1Z wrote:
> > > 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.
Peter, when you said that the physical might be 'relations all the way
down', and I asked you what would you find if you went 'all the way
down', you replied 'primary matter'. IOW, you posit primary matter as a
'bare substrate' to which are attached whatever properties theory or
experiment may suggest. Consequently, isn't it the case that you are
defining this 'bare substrate' (which by posit has no properties of its
own) as whatever-it-is that is RITSIAR (i.e. you might say that it's
what exists)? Bruno, aren't you making essentially the same claim for
AUDA, in attempting to derive all properties from it? In your schema,
if AUDA isn't RITSIAR (even if you'd rather define 1-ritsiar or
3-ritsiar separately), then is anything? Are these two views
commensurable at all? Or are you saying that we can only maintain a
Wittgensteinian silence on such questions?
David
> 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/
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Received on Sun Oct 29 2006 - 11:43:46 PST