From: gts (gts_2000@yahoo.com)
Date: Wed Jan 22 2003 - 08:34:43 MST
Lee Corbin wrote:
>gts wrote:
>> I think Einstein was speaking pragmatically. I would paraphrase his
>> statement thusly:
>>
>> "Scientific progress has depended upon two things: 1) formal logic,
>> especially mathematics, and 2) the philosophy of empiricism."
>
> Well, I'd still take out the word "formal". My whole point
> was that formal logic is merely an abstract codification of
> logic.
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").
And, as the saying goes, "Mathematics is the hand-maiden of science."
> Consider Darwin's work alone:
> exceedingly empirical, but so far as I know, entirely
> without mathematics. And he's considered by many, including
> me, to be the greatest scientist of all time.
I doubt very much that Darwin could have arrived at his theory without
an understanding of formal mathematics, even if only of simple
arithmetic.
I admit however that Darwin is an interesting case. You may realize that
your argument here with respect to Darwin is related to one of the
arguments trotted out by creationists: that biological macro-evolution
is not a proper scientific theory in that it has never been observed or
quantified in any empirical way. Micro-evolution (concerning variations
within a species) is a proper scientific theory, they say, but
macro-evolution (concerning the origin of species) is not.
However, after Mendel, I think it is wrong to state that the modern
theory of evolution does not depend on formal mathematical logic. Among
other things, we predict the appearance of genetic traits in formal
statistical terms.
Einstein's statement is, after all, about the *development* of western
science, (as opposed to the origins of scientific insight). In this
respect Einstein was correct even if you are correct about Darwin. The
*development* of the theory of biological evolution has depended heavily
on mathematics.
Einstein's own theory of relativity was conceived intuitively, without
formal mathematics, but it was only via the formal logic (pure
mathematics) of Lorentz that his theory could be developed and
communicated. Imagine Einstein trying to explain relativity to his peers
without recourse to formal mathematics!
-gts
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