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Re: [ontolog-forum] mKR (was Thing and Class)

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 28 Sep 2008 13:22:04 -0500
Message-id: <14371D17-28E3-4C09-821E-36343CA02356@xxxxxxxx>
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.    (01)

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.    (02)

> 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.    (03)

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.    (04)

> 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".    (05)

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 well-known  
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  
logic-based 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.    (06)

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.    (07)

> Hence by my lights formal logic has "pitfalls" as a basis for AI  
> (and mathematics.)    (08)

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.    (09)

> The work of Schmidhuber and Hutter avoid these "pitfalls", by  
> ignoring formal logic and seeking a basis for meaning in prediction/ 
> probability.    (010)

I doubt very much that they are "ignoring" formal logic, as they still  
have to implement certain forms and patterns of reasoning.    (011)

> 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 "many-body 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.).    (012)

Sounds Very Deep.    (013)

Chris Menzel    (014)

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