1Z wrote: > > > Mark Peaty wrote: >> SP: 'using the term "comp" as short for "computationalism" as something >> picked up from Bruno. On the face of it, computationalism seems quite >> sensible: the best theory of consciousness and the most promising >> candidate for producing artificial intelligence/consciousness' > > What Bruno calls comp isn't standard computationalism, it has > an element of Platonism.
Mark Peaty wrote:
For my benefit, could you flesh that out in plain English please? Regards Mark Peaty CDES [EMAIL PROTECTED] http://www.arach.net.au/~mpeaty/
--------BRUNO's "COMP" INCLUDES ARITHMETICAL REALISM------------- BM: 'The precise comp version is given by a) the "yes doctor" act of faith YD b) Church (Hypo) Thesis CT c) Arithmetical Realism hypothesis AR ' BM:'Now, it is a fact, the failure of logicism, that you cannot define integers without implicitely postulating them. So Arithmetical existence is a quasi necessary departure reality. It is big and not unifiable by any axiomatisable theory (by Godel). (axiomatizable theory = theory such that you can verify algorithmically the proofs of the theorems) I refer often to Arithmetical Realism AR; and it constitutes 1/3 of the computationalist hypothesis, alias the comp. hyp., alias COMP: COMP = AR + CT + YD (Yes, more acronyms, sorry!) AR = Arithmetical Realism (cf also the "Hardy post") CT = Church Thesis YD = (I propose) the "Yes Doctor", It is the belief that you can be decomposed into part such that you don't experience anything when those parts are substituted by functionnaly equivalent digital parts. It makes possible to give sense saying yes to a surgeon who propose you some artificial substitution of your body. With COMP you can justify why this needs an irreductible act of faith (the consistency of COMP entails the consistency of the negation of COMP, this is akin to Godel's second incompleteness theorem. It has nothing to do with the hypothesis that there is a physical universe which would be either the running or the output of a computer program. Hal, with COMP the "identity problem" is tackled by the venerable old computer science/logic approach to self-reference (with the result by Godel, Lob, Solovay, build on Kleene, Turing, Post etc...)' REALISM AND PLATONONISM -------------------------------------------------------------------------------------------------------------- BM: 'Arithmetical Realism (AR). This is the assumption that arithmetical proposition, like ''1+1=2,'' or Goldbach conjecture, or the inexistence of a bigger prime, or the statement that some digital machine will stop, or any Boolean formula bearing on numbers, are true independently of me, you, humanity, the physical universe (if that exists), etc. ' PJ: That's an epistemological claim then.... BM: 'It is a version of Platonism limited at least to arithmetical truth'. PJ: Is it ? But Platonism is an ontoligcal thesis. As a standard reference work has it: "The philosophy of Plato, or an approach to philosophy resembling his. For example, someone who asserts that numbers exist independently of the things they number could be called a Platonist." BM: 'It should not be confused with the much stronger Pythagorean form of AR, AR+, which asserts that only natural numbers exist together with their nameable relations: all the rest being derivative from those relations. If Pythagoreanism is stronger than Platonism in insisting that everything is derivable from (existing) natural numbers, is Platonism weaker than Pythagoreanism in insisting that everything is derivable from existing numbers of all kinds, natural or not? Is Platonism not being taken a s alcaim about existinence here, not just a claim about truth ? BM: "A machine will be said an Arithmetical Platonist if the machine believes enough elementary arithmetical truth (including some scheme of induction axiom)." PJ: Switching back to an epistemological definition of "platonism" BM:'Instead of linking [the pain I feel] at space-time (x,t) to [a machine state] at space-time (x,t), we are obliged to associate [the pain I feel at space-time (x,t)] to a type or a sheaf of computations (existing forever in the arithmetical Platonia which is accepted as existing independently of our selves with arithmetical realism).' PJ: Another use of Realism as a thesis about existence. PJ: And if the pain-feeling "you" exists eternally, how do ever *not* feel pain ? There is an ontological gulf between tokens and types, between the temporal and the eternal, which has been leaped over at a bound here. ------------ BRUNO ADMITS TO (ONTOLOGIAL) PLATONISM ----------------- BM: 'Numbers are not physically real does not entails that numbers don't exist at all, unless you define "real" by "physical real"'. 'I reduce the stable appearance of a "physical universe" to "stable belief" by numbers, which are existing mathematically' 'That is why I explicitly assume the existence of numbers, through RA or PA axioms when I interview the machine, or by accepting the independent truth of arithmetical statements, like in UDA.' ------------ BRUNO ADMITS TO (ONTOLOGIAL) PLATONISM (2) ----------------- PJ: But you *also* think that numbers do have some sort of existence (even if you want to call that "realism" or Plotinism, or something other than Platonism). BM: Yes. Mathematical existence. PJ: Where are these machines? BM: Where you could be, assuming comp, and no fatal error in the UDA argumentation. I was used to call it arithmetical platonia. Logician call it the standard model (logician sense) of PA. I use a generalisation of that for lobian machine. Incompleteness prevent any complete theory describing that. BM: Where the numbers are. ------------ BRUNO DENYING PLATONISM ---------------------- BM: 'I don't need to have that "2" exists. In that sense I am an anti-platonist, if you want. I only need "2 exists", and then it is a simple exercise to derive it from "2+2 = 4": 2+2 = 4 Ex(x+2 = 4 & x = 2) Ex(x=2) Or perhaps you are telling me that an anti-platonist does not accept the quantifier introduction inference rule (from A(t) infer Ex(Ax))??? After all this would be coherent given that I have defined an (arithmetical) platonist to be just someone accepting classical logic (in arithmetic). Lobian machine, like PA or ZF, are platonist, for example. You can see this, in the AUDA part, as a kind of "formalism" if you want. Judson Web, see the ref in my thesis" makes such a case.' -------------BRUNO AGNOSTIC BUT TENDING TOWARDS PLATONISM ---------------------------- BM: Now, many people does take as axiom the unprovable assertion that there is a physical universe. I don't. I am not "atheist" about the universe, but I am agnostic. I believe less in a primitive physical universe (especially as an explanation of physics) than in more general "god-like" or "mathematical-like" reality. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
