Le 29-oct.-06, à 15:27, 1Z a écrit :
> > You do need your UD to exist, or your argument that > I am being generated by it is merely hypothetical. I agree. I need "UD exists", and that is a theorem of PA. I was saying that I don't need "UD" exists in some magical realm. > >> 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))??? > > No, (Anti)Platonism is a philosophical position about > the ontology of mathematical claims, not a mathematical position > about which mathematical claims are true. Such distinction are 1004 fallacies at this stage. learn the theory before quibbling on the terminology. > >> 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. > > 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). Yes. Mathematical existence. > > '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.' > > >> But now, with all my respect I find those metaphysical if not magical >> marmalade a little bit useless. I propose indeed a more precise >> version >> of computationalism than usual, in the sense that I presuppose >> explicitly the classical Church Thesis, which by itself presupposes >> classical logic in the realm of numbers, but then I have made this >> explicit too for avoiding unnecessary complication with possible >> ultra-finitist in the neighborhoods. >> >> Then I propose a reasoning which in a nutshell shows that IF there is >> a >> sense in which a turing machine can distinguish this from that, THEN >> she will will be forever unable to distinguish for sure "real" from >> "virtual" from "arithmetical" possible worlds, or states ... Indeed >> UDA >> already shows that the physical (the observable) must arise from a >> "sum >> on all that the machine can defined". > > Where are these machines? Where the numbers are. 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. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
