Hi Stephen,
On 14 Feb 2012, at 15:53, Stephen P. King wrote:
On 2/14/2012 8:39 AM, Bruno Marchal wrote:
On 14 Feb 2012, at 03:55, Stephen P. King wrote:
The idea of a measure that Bruno talks about is just another
way of talking about this same kind of optimization problem
without tipping his hand that it implicitly requires a computation
to be performed to "find" it.
Because UDA+MGA shows that even if a "real" primary physical
universe exists, it cannot explain anything related to what I can
feel to observe from my 1p view.
Obviously, the appearance of a universe makes it natural to believe
that a simple explanation is that such a universe exists, but this
has been shown to not work at all, once we assume we are Turing
emulable. So f you are right, then there must be flaw in UDA+MGA,
but each time we ask you to point where it is, you come up with
philosophical reason to discard comp (without always saying it).
Hi Bruno,
The flaw is the entire structure of UDA+MGA, it assumes the
existence of the very thing that is claims cannot exist. It is a
theory that predicts that it cannot exist. How? By supposedly
proving that the physical world does not exist. Why is that a
problem? Because without a physical world, it is impossible for that
theory to have any properties. You want to get around this problem
by postulating that the entities of UDA+MGA can and does have a
particular set of properties merely because they exist. OK, but how
does the existence of an entity define its properties?
See Quentin's answer. To insist on this: comp does not say that the
physical reality does not exist. It says that the physical reality is
not a primary notion.
You could as well say that Darwin has shown that higher mammals don't
exist, because he provided an explanation of their appearance from
simpler objects.
I do not blame him as this problem has been glossed over for
hundred of years in math and thus we have to play with nonsense
like the Axiom of Choice (or Zorn's Lemma) to "prove" that a
solution exists, never-mind trying to actually find the solution.
This so called 'proof" come at a very steep price, it allows for
all kinds of paradox.
This is unclear. Comp is axiom-of-choice independent. Even
arithmetical truth is entirely axiom of choice independent. ZF and
ZF + AC proves exactly the same arithmetical truth.
"COMP is Axiom of Choice independent" ... Does this means that
COMP is independent of any particular version of AC or does it means
that the truth of a statement is just the existence of the statement
as an abstract entity in an isolated way?
It means that the first order arithmetical proposition are the same in
the model of set theories with AC than with set theories without AC,
or with ~AC.
I am just trying to be consistent with what I understand of UDA+MGA.
UDA+MGA, as far as I can tell, proposes that the physical world does
not have an existence independent of our experiences and since our
experiences can be represented exactly as relations between numbers,
that all that exists is numbers. Correct?
Not entirely. The physical reality is explained by numbers' dream
coherence, and that is independent of our *experience* of it. So, in a
sense, physical reality is independent of us. But it is still
dependent on all universal numbers and the entire arithmetical truth.
Also, our experience cannot be represented by number relations, by
number relations. I mean, for numbers, their experience are not number
relations. Only at the meta)level, having bet on comp, we can say that
the number experiences are partially axiomatized by relation between
computations and truth, but keep in mind that arithmetical truth
itself cannot be represented by a number relation. (Cf Tarski, Kaplan
Montague, etc.).
If this is correct, then my questions turn on what exactly are
numbers and how do they acquire properties. 1 is a 1, a 2 is a 2,
and 3 is a 3. But what is it that defines what a 1 or a 2 or a 3 is?
To reason, we don't have to know what we are talking about. We just
need to agree on axioms. I gave you the axioms.
We could think of this as a set of different patterns of pixels on
our computer monitors, of marks on paper, or a chalkboard, or
apples, bananas, or trees. But this avoids the question of "what is
it that ultimately gives 1 its one-ness?".
With the axiom given, it can be proved that Ex((x = s(0) & Ay((y =
s(0)) -> y = x)).
Alternatively, we can think of these symbols as physical
representations of sets or classes of objects, but then we have to
define what that means. The easiest way to do that is to point at
objects in the world and make noises with our mouth or, if we are
mute, to make signs with our hands and/or grimaces with our faces.
I think we can use first order logic. It evacuates the metaphysical
baggage, to use Brian Tenneson expression.
Obviously, all of this is taking a 3p or objective point of view
of objects, symbols, etc.
We don't know that. keep in mind that I do not take anything physical
for granted (even without comp). The oneness of 1 is easy, not so for
any physical objects.
but as we know, this is a conceit as we can only guess and bet that
what we observe is "real" in that it is not just a figment of our
imagination that vanishes when we stop thinking of it.
