On Sep 20, 2008, at 12:56 PM, John F. Sowa wrote:
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.
Thanks, though Im not sure what you mean exactly by a 'discrete category'.
I agree that in principle one might conceive of using a Tarski
style of model theory to relate statements about liquids to the
Um... wait a second. "In principle" , "might conceive"? But (of course) that is exactly hat is done by the 'ontology of liquids' , since that ontology is phrased in FO logic, which has a Tarskian semantics. So it certainly can be done and indeed has been done, apparently (see above) with your approval.
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.
Im not sure what you are talking about. Tarskian semantics does not require any functions to be 'evaluated', whatever that means. Its not a computational theory. Take a statement from the liquids ontology, a simple one such as the axiom that lists the possible ways that liquids can occupy space. This talks of liquids and spaces and ways that the liquid can occupy the spaces, and it - the axiom - has a perfectly conventional Tarskian semantics. What is "not being done" here, according to you?
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:
Of course. Both continuous and discrete, in fact. So what is your point? Nobody, not even Tarski, claimed that meaningful discourse was impossible before his paper was written. All he did was set out to give an analysis of the semantics of such representational uses of language.
1. Those methods achieved a high degree of sophistication
by the end of the 19th century.
2. They were developed to a much higher level during the
20th century for designing airplanes and predicting
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.
If by semantics you mean a theory for evaluating the truth or
falsity of statements in terms of the world, I
Not "evaluating" truth. Semantics is concerned with a deeper, prior issue: defining
truth in the first place. It is probably good to do this before trying to evaluate it, IMO.
that the continuous math used by physicists and engineers has
proved to be far more valuable than Tarski's theory.
This isn't a meaningful claim. There is no contrast here. All that continuous math (all math, in fact) uses
representational language. Tarski was concerned with semantics, with giving an account of how representational languages relate to the worlds they describe. Now, one might claim that Tarski's theory is inadequate because it doesn't apply to the case of continuous math (which is false, but one could claim it); but it simply makes no sense to claim (as you here seem to) that semantics is a different way of describing the world than that used by continuous mathematics. Just ask yourself: could any of that continuous mathematics be written as logical axioms? (Yes.)
I would also claim that Tarski's theory was of ZERO help to
the mathematicians, physicists, and engineers who developed
and used those methods.
No doubt. They weren't doing semantics, and he was. But thats not an interesting observation, nor is it a critique of Tarski (which I gather it is intended to be?)
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