From: Lee Corbin (lcorbin@tsoft.com)
Date: Wed Jan 22 2003 - 18:23:07 MST
gts writes
> I'm sure you'll agree that mathematics of any kind is properly defined
> as a type of "formal" logic (if not, then I have no idea what you mean
> by "formal").
No, people don't usually consider arithmetic to be formal logic,
for example. IN all the cases I've encountered, formal logic
means the use of sentences of the predicate calculus, or at
least the statement calculus.
For example, http://dec59.ruk.cuni.cz/~peregrin/HTMLTxt/log&mea.htm
"At approximately the same time at which the linguistic turn was finding expression in the writings of Russell, Wittgenstein, Carnap
and others, another important event, closely connected with it, took place as well. This was the birth of formal logic in the strict
sense.
To avoid misunderstanding, let us stress the difference between formal logic and logic that is merely symbolic. Both formal and
symbolic logic are based on the substitution of symbols for natural language statements and expressions; however, whereas within the
merely symbolic approach symbols are employed solely for the purpose of regimentation (in Quine's sense), i.e. of suppressing those
aspects of natural language expressions which are considered irrelevant for the analysis of consequence, within the truly formal
approach the resulting systems of symbols - logical calculi - are taken to be abstract algebraic structures. Aristotle used letters
to represent unspecific terms; hence he could be considered an early symbolic logician. Frege and Russell were symbolic logicians
par excellence; but neither of them was a formal logician.4
It was Hilbert who for the first time viewed logic as a strictly formal matter..."
Or you can do other Google searches and see what "formal logic"
usually means.
> I doubt very much that Darwin could have arrived at his theory without
> an understanding of formal mathematics, even if only of simple
> arithmetic.
You could be correct, psychologically. I really don't know.
But I do know that in his writings he practically never brings
up mathematics. So far as I know.
But I don't think that the meaning of "formal logic" changed while
Einstein was alive. I think that he simply misspoke.
Lee
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