few examples, the first modern experimental psychologist in the
Americas, the first metrologist to use a wave-length of light as a
unit of measure, the inventor of the quincuncial projection of the
sphere, the first known conceiver of the design and theory of an
electric switching-circuit computer, and the founder of "the economy
of research." He is the only system-building philosopher in the
Americas who has been both competent and productive in logic, in
mathematics, and in a wide range of sciences. If he has had any equals
in that respect in the entire history of philosophy, they do not
number more than two.
Max H. Fisch in Sebeok, The Play of Musement

Source:http://www.peirce.org/life.html

F.

--

E-mail: info<at>simple-line<dot>de

I think the logic began since the Syllogism invented by Aristotle at
300 B.C. There are a few logic laws were the research base of logic.
What is the base of the Syllogism? This law came from God or not. If
not, where was this law came from? Now all of the logic laws that
people used more than two thousands could be proved on concept
algebra. That may be decided the logic belong to mathematics.

As we know the concept is the least element of logic. The A, B and C
in syllogism "If A is B and B is C then A is C" ear the concepts. The
connect verb "is" is an compound operation on concept algebra. The
expression of the syllogism on concept algebra is as follows
(C < A) / ((B < A) * (C ) )
The same expression on logic operation on logic algebra (Book "concept
algebra" Part Three) can be expressed as
((A < B) & (B < C)) -> (A < C)
The sign "<" is a compound operation on logic algebra. These two
expressions could be proved as the theorem on different algebra. Which
is the logic base must be clearly if all of the logic laws can be
proved on one kind of the mathematics.

The conclusion is the logic belongs to mathematics.

Conbra

.

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