[FOM] still more on Hilbert's #6

Harvey Friedman friedman at math.ohio-state.edu
Sun Jan 25 05:33:58 EST 2004

While perhaps becoming intoxicated over our major agreements, maybe we
shouldn't ignore some significant disagreements.

I'm sure you are tired of this topic, and I don't blame you.

But I think there are some controversial points that the readership may
enjoy thinking about.

I think you are in the happily content silent majority in the world of
scholars today, but there may be something here that is holding back serious
advances in foundations outside math.

On 1/25/04 12:51 AM, "Martin Davis" <martin at eipye.com> wrote:

> This started when I submitted a brief message suggesting that one should
> pay attention to the context in which Hilbert proposed this problem, noting
> that revolutionary developments that Hilbert  couldn't have anticipated
> were just around the corner.

Revolutionary developments sitting on top of halfsense does NOT make the
conversion of the earlier halfsense into sense of any less interest. If
anything, it makes the conversion of the earlier halfsense more urgent -
since it is hopeless to make sense out of halfsense that builds on earlier
halfsense that already has defied efforts to be made sense of.

Of course, I do not want to put people in jail for doing exciting halfsense.
I believe in some reasonable division of labor.

Let me make a counterpoint on your side. It can be argued that, say,
classical physics is so off the mark and wrongheaded that trying to make
sense out of it is doomed, or is at best an exercise which will be useless
for making sense out of revolutionary physics.

I don't think this is true, partly because there is nothing all that wrong
about classical physics, and major ideas from it are essential components in
all later physics. See paragraph *) below. I sincerely hope that it is not
true, as it would make it even harder to make sense of more modern physics.
> I think the problem of the foundations of classical mechanics would have
> seemed much less interesting to Hilbert had he realized it was only a very
> crude approximation to the truth. Harvey thinks otherwise. Short of a
> seance, we aren't going to resolve this question.

Every theory, including relativity theory and quantum mechanics, is a crude
approximation to the truth. There will always be expansions of the frontier.
So under (a strong form of) your way of thinking, I don't see how
foundations of physical science is going to seriously get off the ground.

Classical mechanics, as well as other crude approximations to the truth
called relativity theory and quantum mechanics and string theory and quantum
gravity and big bang theory and "ewqfiqwefhfirterwehf", are in fact known to
be, or undoubtedly are going to be known to be, incorrect in important or
yet to be important contexts. I believe that this in no way diminishes the
importance of converting their halfsense into sense.

*) The fact that various theories are false if not weakened appropriately,
is not decisive. For example, there should no problem making classical
mechanics true provided one puts some appropriate inequalities in.

Coming back to your example of foundational commentary of the philosopher
Berkeley versus Euler's bulling forward with halfsense, I missed an
opportunity to make the following response.

I have always drawn distinctions between talk and criticism, versus real
progress. Suppose Berkeley turned the calculus from halfsense into sense via
epsilon/delta? Then there is no way I would rank the wild calculus
applications of Euler that you referred to, automatically higher. Of course,
there is a lot more to what Euler was able to do, and there is an enormous
quantity as well.  

> What is more important is that it is clear from the last pair of postings
> that Harvey and I are in essential agreement on what counts.
Probably largely true.

Harvey Friedman

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