|
Author
|
Topic: Cosmogony, Holography and Causality
|
chimp
Member
Member # 333
|
posted 14. November 2003 02:02
quote:
Gedankin:
Only in a model concept does the atom "decay or not decay". In the real world, the decay is detected by the detector, and the issues are of the detector, not the atom.
In effect, you are saying that we create the universe, as we observe the universe? Is the moon not there if we are not looking at it?
So, reality must be self referential, which means Gedankin and Rex agree with the CTMU after all.
quote:
Rex:
And the imprecision in definitions is important, too, even in areas of apparently pure mathematics.
Let N be the smallest positive integer that cannot be defined in English in 120 characters or less.
Looks like a perfectly good definition of N to me. Now, count the characters. Oops. A & ~A?
What do you propose is going wrong here?
First order logic is complete. According to Goedel, arithmetic will always be "incomplete" though. So your post is not news.
The Abstract State Machine:
http://www.uni-paderborn.de/cs/asm/Available_Materials/intro.html
http://www.di.unipi.it/~boerger/ASMTutorialEtaps.html
http://www.eecs.umich.edu/gasm/
quote:
The ASM thesis is that any algorithm can be modeled at its natural abstraction level by an appropriate ASM. Based upon this thesis, members of the ASM community have sought to develop a methodology based upon mathematics which would allow algorithms to be modeled naturally; that is, described at their natural abstraction levels. The result is a simple methodology for describing simple abstract machines which correspond to algorithms. Plentiful examples exist in the literature of ASMs applied to different types of algorithms.
Faithfulness.
Given a specification, how does one know that the specification accurately describes the corresponding real system? Since there is no method in principle to translate from the concrete world into an abstract specification, one needs to be able to see the correspondence between specification and reality directly, by inspection. ASMs allow for the use of the terms and concepts of the problem domain immediately, with a minimum of notational coding. Many popular specification methods require a fair amount of notational coding which makes this task more difficult.
[ 14. November 2003, 02:06: Message edited by: Russell E. Rierson ]
IP: Logged
|
|
Aliet Jacob
Member
Member # 908
|
posted 14. November 2003 02:03
This statement is false.
False v~False.
If false, not false, if true, not true.
This statement is unprovable.
Provable v~ provable
If provable, not provable if unprovable, not unprovable.
Godel was right. ![[Big Grin]](biggrin.gif)
[ 14. November 2003, 02:07: Message edited by: Aliet Jacob ]
IP: Logged
|
|
Aliet Jacob
Member
Member # 908
|
posted 14. November 2003 02:09
quote:
First order logic is complete. According to Goedel, arithmetic will always be "incomplete" though. So your post is not news.
It should be news to you because all your statements point to the fact that you are either oblivious of it, or regard it as immaterial.
IP: Logged
|
|
Aliet Jacob
Member
Member # 908
|
posted 14. November 2003 02:18
quote:
So, reality must be self referential, which means Gedankin and Rex agree with the CTMU after all.
With the phrase 'self-referential' (M=R) you are again comitting the fallacy of composition, of which you either are unaware, or regard as immaterial.
[ 14. November 2003, 02:20: Message edited by: Aliet Jacob ]
IP: Logged
|
|
|
|
The Pixie
Member
Member # 548
|
posted 14. November 2003 09:07
jasonyoung
quote:
From the principle of syndiffeonesis we know that our perceptual and cognitive systems must share a common syntax with reality in order for our cognitive and perceptual systems to process it.
As far as I am aware, syndiffeonesis is based on the fact (the paradox according to CTMU) that any two things are similar (having in common their existence in reality) and yet different (they are two things, and not one thing). Is there more to it than this? How do we get from here to a common syntax between perceptual-cognitive systems and reality?
Pixie
IP: Logged
|
|
Aliet Jacob
Member
Member # 908
|
posted 14. November 2003 10:13
Rational Holism is NOT M=R. M=R and statements like "self-referencing" as a description of reality are based on the fallacy of composition.
quote:
Goedel also proved the completeness of first order predicate calculus:
Therefore?
More to the point, fopc is incomplete.
Unless you want to argue that fopc is not "sufficiently strong to allow one to do basic arithmetic"?
