Juergen Schmidhuber wrote

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> Russell Standish wrote: >> I never subscribed to computationalism at any time, >> but at this stage do not reject it. I could conceive of us living in >> a stupendous virtual reality system, which is in effect what your GP >> religion Mark II is. However, as pointed out by others, it does suffer >> from "turtle-itis", and should not be considered the null >> hypothesis. It requires evidence for belief. > >By turtle-itis you mean: in which universe do the GP and his computer >reside? Or the higher-level GP2 which programmed GP? And so on? But >we cannot get rid of this type of circularity - computability and >mathematical logic are simply taken as given things, without any >further explanation, like a religion. I disagree. Comp could not have any pretension with respect to the search of a TOE without Church thesis. And we can argue for Church Thesis. (The two main and very different types of argument are: a) The empirical fact that all definitions of computable functions leads provably to the same class of functions. b) The closure of that set for the "most transcendant" operation in mathematics: diagonalisation. It is really the closure of the set of computable functions for the diagonalisation which save comp from any form of *turtle-itis*. That closure provides the fixed point for all computable and self-referencial transformations (from which in particular G and G* an G* minus G can arise). >The computable multiverse, or >the set of logically possible or mathematically possible or computable >universes, represents the simplest explanation we can write down formally. Except that I still don't know what you mean by "universe". >But what exactly does it mean to accept something as a formal statement? >What does it mean to identify the messy retina patterns caused by this >text with abstract mathematical symbols such as x and y? All formal >explanations in our formal papers assume that we agree on how to read >them. I disagree. Axiomatic has been invented and developped for being able to see the validity of our reasoning independently of our interpretations of it. Of course we bet on the ability to distinguish things, and O/1 in particular, but that's another level. >But reading and understanding papers is a complex physical and >cognitive process. So all our formal explanations are relative to this >given process which we usually do not even question. You are mixing levels of description. It is not because I take for granted that you can read english, that I will take for granted that you have a brain made of wave/particle or *any* physical description. This confirm your *use* of the GP suffers turtle-itis. I should have ask you what you mean by universe much earlier. My feeling is you are presupposing some conception of the universe. The UDA gives at least a road making the reasoning immune with respect to such preconception (with the exception of the preconception of natural numbers). >Essentially, the >GP program is the simplest thing we can write down, relative to the >unspoken assumption that it is clear what it means to write something >down, and how to process it. The miracle of Church Thesis is that the "how to process it" is defined in the arithmetical relation themselves. That is what make possible to study the possible discourse of the machines themselves, about they most probable relative computation states and stories. I guess we agree on the importance of intuition about the finitary, the finite things. >It's the simplest thing, given this use >of mathematical language we have agreed upon. But here the power of the >formal approach ends - unspeakable things remain unspoken. I disagree. I would even say that it is here that the serious formal approach begins. Take "unprovable" for "unspeakable", we can meta-reason (informally or formally) and study the logical structure of the set of unprovable sentences by sound universal machines. Although unprovable by the UTM, those sentences are anticipable. Note that "there is a universe around me" is probably such a (psycho) logical anticipable sentence, not a provable one. Bruno