Pat, (01)
These are important discussions regarding things like formal semantics and real
world semantics. So I'd like a bit more help here. (02)
Concerning what the "Tarskian universe" is about I've seen write ups like the
one below from "Semantics for the WWW" Dieter Fensel1, Jim Hendler, Henry
Lieberman, and Wolfgang Wahlster. (03)
" The most common classic formalism, also the most amenable to the use of
ontologies, is so-called
declarative or Tarski semantics as may be found in various places in the
database and AI
literature, as in Reiter's seminal paper [Reiter, 1988] or in the book
[Genesereth & Nilsson,
1987]. Essentially it replaces "reality" (the domain) by a conceptualization, a
mathematical
object that typically consists of very elementary constructs such as a set of
objects and of
(mathematical) relations. Semantics is then formally defined simply as an
interpretation
mapping from the system (or rather from the language describing a system
instance in some
syntax) to this conceptualization." (04)
Do you find this consistent with your interpreation? (05)
On Tarski's main example that snow is white, and he was talking about snow, not
a mathematical simalcrum of snow ("snow") there seem to be people who argue
that one needs something interpretive between the real and formal concept, as
in the paragraph below from Chapter 4 pg 80 (Truth Values) of Joseph Margolis'
A Conceptual Primer for the Turn of the Millennium/ (06)
disquotational theory of truth, I mean that theory that accepts as its paradigm
(disputatiously attributed to Tarski the formula: 'Snow is white' is true if
and only if snow is white. To ascribe truth, it is said (notably by Quine, who
accepts the formulation), one merely "cancels the quotation marks." My own view
is that the disquotational theory is either utterly vacuous (in the form just
given), privileged (if taken as correct as far as it goes, as on Davidson's
reading of Tarski , or else flatly false (since, admitting intransparency, some
interpretive tertium will be needed). The objective of these strenuous (but
ineffectual) moves against the legitimation of truth (a fortiori, the
legitimation of truth-value assignments)-on which Quine and Davidson agree-is
simply to endorse what has come to be called "naturalizing." (07)
Gary Berg-Cross (08)
________________________________ (09)
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx on behalf of Pat Hayes
Sent: Fri 9/26/2008 4:01 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Reality and semantics. [Was: Thing and Class] (010)
On Sep 26, 2008, at 12:29 AM, John F. Sowa wrote: (011)
Pat, (012)
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." (013)
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. (014)
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. (015)
PH> Are you claiming that logical positivism represents an (016)
alternative theory of truth, one that you believe is more (017)
appropriate than Tarski's theory for ontology engineering? (018)
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 (019)
OK so far I agree, but you then take a wrong turn: (020)
,
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. (021)
WRONG. The fact that Tarsi's semantic metalanguage 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. (022)
Nobody has ever made a serious case for the real world as
a model. (023)
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. (024)
The most one can claim is that a Tarski-style model
might be a useful approximation to the world for some purpose. (025)
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) (026)
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. (027)
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. (028)
If you can find any serious
publication that says otherwise, please send quotations. (029)
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. (030)
PH> There is a well-defined technical area called 'semantics'... (031)
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. (032)
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. (033)
Otherwise, it is
nothing but a semantics of imaginary castles in the air. (034)
John, you simply DO NOT UNDERSTAND semantics. I give up on you. Remain mired in
your ignorance. (035)
Pat (036)
John (037)
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