Fwd: Foundations and Foundationalism

[Harvey Friedman]

On Fri, Jun 24, 2022 at 6:40 PM Timothy Y. Chow <tchow at math.princeton.edu>
wrote:

> Harvey Friedman wrote:
> > I don't have the slightest doubt that the great success of
> > foundationalism in mathematics and computer science and electrical
> > engineering can be had in all of science and engineering and possibly in
> > art as well. It's just more difficult to accomplish than in mathematics.
> [...]
> > The reason that foundationalism is so difficult and slow to achieve is
> > that it requires very high levels of disparate abilities that rarely
> > flourish in a single individual. Whereas we all know people in
> > mathematics with uncanny power, and we also know perceptive scholars
> > with strong philosophical instincts, we don't know too many that not
> > only have both but also know how to use them together. The primary
> > example from the 20th century that we all think of is of course Goedel.
> > And in a different realm, there is obviously Einstein.
>
> The main reason I don't believe this is that, other than in mathematics,
> there is no way to settle disagreements definitively.  (Well, there is
> always the oldest and most powerful way of settling disagreements: kill
> those who don't agree with you.  But I mean besides that.)
>

Prospects for settling disagreements at the basic fundamental level in many
fields are actually reasonably good.

Even in f.o.m. there is still a lot of disagreements about the ISMS. But
what we do is move to coherent explanations of the ISMS. Even in f.o.m one
does not literally refute any ISMS. But there is great work that moves to
clarify and delineate ISMS.

Similarly, the prospects are quite good in doing this outside mathematics.
Particularly with sufficiently multi talented people who have the right
incentives.

We have already seen this definitely in computer science. And there is a
hot of hot disagreements about the possibility of using QM to radically
upgrade the capabilities of computer systems. There is slow steady
progress in understanding the prospects of this.

There are major disagreements in statistics, both pure and applied. For
instance so called objective and subjective probability and Bayesian
inference and so forth. Real possibilities for revolutionary work here
also.

Even in Political Philosophy. Just like the Goedel hierarchy in f.o.m.,
there is a spectrum of political philosophies ranging from free market
extremism (the only role of govt is to enforce contracts and control crime)
to Communist extremism (radical forms of Marxism). What are the important
intermediary levels, and how should we meaningfully and productively
classify them? How do we perform some sort of tests as to their actual
consequences in practice? Prospects for this research is rather good.

How do we apply informal reasoning in practical situations such as Court
proceedings? How do we evaluate the evidence of massive 2020 election fraud
which now involves math, science, engineering, and law? A very rich real
world practical issue.

Prospects for foundationalism seems quite good to me. WIsh I was 23 and not
73.

If there is a way to settle disagreements, then there is no need to have
> individuals who are geniuses in several dimensions at once.  Progress can
> be achieved by a group.  Indeed, group progress is the way progress has
> always been achieved, in any arena of human endeavor.
>

I do not believe in foundational advances by committee. E.g., this was
tried with Algol. What happened to Algol?

When I play a classical piano solo piece and have a new style/effect that
has a striking effect on the listener, this requires a subtle combination
of a mixture of complex musical ideas and technical execution, mixed
together. I cannot imagine coming up with anything groundbreaking in this
respect by a committee or even with two people. There is no division of
labor that we know about here. And if there could be a division of labor.

I can see the role of committees when the basic foundational work is done
at the conceptual level. For instance, basic foundational insights might
suggest the construction of computer systems with certain properties, those
properties never having been considered, and may have profound
consequences. Then specialists in the construction of the relevant computer
systems could get involved without necessarily even caring about any
foundational issues. That is an obvious division of labor.

>
> Conversely, if there is no way to settle disagreements, then
> foundationalism is impossible.  Thousands of philosophers throughout
> history have convinced themselves that they have laid solid foundations
> once and for all, but come on...who are they kidding?  The Standard Model
> of physics is an amazing accomplishment, but once we reach the point where
> disagreements can no longer be settled by experiment, what is there left
> to do?
>
> It is bizarre and anomalous that such a high degree of agreement is
> achievable in mathematics.  Despite the success of f.o.m., I think we have
> no good explanation for this anomaly.  I believe that Kripkenstein, or
> what Friedman likes to call Wittgenstein-inspire skepticism, demonstrates
> that even foundationalism in mathematics has its limits.  If it weren't
> for mathematics, there would be overwhelming evidence that such a high
> degree of agreement is impossible (without a correspondingly high number
> of murders).  Somehow we're lucky to have one success story, but I see no
> grounds to be optimistic about similar successes in other arenas, where
> there is no credible mechanism for settling disputes definitively.
>

in my opinion, I think you are attaching too much importance to the
settling of disputes issue. As I said earlier, we still have profound
disagreements about the ISMS, but foundationalism has led to an intricate
deep understanding of various critical aspects of the ISMS, through RM and
hopefully SRM, and other tools.

Harvey Friedman
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