On 11/2/2012 1:08 PM, Bruno Marchal wrote:
On 01 Nov 2012, at 22:34, Stephen P. King wrote:
On 11/1/2012 11:47 AM, Bruno Marchal wrote:
On 01 Nov 2012, at 01:01, Stephen P. King wrote:
Dear Bruno,
Exactly what do these temporal concepts, such as "explain",
"solve", "interacting" and " emulating", mean in an atemporal
setting? You are mixing temporal and atemporal ideas. ...
Study a good book in theoretical computer science. You told me that
you have the book by Matiyazevich. he does explicitly emulate Turing
machine, which have a quite physical look, with a moving head, and
obeying instruction is a temporal manner, and yet they can be shown
to be emulated by a the existence or non existence of solution of
Diophantine equations.
Dear Bruno,
That book, full of wonderful words and equations, is a physical
object.
True, but non relevant.
Dear Bruno,
Yes it is relevant as it is the essence of my proof. But let me
quote Russell: http://www.ditext.com/russell/rus12.html
*
"..a belief is/true/when it/corresponds/to a certain associated
complex, and/false/when it does not. Assuming, for the sake of
definiteness, that the objects of the belief are two terms and a
relation, the terms being put in a certain order by the 'sense' of
the believing, then if the two terms in that order are united by the
relation into a complex, the belief is true; if not, it is false.
This constitutes the definition of truth and falsehood that we were
in search of. Judging or believing is a certain complex unity of
which a mind is a constituent; if the remaining constituents, taken
in the order which they have in the belief, form a complex unity,
then the belief is true; if not, it is false.
Thus although truth and falsehood are properties of beliefs, yet
they are in a sense extrinsic properties, for the condition of the
truth of a belief is something not involving beliefs, or (in
general) any mind at all, but only the/objects/of the belief. A
mind, which believes, believes truly when there is
a/corresponding/complex not involving the mind, but only its
objects. This correspondence ensures truth, and its absence entails
falsehood. Hence we account simultaneously for the two facts that
beliefs (/a/) depend on minds for their/existence/, (/b/) do not
depend on minds for their/truth/.
We may restate our theory as follows: If we take such a belief as
'Othello believes that Desdemona loves Cassio', we will call
Desdemona and Cassio the/object-terms/, and loving
the/object-relation/. If there is a complex unity 'Desdemona's love
for Cassio', consisting of the object-terms related by the
object-relation in the same order as they have in the belief, then
this complex unity is called the/fact corresponding to the belief/.
Thus a belief is true when there is a corresponding fact, and is
false when there is no corresponding fact.
It will be seen that minds do not create truth or falsehood. They
create beliefs, but when once the beliefs are created, the mind
cannot make them true or false, except in the special case where
they concern future things which are within the power of the person
believing, such as catching trains. _/What makes a belief true is
a/__//__/fact/__/, and this fact does not (except in exceptional
cases) in any way involve the mind of the person who has the belief/_. *"
I do not see Russell accepting the idea that Truths have definite
valued in the absence of beliefs and the definiteness of belief in the
absence of minds. Why do you accept such an idea? Facts require possible
worlds.
That physical object is, in my thinking, an example of an
implementation of the "emulation of a Turing Machine..." just as the
image on my TV of Rainbow Dash and her friends is a physical
implementation of magical Ponies. You seem to ignore the obvious...
You assume physical objects, but this contradict your own theory (on
which you point to, but without ever giving it).
I do not pretend to have a "theory of Everything". I am merely
trying to show you where there is an obstruction in your result that
results in the problem of an arithmetic body. It is strange that you
openly admit to a problem but do anything to prevent its solution!
But this is already no more an enigma for many physicists which
agree that temporality is just an illusion resulting from projection
from higher dimension.
