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Re: [ontolog-forum] Truth

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Wed, 11 Jul 2012 18:58:58 -0400
Message-id: <4FFE0532.5010501@xxxxxxxxxxx>
Chris,    (01)

Our disagreement is not so much about names, but about the nature of
models in model theory.  In the Tractatus, Wittgenstein assumed that
the real world was the model:  "The world is everything that is the
case."  Then atomic sentences have a one-to-one mapping to facts.    (02)

But in his transitional period, he abandoned that mapping of
sentences to facts.  Instead, he mapped theories (Satzsysteme)
to the world.  From his _Philosophical Remarks_ of 1929-30:    (03)

> The Satzsystem is like a ruler laid against reality. An entire
> system of propositions is now compared to reality, not a single
> proposition.    (04)

In model-theoretic terms, LW's "ruler" is a Tarski-style model that
is composed of surrogates that represent individuals.  Then that
model is treated as an approximation to the reality.  For a diagram
that illustrates that mapping, see Slide 23 of    (05)

    http://www.jfsowa.com/talks/dynolang.pdf    (06)

The real world is on the left, and the theory (Satzsystem) is
on the right.  The graph in the middle is a model of the theory.
The denotation {true, false} is determined by relating the
theory to the model.  The approximation {good, fair, poor} is
determined by observations that relate the model to the world.    (07)

> Then they don't have a naming relation in their language. At best they
> have some shadow thereof whose meaning is not encoded in the formalism
> but which is interpreted pragmatically by the users, much the way box
> and arrow diagrams can be useful to a select group of modelers who
> understand the unstated semantic conventions of their diagrams.    (08)

Absolutely!  That is all we can ever have in our computers -- or in
our brains.  We have shadows in the computer, and technicolor pictures
in the brain.  They're called "mental models", and the neural evidence
for them shows that the cognitive scientists were right all along.    (09)

> But that's not a logical solution to the problem.    (010)

Of course not.  It's impossible to have a logical solution to an
empirical problem.  A theory of context is an empirical theory
about language use.    (011)

> There is nothing in the logic  of the DB to ensure that the intended
> semantic relation holds. It is  simply understood by the users.    (012)

The best that any database can do is to accept whatever we tell it.
And that is all that people can do for anything they have not been
able to observe for themselves.    (013)

> Database administrators have probably faced more such examples
> than philosophers have dreamed of.    (014)

> I highly doubt it.    (015)

I recommend Bill Kent's book _Data and Reality_, not as a book on logic
or philosophy.  But it is loaded with good examples that illustrate
the kinds of issues that DB administrators (or practical ontologists)
run into.    (016)

> But please, don't start citing your books as if you've solved these
> problems and don't start citing journal papers as if I don't know
> this literature or understand these issues.    (017)

I was citing my own work to indicate that this is not just a hypothesis
I dreamt up this morning.  And I believe that Ludwig W. was absolutely
right in dropping the claim that NL sentences can be mapped directly
to the real world.    (018)

If you have any examples of paradoxes that cannot be solved as well or
better in terms of the diagram in my slide 23, I would really like to
see it.  I don't believe that you can find any, but I would very much
like to know of any that test the hypothesis.    (019)

John    (020)

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