Radioactive Rivers
andrew at cee.hw.ac.uk
andrew at cee.hw.ac.uk
Wed Mar 12 04:43:00 CST 1997
David Casseres writes:
> I wuz all
> >> BTW it's not that math is art rather than science -- it's that math is,
> >> well, math. More closely related to logic than to any other discipline.
> Now Andrew sez
> >Err, . . . logic is what a few mathematicians do, not what all of them
> >do. What the mathematicians who don't do logic *do* do is in no way
> >contradictory to or competitive with logic,it just isn't logic.
> Quite so -- I only meant that the mathematician's mental processes (from
> what I can understand of them) are more *like* logic than like other
> disciplines.
Now I am going to have to be doubly anal. What do a mathematician's
mental processes and logic have to do with each other? Are you
labouring under some peculiar delusion that logic is the form of
thought? Or maybe you are hedging with the idea that it is (sometimes)
a close approximation? Well, if so you've run up against the mother of
all category mismatches. Logic can be used to formulate certain
reasoned arguments, particularly mathematical proofs. What does this
have to do with `mathematician's mental processes' (whatever they
are)?
Don't tell me, since mathematicians produce proofs when they reason
then what they are doing must be involve some mental activity which
follows a similar order and organization to the proof. nix? That's
about as dumb as saying that a photographer must visualize every photo
s/he takes in order to be able to take it. Most mathematicians have
attested to the experience of sitting out a proof while the thinking
goes on in the backgrond and then the sudden click as they understand
the real nature of their problem and its solution (not really any such
dichotomy - more that your vision of a certain area crystallizes and
clarifies). Writing out the proof is merely a question of traversing
familiar ground and talking about it in a familiar, almost native,
language. You don't think about the grammar or syntax of a proof
(i.e. the results inferred at each stage and the rules of inference
employed) as you write it, just as you don't think about the grammar
and syntax of your native tongue as you speak. This myth of logic as
the form of thought is one of the most pernicious evils in our Greek
heritage. Logic merely serves as a vehicle for the *expression* of a
small and tightly circumscribed family of arguments. It's a nice
formalism in its place. Out of it it's the biggest fly trap I have
ever encountered.
> Cheers,
> David
Cheers. I'll have pint of Guinness.
Andrew Dinn
-----------
And though Earthliness forget you,
To the stilled Earth say: I flow.
To the rushing water speak: I am.
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