Dear Bruno, please, don't even read this: (This is not a personal attack on you or YOUR theory, it is a common belief and I question its usability - not by opposing, just curious to find a way to accept it and experience the happiness of the mathematicians).
It is a retardating barrier for me to jump from thinking about reasonable (problematic?) topics into 2+2=4 or 3x17=367 or that 17 is a prime number. Could we talk 'topics' without going into trivialities what every child knows after the first visit to the grocery store? As long as we cannot identify what a 'number' is, it does not contribute to an understanding of reason. What is '3' without monitoring something? Why is it not the same as 35.678? or 5? (of course they are, just set the origo and the scale accordingly). And this 'meme'based illusion is used to explain 'serious' features (not quantized, counted, equated or compared values they refer to. Please remember these 3 last words!) As you can see, I have no idea about number theory. Whenever I tried to read into it, I found myself (the text) inside the mindset which I wanted to approach from the outside. Nobody offered so far a way to "get in" if you are "outside" of it. It is a magic and I do not like magic. I propose a test: Next time when I ask "how can you describe the taste of vanilla by manipulating ordinary numbers"? TRY IT. With friendship and ignorance John ----- Original Message ----- From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <firstname.lastname@example.org> Sent: Friday, July 21, 2006 10:37 AM Subject: This is not the roadmap This is not the roadmap. I think aloud in case it helps (me or someone else). Le 21-juil.-06, à 15:01, I wrote > This can be made precise with the logics G&Co, but for this I should > explain before the roadmap George has suggested (asap). My problem. How much should I rely on Plotinus? When people asks me for a non technical version of my saying, Plotinus' Enneads are quite close to that. You should not take his examples literally, but only its logic and the difficulties he encouters. I must think. Strictly speaking, math is what makes the explanation easier. In a nutshell I could perhaps try to put it in this way: One (among many) possible description of the comp ontology of a comp TOE, is just: Classical logic + the (recursive) definition of addition and multiplication. This gives Robinson Arithmetic (RA), one of the weakest theory possible. RA can prove that 4 + 5 = 5 + 4, but is already unable to prove that this is true for any number n. RA cannot generalize. It can prove that the sum of the first ten odd numbers 1+3+5+7+9+11+13+15+17+19 = 10 * 10, but RA cannot prove that for any n the sum of the n first odd numbers gives always the perefct square n * n. Yet, RA has enough existential provability ability so as to be able to represent the partial recursive functions, and from a recursion theorist point of view RA can be seen as a universal machine, and RA's theorem codes the generation of a universal dovetailing. (Technically RA is able to prove all true sigma-1 sentences, those which are like ExP(x) with P decidable). Now if I stop here, I would fall against a critic David Deutsch once made against Schmidhuber's "computationalist view of everything". It would be quasi trivial. So I add an epistemology: this concerns what richer machine's can prove. Those richer machines are emulated all the time in the sequence of simple existential proposition proved by RA. Then I do what Everett did for quantum mechanics: what can prove the lobian machine whos histories are generated by RA, or any DU, or just the sigma1 truth). (To understand this you need to understand the difference between computation or emulation, and proof). Many people are wrong about this. For example the (very rich) theory ZF can prove that the (rich) theory PA is consistent. PA cannot prove that. But PA can prove that ZF can prove PA's consistency. The main reason fro that, is that the fact that you can emulate Hitler's brain (in platonia) does not entail you will get Hitler's belief. This can be related to Dennett and Hofstadter correct (assuming comp) rebutal of Searles in the book "Mind's I". Even RA can prove that ZF can prove that PA and RA are consistent! But RA and PA and ZF can hardly prove that they are respectively consistent (no theories which can talk about addition and multiplication can prove their own consistency, but richer lobian machine can prove many things on simpler lobian machine, including what is true about the simpler machine that the simpler machine cannot prove). The lobian machine, my epistemology, is thus richer than the TOE comp basic ontology (given by RA or the UD). A typical lobian machine is given by the theory (or its corresponding theorem prover program if you prefer) PA (Peano arithmetic). It is given by -Classical logic -the (recursive) definitions of addition and multiplication -The infinity of induction axioms (read "A" "for all") like [P(0) and An(P(n) -> P(n+1))] -> AnP(n) This provides PA with incredible introspective abilities, enough for enabling it to discover its limitations and the geometry of those limitations. and eventually to correctly infer, from the logic of provability (note the "v) the logic of "probability" (note the "b") bearing on the collection of all their consistent extensions. And more. At least enough for discovering two, and then 4, 8, 16, ... plotinian-like hypostases (person notions), including the one which justify matter, both in the UDA sense, and in the plotinian sense (a "slight platonist correction of Aristotle theory of matter actually (I begun the reading of Aristotle at last). Note that the first primary hypostasis, truth, could aptly be called the zero person point of view. That could perhaps be related with Nagel's "point of view of nowhere". It is really here that Plotinus contradicts the more Aristotle, which first hypostasis, seems to be a 1-person, especially in the treatise (5.6) which has been abridged out in the pengwin paperbook Ennead (I guess a coincidence because that point is well explained in many other ennead's treatise, so it is normal to abridged this one for making possible to put the enneads in your pocket without demolishing the pants). I must think, the subject is difficult and goes over many disciplines, Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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