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 <>:

"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 <>:

"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 <>:

"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?



"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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