On Sep 26, 2008, at 12:29 AM, John F. Sowa wrote:
As I said, we have no disagreement about Tarski's semantics for
FOL (or extensions of it to other versions of logic) when applied
to mathematical sets, such as the integers. The title of Tarski's
famous paper was "The Concept of Truth in Formalized Languages."
Because a language is itself formalized, that does not require or even imply that it can only speak of mathematical entities. Tarski's main example was the assertion that snow is white, and he was talking about snow
, not a mathematical simalcrum of snow.
Maybe this misapprehension is the source of your blind spot with regard to semantics. FOL is not restricted in its subject-matter to only speak about mathematical sets. The Tarskian universe is a set, but that isn't what the formalism talks about. It talks about the elements of that universe, and those elements can be anything.
PH> 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?
No. I am claiming that Carnap, Popper, et al. were addressing
the question of how scientific methodology can observe objects
and events in the world and relate them to mathematical models
OK so far I agree, but you then take a wrong turn:
among which are the Tarski-style sets and relations. Without
such a methodology, a Tarski-style model has no relationship
whatever to anything that exists in the world.
WRONG. The fact that Tarsi's semantic meta
language uses set theory, does not entail that it can only speak of mathematical abstractions. The elements of the 'universe set' can be literally anything. A set of pieces of steel reinforcing cable is just as much a set as a set of integers. Set theory is not restricted to speaking only of sets of abstractions.
Nobody has ever made a serious case for the real world as
Every writer on semantics (other than you) presumes this, without needing to have a case made. Certainly this is what Tarski intended, in any case.
The most one can claim is that a Tarski-style model
might be a useful approximation to the world for some purpose.
I claim, and I believe it is impossible to refute this claim, that a Tarski-style model can BE an actual part of the real world, not an approximation to, or representation of, anything. You and I, and the relationship of being engaged in an ongoing argument by email, constitute a part of the actual world. And this part is
- literally, actually, is, no metaphors here - a Tarskian interpretation of the atomic assertion:
(Continually-arguing-by-email John Pat)
To claim that the tuples of a Tarski-style model consist of
actual objects in the world is somewhere between a colorful
metaphor and pure fantasy.
Nonsense. It is literally correct. What makes you feel it must be a fantasy? Do you think it is incoherent to speak of, say, sets of people or sets of rivets or sets of galaxies? Nobody else I know or have ever read, which by now amounts to quite a lot of people, believes that set talk is limited in some way. None of those who invented it believed this.
If you can find any serious
publication that says otherwise, please send quotations.
You have made this challenge on other occasions and I have found quotes from Russell, Quine, Church, Tarski, Carnap and others all making it vividly obvious that they had what one might call the 'realist' view of sets. That this view is mainstream is simply obvious to anyone who has studied the subject. This of course does not establish that it is correct, but it does respond to your challenge.
PH> There is a well-defined technical area called 'semantics'...
For abstract sets, yes. But for things and events in the real
world, Tarski's models must be supplemented with a methodology
for mapping those abstract sets to the world.
You keep asserting this over and over again, without argument, and it is COMPLETE NONSENSE. Sets need not be sets OF ABSTRACTIONS. A set of people contains real, live, breathing, sweaty people. A set of sodium atoms contains real sodium atoms. Tarski's models can BE parts of the real world. You are simply stuck with a limited and mistaken grasp of the scope of set theory.
Otherwise, it is
nothing but a semantics of imaginary castles in the air.
John, you simply DO NOT UNDERSTAND semantics. I give up on you. Remain mired in your ignorance.
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