Bruno Marchal wrote: > 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.
If it doesn't exist anywhere, it is not generating me. > > > > >> 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. OK. Question one: where is the UD running? > > > > > >> 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. Which is...? Presumably the answer is not "on blackboards" or "in the minds of mathematicians". Apparently its not a "magical realm" either. > Where you could be, assuming comp, and no fatal > error in the UDA argumentation. I was used to call it arithmetical > platonia. So.. you didn't stop being a Platonist (in the standard sense) you just stopped calling yourself one. > 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 -~----------~----~----~----~------~----~------~--~---
