FOL forces you email@example.com (Fritz Lehmann)
Date: Sat, 24 Sep 94 05:49:28 CDT
From: firstname.lastname@example.org (Fritz Lehmann)
To: email@example.com, firstname.lastname@example.org, email@example.com
Subject: FOL forces you too
Cc: firstname.lastname@example.org, email@example.com
Pat Hayes, responding to Paul van der Vet, wrote:
thinking we often seem able to accept a general proposition as being
consistent with several minor exceptions. This has been modelled by default
logics, nonmonotonic logics, probabilistic logics, etc etc.; but Ive never
seen a really convincing account of it. Repeated use of any one of these
formalisms will gently warp the way you think about how to organise
knowledge: you will becomne sensitive to the order in which things are
asserted; or you will come to think of every universal quantifier as
basically probabilistic and then become worried about how to axiomatise
arithmetic; or you will start to routinely qualify things with 'unless
exceptional' predicates, or whatever. I dont know how to "think it out" for
myself in a completely neutral way, uninfluenced by the formal tool I am
using to write the oprganisation down with, and I suspect it can't be done.
(It may not even make sense, in fact.) Maybe these are only 'very global'
restrictions, but they may nevertheless (or even for just this reason) be
also very pervasive distortions of how we are able to organise things.
Pat, I think you're right (and maybe being charitable) about
those logics, but it's only fair to note that regular logic causes
its own troubles. That's (one reason) why the others were invented.
Your recent email about reconciling the different axiomatizations
of time, which are inconsistent you say (apparently due to effects
of infinitesimals and the like), is disturbing because we know
those differences in extreme borderline cases are non-issues
for us at the commonsense level. We don't care -- we want to get
on with it (except as an interesting logical exercise of course).
Except in the extreme cases, "we know what we mean". It seems that
FOL axiomatization stands in the way of a desired robustness. An
ontology of time for practical use would be _indifferent_ to which
of the base notions are used (points, infinitesimals, discrete
points, intervals, etc.) -- but for the fact that fatal inconsistency
prevents their combination. My stock response has been "Change the
theory -- don't mess with the logic." but this fragility and
sensitivity to rarified decisions during axiomatization gives me
pause to wonder. I'd prefer to discover that a new theory in true
predicate calculus somehow subsumes and harmonizes the competing
time theories, but maybe that won't be possible. Let us know.
Yours truly, Fritz Lehmann
GRANDAI Software, 4282 Sandburg Way, Irvine, CA 92715, U.S.A.
Tel:(714)-733-0566 Fax:(714)-733-0506 firstname.lastname@example.org