Chris, (01)
I perceive this to, indeed, be the argument about my use of the word
"pitfalls" I thought it was. In which case I must leave you to make
what arguments you wish. (02)
Rob (03)
On Mon, Sep 29, 2008 at 2:22 AM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
> On Sep 27, 2008, at 1:24 AM, Rob Freeman wrote:
>> If you are really confused by my reference to the "pitfalls of
>> formal logic" I apologize.
>
> No apology needed, unless it is for what appears to be an attempt to
> deflect attention away from your refusal to answer my simple question
> about what you had in mind by the "pitfalls of formal logic" by
> depicting me as confused.
>
>> My comment was most directly in the context of the artificial
>> intelligence work of Marcus Hutter and Juergen Schmidhuber
>> immediately above in my original message.
>
> There is nothing whatever in the work of Hutter and Schmidhuber that
> suggests there are any "pitfalls of formal logic". As proponents of
> approaches to AI that are alternatives to the more traditional logic
> based approach, they no doubt argue that pitfalls await those who
> attempt to *base AI* on formal logic alone. The problem I saw with
> your original post, and which seems to be persisting, is that you
> appear to be attributing the existence of pitfalls that can arise in
> an *application* of formal logic to formal logic itself. That is is
> simply a confusion about the nature of logic (and, in this case AI)
> that I think it is quite important to point out.
>
>> Traditionally AI has been approached as a problem of formal logic.
>> This has proven intractable for reasons which I believe closely
>> resemble those which prevented a basis in formal logic for
>> mathematics, broadly "Gödelian incompleteness".
>
> There are several errors and unclarities here. First, AI has never
> been "approached as a problem of formal logic". Problems of formal
> logic have to do with such matters as the axiomatizability of validity
> relative to a certain semantics, the decidability of validity, the
> expressive power of a certain semantics, the consistency of a certain
> theory, etc. AI, by contrast, is the problem of implementing
> something approaching human intelligence on a computer. That is an
> engineering problem, one that, depending the particulars of your view
> of AI, also bleeds over into a variety of other disciplines including
> cognitive science and linguistics. And there are, of course, many
> points at which one might *apply* formal logic to solve particular
> problems in AI. And here, of course, pitfalls await. The wellknown
> problems of intractability in pure logic of course have implications
> for AI  indeed, these purely theoretical facts lead to perhaps the
> most fundamental challenge to (and, hence potential pitfalls for) a
> logicbased approach to AI. One of the things human do quite well is
> reasoning, drawing valid conclusions from given premises. In general,
> however, the problem of determining when one thing follows from
> another is undecidable (hence intractable). So a serious challenge of
> AI is to figure out how to do useful reasoning in the face of this
> theoretical limitations. But, again, the limitation itself are no
> more a "pitfall" of formal logic than, say, the infinitude of the
> primes is a pitfall of arithmetic.
>
> As for your remark about finding a basis for mathematics in formal
> logic, I'm not sure which of two projects you are alluding to. The
> idea of finding a basis for mathematics in logic sounds very much like
> the logicist project of Frege and (subsequently) Russell. But the
> reasons for the failure of this project had nothing to do with the
> issue of tractability and indeed was largely dead in the water long
> before 1931 when Gödel published his famous paper on incompleteness.
> So I'm thinking that, if anything, what you have in mind here is the
> formalist project of Hilbert, whose failure can indeed be attributed
> to Gödel's work, from which the general intractability of deduction
> noted above follows. Historically interesting, for sure, but I'm not
> seeing any clear point.
>
>> Hence by my lights formal logic has "pitfalls" as a basis for AI
>> (and mathematics.)
>
> Once again, that there may be is exactly the point I made (more
> generally) in my original reply: there may well be pitfalls in any
> attempt to *apply* formal logic to solve a problem. It might simply
> be the wrong framework for the problem at hand.
>
>> The work of Schmidhuber and Hutter avoid these "pitfalls", by
>> ignoring formal logic and seeking a basis for meaning in prediction/
>> probability.
>
> I doubt very much that they are "ignoring" formal logic, as they still
> have to implement certain forms and patterns of reasoning.
>
>> It is interesting to compare this with, e.g. Greg Chaitin's work on
>> mathematical randomness...As I said in the "Axiomatic ontology"
>> thread I personally prefer to look for a basis for this randomness
>> in something like Vitiello's "manybody system" approach (or Chris
>> Anderson's "Google"/Robert Laughlin's "bottom down", crystalline
>> structure inspired, physics.) But the different approaches don't
>> conflict (no less the success of "transformation invariance", as a
>> fundamental parameter for understanding the world, in "geometric"
>> models.).
>
> Sounds Very Deep.
>
> Chris Menzel (04)
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