Those physicists are wrong in their belief. This is argued well in
this paper http://xxx.lanl.gov/abs/gr-qc/9708055 and in any other
places. I recall a long chat that I had with Julian Barbor. In it I
tried to ask him about the computational complexity of implementing
his 'time capsule' and 'best matching' ideas, he seemed to not
understand what the heck I was talking about and yet bemoaned the
very problem at length in one of his papers on the idea!
From pg 52 of http://www.platonia.com/barbour_hrp2003.pdf
"About ten years ago, I did some computer calculations to find such
configurations with the Macintosh computer I then possessed. I was
able to
do exhaustive calculations up to N = 27, which took the computer
about three
days. Because the number of combinations that must be checked out grows
exponentially with N, even with a modern supercomputer I doubt that
calculations much beyond N = 50 would be feasible."
BTW, it was reading this paper that opened my eyes to the NP-Hard
problem of Leibniz' Pre-Established Harmony.
I thought you agree that physics (and thus time) is not primitive.
I agree, physics (and all that it such as particles, forces,
matter, energy) impels cannot be ontologically primitive. But it must
exist nonetheless. My challenge is showing how. I start with a notion
of a property neutral "totality of all that exists"
But what exists has properties, and besides, we don't know what exists
(beside our consciousness), so you take for granted much too much,
exactly what we have to explain.
No. Mere existence does not inform properties, it merely denote
necessary possibility. You are using a materialist's definition of
"existence" and not a philosophical definition. It seems that you need
some remedial education in philosophical concepts!
Existence is not a property that can be measured or otherwise
determined by some means. This is because existence is not contingent
nor supervening on anything else. Existence is ontological and
axiomatic. When we observe, measure or infer the possibility of such, we
are denoting the properties of objects. When we think of or deduce a
concept, we are not "causing the concept to come into existence", we are
merely determining its properties. Existence is not a property, it is
the only a priori synthetic as all other considerations demand it.
If we consider properties, such as the oneness and unity of 1, and
the twoness of 2, etc. we are apprehending the proprieties of concepts
and not magically gaining information of some immaterial object. My
proof of this claim is the simple demonstration that if you cannot
represent a concept or an object to both yourself and some other entity,
then you cannot know anything at all about it, nor can you even
conceptualize it. This undermines the very idea that there exists object
outside of our ability to know of them, at least in the potential sense
of a priori, since we cannot even speculate about their existence.
Truth is not an object, it is the result of an evaluation by a
mind, but it is such that it does not depend on any particular mind.
There is no such thing as a "private truth" other than the 1p aspect of
the apprehension of qualia.
and consider how from that ground two aspects emerge simultaneously,
the physical and the mental as mutually distinct dual aspects that
when added together yield back the neutrality. This idea is very
similar to Russell Standish's Theory of Nothing.
I have no clue what you mean.
Try harder, it is not that difficult. What is the basic result of
Standish's thesis? http://www.hpcoders.com.au/theory-of-nothing.pdf
"There is a mathematical equivalence between the
Everything, as represented by this collection of all possi-
ble descriptions and Nothing, a state of no information.
That some of the descriptions must describe conscious
observers who obviously observe something, gives us a
mechanism for getting Something from Nothing: Some-
thing is the "inside view" of Nothing."
and
"The ontology of bitstrings has no possible "God's
eye" viewpoint. Since the ensemble of bitstrings
have zero information, nothing can be learnt from
observing it from the outside."
There is no external Truth other than what might be possibly known
by some entity within the totality of what exists and thus truth does
not 'float-free' of the means that could exist of determining it.
This means that they can and need to be explain from non temporal
notion.
Arithmetic is the bloc mindspace.
Is it a Singleton?
No.
Then what partitions it into mutually exclusive statements?
Can it be exactly represented by a Boolean Algebra?
Yes.
Then it has a dual that is a topological space. My thesis is that
"physical worlds" are nothing more that elaborations and relations on
these topological spaces that are dual to arithmetics. This makes
arithmetics and physical worlds (representable by Stone spaces) to be
co-existent and dual aspects of a fundamental ontological primitive that
has no particular properties nor truth values.
