Dear All :-
That was a good thread. Imprecise probabilities and direct inference have
been thoroughly and engagingly treated.
As to the remaining issue, it turns out that all along there have been
probabilistic accounts of bivalent propositions containing qualitative
descriptions, e.g. Cox's 'short, fat old man.' Even Boole trafficked in them.
It is not so bad that some other probabilists disagree with those
accounts. "Probabilists fail to agree" stops no press. What matters
more is that there really is a technically rich alternative to the
abandonment of familiar notions of truth as the price for speaking and
listening as human beings familiarly do.
With a concrete alternative comes the possibility of pragmatic
investigation of otherwise hopeless theoretical wrangles. Does the
speaker of "short, fat old man" intend to testify truthfully, or only
sort-of truthfully? Is it advantageous or disadvantageous that the
listener has a choice between treating that utterance near-enough
categorically or by goodness of fit? If goodness of fit is chosen, are
the best rules for that always compositional, or is flexibility in
representing dependencies often important?
Despite appearances, those are not rhetorical questions. Nature
has surprised all of us before. What the questions are is a big step
up from "we have nothing to say to one another, except that you are
irrational (respectively, unfit to live in the real world) and wrong."
Best to all, regardless of commitments. Special thanks to
Professor Zadeh for his energy in afflicting the comfortable with
exquisite personal grace.
Paul
