Bruno writes: > I will think about it, but I do think that CT and AR are just making > the YD more precise. Also everybody in cognitive science agree > explicitly or implicitly with both CT and AR, so to take them away > from YD could be more confusing.
I think that is probably true about the Church Thesis, which I would paraphrase as saying that there are no physical processes more computationally powerful than a Turing machine, or in other words that the universe could in principle be simulated on a TM. I wouldn't be surprised if most people who believe that minds can be simulated on TMs also believe that everything can be simulated on a TM. (I don't see the two philosophical questions as absolutely linked, though. I could imagine someone who accepts that minds can be simulated on TMs, but who believes that naked singularities or some other exotic physical phenomenon might allow for super-Turing computation.) But isn't AR the notion that abstract mathematical and computational objects exist, to the extent that the mere potential existence of a computation means that we have to consider the possibility that we are presently experiencing and living within that computation? I don't think that is nearly as widely believed. That simple mathematical objects have a sort of existence is probably unobjectionable, but most people probably don't give it too much thought. For most, it's a question analogous to whether a falling tree makes a noise when there's no one there to hear it. Whether the number 3 existed before people thought about it is an abstract philosophical question without much importance or connection to reality, in most people's minds, including computationalists and AI researchers. To then elevate this question of arithmetical realism to the point where it has actual implications for our own perceptions and our models of reality would, I think, be a new idea for most computationalists. Right here on this list I believe we've had people who would accept the basic doctrines of computationalism, who would believe that it is possible for a human mind to be "uploaded" into a computer, but who would insist that the computer must be physical! A mere potential or abstractly existing computer would not be good enough. I suspect that such views would not be particularly rare among computationalists. Hal Finney