On 09 Dec 2011, at 17:55, Stephen P. King wrote:
I take Occam to say "in any explanation do not multiply entities
See Brent's answer.
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.
Occam razor asks for the minimal number of assumption in a theory.
It does not care about the cardinal of the models of the theory.
That is why the many worlds is a product of occam principle.
Sure, but the necessity of the plurality of "actual worlds"
given that we can only observe one
Nobody can observe one universe. Physicists measure numbers and
relates those numbers by inductive inference on quantitative relations
requires additional evidence.
"one physical universe" requires as much evidences and explanations
than 0, 2, 3, infinity, ... The everything idea is that "all possible
universes" is conceptually simpler than one real universe among all
the possible one.
Some say that the interference of particles "with themselves" in the
two-slit experiment is amble evidence for these, but MWI does
nothing to explain why we observe the particular universe that we do.
Comp explains this completely, by explaining why you cannot understand
that you are the one ending in Washington instead as the one ending in
Moscow. It explains contingencies by consistent extensions.
It has its basis problem as your result has its measure problem.
I don't think there is any basis problem in the quantum MW, nor is
there any "initial theory" problem in comp. And the mind-body problem
is transformed into a body problem, itself becoming a measure problem,
but that is what makes those theories interesting.
I suspect that these two problems are in the same family.
Even when we reduce this to a countable infinite of entities,
Which is indeed the case for the comp ontology, but the
epistemology can and will be bigger. It is a sort of Skolem
phenomenon, that I have often described.
the need for necessitation remains unanswered. Why do numbers exist?
Nobody can answer that. We cannot prove the existence of the
numbers in a theory which do not assume them at the start,
implicitly or explicitly.
So it is OK to postulate that numbers exists
We need only to postulate that zero (or one if you prefer) is a
number, and that the successor of a number is a number. This is less
than postulating sets or categories, as you need for talking about
and from such argue that the physical world is unnecessary
It is a phenomenon. Why would it be an epiphenomenon? I have argue
that this does not make sense.
and yet is required for your result to run.
The phenomenon is required. Not its primitivity.
All I ask is that you consider the world of numbers to not have an
existence independent of the possibility of knowledge of it.
In which sense. With comp, the numbers (N, +, *) entails the existence
of the knowledge of the numbers by some universal numbers. The "Bp &
p" concerns numbers relatively to universal numbers.
I separate "existence" from "properties".
Me too. Existence is handled by the quantifier "E", and properties are
handled by arithmetical predicate.
The mere existence of an object does not necessitate any propeties
whatsoever. Numbers have properties, they have relative value...
Where do those properties derive?
From the (non trivial) additive and multiplicative properties, which
are among the postulates (recursive laws of addition and
Why numbers and not Nothing?
Because with Nothing in the ontology, you can't prove the existence
of anything, not even illusion which needs some illusionned
subject. That is why all fundamental theories assumes the numbers,
(or equivalent) and with comp this can be shown to be enough.
I merely start with the assumption that "existence exists" and
go from there.
We have discussed this. "existence exists" does not make sense for me.
Existence of what? You are the one transforming existence into a
To postulate one particular type of entity and not any other
requires special explanations.
We assume simple principles and no more than what we need, and with
comp we need only combinators, of lambda-terms, or natural numbers.
What makes numbers special over spaces?
They are conceptually far simpler.
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.
Assuming different instances of boolean algebra is assuming more
than the natural numbers (like assuming finite and infinite sets).
Are two Boolean algebras that have different propositional
content one and the same? If this is true then there is no variation
is algorithms, it is to say that all algorithms are identical in
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.
Not all. The relevant part of computer science is embedded in
arithmetic. The one doing the comprehension are the universal
numbers, and they need only addition and multiplication for doing
that. That can be derived easily from Godel's 1931 paper.
The notion of computation is not inherent in the independent
existence of numbers.
It is. This is a consequence of Church thesis.
You are making the mistake of thinking that "independent of any
particular physical implementation" is equivalent to "independent of
I do not assume this. This is what the MGA proves or is supposed to
prove. Perhaps that is the error of Benjayk, and other people who does
not see that immateriality is proved in the 8th step, and not use
thus you are free from any physical constraint on the notion of
computation and then when tyros like me fail to understand how such
an idealist model can have any causal efficacy or limit, then I
wonder about its validity.
The causal efficacy comes from the fact that addition and
multiplication makes the basic ontology Turing universal. Machines
have causal efficacy by themselves.
You need to agrees Deutsch's critique directly as to how it is
possible for an abstract form of theory proving is possible.
It is up to Deutsch to explain what is the role of primitive stuff in
our experience. With comp, MGA prevents such kind of explanation.
My point is that we cannot tacitly assume the existence of
entities that can make the distinctions (for example, between
difference Goedelian numberings)
Arithmetical (sigma_1) truth dovetails on all Gödel numbering. The
inability for a universal number to really know its coding is part
of the reason why their is a first person indeterminacy in
arithmetic, and that is part of the explanation of why physical
laws will be apparent from the universal numbers points of view.
What you just wrote and its meaningfulness vanishes if there is
not physical implementation of it.
On the contrary, if you introduce primitively physical implementation
you have the problem to explain what you mean by that, and how to
relate them with consciousness. this is explained entirely in the comp
theory. Primitive matter is used by materialist like a God-explanation
gap. It is a postulate of something on which we are asking to not ask
further question. Even if comp did not detroy that notion, I would not
find it as having an explanatory purpose.
You cannot dismiss the material world and keep its properties.
Why? I can explain its properties without introducing an
unintelligible primitive matter in the picture.
and thus the insistence that the physical not exist at the same
level as numbers seems to be an error.
The numbers (or other finite entities belonging to universal
systems) have to be primitive (they are not derivable by less than
themselves). This is *necessary* not the case for physics, *by the
No, UDA only proves that the physical world cannot be monic and
allow for computations. It does not prove that an idealism can work.
It proves that IF mechanism is true, only idealism can work. Anything
we might add will be like invisible horse. Remember that nobody has
ever seen "primitive matter": it is a theological abstract notion. It
is not even used in physics, except as a way to put the mind-body
problem under the rug, usually with mechanism. My main point is
negative: that can't work.
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
You are not even showing a valid proof here. Refuting Deutsch's
assertion would effectively make Yes Doctor vanish,
Why? The contrary is more plausible. "Yes doctor" should a priori
refute Deustch thesis.
If Deutsch is wrong, digital substitution vanishes
and so does your result.
I have no clue about what you are saying.
leaving your result vacuous. Removing all traces of the physical
world removes all possibility of distinguishing a false proof from
a true proof.
Trivially so. But comp does not remove any *trace* of the physical
worlds. Only the pretension that the physical has a primary ontology.
Two different meanings of the world trace. Please don't play
You might elaborate. I thought I was using trace in your sense.
How are numbers more primitive than spaces?
Which spaces? Define them axiomatically, so we can compare. But either
you will axiomatize a very poor notion of space (porr= non Turing
universal), or you will define just another universal system, which
will be equivalent (ontologically) with the numbers.
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