[FOM] Tangential Epistemological Comment
a.hazen at philosophy.unimelb.edu.au
Mon Mar 15 23:10:38 EST 2004
Harvey Friedman, writing about a hypothetical alien artifact that
purports to be a hypercomputer, says:
"...experiments are done on the device as a "black box" with absolutely
no understanding whatsoever of its internal mechanism.
"I claim that we would then obtain a "proof" that Goldbach conjecture
is false, that is not as convincing as one would hope, but
substantially more convincing than any knowledge that we presently
have in the sciences and engineering outside mathematics."
I would like to applaud the scare-quotes he has put around "proof"
here. If I were writing very carefully, and not in an informal
symposium like FoM, I would prefer to put his thought by saying that
the experiments would provide EVIDENCE, rather than proof (and go on
to say that this evidence was more convincing than blah blah, and
even that it justified a higher degree of confidence than most
I think we have (as part of the conceptual resources provided by
what philosophers call "ordinary language") a variety of ways of
classifying and evaluating kinds of evidence (in the broadest sense
of the word: grounds for rationally changing our degree of belief in
various propositions) and that it is ***NOT*** the case that they fit
into a single hierarchy of more-to-less convincing (or more-to-less
conclusive). PROOF is a special kind of evidence that is available in
mathematics. Being presented with a proof doesn't automatically
justify complete, 100%, confidence in the truth of the claimed
theorem: authors, and editors and referees, make mistakes. Sometimes
a non-proof may be more convincing (and RATIONALLY more convincing)
than a proof.
Compare legal proceedings. I can readily imagine cases in which
hearsay evidence would raise my degree of subjective confidence in
the guilt of the defendant more than eyewitness testimony, and I
think rationally. (I have good grounds to believe in the reliability
and probity of the person reporting the overheard conversation, I
know the eyewitness's vision is no better than mine ....)
Nonetheless, the eyewitness testimony is, and the hearsay is not,
"admissible in evidence."
(((Apologies for going off on a philosophical tangent not
directly f.o.m.-relevant. I'll try to be good in the future.)))
University of Melbourne
More information about the FOM