http://groups.google.com/group/everything-list/t/37514d7224e09703

Discussion that I have started on the everything-list. Below some answers from Bruno.

Embryogenesis fits very well. The second recursion theorem of Kleene provides the conceptual solution of a problem given by Descartes: how to build a machine capable of self-reproduction. I have explained the ‘trick’ sometimes. I use a generalisation by John Case to program ‘planarias”, that is programs which are ble to regenerate themselves when cut in parts. I illustrate that embryogenesis can be described by case’s generalization of Kleene’s recursion theorem. In fact in computer science, Kleene’s theorem can be seen as the most fundamental theorem of ‘abstract biology’.The quitessence of the trick is to apply a duplicator D to itself. If Dx gives xx, DD gives DD.

The same trick is used for handling self-reference by machines and theories, or belief systems, and this leads to G and G*, and their variant.

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I was talking on the multicellular planaria:

http://www.youtube.com/watch?v=J9EuFuJF9N0

http://www.youtube.com/watch?v=vXN_5SPBPtM

My self-regenerating program PLANARIA was made of many cells, subprograms occupying different locations (in the code), and having different functions. Yet you can cut it in many pieces as little as one cell, and any such one cell regenerates the entire program!

It is described in the volume 2, 2, here:

http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html

(That work describes theorem provers, in LISP, for each hypostasis).

The recursion theoretic answer to self-regeneration gives the conceptual solution to embryogenesis, as that one cell regenerating complete “planaria” illustrates.

Of course the whole thing is far more sophisticated for the carbon implemented local living beings.

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I start from the mind body problem, and from the digital mechanist hypothesis. I show this makes us *very* ignorant.

So I will be franc. The problem of interaction is not solved at all, even between third person describable objects. And the problem of how many first person “really” exist is also an open problem, although I tend more and more to believe that there is only one first person: the universal person described by the arithmetical hypostases. Although personal consciousness is not an illusion, self-identity can be. But, please note that I am speculating here. And there do exist some evidence that the numbers of person could be at least two. That would be the case if the “whole truth” is a sort of person. Very complex question.

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Beautiful and wonderful.Astonishing? I know I will perhaps look presumptuous, but I think that Kleene’s second recursion theorem provides the conceptual solution of the Descarte-Driesch self-reproduction problem, I can argue that a generalization of Kleene’s theorem provides the conceptual solution of embryogenesis, even of self-regeneration. I wrote a paper on that for the first european meeting on artificial life (“Amoeba, Planaria and Dreaming Machine”). I wrote a program ‘planaria’, having a lot of different subroutines, and which is such that when a subroutine (any of them) is isolated and given some flag as input, it regenerates the entire program. I even programmed an infinite planarian.

For theology, fortunately, or perhaps unfortunately, all the use of the second recursion theorem is encapsulated in the theorem by Solovay, linking the modal logic G and G* to the self-reference abilities of what I call the Löbian entities (notably the Löbian numbers , the Löbian theories, the Löbian machines, and a large spectrum of Löbian ‘supermachine’).

In “conscience et mécanisme”, the long version of my PhD thesis, I do both the abstract biology and the abstract theology. Abstract biology takes the second recursion theorem as a fundamental theorem. Abstract theology takes as fundamental theorem the fact that some machine can prove a form of the second recursion theorem. It is known in the literature as the “Gödel’s diagonalization lemma”.

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