>All:�
>
>Folks might enjoy the Soloman Feferman�lecture
><http://math.stanford.edu/~feferman/papers/godelnagel.pdf>Goedel,
>Nagel, Minds and Machines.�After recounting�an
>exchange between Godel and Nagel�circa 1956,
>�Feferman describes the implications of the
>minds vs. machines dichotomy ensuing from the
>exchange. (01)
There has been a LOT of material written on this
general topic since 1956. At that date, AI
systems in the modern sense did not yet exist, so
the discussion was not particularly well-informed. (02)
> To avoid the impass�resulting from the
>dichotomy, Feferman proposes the redefinition of
>a formal system to an �open ended schematic
>axiomatic system.� He claims�this redefinition
>is a constructive step towards an �informative,
>systematic account at a theoretical level of how
>the mathematical mind works�that squares with
>experience.� (03)
Yes. His idea was subsequently formalized and
then quite rapidly shown to suffer from the same
limitations as the simpler Goedel notion. So
considered as an end-run past Goedel, it did not
succeed. It is now generally accepted that all
such attempts to sneak past the Goedel result are
doomed to failure, and this topic is considered
to be closed. However, none of this has any
bearing on AI, contrary to what Penrose and
others (including Goedel) believe. For a fairly
thorough refutation of the Goedel-based attack on
AI, see: LaForte, Hayes & Ford (1998) "Why
Godel's theorem cannot refute computationalism"
Artificial Intelligence 104 (1998) 265-286 (04)
> He stresses the importance of�a�subject neutral
>theory of operations�with basic schemata for
>language, arithmetic, set theory that�would
>amount to a version�of an untyped lambda
>calculus.�Feferman concludes by�rejecting any
>effective machine representation of�mind as
>contemplated by Nagel, Penrose & others.��
>
>So, what does this mean to Common Logic and LBase ?� (05)
Absolutely nothing. (06)
>Seems to me that efforts
>like�<http://cl.tamu.edu/>Common Logic and
><http://www.w3.org/TR/lbase/>LBase would either
>have to a) be�defined within this type of an
>open ended system, let�s say as the natural
>language description of the constraints to which
>the axioms�that make�up the theory of such a
>system would �adhere; or b)�evolve into�an open
>ended system�that exhibits�characteristics
>of�transformation across languages, logics,
>models and theories. (07)
No, neither. Common logic is simply a modernized
Net-savvy restatement of first-order logic, in an
attempt to get past the interoperability problems
arising from the huge variety of surface
notations in use. LBase is (was, better, as it
seems to have been widely ignored) an earlier
attempt to do this for the W3C family of semantic
web languages. Goedel's incompleteness result,
which gave such a shock to foundations of
mathematics, has no relevance to the completeness
of first-order logic (which was also first proved
by Goedel, by the way.) (08)
Pat (09)
>
>Rick
>
>
>
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