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Re: [ontolog-forum] Approximation

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Mon, 25 Jan 2010 16:08:03 -0800
Message-id: <20100126000806.97425138D10@xxxxxxxxxxxxxxxxx>

John and Pat,



Rich Cooper


Rich AT EnglishLogicKernel DOT com


Your discussion is interesting, but it doesn’t fully reflect the two ended nature of communications, IMHO.  The “accuracy” or “fuzziness” of a concept has another aspect.  It can also be explained by iteratively communicated observations from different people; each one in the grouop perceives the world slightly differently, yet communicates it with a supposedly shared word in a supposedly shared language.  The approximations can be, at least in part, due to the wear and tear of concept definitions in communications among the group.  For each participant, a most recently chosen definition is only one in a sequence of changing definitions as the concept is viewed from subjective angles.  The sequence of facts discovered and deduced changes the possible world of that person as the conversation progresses.  


Engineering the (m,t) pairs just sharpens the confusion.  The real issue is to represent the totality of all the viewpoints in a group so that the members can be tracked in a single association with the group.  


So the possible world is constructed inside each listener’s expectations.  The task of a good speaker is to predict the listener’s reactions, and to adapt to them, as needed to communicate the concept as clearly as the speaker can present it.  But each listener in a group still has a different possible world in mind from the next listener, or from the speaker, when the discourse has run.  






I agree with your point, but one could adopt another solution

that does not require a metalevel discussion of possible worlds.


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


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.


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.


Therefore, the statement "That car weighs 2 tons" would imply

that the weight w is in the range 1.5 < w < 2.5 tons.


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.


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.





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