Volker.Halbach at uni-konstanz.de
Mon Apr 19 22:53:28 EDT 1999
>Please keep talking
I do not want to act as a "Shapiro surrogate", but I will try to
explain why many philosophers became anti-foundationalists and why
anti-foundationalism is perhaps not so mad as some people on this
I will try to stick to a definition of foundationalism (in
epistemology) as it can be found in textbooks. Epistemology is
concerned with explaining what makes beliefs justified. Basic
beliefs are beliefs that do not rely on any other beliefs in their
justification (relative to an epistemic agent and time), i.e.,
they are "self-justifying". Foundationalists claim that there are
basic beliefs and that all justified are somehow derived from
these basic beliefs.
Now philosophers tried to find basic beliefs from which at least
all our empirical knowledge is derived (perhaps not in a strict
logical sense). But beliefs like "There is a computer in front of
me" are not basic, because these beliefs are supported by other
beliefs ("I am not dreaming", "This isn't an imitation of a
computer, because I can run TeX on it"). On the other hand, more
modest beliefs like "I have the impression that there is a
computer in front of me" are perhaps basic, but not sufficient as
foundations for empirical knowledge.
Anti-foundationalists do not have to deny that there are commonly
accepted beliefs where discussions stop. But even these commonly
accepted beliefs are in need for justification.
I suppose that many philosophers became anti-foundationalists,
because nobody was able to present basic beliefs acting as
foundations of our knowledge.
I hope this gives at least a clue why anti-foundationalism is now
a strong movement in epistemology.
Now back to maths: As (I think) Friedman pointed out, a statement
is accepted if it is derived from the ZFC axioms. In fact there
are many more commonly accepted beliefs among mathematicians to
which they appeal in proofs but they are hopefully all theorems of
ZFC. But the anti-foundationalist will still ask why you are
justified in your acceptance of the ZFC axioms.
Question for the foundationalists: Do you believe in the axioms of
ZFC and claim that they are self-justifying or self-evident and
not in need of any justification by appeal to some other
principles? And if they are not, what are your basic beliefs?
The anti-foundationalist will claim that there are arguments for
the axioms, perhaps not logically cogent arguments, but at least
some arguments for their plausibility. In fact, there are enough
papers that purport to provide evidence for the ZFC axioms. Thus
the ZFC axioms are not basic beliefs: they are justified by appeal
to other beliefs.
I am not anti-foundationalist, but I also find it very
unsatisfying to accept axioms without having any reason to do so.
I also do not believe that anti-foundationalism and second-order
logic are tied together in some way.
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