Pat, (01)
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. (02)
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. (03)
PH> Maybe they did. However, IMO they were mistaken. (04)
I believe that Carnap et al. were mistaken about many issues,
but not about that one. (05)
PH> Semantics does not talk about 'starting assumptions' or
> 'observed values' or 'unknowns of interest'. Whatever you are
> talking about here is not semantics. (06)
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
methodology. (07)
PH> The commonest textbook notions of limits and continuity are
> written in terms of interval sizes (the familiar delta-epsilon
> definitions).... (08)
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. (09)
In summary, restricting the word 'semantics' to a theoretical
notion that cannot be determined in practice is, I believe, odd.
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. (010)
John (011)
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