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Re: [ontolog-forum] Approximation

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Mon, 25 Jan 2010 15:32:43 -0500
Message-id: <4B5DFFEB.8040600@xxxxxxxxxxx>
Pat,    (01)

I agree with your point, but one could adopt another solution
that does not require a metalevel discussion of possible worlds.    (02)

RS>> Suppose we replace true and real these two words with a prefix
 >> "approximately", what opens up as additional attributes that are
 >> required to complete model theory or a model of whatever    (03)

PH> Good question. There is no definitive answer, but one that can
 > (and has) been given, is that to be approximately true is to be
 > true (in the original, exact, model-theoretic sense) of an
 > approximation, ie of a world which is in some appropriate sense
 > 'sufficiently like' the actual world (assuming that there is
 > a notion of a precise actual world available, of course.)  The
 > great utility of this is that it keeps the semantic theory intact
 > (and unchanged), and simply adds to it a notion of approximation
 > or closeness between worlds.    (04)

Another way to formalize the problem is to add an extra argument
to physical measurements to specify the expected error range.
For example, a common convention is to assume a default error
range of one half of the last significant digit, unless a
different error range is explicitly specified.    (05)

Therefore, the statement "That car weighs 2 tons" would imply
that the weight w is in the range 1.5 < w < 2.5 tons.    (06)

This approach would require the ontology of measurements to
be specified as a pair of numbers (m,t), where m is the mean
value and t is the tolerance or error range.    (07)

Both approaches multiply entities beyond the Ockham limit.
One adds "worlds", and the other adds "error ranges".
It would also be possible to add entities called emotions,
goals, etc.    (08)

John    (09)

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