# Re: Numbers, Machine and Father Ted

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Le 29-oct.-06, à 12:21, 1Z a écrit :```
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> 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.

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))???

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 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".

... 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

Bruno

http://iridia.ulb.ac.be/~marchal/

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