Re: Epistemology 201: The Science of Science

From: Wolf Kirchmeir (wwolfkir_at_sympatico.ca)
Date: 02/09/05 

Date: Tue, 08 Feb 2005 20:25:47 -0500

Albert wrote:
> Wolf Kirchmeir wrote:
>
>> Albert wrote:
>> [...]
>>
>>>
>>> Logic was not an invention of mathematics, but rather philosophy.
>>> Mathematics added a new twist to logic with the introduction of
>>> probability logic. I was referring to classical logic. You are
>>> referring to probability logic. FWIW, I totally agree with you that
>>> "mathematics is the study of measurements and their relations."
>>
>>
>>
>> More silliness.
>
>
> Which part?

a) the bit about the invention of logic. A philosopher invented formal
logic, but that doesn't mean logic is a product of philosophy, if onlyu
becasue "philosophy" on Aristotle's time isn't at all what "philosophy"
means nowadays. It would be far more accurate, both historically and
ontologically, to say that logic is the product of Greek science (which
they termed "philosophy"). Or so it seems to me. It's been a long time
simce I read Aristotle and Plato, or commentaries on them.

b) The bit about math. Math is only partly about measurements. In fact,
there is a slew of math which deals with nothing but measurements. Since
measurement in actuality entails errors, this area of math has perforce
expanded into error-correction theory, and is extremely useful, as well
as theoretically intersting. I had to learn a fair *** of measurement
theory when I did engineering (which I didn't finish, since pool and
poker interested me more than practicing problem-solving. I was very
young, you see. :-)) -- FWIW, I suspect that the use of "metric" in ref
to certain spaces has misled you, but without a clearer definition of
what you mean by "measurements", I can't really tell.

[...]
> Well, there seems to be confusion on both sides. You seem to believe
> that all calculation belongs in applied math and that *authentic* math
> is only possible for certain rare and highly gifted persons, such as
> yourself, who have no problem accepting logical absurdities in the name
> of logic.

Well, it seems there is.

I think that arithmetic isn't math, but figuring why arithmetic works is
math. (That's all in NL terms, as far as I can tell. :-)) The Sumerians
and Egyptians knew a lot of integer solutions to a^2 + b^2 = c^2: they
clearly did a lot of arithmetic. We don't know whether they did any
math, ie ask a the general questions about integer triplets that satisfy
that equation, but on the evdince, they never did. Pythagoras did. He
did math. Ditto Euclid, Archimedes, and many other Greeks.

And of course doing math requires calculation, sometimes. But
"calculate" is a vague term here. I myself have used it to mean
"determine the truth values of a complex truth function", which isn't
exactly the same kind of process as summing an infinite series.

Classical logic (I assume you mean Aristotle's rules) has been subsumed
by Boolean algebra, which has been subsumed by set theory. But that's
OK, it's all math. Or all logic, if you like. Sometimes I prefer one
view, and sometimes the other. Depends on the weather, perhaps - I
haven't kept careful records. :-)

As to gifts: I have only average gifts in math, and make many errors,
some which others have been kind enough to point out. (See stephen's
comment on my muddled characterisation of countable/uncountable sets.)
I'm a spectator at a sport that I don't do very well, but know enough
about to admire the skill of the pros. Like hockey. Where I differ from
you, it sometimes seems, and Zick for sure, is that I'm willing to take
correction and coaching when I utter opinions. I don't insist that my
understanding of what a mathematical term "really means" must be right,
nor do I insist that my insight must be true because everybody else
thinks it's daft; etc.

Most mathematicians have rather specialised gifts - it's for example
rare to find that a whiz at number theory is equally adept at topology.

In any case, I enjoy math, I enjoy reading about it, I even from time to
time work through a proof just get a better glimpse of how it really
works. Mathematics is beautiful.

I could now maunder on about the beauty of other arts and sciences, but
that would be getting really off topic for this forum.

HTH

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