Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!swrinde!zaphod.mps.ohio-state.edu!think.com!snorkelwacker.mit.edu!stanford.edu!csli!csli.stanford.edu
From: levesque@csli.stanford.edu (Hector Levesque)
Newsgroups: comp.ai
Subject: logic and related stuff
Keywords: logic, truth, Minsky
Message-ID: <20018@csli.Stanford.EDU>
Date: 18 Jun 91 19:48:34 GMT
Sender: levesque@csli.Stanford.EDU
Organization: CSLI, Stanford University
Lines: 67

I've never posted to comp.ai before (and may regret it!), so please forgive
violations of protocol.  But these attacks on logic and truth, though maybe
familiar in AI from about 15 years ago, deserve some comment.

First, a minor complaint about Minsky's post about logic.  I agree
completely that universal generalization could end up playing a very minor
role in our cognitive life.  But I disagree completely that the utility of
logic is somehow thereby compromised.  One very popular logical theory,
sometimes called "quantification theory" is indeed concerned with
expressing in logical terms the properties of "for all" and "for some."
But even existing logical theories go well beyond this.  The theory of
generalized quantifiers, for example, examines properties of quantifiers
like "many", "most," "almost all" and the like that stand to play a much
more important role in expressing what we believe.  Then there are the
statistical/probabilistic accounts (a la Bacchus/Halpern), the nonmonotinic
accounts etc.  To say that logic lives or dies with generalization and
instantiation is like saying it lives or dies with exclusive-or.

Another point: I think it is a simple mistake (of logic!) to conclude that
because we can never be *certain* about what we mean when we say something,
or what we are agreeing about, or what is true, that somehow the truth of
the matter is thereby open to negotiation or interpretation, or that we can
decide to act in a way that does not take it into account.  If I tell you
"there's a truck coming towards you from behind", I may have no way of
knowing for sure that my statement is correct, and you may have no way of
being sure either of what I'm getting at or (assuming you've figured it
out) of whether or not what I am saying is true.  But it's a mistake (and a
dangerous one) to conclude from this lack of certainty that the truck issue
is somehow thereby reduced in importance, or that what ultimately matters
is your goals and desires, or our linguistic conventions, or even that one
opinion on the issue is as good as another.  None of these follow from
admitting that we may never know for sure one way or another if there is a
truck.  A skeptic may choose to focus on what I said, question what I mean
by a "truck" (a toy truck?), or just observe the loaded context dependency
and unavoidable subjectivism in how I perceive and report things.  But if
he or she after all this doesn't get it, and does not come to appreciate
very clearly the relevant issue, all is for nought, and the world will do
the rest.  You don't have to *know* what I said, and you don't have to
*know* if what I said is true, but for your own safety and comfort, you'd
better be able to figure out what it would be like for it to be true.

This, I assume, is what logic is for, at least for AI purposes.  Focussing
on Truth in some abstract, all-or-nothing, eternal, godlike sense, is a bit
of a red herring.  What matters I think in AI is being able to explore the
consequences of things being one way and not another, even while admitting
that much of our view of the world is not going to be right (even by our
own terms), and that there is no way to achieve certainty about almost all
of it.  We need to be able to ask ourselves "according to what I now
believe, what would things be like if P?"  The fact that we first use
natural language typically to express a P, and that this language is
infinitely rich and open to endless interpretation and uneliminable context
dependency and bla-bla-bla should really not fool us into thinking that
there is no issue to settle regarding the way the world is.  To fall for
this, as far as I can see, is to undervalue the difference between being
right or wrong about the truck, for example, and to guarantee for oneself a
hermeneutically rich but very short life.

The fact is, I don't think anyone takes this position too seriously except
when assuming a philosophical stance.  Show me a philosohper that doesn't
fall into realism of the most naive sort when confronted with memos that
say "I'm sorry, but your salary will be reduced by 50%."  Under the right
circumstances (having nothing to do with mathematics or formal artificial
domains!) relativism is put on hold, and the ordinary objective truth about
what might appear to be hopelessly vague imponderables suddenly becomes
very crisp, very precise, and very relevant to action.

Hector Levesque