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/
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Received on Sun Oct 29 2006 - 10:46:22 PST