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From: daryl@oravax.UUCP (Steven Daryl McCullough)
Newsgroups: comp.ai
Subject: Re: Searle and Radical Translation (was: Re: Searle and Biology)
Summary: Humans don't have a consistent, complete definition of truth, either.
Message-ID: <1604@oravax.UUCP>
Date: 18 Jul 90 23:31:47 GMT
References: <14265@enera.isi.edu> <602@ntpdvp1.UUCP> <1595@oravax.UUCP> <606@ntpdvp1.UUCP>
Organization: Odyssey Research Associates, Ithaca NY
Lines: 64

In article <606@ntpdvp1.UUCP>, kenp@ntpdvp1.UUCP (Ken Presting) writes:

> Searle does not say much about how to determine whether symbols
> have any semantics attached, but he is unlikely to object strongly
> to the "Radical Interpretation" of Davidson (and Quine), which is
> well-known and very influential among philosophers of language.

> Radical Interpretation *is* based on observations of behavior.  (Cf.
> WVO Quine, _Word and Object_, and D. Davidson, _Inquiries into Truth
> and Interpretation_) Radical Translation involves adopting the
> hypothesis that the symbols generated by a system are *true
> sentences* (among other assumptions), and iteratively modifying a
> tentative semantics for the system, hoping to preserve the
> hypothesis. The interpretation "succeeds" if some symbol in the
> system's vocabulary gets assigned the semantics of the concept
> "truth".

This is a very interesting idea until the last sentence. Why not say
that the interpretation succeeds if there is any interpretation which
makes all the sentences true? Why must there be a word for the notion
of truth?

> (This is a very quick sketch of a very complex and interesting theory,
> which was never intended to be applied to AI.)
> Note that no mere implementation of a Turing Machine could pass
> this test, because truth (like "halting") cannot be represented by a
> computable function.

Now I see why you added the last sentence! You had your theorem "no
mere Turing Machine may pass the test" in mind before you set out the
rules.

> IMO, real computers are more than mere TM implementations, so
> Tarksi's theorem does not prohibit real machines from representing
> truth.

Ken, IMHO, it is completely bogus to use Tarski's theorem to "prove"
that there is some notion of truth that physical objects can know but
Turing machines can't. Tarski's undefinability of truth has just as
much force when applied to humans:

     Theorem: No human being can have a definition of truth and still
     be consistent.

     Proof: Consider the sentence "This statement is not true". There
     is no consistent truth assignment to the sentence if we are to
     assign the word "true" its usual meaning.

My guess is the human's are just inconsistent.

Notice, however, that if we weaken our claim to having a definition of
absolute truth to having a subjective definition of truth, then the
paradox is resolved:

     Consider the sentence: "This sentence will never be considered
     true by Ken Presting"

The above sentence could very well be true, but if so, then there is
at least one sentence that is true, but Ken Presting doesn't consider
to be true. Therefore Ken Presting doesn't have a definition of real
truth. On the other hand, the above sentence could be false. Then Ken
Presting will consider it to be true, and so again Ken Presting's
notion of truth is not real truth.

Daryl McCullough