[FOM] Re: Tangential Epistemological Comment

[Don Fallis]

Quoting Allen Hazen:
>     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."

Evidence is used by both mathematicians and juries to determine what the
truth is.  However, in both cases, certain types of evidence are
"inadmissible" when it comes to making this determination.  But, beyond
that, it is not clear to me that your analogy works.  That is, it is
not clear to me that the reason for the inadmissibility of hearsay
evidence in court is anything like the reason for the inadmissibility
of non-deductive evidence in mathematics.

It is my understanding that hearsay evidence is inadmissible because of
the risk that juries will be misled by such evidence.  For example, if
hearsay evidence of a crime were admitted in court, then the defense
would not be able to cross-examine the person that actually witnessed
the crime ("Was there good lighting?", "Do you wear prescription
lenses?", etc.).  As a result, juries might end up putting too much
faith in such evidence.

Of course, as you suggest, hearsay evidence is nevertheless evidence,
and may often be even more reliable than a lot of evidence that is
admitted.  Even so, juries are not allowed to hear such evidence
because (we believe that) they are generally not able to accurately
judge its probative value.  But it is not clear that there is an
analogous explanation of the inadmissibility of non-deductive evidence
in mathematics.  Are mathematicians only able to accurately judge the
probative value of deductive evidence?

take care,
don

PS.  Of course, even if mathematicians can accurately judge the
probative value of non-deductive evidence, they still might want to
restrict themselves to "a special kind of evidence."  But then what is
the unique epistemic value of deductive evidence if it is (at least
sometimes) less rationally convincing?

Don Fallis
School of Information Resources
University of Arizona
http://www.sir.arizona.edu/faculty/fallis.html