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.
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
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.
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