The post is addressed to George, but concern "my thesis". May I make some comments?
I put "my thesis" in quotes because it is really the Sound Universal (Turing) Machine's thesis, you know. ... or will know ;)
"Turing" is under quotes thanks to Church thesis. It is Church thesis which makes the notion of universal machine independent of which precise machine is used to define it. After denying the Church Turing Post Markov ... thesis for some time Godel will eventually accept it and he will call it an epistemological miracle (in its Princeton talk, see Davis 1965).
Church thesis makes the intuitive notion of computability -machine or -reference frame totally independent. We can also say that the notion of computability is formalism independent.
After having accepted Church thesis, Godel will look after a corresponding machine or formalism independent notion of provability. This is curious, because at that time Godel did show, by its own incompleteness phenomenon, that provability is an essentially machine or formalism dependent notion. At the same time, by its very reasoning Godel will provide tools for studying what *is* universal and machine independent concerning the provability notion. This gives rise to the logic of provability, also called the logic of self-reference, which has made tremendous and continuous progress since its birth.
After this introduction I want to comment Stephen's genuine remarks in some sufficiently precise
way so that we can avoid future misunderstanding.
> The problems that I have with Bruno's thesis is Digital
>substitution and that it does not address the problem of
>epiphenomenona found in both Idealism and Materialism.
Giving that the Comp, through the UDA (for exemple) , leads to Monistic idealism, I think the use of the word "epiphenomenon" could be misleading (it is used more in the non interactive dualist approach of the mind body problem, as far as I know). It is better to to talk about simply phenomena, and I guess you pretend I don't address them (which imo is a little bit unfair as I will try to explain).
>Digital substitution seems to assume that consciousness
>and awareness and related notions can be completely
>explained in terms of how one number relates to another.
Here is an "important error", on which ultimately Godel's theorem will put light.
Saying "yes doctor" for a digital brain substitution does not mean you or the surgeon or the international scientific community has *explained* how consciousness is related to
numbers or machines. As I insist, comp needs an act of faith. It says there is a level where we can survive (in the grandmother sense) to a digital subtitution, but then it justifies why an ignorance gap remains and must remain. That is: IF there is a level where we survive the subtitution, then we can never pretend to know that level. Please remember that Godel's theorem shows that provability by a machine and truth about that machine are different from the machine perspective. Yes the comp practionners believe its own consciousness can be reduce in some way to relations between numbers, but he/she does not pretend that, even if the correct realtions are given to him, that he can take them as a complete explanation. Comp + Godel will justify why he would became inconsistent would he find such an explanation.
It helps to keep this in mind to understand the explanation of where the physical appearance comes from, because in some sense the physical appearances will come from our sharable border of that necessary ignorance, where "our" refers to *us* the hopefully sound universal machines.
>I think that your would agree that Bruno's thesis
>is a very sophisticated form of Idealism.
OK. Although I'm not so sure it is so sophisticated. I could argue it is just the consequence of George Boole's laws of thought. But OK.
>It is widely recognized that "matter" and physicality in
>general is an epiphenomenona within any Ideal theory.
You say that again. Perhaps you are right. I would be please to know some references.
In the case of monistic idealist theory I do think "phenomena" or "appearances" are less misleading terms.
>This in turn makes the notion of a physical substrate
>suspect as it does not exist apart from its properties
>as encoded in numbers, e.g. our consciousness is
>merely information thus what that information is
>"encoded" in is irrelevant.
I do not quite agree with the saying "consciousness" is merely information. I will at some point suggest that consciousness is true and partially automated anticipation of our own consistency, but it is premature to do it now (without first explaining Godel's theorem and the Solovay's extensions with G, G* etc.).
> What I am trying to do is to make the point that it
>is not sufficient to just take as an article of faith
>or postulation the idea that digital substitution is
>actually possible, especially when the epiphenomenona
>problem is not even addressed! OTOH,
Please remind me what means "OTOH" I always forget this one!
It is not sufficient to make that act of faith to solve the mind-body problem, I agree. Although it is sufficient for surviving the digital brain transplantation (if comp is correct).
But I'm afraid the (epi)phenomena are addressed. I can even sum the technics up in one short sentence: just apply the Theaetetus' definition of knowledge from opinion with opinion defined by machine's formal provability.
if it can be shown that digital substitution is possible in practice then Bruno's thesis will go along way to explaining many things. But there is more to my difficulties than this! Copying, to me, implies that something is doing the copying. What is that
I do not think that the notion of "possible in practice" is relevant for the issue here.
I am not sure I understand either why you need that something does the copying. Where would that something come from?, and what would it be?, as you ask yourself. I am not building from nothing, I take granted arithmetical truth. It is a part of comp, and it's enough to grant the computational histories, and stable machine discourses including some necessary interrogations. The phenomenal qualities will be handled by logical *modalities*, those isolated from variant of the Godel Lob logic of self-reference.
Stephen, thank you for your frank remarks which helps me to be aware all this is not so easy.
I suspect you make the Lucas-Penrose confusion, consisting to confuse "believing we are a machine", and "believing we know which machine we are". In the case of consistent or sound machines the truth of the first proposition entails the falsity of the second one.