> 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.