On 03 Aug 2012, at 20:43, Stephen P. King wrote:

On 8/3/2012 8:27 AM, Bruno Marchal wrote:

On 03 Aug 2012, at 11:43, Stephen P. King wrote:

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."

Most machine's possible properties are way beyond the recursively enumerable. For example the property of being able to compute the factorial function is itself not computable.

Dear Bruno,

Yes, and this is why properties (resulting from process!) are "special". Those that are not recursively enumerable form the orbits (?) within which the Perfect named objects are stable.

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!

Here you are too fuzzy for me. Sorry. *In* the comp frame, and we cannot take for granted notion of physical objects.

Yes, we cannot take for granted the notion of physical objects. In the theory that I am exploring, physical objects are (only!) those that can be represented by Stone spaces, which are in turn Stone dual to some Boolean Algebra if we consider only a timeless presentation. In physics these are represented as "bound systems". Those that are evolving and have a measure of time are represented by "Scattering states" of bound systems.

Locally it is plausible that brick "exists" and that they are a lattice of atoms, but this can only be a local relative description of how we conceive a brick.

Yes, and I mean my statement in the sense of your remark . It is only in a local frame of relations that there can exist an exact simulation of a brick such that the self-simulation criteria can be satisfied.

With comp, a brick is quite different sort of objects, for which we have no intuition at all. We can only do the math, as frustrating as that could seem.

Yes, we have to segregate the idea of a "brink" as appearing in a 1p (for example as a part of the environment in Moscow or Helsinki) from a 3p (which is a consensus or commonality of intercommunication observers).

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? ;-)

That illustrates the "lived solipsism" which we are all living, but this does not need to make us believe in doctrinal solipsism. We all feel alone, but we don't have to believe that we are alone.

    I agree.

The trick is to never get stuck in a single point of view of one's world!

That is a good idea, but it cannot be effective. That would give a recipe for intelligence, but you agreed there are none.

But is it really a recipe? Think about what I wrote here; it is not possible to write a precise recursively enumerable version of it! The state of "getting stuck" can only be defined in a relative 1p sense.

Yes. That is why it is not effective, and not a recipe.

There are an infinite number of possible observational bases, why only use one?

If by base, you mean the basic ontology,

No. I mean observational basis. For example, measurements that yield position date are in a position basis.

OK. But with comp we can no more assume observation, position, etc.

we can use only one (like arithmetic) because they are all equivalent, ontologically.

Yes, and that is exactly why I am asking you to reconsider the idea that arithmetic is ontologically primitive! When we reduce a class to the ontological primitive level (meaning that all else supervenes upon that class or some subclass thereof), then we make the relational structure of that class degenerate. We literally eliminate the meaningfulness of the class if we make it uniquely primitive. This is why a primitive class is denoted as "neutral". It cannot be "any particular thing", it is either "Everything" or "Nothing" or both simultaneously (depending on your pedagogical stance).

I cannot give sense to that paragraph.

Physics and theology/psychology/biology is independent of the choice of the base.

Yes, but not the names of the objects in them. Consider the contrary case. Assume that the names of objects within a physics theory or a theological schemata or a psychology or a biological taxonomy to be a priori definite or "given by necessity". It would then be impossible to rename the objects to take into consideration any novel condition as we can define by diagonalizations. Thus names cannot be a priori definite. QED.

But the ontology is not concerned by the names given to the object.

Epistemologically, we have the complete opposite. Special systems get special role, and we have to learn to live with the different points of view inside us and inside others.

I agree, but this is only in the case when we are considering the multiple minds of many 1p, each having some non-empty set of bisimilarity relations with each other.


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."

Except that with comp, extension in space is only an intensional notion. of course this is highly non trivial, and is a counter- intuitive consequence of computationalism. With comp, space and time are intensional notions.

Yes, but only when you are assuming Arithmetic Realism as you define it. My claim here is that your AR is wrong, objects (whether material or immaterial) cannot have a priori definite properties!

I assume the audience understand that 2+2 = 4, that 17 is prime, that phi_i(j) is defined or is not defined, etc. Nothing more.

If AR is wrong, absolutely all theories are wrong, except the physicalist ultrafinitist one.

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?

Er well, trivially once you get the point that incompleteness makes the correct machine able to justify the existence of (many) modalities/points of view. I mean that your statement here is very general. It concerns the whole modal logic approach, not just the modal approaches forced by comp and computer science. But OK.

    Yes, I was making a very general claim.




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