Bruno Marchal wrote:
> Le 29-oct.-06, à 12:21, 1Z a écrit :
> > That's in the sense of abstract truth, not in the sense
> > of real existence, then. (Remember: anti-Platonists
> > agree that "2+2=4" is a necessary apriori truth,
> > they just disagree that "2" exists).
> I don't need to have that "2" exists.
You do need your UD to exist, or your argument that
I am being generated by it is merely hypothetical.
> 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)
> 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.
> 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).
'Numbers are not physically real does not entails
that numbers don't exist at all, unless you define "real" by "physical
'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
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?
> ... so that *betting on comp" at her tour, she can infer abductively
> from it that her basic reality is arithmetical, that her physics is
> comp-arithmetical, and that this is empirically testable. Indeed I get
> the logic of the observable propositions from interviewing her.
> Peter, I got this in the seventies (except for theorem 14 in my french
> thesis), I defended this as a PhD thesis in France in 1998. I thought
> "acomp" to be refuted in the year. Some people have *pretended* that.
> It is a mathematically very transparent and clearly empirically
> falsifiable theory of quanta and qualia, but mathematically not so easy
> (I guess that was the price). Yet the first open problem (the
> axiomatization of "intelligible matter") has been solved recently: the
> logic Z, Z*, Z1; Z1* has been axiomatized. My initial and still basic
> goal consists just in showing that the mind body problem is open, but,
> through some class of hypothesis (theories), mathematically
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