From: Eschatoon Magic (eschatoon@gmail.com)
Date: Mon Feb 16 2009 - 01:12:36 MST
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.
I think since the only evidence in favor of the Goldbach conjecture is
that it holds for all even numbers that have been tries so far, and
since the measure of this set is zero compared to that of the set of
all even numbers, the probability of its being true is zero.
Do I agree with "We should strive to preserve endangered human
languages."? Yes, I do.
Why? The only answer I can give is "because".
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.
On Sun, Feb 15, 2009 at 9:19 PM, Johnicholas Hines
<johnicholas.hines@gmail.com> wrote:
> On Sun, Feb 15, 2009 at 2:56 PM, Eschatoon Magic <eschatoon@gmail.com> wrote:
>> What is the relationship between mathematics and ethics/morality?
>> Simple: there is no relation. They are non-overlapping domains of
>> thought.
>
> I agree with you the two domains do not overlap. However, they are
> similar in that they are both distinct from Science.
>
> Mathematics is not falsifiable by experiment. Similarly, Ethics is
> also not falsifiable by experiment.
>
> One person, Alice, cannot convince another person, Bob, of a
> mathematical statement like "There are infinitely many primes.", if
> Alice and Bob do not both believe some basic statements about primes,
> natural numbers, or set theory.
>
> Similarly, Alice cannot convince Bob of an ethical judgment like "We
> should strive to preserve endangered human languages.", if Alice and
> Bob do not both believe some basic judgments about what are good
> actions or good goals.
>
> Johnicholas
>
-- Eschatoon Magic http://cosmeng.org/index.php/Eschatoon aka Giulio Prisco http://cosmeng.org/index.php/Giulio_Prisco
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