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From: blenko-tom@cs.yale.edu (Tom Blenko)
Newsgroups: sci.math,comp.ai
Subject: Re: musings on Godel's theorem
Message-ID: <27399@cs.yale.edu>
Date: 26 Nov 90 04:27:06 GMT
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In article <1990Nov25.204513.24169@nntp-server.caltech.edu> morphy@nntp-server.caltech.edu (Jones Maxime Murphy) writes:
|news@ccncsu.ColoState.EDU (USENET News) writes:
|
|>This link between an axiomatic system and computation seems rather ill-defined
|>and tenuous!  (The philosopher Searle may be taking advantage of this with his
|>...
|
|The link is hardly tenuous. A machine is defined by it's changes of state in 
|response to sentences from the language it accepts. The primitives of it's
|language correspond to axioms, and syntax corresponds to an inferential
|mechanism for extracting state changes from combinations of primitives.

You've left me mystified. A computing machine reads a sequence of
inputs, producing a sequence of outputs and halting or not halting.  A
logical theory consists of a set of axioms, rule(s) of inference, and a
collection of theorems derivable from the axioms.

Now, what is the "link"? What corresponds to the inputs, what
corresponds to the outputs, and what corresponds to the computing
machine?


|I presume the one "truth" being referred to here is the impossibility of 
|a finistic proof of the consistency of arithmetic that can be embedded in the
|language of arithmetic and the first-order predicate calculus. In addition to 
|simple culture shock at the news that "logic" as we know it is no longer
|omnipotent in it's domain of inquiry, the fact is that we must now be wary in
|the quest for artificial intelligence.
| A great deal of human intelligence derives from self-reference, and weaknesses
|in self-referential analysis in the inferential mechanisms of computing machines
|which at the moment all rely on 1st order predicate calculus must be taken
|seriously.

Again, this argument is opaque. Intelligent entities exist, and their
evolution/development presumably has proceeded with no prior knowledge
of logical truths.

If you wish to *describe* intelligent entities, artificial or
otherwise, or to describe automobiles, toasters, or houseplants for
that matter, you may find that some or all logics are unsuitable. If
so, this is not a problem of automobiles, toasters, or houseplants, but
a limitation of the logics in question.

	Tom