On 01 Aug 2011, at 20:11, Craig Weinberg wrote:

On Aug 1, 1:55 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
On 01 Aug 2011, at 01:12, Craig Weinberg wrote:

What machine attributes are not Turing emulable? I thought Church says
that all real computations are Turing emulable.

But for Church the "real computations" are what can do a finite mind
with a finite set of transparent instructions, in a finite time, but
with as much memory and time he needs. It is the "intuitively
computable functions".

I didn't realize it was that limited.

It is not that limited. It is the only effective set (you can generated it) which is close for the most trancendental operation known in math (diagonalization). Just this makes that set explicatively close.

I wasn't thinking of real in the
sense of only physical, but if Church posits a finite 'mind' with
transparent 'instructions' then it would seem useless for emulating

I guess that is trivial assuming your non-comp theory.

Does a mind include sensation and perception?

It does not exclude it, but that is only elementary relevant. A Turing machine must be able to recognize if some symbol is on its tape or not, and act in a way depending on its state, but above that nothing much is needed. Indeed the goal is to explain the complex (sensation and perception) from the simplest (elementary perception and obeisance to elementary laws). If not this is a bit like a treachery, as far as we look for an explanation, perhaps even partial.

It seems very

It is not, by result in computer science, we know what the simplest thing can get awfully bizarre, unpredictible, deep and sophisticated. We can only scratch on the surface, and provably so, assuming comp.

and special case begging.

You are the one supposed to motivated us for a non-comp theory.

There is no reference at all with any idea of
"real" in the sense of physically real, which is something never
defined. David Deutsch has introduced a "physical" version of Church
thesis, but this has no bearing at all with Church thesis. Actually I
do think that Church thesis makes Deutsch thesis false, but I am not
sure (yet I am sure that Church thesis + "yes doctor" leads to the
existence of random oracle and local violation of Church thesis by
some physical phenomena (akin to iterated self-multiplication).

So if there are machine aspects that are not Turing emulable, why
aren't they primitive?

Because we recover them in the epistemologies, or at the meta-level, when we listen to the average LUMs in the tiny UD, or sigma_1 arithmetical truth. They are either definable or derivable. From inside it is bigger than Everett multiverse (and that might be a "real" problem for comp: the white rabbit problem which is equivalent with the problem of justifying the stability and sharability of the physical appearances from numbers and addition+multiplication).



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