Wei Dai wrote:
>No, it's very helpful. I'll have more feedback after digesting the
>information and reading the books on metamathematics.
OK. Note that UDA needs only some passive knowledge of Church thesis.
This is need to understand that the Universal Dovetailer is *really*
universal. More elaborate Metamathematics is need for the Arithmetical
translation of the Universal Dovetailer Argument: AUDA.
My thesis is really just UDA + AUDA.
>A couple of suggestions in the meantime. In your future papers you may
>want to define some of the terms that you use. For example what you mean
>by "computationalism" seems to be a very specific kind of
>computationalism, as the term is commonly used. This page
>defines computationalism only as:
>> The notion that the operation of the mind can be explained entirely in
>> terms of the formal, or functional, properties of a computational
Thank you for the suggestion. In CC&Q comp is defined in a footnote:
bad idea I understand. Different form of comp are of course related.
We can discuss it later. Perhaps I should use another acronym,
like "icomp"? (for "I"-comp, or Indexical-Comp)
>You should also get a local colleague to review your papers before
The version which has been published has been so reviewed. I realise
the one in my web page has not. Oops. (Thanks for making me
>> The best book is Boolos 1993 "The logic of provability" (ref in my
>> thesis, or look at "Boolos" in the archive).
>> A good intro is Boolos and Jeffrey.
>> A textbook is Smorynski "Self-reference and Modal logic".
>> A popular introduction is Smullyan's "Forever Undecided".
>What about _Introduction to Metamathematics_, by Stephen Cole Kleene. Is
>that any good?
Oh! It is my favorite "pre-lobian" one. It precedes the 1955 discovery by
Lob of the truth of the propositions which assert their own provability.
And of course it preceeds the work by Solovay (1976). Solovay has shown
that metamathematics can be formalised in Modal Logic, notably by the
modal system G and G*. G captures (soundly and completely) the abstract
pattern of what a sound self-referential machine can prove, and
G* captures, crazily enough, all the true, even if not provable by the
machine, self-referential propositions (at some propositional level).
>> 2) Church Thesis: Anything computable is Turing computable. I give
>> the conceptual reason for this at
>You refence a "G*" in this post. What does that mean? May I suggest that
>you put a list of such terms and definitions on your web site for
>reference? You probably defined it in an earlier post, but again it's hard
>to read 500 posts. Perhaps you could also give a list of essential posts
>that explain your ideas as concisely and clearly as possible and the order
>that is best to read them in, and put that on your web site as well.
I have still some technical problems for modifying easily my iridia
web page, but I will take your suggestion into account. In the
meantime, for G and G* you can look at
and its errata: http://www.escribe.com/science/theory/m2840.html
>> Also, when you say that QM should be the shortest algorithm, I am
>> afraid you share with Schmidhuber a proposition on the mind body
>> relationship which I show to be inconsistent with comp. You seem
>> to believe that the mind brain relation is one-one.
>No I don't believe that. What I meant was that QM plus a translation
>algorithm (into some abstract description of observer-moments) is the
>shortest algorithm. I think that multiple distinct brains can translate
>to the same abstract description.
Nice. That will help for the sequel.
>On the other hand, from a decision theory perspective, this question may
>be irrelevent or just a subjective value judgement.
I think it will be relevant, not only with respect to some
computationalist practice (accepting a digital prosthesis made at
this or that level), but also because the reasoning I propose
should lead to our aknowledgement of a bigger form of ignorance, and
this could encourage us to be more cautious with judgments
and decisions in general. Shakespeare said that "Conscience make us
Coward" (Hamlet), I believe comp justifies this in some way.
>The reason I'm so
>interested in a decision theoretic approach is that it may help us figure
>out which are the essential questions, and which may just be empty
I agree with you.
>If the answer to a question is irrelevent to choosing actions,
>does the question mean anything? If the answer only affects the utility
>function, does that mean it has no objective answer and there is no point
>in arguing over it?
The answer to a question, or the absence of such an answer, can
be relevant in choosing actions for general reasons. I think that an
overview of "reality" can help in the shaping of beliefs and
decisions in some indirect and negative way. Because now we
can bet, with comp, that if our knowledge grows our ignorance grows
more. We become more fallible, we get more doubts, and at the same
time that necessary ignorance space got some invariant
geometry related with that reality. Comp owes to Descartes who
sees the powerfullness of systematic doubting for raising solid
fixed point. Metamathematics can make this precise.
>P.S. Happy Thanksgiving everythingers. Right now I'm very thankful that I
>live in a world that affords me the opportunity to think and talk about
It is a big pleasure sharing our interest. Deep thanks for giving us
that opportunity, Wei. Happy Thanksgiving Everyone.