Dear Bruno,
On 8/3/2012 3:55 AM in post "Re: Stephen Hawking: Philosophy is Dead",
Bruno Marchal wrote:
There is no recipe for intelligence. Only for domain competence.
Intelligence can "diagonalize" again all recipes.
A very good point! Intelligence is thus forever beyond a horizon or
boundary within which recursively countable is possible. This is exactly
the idea that I see implied by "relativizing" the Tennenbaum theorem.
For any kind of "something" ( I do not know what it is named at the
moment) there is always a recursively countable name that that something
has for itself. Recall what Wittgenstein wrote about names
<http://en.wikipedia.org/wiki/Naming_and_Necessity>:
"According to descriptivist theories, proper names either are synonymous
with descriptions, or have their reference determined by virtue of the
name's being associated with a description or cluster of descriptions
that an object uniquely satisfies. Kripke rejects both these kinds of
descriptivism. He gives several examples purporting to render
descriptivism implausible as a theory of how names get their reference
determined (e.g., surely Aristotle could have died at age two and so not
satisfied any of the descriptions we associate with his name, and yet it
would seem wrong to deny that he was Aristotle). As an alternative,
Kripke adumbrated a causal theory of reference, according to which _/*a
name refers to an object by virtue of a causal connection with the
object as mediated through communities of speakers. He points out that
proper names, in contrast to most descriptions, are rigid designators: A
proper name refers to the named object in every possible world in which
the object exists, while most descriptions designate different objects
in different possible worlds.*/_ For example, 'Nixon' refers to the same
person in every possible world in which Nixon exists, while 'the person
who won the United States presidential election of 1968' could refer to
Nixon, Humphrey, or others in different possible worlds. Kripke also
raised the prospect of a posteriori necessities --- facts that are
necessarily true, though they can be known only through empirical
investigation. Examples include "Hesperus is Phosphorus", "Cicero is
Tully", "Water is H2O" and other identity claims where two names refer
to the same object."
A name is "perfect" if it is a recursively enumerable
representation of an object. This definition is required by the
postulate that "reality is that which is incontrovertible" for all
inter-communicating observers". We could define an observer as any
system capable of implementing in its dynamics a computational
simulation of itself. Most objects that exist cannot do this on their
own, a brick for example. But consider that at a deeper level, a brick
is a lattice of atoms that supports an entire level of dynamics - the
electrostatic interactions of the electrons and protons for example -
and at this level there is sufficient structure to support an
organizational equivalent of a computation of a brick.
This takes your "substitution level" idea another step!
Even for competence, effective recipes are not tractable, and by
weakening the test criteria, it is possible to show the existence of a
non constructive hierarchy of more and more competent machines. It can
be proved that such hierarchy are necessarily not constructive, so
that competence really can evolve only through long stories of trial
and errors. Intelligence is basically a non constructive notion. It is
needed for the development of competence, but competence itself has a
negative feedback on intelligence. Competent people can get easily
stuck in their domain of competence, somehow.
They can get stuck in a recursive loop where they are unable to
"see" outside of their dreams about themselves. Nice example of
solipsism, no? ;-) The trick is to never get stuck in a single point of
view of one's world! There are an infinite number of possible
observational bases, why only use one?
If you are interested in theoretical study of competence, you might
read the paper by Case and Smith, or the book by Oherson, Stob,
Weinstein (reference in my URL).
I will look for this. As I was checking down links, I found
<http://en.wikipedia.org/wiki/Intensionality>:
"In philosophical arguments about dualism versus monism, it is noted
that thoughts have intensionality and physical objects do not (S.E.
Palmer, 1999), but rather have extension in space."
and further <http://en.wikipedia.org/wiki/Intensional_logic>:
"Intensional logic is an approach to predicate logic that extends
first-order logic, which has quantifiers that range over the individuals
of a universe (extensions), by additional quantifiers that range over
terms that may have such individuals as their value (intensions). The
distinction between extensional and intensional entities is parallel to
the distinction between sense and reference."
Is not what you are arguing for here in your post exactly what
Intensional logic was found to do?
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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