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Re: [ontolog-forum] Reality and semantics. [Was: Thing and Class]

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 24 Sep 2008 00:07:45 -0400
Message-id: <48D9BD11.6050003@xxxxxxxxxxx>
Pat,    (01)

I agree that Tarski's evaluation function is a formal construct.
Whether or not one applies that function to a sentence s to get
a value of T or F is a separate issue.  But in the case of finite
models (such as the tables of a relational DB for a closed world),
computational methods logically equivalent to Tarski's are used
to answer questions.    (02)

JFS>> I agree that in principle one might conceive of using a Tarski
>> style of model theory to relate statements about liquids to the
>> world.    (03)

PH> wait a second. "In principle", "might conceive"? But (of course)
> that is exactly what 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...    (04)

I agree that you assumed a Tarski-style model for your ontology, which
is very good of its kind.  But most engineering work with fluids uses
continuous math, such as differential equations.    (05)

JFS>> 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.    (06)

PH> 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.    (07)

I agree.  But if it is to have any kind of relevance to practical
applications, those functions must be evaluated on actual sentences.    (08)

PH> 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?    (09)

Solving the kinds of problems that are routinely done with the
continuous methods of fluid mechanics.    (010)

PH> 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.    (011)

I'll admit that there may be good reasons why the truth value for
a given sentence cannot be determined.  But a fundamental *goal*
of any semantic theory is to determine whether sentences are true
or false.  I don't have much sympathy for "deep" semantic theories
that cannot be used in practice.    (012)

PH> 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.    (013)

No.  I am claiming that Tarski's evaluation function is useless
for the differential equations used by physicists and engineers.
And I would claim that the continuous methods for determining the
truth of such equations are just as "semantic" as Tarski's function.    (014)

I admit that a collection of differential equations could be
considered a conjunction to which Tarski's method might be used.
But I suggest the following approach, which is what physicists
and engineers have been using informally for centuries:    (015)

  1. For any equation q, use the traditional methods of applied
     mathematics to determine the truth value of q in terms of
     a traditional *engineering model*.    (016)

  2. For any statement s that combines equations with quantifiers
     and Boolean operators, use a Tarski-style method to reduce s
     to equations (as in #1) instead of atoms (as in Tarski models
     with a set of entities and a set of relations over them).    (017)

  3. After s has been reduced to equations, each of them can be
     evaluated in terms of the domain to determine a value T or F.    (018)

This method is every bit as "semantic" as anything that Tarski
ever did, and it is compatible with the practices of physicists
and engineers since the time of Newton and Leibniz.  Furthermore,
it avoids any claim that the world consists of tuples.    (019)

I'm not saying that Tarski's evaluation function is bad for what
it can do.  But I would claim that for many kinds of statements,
there are better methods for determining their truth in terms
of the world.    (020)

John    (021)

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