On Sep 25, 2008, at 3:18 PM, John F. Sowa wrote:
I entirely agree that a mathematical theory, such as Tarski's,
is independent of computation. But any ontology and reasoning
method that is relevant to engineering, computer science, AI,
or the Semantic Web must be computable.
Of course the reasoning methods must be computable, but that does not require a computable semantic
theory. That notion is close to incoherent, in fact, as it would suggest that it is impossible to refer to uncomputable things. But of course we do this all the time. Distant galaxies and sodium atoms are not 'computable', whatever that could possibly mean, but we still can, and indeed do, refer
JFS>> The old logical positivists said that the meaning of a
sentence is its method of verification. Popper emphasized
falsification. But either way, they considered testing
truth values to be an integral part of a theory of meaning.
PH> Maybe they did. However, IMO they were mistaken.
I believe that Carnap et al. were mistaken about many issues,
but not about that one.
Perhaps I have misunderstood what you meant here. Are you claiming that logical positivism represents an alternative theory of truth
, one that you believe is more appropriate than Tarski's theory for ontology engineering?
PH> Semantics does not talk about 'starting assumptions' or
'observed values' or 'unknowns of interest'. Whatever you are
talking about here is not semantics.
Those are topics that were discussed in detail by Carnap and
his friends. Their most common term was 'observable', and they
discussed in detail how observables were related to scientific
Quite. Scientific methodology, and semantics are two different subjects. Popper is usually cited as a philosopher of science.
PH> The commonest textbook notions of limits and continuity are
written in terms of interval sizes (the familiar delta-epsilon
In previous notes, I agreed that such an approach is used in
foundational studies. But practicing mathematicians ignore
those studies as useless for anything they do.
? Do you actually know the mathematical theories of continuity? I was citing mathematical
notions (of limit) here, not 'foundational'.
In summary, restricting the word 'semantics' to a theoretical
notion that cannot be determined in practice is, I believe, odd.
There is a well-defined technical area called 'semantics'. It has a clear focus and a well-established theory and set of methods. It is in constant use. For example, all the recent W3C Web ontology language standards use it in one way or another, as do the fields which developed the dominant inferential machineries in widespread industrial use (including SQL, Prolog and description logics) and it applies directly to the formalisms used throughout ontology engineering. It is not a "theoretical notion" In what is obviously intended by you to be a contemptuous sense (as in "mere theory"). One ignores it at one's peril when writing technical specifications, for example, as many have discovered. And, to repeat, it is called "semantics". Apparently you would prefer that this word have a different meaning: but that is not really a very important issue, seems to me. The fact is, this field, whatever you call it, is of central importance; and we might as well call it by its common name, if only to keep our discussions clear.
I'd be happier with Carnap's idea of 'meaning' as something that
could actually be determined. In any case, there is no point
in continuing to debate our preferences on this issue.
As you wish, but it would be useful if we could at least agree on terminology.
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