From: "Phil Roberts, Jr." 
Subject: Re: Robot Evolution
Date: Fri, 12 Jan 2007 12:46:17 -0500 (EST)

Tim Tyler wrote:

> Phil Roberts, Jr. wrote:
>  > But I have been assuming that your disagreement has been
>  > with Hofstadter who I quoted as someone who had offered
>  > "one of the most lucid statements of the Lucas/Penrose
>  > PERSPECTIVE".  Here is a repeat of what started the whole
>  > ruckus, and in which I have taken the liberty of including
>  > some of Hofstadter's rationale:
>  >

> I had been wondering how on earth you had managed
> to conclude that Hofstadter, Dennett and Chaitin
> were remotely on the same side as Penrose on
> the issue of potential cognitive capacity of
> machines.


In hindsight, I added to this confusion by quoting
from Lucas and Penrose in response to various
objections raised by yourself and others.  But on
the other side, I really did make quite a fuss
about the fact that I was not viewing Godel
as a proof or a formal argument that minds
are different from machines, but rather more like
a controlled experiment, or as Hofstadter puts it,
as a SUGGESTION when "looked at this way".  This is
a much softer stance than that of Lucas and
Penrose, and one which I have tried to buttress
with evidence from other spheres of experience,
some of which I have yet to present, and which is
a considerably different approach from the one
taken by either of my esteemed (by me at least)
allies (Lucas and Penrose).  Here is a little more
of the Hofstatder rationale that preceded the
passage I have already quoted:

    Godel's proof offers the notion that a high-level view
    of a system may contain explanatory power which simply
    is absent on the lower level.  By this I mean the
    following.  Suppose someone gave you G, Godel's
    undecidable string, as a string of TNT [or Peano
    arithmetic].  Also suppose you knew nothing of Godel
    numbering.  The question you are supposed to answer is:
    "Why isn't this string a theorem of TNT?"  Now you are
    used to such questions; for instance, if you had been
    asked that question about S0=0 [successor of 0 = 0],
    you would have a ready explanation: "Its negation,
    ~S0=0 [no successor of 0 = 0] is a theorem."  This,
    together with your knowledge that TNT is consistent,
    provides an explanation of why the given string is a
    nontheorem.  This is what I call an explanation on the
    TNT level...

    Now what about G?  The TNT-level explanation which
    worked for S0=0 does not work for G, because ~G is NOT
    a theorem.  The person who has no overview of TNT will
    be baffled as to why he can't make G according to the
    rules, because as an arithmetical proposition, it
    apparently has nothing wrong with it.  In fact, when G
    is turned into a universally quantified string, every
    instance gotten from G by substituting numerals for the
    variables can be derived.

    The only way to explain G's [G = Godel sentence]
    non-theoremhood is to discover the notion of
    Godel-numbering and view TNT [or Peano arithmetic] on
    an entirely different level.  It is not that it is just
    difficult and complicated to write out the explanation
    on the TNT-level; it is IMPOSSIBLE [my emphasis].

> Those guys normally have their heads screwed on -
> and Hofstadter and Dennet are AI proponents, well
> known for advocating the opposite viewpoint.

Yes.  And in fairness, Hofstadter continues with a paragraph
in which he seems to be holding out hope that the higher
level explanation issues might themselves be addressed
without necessarily abandoning the assumptions of the
AI advocates:

    But it is important to realize that if we are being
    guided by Godel's proof in making such bold hypotheses, we
    must carry the analogy through thoroughly.  In particular,
    it is vital to recall that G's nontheoremhood DOES have an
    explanation -- it is not a total mystery!  The explanation
    hinges on understanding not just one level at a time, but
    the way in which one level mirrors its metalevel, and the
    consequences of this mirroring.  If our analogy is to hold,
    then, "emergent" phenomena would become explicable in terms
    of A RELATIONSHIP [my emphasis] between different levels in
    mental systems (Douglas Hofstadter, GEB, p. 708)

Or, in the words of Hofstadter's cohort, D.C. Dennett,

    "And then a miracle happens."  :)