We can hope. But even if it is real, comp makes it not primitively real.
I am being intentionally absurd to illustrate a problem that I see.
If we are going to claim that the physical world does not exist then
we have to be consistent with that claim and cannot use any concepts
that assumes the properties of a physical world.
Fortunately comp never would assert such an absurd statement. Please,
try to always separate "primitive phsyical reality" and "physical
reality". Comp forbids the first, and explains the later.
My claim is that UDA+MGA violates this requirement by using concepts
that only have a meaning because of their relation to physical
processes and yet claiming that those very processes do not exist.
Then read the argument more carefully. You introduce assumptions which
are not there. Comp assumes doctor, brain, machines, etc. But it does
not assume primitively real doctors, brains, machines, etc.
A possible solution to this problem, proposed by many even
back as far as Heraclitus, is to avoid the requirement of a
solution at the beginning. Just let the universe compute its least
action configuration as it evolves in time,
This does not work, unless you define the physical reality by
arithmetic, but this would be confusing. It seems clearer
and cleare that your "existence" axiom is the postulate that there
is a physical primary reality. But then comp is wrong.
What I see as wrong about COMP is how you are interpreting it.
You are taking its implied meaning too far. I claim that there is a
limit on its soundness as a theory or explanation of ontological
nature, a soundness that vanishes when it is taken to imply that its
communicability becomes impossible - a situation which inevitably
occurs when one interprets COMP as a claim that the physical world
does not exist.
It is a bit annoying because some people have purposefully lie about
this in Brussels and Paris. In our context, it is fundamental to
distinguish between a physical universe (which of course is the kind
of things I tend to believe in), and a primary physical universe (the
ontological root of physicalism). Comp implies that physics is a
branch of number theory, this justifies more the existence of a
physical universe than any extrapolation on observation (we might be
dreaming). So the physical worlds is made much more solid and founded
with comp than without, at least until comp is refuted.
At least Craig is coherent on this. he want some primitive matter,
and he abandons comp. His theory is still unclear, but the overall
shape make sense, despite it explains nothing (given that he assume
also a primitive sense, and a primitive symmetry).
Bruno
I do not want primitive matter, as this would put us into the
situation that the material monist are in, with the epiphenomenal
nature of consciousness. I just want abstract representations and
physical object on the same level.
That's arguably the case with comp. representation are in the mind of
person, and matter appearance too.
I think that we can agree that the physical world cannot be
primitive in the ontological sense,
So I have no clue of what problems you allude to in comp.
but can you not see that representations cannot be primitive either
Indeed, they are not.
if only becuase to claim that, for instance, that only numbers are
primitive
That's different. numbers are not representation. They are the object
obeying to the axioms I gave you. representation will be more complex
things related to the relative "behavior" of the universal numbers.
eliminates the possibility that one number has a particular set of
properties that makes it somehow different from another number.
This contradict elementary arithmetic. PA proves that 1≠2.
Also, you have been using the word "neutral" to mean
"indifferent" in a way that is similar to "I am indifferent to
whether cows prefer chocolate ice cream over vanilla ice cream". I
mean neutral to mean "not having any bias for some set of properties
over any other".
This is a requirement preventing to do science. In cognitive science
or philosophy of mind, "neutral" means "not having bias toward matter
or mind".
These two meaning are very similar but the latter is more general
than the former because the latter is not considering the entity
that might have a particular set of properties (which implies a
choice of properties and thus my comments about the axiom of choice)
You mix too much non relevant things here.
while the former is taking the case of indifference about some
particular state of affairs given from a particular point of view.
It is a 1p versus a 3p difference. No?
That paragraph is too much unclear for me. Sorry.
At issue is the question of how does the definiteness of the
properties of an object, be it abstract - like the concept of a
number - or concrete - like the keyboard that I am typing on, come
to be what it is. You seem to claim that properties are defined by
the mere existence of an object. I am not understanding how you
think that such is possible.
I don't make any claim of that kind. The property of numbers are
defined by the laws to which they obey, not their singular existence.
5 is prime because we can prove using the add and mult laws that 5 has
no non trivial divisors.
We can make claims that A exists and that A is A, but what is A
independent of any claims we might make of it?
That question is not clear.
Bruno
http://iridia.ulb.ac.be/~marchal/
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