Re: clarifying clarifying email@example.com (Pat Hayes)
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Date: Fri, 28 Jul 1995 11:58:03 -0500
To: firstname.lastname@example.org (Fritz Lehmann), email@example.com, firstname.lastname@example.org,
From: email@example.com (Pat Hayes)
Subject: Re: clarifying clarifying ontologies
At 8:09 PM 7/26/95 -0500, Fritz Lehmann wrote:
> Pat Hayes wrote:
> Well, mushy philosophizing at the upper end is one hazard to
>be avoided, but getting mired in formal details at the lower end is
>another hazard to be avoided. For example, Hayes himself has pointed out that
>almost all of those formal incompatibilities among his time axiomatizations
>are IRRELEVANT to almost all practical, human-scale activities -- they
>arise only in the extreme borderline cases, where EXACT identity of
>time periods is involved, for example. They involve issues of
>a discrete time-line of tiny moment-points versus a dense line
>like the rationals versus a supposedly Cantor-continous line like
>the Reals. Joe Blow, who needs ontologies of business systems,
>calendars, etc. couldn't care less, particularly since all time
>measurements, like other physical meaurements, are necessarily
>approximate anyway. It is only in the rarefied world of precise
>logic and mathematics that these "continuum" problems even arise
>at all. That's a _drawback_ of typical logical axiomatization.
I agree that Joe shouldnt need to be bothered by issues like these. But he
HAS to be, because if he is careless about them, he is going to get
ensnared in inconsistency and (what seems like) paradox. It all SEEMS
obvious. There are intervals and points, intervals are sets of points and
intervals can meet one another at points...already we are in deep, deep
trouble. Already it seems like we have to make all kind of non-Joe-Blowish
distinctions (between open and closed intervals, things true-AT a point or
happening-AT a point, etc.) and it all gets very murky and complicated. Joe
Blow might not want to be concerned with all this, but he doesnt have the
option, because even apparently quite ordinary, harmless assumptions turn
out to committ him to taking a position in some "rarefied" debate.
I think you have the idea that there is a kind of good robust common-sense
middle ground which we ought to be able to get clear, and then there is a
lot of exotic fussing which is of interest only to mathematicians, and is
just a kind of intellectual decoration, angels-on-pinhead stuff. But this
isnt how it works. The middle-road stuff DOESNT WORK PROPERLY, and we need
to look more closely to try to find out why not, and fix the bugs. That
catalog of mine started with very straightrforward axoims, and was forced
into the 'rareified' world of mathemtaics in order to get the ordinary
intuitions clear. In any case, mathematics isnt rarified in its
subjectmatter, only its methods. The modern mathematical theory of the
continuum is based on very 'common-sense' intuititions about smoothness.
It may be that this is all an artifact of our having to use 'exact logics'.
But we dont have any option, since we dont have any inexact logics (fuzzy
logic, just to make things clear, is MORE exact in this sense), and this
applies to your robust everyman knowledge just as much as to everyone else.
Notice by the way that it ISNT to do with the fact that most measurements
arent exact. One can reason 'exactly' (ie deductively) about imprecise
measurements. Its the consistency enforced by the logic that forces one
into getting the math straight.
> I'm in favor of both kinds of ontologizing, top-down and
>bottom up. I'm even more in favor of figuring out the middle
OK, lets see some examples. I think you will admit most of my temporal
axioms as pretty middling: things like that 'before' is transitive, that if
two intervals both meet an interval then each meets any interval that one
meets. All straightforward gross-topological stuff, which would typically
be built into the machinery of a Joe Blow calendar system.
> (Meanwhile, we really do need a servicable theory of
>approximation. Tolerance theory, Topaloglou's "haze space/time",
>Cohn's and my EGG/YOLK theory, the method of the Rome Planning
>Ontology, and ideas from Measurement Theory may help.
I agree, this is a central need. Ive been trying for a while, and would
welcome any ideas.
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