Greetings :-
Thanks to Jason for distributing Professor Zadeh's proposed
solution, which was originally omitted because of prudent list policy
against distributing attachments.
While his proposal was unsurprising, Professor Zadeh did supply
something which has been missing from this long discussion, and whose
absence has been keenly felt: his specific standard for what
constitutes a 'solution'.
> Note also that the fuzzy logic solution is a solution in the sense that it
> reduces the original problem to a well-defined mathematical problem.
Jason has met this standard, as have eight other probabilists who
offered their solutions to similar problems in these threads, along
with countless other probabilists throughout the decades in the
literature. Professor Zadeh, of course, has also met his standard.
This is progress, because we find ourselves in that most familiar
of situations in non-demonstrative reasoning: people differ about
which 'well-defined mathematical problem' provides the most useful
insight into the challenges posed by the 'original problem'. Further
progress would plausibly occur by comparing the insights offered by
the competing solutions.
To foster that progress, I ask Professor Zadeh to provide one more
definition. What is 'partial truth'? That appears to be the crucial
attribute which, in his opinion, distinguishes his kind of solution
(which does, to his satisfaction, accommodate partial truth) from
probabilistic or otherwise bivalent ones (which, it is said, do not
accommodate partial truth).
If Professor Zadeh obliges, then I ask that his definition move
beyond examples. I confess that I do not see a difference in kind
between the canonical 'Sven is tall' and the usual alternative 'Sven
stands 190 cm.' I understand that the two reports differ in precision,
but understand neither as categorically precise.
The 190 cm. statement even resembles Jaynes' offense, i.e. one
suspects that a physical quantity is being accurately described with
just that precision which could make any difference in the setting
where it is being discussed. Then again, the same might be said of
the first statement, depending upon its setting That would recall Cox'
and Polya's offenses, going way back.
Fond regards.
Paul
