Hi David,

Le 02-sept.-07, à 17:00, David Nyman a écrit :

> On 02/09/07, Bruno Marchal <[EMAIL PROTECTED]> wrote:
>> You could have chosen a better moment because next week I have exams
>> and will not be in my office, but the week after I will try to explain
>> this. It is necessary to get the UDA, and even more for the AUDA (the
>> lobian interview).
> Hi Bruno
> Given your current commitments, I'll continue my reading, and also
> thinking about the various issues recently posted.  Let's continue the
> dialogue the week after the exams.

No problem. I hope you don't mind if I give little exercises from time 
to time. My goal is not to teach logic on the list but only to explain 
the minimal amount so that I can explain better some result, so that 
people are not mislead by the vocabulary. It is just OK to ask me for 
answesr if only for the benefits of the others. It is obvious that comp 
makes sense only through some COMPuter science ...

> BTW, I've also been intermittently reading Schopenhauer (and Bryan
> Magee's book on him) and ISTM that maybe comp is a way to approach the
> Kant-Schopenhauer noumenon, at least in the sense that what is below
> our substitution level is indiscernible, and hence in that way
> inescapably 'noumenal', for us (i.e. it's constitutive of us, but
> never an object of our knowledge).

It is bit more complex, in the sense that it is not just because those 
sublevel substitution are indiscernible, but also because we have to 
bet on a substitution level at the start: so, eventually, the 
theological part is more related to the G/G* distinction than to the 
unknowability of what happens below the subtitution level, but again we 
are anticipating ... Of course those points are related.

> Is this in any way similar to what
> you mean by machine 'theology', in the sense that its theology (or
> noumenon) is equivalent to a machine's beliefs about its ontology
> (i.e. its constitutive or 'substitution' level), but that these
> beliefs can never be formulated as proofs about its epistemic (or
> 'phenomenal') world?

It is related. Actually I am not yet sure about the best way to define 
this 'machine theology'. But the simplest way is to define the theology 
of machine M by the difference between TRUTH ABOUT the machine M, and 
what the machine M can prove about herself, once she bets on some 
substitution level (and once she bets on comp, also).
This is a non normative definition of theology. Nobody pretends to know 
truth about us. But it is a fact that rich lobian machine can *prove* 
everything about simpler machine theology (at the propositional level).

> If so, the content of such a belief would then
> be what Wittgenstein, taking his lead from Schopenhauer, claimed
> (though he stressed its primacy) that we couldn't make intelligible
> statements about (i.e. the mystery *that* the world is); but the
> notion of substitution level in comp would in fact give us a way of
> speaking about it in a relative way.

Yes, again this is related. In "CONSCIENCE ET MECANISME" I make that 
relation explicit. I take as axiom what I did call the WITTGENSTEIN 
principle: such content is an x such that, well not only we cannot 
prove x, but the truth of x entails the non-provability of x. That is, 
we have both:

~Bx, and
x -> ~Bx

with "B" meaning "provable by M", in the language of the (ideally 
correct) machine M. Note that any falsity, like "0 = 1" satisfies the 
first formula trivially: ~B'0=1' is true for an ideally correct 
machine. But that very fact is a truth which, by the second 
incompleteness result, cannot be given by the machine. So x = 
consistency (x = ~B'0=1') statisfies the second formula: ~B"0=1' -> 
~B(~B'0=1'), or ~Bf -> ~B(~Bf). OK?

To sum up: theology of machine M = truth about M minus provability by M 
about M. (Tell me if this makes some sense for you, or nothing, but 
again we are anticipating).




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