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From: marcel@uiucdcs.UUCP
Newsgroups: net.ai
Subject: Re: A topic for discussion, phil/ai pers - (nf)
Message-ID: <32300026@uiucdcs.UUCP>
Date: Wed, 16-May-84 13:57:00 EDT
Article-I.D.: uiucdcs.32300026
Posted: Wed May 16 13:57:00 1984
Date-Received: Fri, 18-May-84 00:29:42 EDT
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Nf-From: uiucdcs!marcel    May 16 12:57:00 1984

#R:wxlvax:-27700:uiucdcs:32300026:000:2437
uiucdcs!marcel    May 16 12:57:00 1984

The problem is one of identification. When we see one object matching a
description of another object we know about, we often assume that the object
we're seeing IS the object we know about -- especially when we expect the
description to be definite [1]. This is known as Leibniz's law of the
indiscernability of identicals. That's found its way into the definitions
of set theory [2]: two entities are "equal" iff every property of one is also
a property of the other. Wittgenstein [3] objected that this did not allow for
replication, ie the fact that we can distinguish two indistinguishable objects
when they are placed next to each other (identity "solo numero"). So, if we
don't like to make assumptions, either no two objects are ever the same object,
or else we have to follow Aristotle and say that every object has some property
setting it apart from all others. That's known as Essentialism, and is hotly
disputed [4]. The choices until now have been: breakdown of identification,
essentialism, or assumption. The latter is the most functional, but not nice
if you're after epistemic certainty.
	Still, I see no insurmountable problems with making computers do the
same as ourselves: assume identity until given evidence to the contrary. That
we can't convince ourselves of that method's epistemic soundness does nothing
to its effectiveness. All one needs is a formal logic or set theory (open
sentences, such as predicates, are descriptions) with a definite description
operator [2,5]. Of course, that makes the logic non-monotonic, since a definite
description becomes meaningless when two objects match it. In other words, a
closed-world assumption is also involved, and the theory must go beyond first-
order logic. That's a technical problem, not necessarily an unsolvable one [6].


[1] see the chapter on SCHOLAR in Bobrow's "Representation and Understanding";
    note the "uniqueness assumption".
[2] Introduced by Whitehead & Russell in their "Principia Mathematica".
[3] Wittgenstein's "Tractatus".
[4] WVO Quine, "From a logical point of view".
[5] WVO Quine, "Mathematical Logic".
[6] Doyle's Truth Maintenance System (Artif. Intel. 12) attacks the non-
    monotonicity problem fairly well, though without a sound theoretical
    basis. See also McDermott's attempt at formalization (Artif. Intel. 13
    and JACM 29 (Jan '82)).

					Marcel Schoppers
					U of Illinois at Urbana-Champaign
					uiucdcs!marcel