[FOM] 23.99 Carat Gold; foundationalism vs. coherentism

[mjmurphy]

> My knowledge of the history of philosophy is rudimentary.  But it
> seems to me that the original foundationalist was Aristotle, with his
> detailed blueprints on how to organize sciences deductively from first
> principles (archai).  Of course Aristotle recognizes the importance of
> choosing the right axioms or starting points for each science.  He
> develops various methods for doing so, and he says that this is
> ultimately a matter for dialectic.
>
> Foundationalism versus anti-foundationalism is obviously a core
> philosophical question.  All sciences beg to be organized
> foundationally, but mathematics is the one science where the
> foundationalist program has been carried out most fully.  Thus
> mathematics emerges as the grand laboratory of foundationalism.  This
> is why philosophers through the ages have been so intensely interested
> in mathematics, and why philosophy of mathematics has so often been
> dominated by arguments concerning foundationalism, pro and con.

Stephen, this seems incorrect.

It is not the case that the sciences, or scientists at least, "beg to be
organized foundationally".  The position of their science within some
philosophically concocted hierarchy of knowledge is seldom on the mind of
your typical scientist.  Nor is it the case that foundationalism has been
executed "less fully" in the case of, let us say, physics or chemistry, than
in the case of mathematics.  It is probably closer to say that
foundationalist programs have either failed miserably in the former cases,
or failed to produce anything in the way of useful knowledge, and have come
to be generally ignored.

One thing to understand concerning attempts to found empirical knowledge is
that the project was often an attempt to articulate an ars artium, a science
of sciences, which would be written in the language of logic.  Once you have
your ars artium, then it becomes possible to judge a theory of the other
sciences based on the ability to translate the language of this latter
science into the language of the ars artium.  If such a translation is
possible, then the theory is well-founded; if not, then not.  Thus Hume is
willing to consign the works of the scholastics "into the flames" because
definitions of their concepts do not terminate in concepts directly
referrable to sensory experience.  Carnap's critique of Heideigger is based
roughly on the same principle, and the logical positivist division of
language into sense and nonsense (with the language of physicists on one
side and, for example, the language of Freud and crew on the other).
Popper's demarcation principle functions similarly.

Now, before going on, its worth pointing out that such a project is quite
likely to irritate both practitioners of the special sciences and
philosophers of the special sciences, who are apt to wonder how someone
whose competence lies in slinging the symbols  FOL should be qualified to
speak of biology, or sociology, or whatever.  Indeed, Popper for example
managed to say some immensely silly things about evolutionary theory (that
it was not properly empirical) and economics (that it was, at least as
practiced by Hayek).  So the foundationalist comes to look like a kind of
universal kibitzer.

Now, when I say foundationalism with respect to the empirical sciences has
failed miserably or is useless, I mean that 1) people like Carnap (in places
like "The Unity of Science") while arguing that the language of all the
sciences be reduced to a protocol language using only the language of
physics, plus logic and the language of immediate experience (which may or
may not be a sub-language of physics), was forced to admit that it was
impossible to discard the language of the special sciences (even in
principle).  So the reduction or translation amounts to arranging the
special sciences in a hierarchical structure with physics at the bottom.
This is, as I mentioned to Neil Tennent, all quite lovely, but where does it
get you, other than making physicists feel especially special?  I also mean
things like 2) while Carnap had a means by which one could "measure the
degree of confirmation" of a theory in the special sciences, he also
admitted that this measure was in practical terms quite useless in helping
you judge which of two theories were in some sense "better".  And also
things like 3) Hempel's paradox, which is a pseudo-problem generated by this
kind of (logicist) approach to the sciences, not a problem in the sciences
themselves (No scientist would take a purple cow as evidence that all crows
are black).

Stephen concluded:

>Thus mathematics emerges as the grand laboratory of foundationalism.  This
>is why philosophers through the ages have been so intensely interested
>in mathematics, and why philosophy of mathematics has so often been
>dominated by arguments concerning foundationalism, pro and con.

My take on modern philosophy of science is that foundational issues have
simply receded in importance.
Competence here is signaled more by an intense awareness of the history of
the special sciences than the ability to whomp up formalizations.

Neil has yet to respond to my earlier question, so let me ask you.  If set
theory is the foundation of mathematics (the ars artium of mathematics), why
is it that all math is not done in set theory?  Should the other mathies
simply throw in the towel?

Cheers,

M.J.Murphy