From: Johnicholas Hines (johnicholas.hines@gmail.com)
Date: Mon Feb 16 2009 - 05:05:41 MST
On Mon, Feb 16, 2009 at 3:12 AM, Eschatoon Magic <eschatoon@gmail.com> wrote:
> If Alice tries to persuade Bob that "every even number is the sum of
> two prime numbers", Bob could in principle refute her with
> "experimental evidence" (that is, a counter example, which we have not
> found so far). In this sense, mathematics is very much like an
> experimental science, and Godel has proven it.
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.
I was trying to focus on the fact that Mathematics is a separate
domain from Science. We can use scientific methodology (as opposed to
the usual proof-based methodology) INSIDE of this separate domain. But
could any physical experiment CAUSE a mathematical statement to be
true or false? I think not.
> The sentence relates positively to things that I have chosen to hold
> as important values, but there is no way I can "prove" it. I could
> just as easily argue in favor of the opposite, that the sooner we
> adopt a single language the better for everyone. There are things that
> one likes because he does, and most "ethical" or moral statements
> belong to this category.
My analogy is this: If you wrote a moral argument, an attempt to
persuade someone else to action, then you would justify that action by
appealing to more basic moral values. However, if your listener does
not share your more basic moral values, then you will not be able to
persuade them.
This is similar to a mathematician writing a proof, and a listener not
admitting the conclusion because they do not believe the premises.
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.
Johnicholas
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