Pat, (01)
I like your ontology of liquids, which I discussed in my KR book.
It is a very good illustration of the complex issues about mapping
discrete categories to a continuous world. (02)
I agree that in principle one might conceive of using a Tarski
style of model theory to relate statements about liquids to the
world. But in practice, the exercise of evaluating Tarski's
function to determine whether any particular statement about
liquids is true or false in terms of the world is never done. (03)
But long before Tarski published his famous paper, physicists,
mathematicians, and engineers had been applying continuous
methods to make generalizations about fluids, make measurements
in terms of them, and reason about them: (04)
1. Those methods achieved a high degree of sophistication
by the end of the 19th century. (05)
2. They were developed to a much higher level during the
20th century for designing airplanes and predicting
the weather. (06)
3. Those methods make accurate predictions of the truth or
falsity of many important statements about the world,
and the experimental methods confirm their accuracy. (07)
If by semantics you mean a theory for evaluating the truth or
falsity of statements in terms of the world, I would claim
that the continuous math used by physicists and engineers has
proved to be far more valuable than Tarski's theory. (08)
I would also claim that Tarski's theory was of ZERO help to
the mathematicians, physicists, and engineers who developed
and used those methods. (09)
John (010)
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