Klarinet Archive - Posting 000260.txt from 2009/02

From: Michael Nichols <mrn.clarinet@-----.com>
Subj: Re: [kl] Fair Use
Date: Thu, 12 Feb 2009 00:27:13 -0500

On Wed, Feb 11, 2009 at 10:03 PM, Alexander Brash
<brash@-----.edu> wrote:

> Yikes! I'm sure I'm getting a reputation for being Jonathan's lapdog, but
> seriously, the guy has a Physics degree from Harvard, trust me he doesn't
> need you to derive DeMorgan's laws for him.....

Are you saying that if I use logic to refute a fallacious argument he
makes then I'm wasting my time because, as someone with a Physics
degree from Harvard, he already knows what he's saying is baloney?
Maybe you're not such a lapdog after all! :-)

> On Feb 11, 2009, at 10:49 PM, Michael Nichols wrote:

>> Truth and provability are not one and the same.
>> Ever heard of Goedel's Incompleteness Theorem?
>
> Which has nothing to do with the matter at hand - you're simply trying to
> show off?

No. Jonathan challenged the list to prove that his statement is
false, implying that if no one can, it must be true. I'm saying that
just because you can't prove something with logic (like the falsity of
Jonathan's statement) doesn't mean it isn't true (i.e., just because
you can't use logic prove Jonathan's statement is false doesn't mean
that it isn't false).

Goedel's theorem is a special case of this phenomenon. Informally
speaking, Goedel says that any formal system that is sufficiently
expressive to describe the natural numbers will contain true
statements that cannot be proven within that system. You can
generalize from this that just because you make a statement in a
formal system and fail to be able to prove it within the bounds of the
system, that doesn't mean it isn't true. In other words, whether
something is provable and whether something is true are two entirely
different questions.

> See, I can read the GEB too!

Actually, I've never read that book. I did take a course on
computability theory (a topic germane to computer science), though,
where we learned about Goedel numbering and the Incompleteness
Theorem.

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