On 12/9/2011 4:34 AM, Stephen P. King wrote:
On 12/9/2011 4:06 AM, Bruno Marchal wrote:
On 09 Dec 2011, at 08:47, meekerdb wrote:
On 12/8/2011 6:35 PM, Stephen P. King wrote:
On 12/8/2011 9:01 PM, meekerdb wrote:
On 12/8/2011 5:48 PM, Stephen P. King wrote:
On 12/8/2011 6:45 PM, meekerdb wrote:
On 12/8/2011 3:04 PM, Craig Weinberg wrote:
On Dec 8, 4:44 pm, "Stephen P. King"<stephe...@charter.net> wrote:
On 12/8/2011 4:22 PM, Craig Weinberg wrote:
To suppose computation requires a material process would be
materialism, wouldn't it?
Hi Craig,
Not quite, a dualist model would require that some form of material
process occur for computations and would go even further in prohibiting
computations from not having a physical component but would not specify
which it was. This way we preserve computational universality without
having to drift off into idealism and its own set of problems.
True, it could be dualism (or an involuted monism) too, but I wouldn't
call a theory of mind which depends on material processes
computationalism.
You might if you thought that's all that was needed to make a mind, in contrast to
some supernatural soul stuff. It basically boils down to whether you suppose
there are some things that are real (e.g. some things happen and some don't, or
some stuff exists and some doesn't) and some aren't or you suppose that everything
happens and exists. In the latter case there's really no role for ur stuff whose
only function is to mark some stuff as existing and the rest not.
Brent
Hi Brent,
Interesting role that you have cast the physical world into, but ironically
"stuff whose only function is to mark some stuff as existing and the rest not" and
"everything happens and exists" do not sleep together very well at all. The
"everything happens and exists" hypothesis has a huge problem in that is has no way
of sorting the "Tom sees this and not that" from the " from "Dick sees this and not
that" and "Jane sees this and not that", where as the "stuff whose only function is
to mark some stuff as existing and the rest not" can be coherently defined as the
union of what Tom, Dick and Jane see and do not see.
The idealists would have us believe that along with numbers their operations
there exists some immaterial stratifying medium that sorts one level of Gedel
numbering from another. I am reminded of a video I watched some time ago where a
girl had three sealed jars. One contained nothing, one contained 4 6-die and the
third contained 1,242,345,235,235 immaterial 6-die. ...
The physical world is very much real, even if it vanishes when we look at it
closely enough. But we might consider that just as it vanishes so too does the
ability to distinguish one set of numbers from another. If the ability to
distinguish this from that itself vanishes, how are we to claim that computations
exist "independent of physics"? Seriously!?!
Where did I claim that. I was just pointing out the genesis of "everything
theories"; you did notice that this is called the "everything-list" didn't you?
Brent
HI Brent,
I commented on what you wrote. Care to respond or will you beg my question? How
does immaterial based "everything theories" deal with this problem that I just outlined?
You should ask a proponent of such theories; like Bruno. But as I understand it, the
ultimate application of Ocaam's razor is to refuse to make any distinctions, so that
we theorize that everything exists. But the unqualified everything doesn't seem to be
logically coherent. So Bruno backs off to an "everything" that is well defined and
still possibly comprehensive, i.e. everything that is computable. Within this plenuum
there are various states (numbers in arithmetic) and some principle will pick out what
part we experience. Computation includes an uncountable infinity of states and
relations between states - so whatever we experience must be in there somewhere.
Good answer. The distinction asked by Stephen King are done, in the relative way, by
the universal numbers themselves.
Hi Bruno and Brent,
Sorry, I do not accept that as a "good answer" since it would be cut to shreds by
the razor itself. Postulating that everything exists without a means to even demostrate
necessity is to postulate an infinite (of unknown cardinality!) of entities, in direct
contradiction to Occam's razor.
I think you have a mistaken conception of Occam's razor. Although Occam may have had
physical objects in mind when he enunciated his principle, no one uses that razor any
more. Occam's razor advises to make one's *theory* as simple as possible. For example
the atomic theory of matter entails an enormous number of objects - but it is a simple way
to explain the existent of different materials, thermodynamics, fluid dynamics,
bio-energetics,...
Even when we reduce this to a countable infinite of entities, the need for necessitation
remains unanswered. Why do numbers exist? Why numbers and not Nothing?
Bruno's theory doesn't depend on numbers; it only assumes computation. Arithmetic is a
convenient and familiar example for purposes of exposition.
At least with the Stone-type dualism we have a way to show the necessity of numbers via
bisimulations between different instances of Boolean algebras and, dually, via causality
between Stone spaces and thus do not violate Occam blindly.
Which seems to me a more complex structure than arithmetic.
Comprehensability requires the co-existence of that which is comprehended with that
which is doing the comprehension, that numbers can comprehend themselves without
additional structure seem to me to be ruled out even by your result.
I don't understand how comprehension is modeled in Bruno's theory. It's unclear to me
whether it a relation of deducing one number from another.
My point is that we cannot tacitly assume the existence of entities that can make the
distinctions (for example, between difference Goedelian numberings) and thus the
insistence that the physical not exist at the same level as numbers seems to be an error.
I'm intrigued by David Deutsche's assertion that different physics implies that
different things are computable, but I'm doubtful that it's true.
I agree, it is total non sense. Not only it would contradict Church thesis and the
immunity of computability for diagonalization, but thanks to David Deutsch quantum
computer, it does not even make sense with what we know currently believed in physics,
and such a position is a sort of revisionist definition of what is a computation.
That's is why I prefer to call Deutsch's "Church Turing principle" the "Deutsch's
thesis". And it is an open problem if such a thesis is compatible with Church's thesis.
You are not even showing a valid proof here. Refuting Deutsch's assertion would
effectively make Yes Doctor vanish, leaving your result vacuous. Removing all traces of
the physical world removes all possibility of distinguishing a false proof from a true
proof.
That was essentially Peter Jones argument, except he argues that some things exist and
some don't and "matter" is marker of what exists.
To contradict this one must show how a "theory of abstract theorem proving" is
self-consistent in the absence of a means to distinguish one proposed proof from
another. Only the physical world with its chalkboards, computer screens sound waves,
etc. offers a medium on and in which we can communicate abstract ideas and concepts such
as your result.
To believe otherwise is to similar to the belief in perpetual motion machines as it
would allow us to do work in contradiction to thermodynamics. The acquisition of
Knowledge, via computation or other, requires the generation of entropy. Information is
not gained for free. If numbers have a unique and a priori existence and the physical
world emerges from it then even thermodynamics itself is emergent but this still does
not allow us to get 0 to equal 1.
I am sorry to seem so harsh in my critique but this problem that I am pointing out
is far to obvious to be so lackadaisically dismissed. I believe in your result, but it
does not prove the physical world to not exist as it requires the existence of the
physical world to be communicated. That fact alone should be clear.
Although Bruno often talks as though he has proved matter doesn't exist, his theory is
just that it is not fundamental, that it can be explained in terms of universal
computation, i.e. it can be picked out of the computational everything along with why we
have experience of it. However, I don't think he has shown how that can be done.
Brent
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