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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: Fri, 26 Sep 2008 20:05:19 -0400
Message-id: <48DD78BF.6040400@xxxxxxxxxxx>
Pat,    (01)

That is true:    (02)

PH> 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.    (03)

First, Tarski's example "Snow is white" was an unfortunate choice
because it introduced several complex issues he did not explain in
that paper: (a) continuous substances such as snow, (b) a generic
statement without the use of quantifiers, (c) the question of how
FOL could be used to talk about continuous stuff, and (d) the
question of how a statement in ordinary language could be related
to the formal notation for which he defined his semantics.    (04)

Second, even in that paper, Tarski discussed the problems about
natural languages and explicitly admitted that a great deal more
work would be needed to apply his approach to those languages
and that he wasn't sure whether such an application was possible.    (05)

In that paper and in his later work (1944), he did not get into
details about many issues that are critical for relating any
symbols (formal or informal) to things and events in the world.
He certainly did not discuss *symbol grounding* which was the
subject of much debate a few years ago.  Nor did he claim that
by using set notation the symbol grounding problem was avoided
or magically solved.    (06)

In my earlier note, I mentioned Carnap, Popper, and others who
recognized that some such methodology is a necessary component
of a theory of meaning.  It can be a supplement to Tarski's
models, but it is a necessary supplement.    (07)

PH> Maybe this misapprehension is the source of your blind spot
 > with regard to semantics.    (08)

I respect your technical knowledge, but I believe that you're
the one with the blind spot about the need for some kind of
mapping to ground the symbols of a formalism.    (09)

JFS>> Without [a methodology for relating symbols to reality],
 >> a Tarski-style model has no relationship whatever to anything
 >> that exists in the world.    (010)

PH> WRONG. The fact that Tarski's semantic metalanguage uses set
 > theory, does not entail that it can only speak of mathematical
 > abstractions... Set theory is not restricted to speaking only
 > of sets of abstractions.    (011)

I agree that the phrase "a set of apples" is as legitimate in
English as the phrase "a bushel of apples".  But there's a big
difference between talking about integers and apples:    (012)

  1. Peano's axioms for arithmetic determine criteria for finding
     an integer n that has a property P(n) and for determining
     whether two integers n and m are the same, n=m.    (013)

  2. But I can't accept a proposed model with a physical entity
     x and no methodology of any kind for determining whether a
     property P(x) is true in the actual world or whether two
     variables x and y represent the same entity in the world.
     Without such "grounding", it is absurd to claim that any
     claims of truth or falsity about the world are credible.    (014)

I realize that point #1, which can be solved by an explicit
enumeration with a countable universe, becomes more difficult
to formulate with an uncountable universe.  But for physical
domains, I'd like to see a methodology for #2 that acknowledges
the symbol grounding issues and presents at least a partial
answer to the two questions about the world:  P(x)?  and  x=y?    (015)

PH> 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.    (016)

All I'm asking for are some quotations that acknowledge the issues
in point #2 above and suggest some methodology.  You can start with
Tarski's 1944 paper, which I posted on my web site several years ago:    (017)

    http://www.jfsowa.com/logic/tarski.htm    (018)

If you can't find clear evidence there, then please send some clear
quotations from some other source that explain the matter.    (019)

PH> Do you think it is incoherent to speak of, say, sets of people
 > or sets of rivets or sets of galaxies?    (020)

It's not incoherent.  But when people use such language, they can
usually state, if asked, how an entity x with a property P(x) could
be found and how to answer a question of the form x=y?    (021)

Airline personnel, for example, talk about reservations, flights,
and passengers in a database, even though the database actually
contains unique identifiers for the entities, not the entities
themselves.  But they maintain a clear methodology for relating
the symbols in the DB to the physical objects and events (e.g.,
a phone number to call a passenger in case of a cancellation).    (022)

PH> 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.    (023)

Yes, Russell was notorious on that point.  He claimed that a
"proposition" about Mont Blanc actually contained the physical
mountain with all its rocks and snow.  The fact that Frege was
incredulous about Russell's claim indicates that Russell was
mixing physical and abstract entities in an unusual way.    (024)

PH> You are simply stuck with a limited and mistaken grasp of
 > the scope of set theory... John, you simply DO NOT UNDERSTAND
 > semantics. I give up on you. Remain mired in your ignorance.    (025)

No. I believe that you have taken a system that Tarski developed
for "formalized languages" and applied it to the real world
without including a methodology for answering the kinds of
questions that are routinely answered for mathematical systems,
such as P(x)? and x=y?    (026)

John    (027)

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