From: Stuart Armstrong (dragondreaming@googlemail.com)
Date: Tue Feb 17 2009 - 07:57:06 MST
> That's an interesting point. Thank you for the description of Godel's
> incompleteness as "Mathematics is an experimental science.", it is an
> intriguing way of looking at it.
Maybe, but it's also false. You can see mathematics as an experimental
science in some ways, but Godel has nothing to do with it. He
demonstrates simply that there exists statements in arithmetic that
cannot be proved or disproved algorithmically; Turign then extends the
result to show that not only does there exists statements of the above
type - but that you cannot be sure to identify one if you meet one.
This has a whole load of philosophical consequences, but bringing in
experiments to mathematics isn't one of them (in fact it shows that
certain questions cannot be decided by any experiment). Mathematical
experiments are a seperate issue, and one that predates Godel.
> The analogy seems obvious, but why should anyone care? I was trying to
> convince people that using moral arguments (normative speech) in a
> community is a perfectly reasonable (rational) thing to do, if the
> community has some shared values that the argument can be based on.
Indeed. And the main thing that underpins all this is that we might
agree, in theory, that values are arbitrary, but, in practice, our
values are very very close together. That's why we can have
constructive arguments; the tension is that it is not clear to people
(especially at the beggining of an argument) what differences come
from slight differences in values and what comes from major
differences in understanding of the consequences.
That's why is and ought are so mixed up in standard discourse, and why
we should try and keep them seperated even when doing "ought" type
arguments. (there's also a certain cowardice behind the distinction -
presenting "is" type arguments means you don't take risks by putting
forwards your values and having arguments about them, and you can
always take refuge by saying that you are simply considering options
or possibilities).
Stuart
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