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Re: Reification

From: Drew McDermott <drew.mcdermott@yale.edu>
Date: Mon, 9 Apr 2001 17:15:03 -0400 (EDT)
Message-Id: <200104092115.RAA24570@pantheon-po01.its.yale.edu>
To: www-rdf-logic@w3.org

Warning: This message concerns philosophical issues that are perhaps
not very germane to anything practical.  Eminently skippable.

   [Seth Russell]
   If someone creates a formal system in which all axioms, syntax, and
   operations are specified;  then the statements of such a system can be
   considered True\False and we can operate on that state with negation.  I
   would call such a system "closed".  The opposite situation is where the
   axioms and operations are not all known - perhaps the only thing that is
   known is the syntax of the statements.  I would call such a system "open".
   My thesis, of course, is that the real world, that world in which we human
   agents seem to live and also the world we inhabit when we surf the web, is
   open and that there does not seem to be any absolute or formal meaning to
   the description of statements as True\False or the negation of that
   description.  In other words Truth in the real world and on the web is
   relative.

I think how a classical logician/philosopher (let's call him or her
Pat) would object goes like this: If you know the *meanings* of the
expressions of the language as well as their syntax, then for each
statement P of the language you know what the world would be like if P
were true.  That's because knowing the truth conditions of P *is*
knowing the meaning of P as far as Pat is concerned.  Furthermore, if
you know the meaning of P, you must know the meaning of (not P),
because the world is constrained by (not P) to be a certain way if and
only if it would be constrained by P not to be that way.  (This is a
bit clumsy, because I'm trying to avoid talking about interpretations
and models.)  Therefore, there is no particular problem with negation.

Let's say an "open system" is a source of statements (a speaker
uttering a series of claims; or the contents of a series of Web pages
you have some reason to ascribe credibility to) such that the source
may emit statements in the future that it hasn't emitted in the past.
It's true that for an open system you don't know the entire claim the
statement source is making.  However, you can certainly know what it
would mean for all the statements you *have* heard to be true.
Further statements will further constrain the way things could be; the
constraints may finally become inconsistent, in which case they don't
describe any possible world.

Is Pat being too glib?  I'm not sure.  One might argue that while one
knows the meaning of terms like "not" and "possibly,"  the meaning of
terms like "conservative" or "mindshare" is too fuzzy to be really
known.  Pat would no doubt counter that if you know anything about the
meanings of those term, what you know must be expressed as explicit
axioms; then those axioms (which use terms like "not" and "possibly")
plus claims from the open system involving the contested terms will
constrain the ways the world could be just exactly as far as they
should be constrained.

I am skeptical about the possibility of expressing everything we know
about the meanings of terms as axioms.  (Because I doubt that
everything we know can be expressed in a deductive framework.)  So I
think there is room to disagree with Pat.  However, I don't think I
would say

   "there does not seem to be any absolute or formal meaning to
   the description of statements as True\False or the negation of that
   description"

as Seth does.  I don't see that there is a problem with truth,
falsehood, or negation.  Those concepts seem crystal clear, whether we
are dealing with an open system or a closed one.  There is a problem
with the meaning of terms like "conservative."  But
"conservative(Antonin)" is true if and only if Antonin is a
conservative.  Is that problematic?  And "not(conservative(Antonin))"
is true if and only if Antonin is not a conservative.

Perhaps Seth meant to say that there doesn't seem to be any way to
*test* whether a statement is true.  But that's a different claim
altogether.

                                             -- Drew McDermott
Received on Monday, 9 April 2001 17:15:05 GMT

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