I see 'mindspace" as one half of the dual aspects.
You pretend to see a flaw. I am not interested in your "theory". You
have to work in the theory you are criticizing, to find the flaw in
that theory. If not you are like someone pretending that abelian group
are ridiculous as you know a non abelian group. Use comp, without
adding any other axioms, please.
The fact that your result has a "arithmetic body" problem is my
proof of a flaw in comp. It is the same problem that Berkeley's
Immaterialism has. There is nothing new in your work other than 1) a
brilliant refutation of material monism, 2) a wonderful modal logical
derivation of the relations of within a mind and 3) a fatal flaw of
assuming what cannot be known to be the subject of a theory. Truth is
not an a priori definite. Only existence can be a priori.
There is nothing more dynamical than the notion of computations,
yet, they have been discovered in statical math structure.
Mathematical objects are the epitome of static objects. I think
that this view of math is blinkered. A description of a dynamic
process may be static, but the evolutionaly Becoming aspect is still
there, just hidden. Just as a photograph acts to freeze a moment in
time...
So you assume a primitive time.
How so? I have repeatedly discussed how time is a measure of
change. Change can exist without a measure. You are conflating the act
of sequencing events with the ordering that this action induces.
This contradicts your "theory" (the few I ahve grasped, but which
becomes more and more confused, when you try to escape some comp's
consequence, for reason which eludes me, as in some post you seem to
have agreed with them.
Well, I cannot be held responsible for the mistakes and
misunderstanding of others. ;-) I can agree with some comment of almost
all people without wholesale agreement with them. I agree with most of
your ideas, Bruno. We fight over a tiny concept, but it is the linchpin
of your entire thesis. You claim that truth is a priori and I claim that
truth is a posteriori. You claim that numbers have particular values
independent of the means to manifest those values and I claim that they
cannot.
I can explain your ideas to other people to the point of their
understanding of them, but you cannot even understand the basic idea of
what is "existence"!!
This is made possible as the statical sequence 0, 1, 2, 3, ...
reintroduces a lot of quasi-time notion, and it is explained how
some of them will play the role of the "observable timing of events"
locally, by relative numbers.
This is where you make the mistake. You are assuming that the
ordering of numbers *is* the dynamic.
No.
Then how can you claim that the ordering of numbers can "run" or
"implement" a computation?
I claim that the ordering of numbers *is a representation* of the
dynamic.
It can be. But the confusion is not made in comp, or in my posts.
Where is it then?
We should be very careful when we identify the map with the
territory! I agree that there are situations when there is an exact
isomorphism between map and territory, but that is only in the case
of automorphisms and fixed points.
We can use sequences of relative numbers, surely, but only when
the conditions to define them occur.
This makes no sense. It leads directly to infinite regress, as the
condition will usually be much more complex than the definition of the
numbers. You are asking to the centipede to understand how its brain
and legs function before walking.
No! Infinite regress is only a problem if it is part of an
explanation. Non-well founded sets are perfectly logical and
non-pathological and include all kinds of infinite regress!
We cannot assume that the properties of relative numbers exist in the
absence of the means to define the "timing", "locality" and
"relations" required.
Then give me your theory of numbers. And make sure it is simpler than
the first order usual arithmetical theories. Good luck ...
Any particular number is the equivalence class of its possible
manifestations. Alternatively, a numbers is the bundle of the properties
that it induces on other numbers and/or objects.
0 = 1-1, 2-2, 3-3, 4-4, ..., the additive identity in some model of
arithmetic, ..., the absence of values, ...
1 = 2-1, 3-2, 4-3, 5-4, ... , the multiplicative identity in some model
of arithmetic, ...
3 = 4-5, 5-4, ..., the observer independent quantitative value of three
objects, ..
...
I assume that truth is something that cannot be communicated but it
can be agreed upon. Truth is 1p. ;-)
--
Onward!
Stephen
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