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Re: [ontolog-forum] formal systems, common logic and lbase

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 28 Nov 2007 12:01:06 -0500
Message-id: <474D9ED2.10408@xxxxxxxxxxx>
I agree with the points that Chris and Pat made about CL and IKL.
But I wanted to add a few more.    (01)

CM> Their (very fine) work is just a small portion of the huge
 > body of research on "post-Tarskian" semantic theories for
 > languages that contain their own truth predicate, stemming
 > (most notably) from Kripke's enormously influential 1975
 > paper "Outline of a Theory of Truth."    (02)

I agree that is good work, but I was recommending a Tarski-style
hierarchy only because it is simpler and, for most KR purposes,
much richer than what most people have been using.    (03)

I have no objections to extensions that have a single truth
predicate for everything, but it is not clear that it is useful
for more than a small number of interesting puzzles.  For natural
languages, for example, the common word 'true' could be interpreted
as an indexical, like 'here' or 'now', which depends on the context
in which it is uttered.    (04)

The word 'language', as used by logicians, is highly confusing to
most people who think that the language "stays the same" as you
add more vocabulary or change the domain of discourse.  But
logicians talk about different languages, even though they may
use identical syntax and have a very high overlap in vocabulary
and domain.    (05)

So the Tarski hierarchy of "languages" can be viewed as just a
single syntax for every level, but an increasing domain (and
truth predicate) as you go up the levels -- i.e., each level
can talk about propositions and truth values of the levels
beneath it.    (06)

That restriction makes it impossible to state the Liar Paradox,
and it's not clear that there are many, if any practical
applications that need more.    (07)

John    (08)

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