If it is, then it is incomplete.
[ 14. November 2003, 10:19: Message edited by: Aliet Jacob ]
IP: Logged
|
|
gedanken
Member
Member # 594
|
posted 14. November 2003 10:32
Strictly in the context of a discussion of the Schroedinger's cat issue, I pointed out that in that setup that the device that deals with the cause in relation to the cat must be based on a sensor. (That device cannot be based on an abstract concept of the truth of a particular nuclear decay--for a devcie to cause an action based on the "decay" or any other situation it must have a sensor or cause and effect chain of some sort.)
Russell responded:
quote:
In effect, you are saying that we create the universe, as we observe the universe? Is the moon not there if we are not looking at it?
No, russell, in effect I am saying that in order to "see" the universe we have to have eyes, to "hear" the universe we have to have ears, to "feel" the universe we have to have touch nerve endings and trigger mechanisms. That has nothing directly to do with the existence of the universe independent of observation.
The mechanism that supposedly (gruesomly) kills the cat has to sense the nuclear decay somehow! It was in the context of that mechanism that I brought up matter of degree, "metastability" issues--discussing an inherent character of these issues in all measurement mechanisms. Russell, are you saying that the Schroedinger's cat setup can exist as proposed, but have no sensing mechanism to control the release of the poison vial?
Now as to the question of whether we create the universe, as we observe the universe? I don't know the answer to that question. But we do seem to have experience of consistency in the universe in terms of causal chain, and to have multiple persons able to come to fairly close agreement about details of events when sufficient care is exercised in observation of the event or causal chain from events. So I accept the existence of some fundamental "reality" that is independent of the individual observer.
But in the ultimate degree I can't answer that. I can't say that we are not part of some elaborate simulation, for example, that only produces the equivalent experiences in our simulated consciousnesses such as to be consistent with a "reality", as opposed to some absolute existence. (But I'm not sure that is a meaningful distinction, either!)
But Russell, you seem to consistently leap to conclusions from what I say by forgetting the context or other aspects that are available to the reader to lead to understanding of my sentences. While these may lead to interesting questions, I do become weary. Am I doing that badly in making myself clear?
[ 14. November 2003, 10:38: Message edited by: gedanken ]
IP: Logged
|
|
chimp
Member
Member # 333
|
posted 14. November 2003 14:19
quote:
Aliet:
Rational Holism is NOT M=R. M=R and statements like "self-referencing" as a description of reality are based on the fallacy of composition.
quote:
Goedel also proved the completeness of first order predicate calculus:
Therefore?
More to the point, fopc is incomplete.
That's relational holism, and, a self reference is not a fallacy of composition.
FOPC is complete, "therefore" the three metalogical axioms endow predicate logical and model theoretic levels with closure also...?
I see that Aliet is grasping at straws...
Materialistic philosophy dulls the wits?
quote:
Gedankin:
Strictly in the context of a discussion of the Schroedinger's cat issue, I pointed out that in that setup that the device that deals with the cause in relation to the cat must be based on a sensor. (That device cannot be based on an abstract concept of the truth of a particular nuclear decay--for a devcie to cause an action based on the "decay" or any other situation it must have a sensor or cause and effect chain of some sort.)
Russell responded:
quote:
In effect, you are saying that we create the universe, as we observe the universe? Is the moon not there if we are not looking at it?
No, russell, in effect I am saying that in order to "see" the universe we have to have eyes, to "hear" the universe we have to have ears, to "feel" the universe we have to have touch nerve endings and trigger mechanisms. That has nothing directly to do with the existence of the universe independent of observation.
This appears to be a game of musical chairs? If you agree that a causal chain exists then you agree that the tautology [X or ~X] corresponds exactly to [Real or not-Real]. If cause then effect.
[Cause or not Cause]----->[Effect or not-Effect]
Therefore the tautology [X or not-X] correspondes exactly to [Real or not-Real]
Gedankin, Rex, and Aliet are refuted.
IP: Logged
|
|
jasonyoung
Member
Member # 432
|
posted 14. November 2003 21:03
Pixie:
quote:
How do we get from here to a common syntax between perceptual-cognitive systems and reality?
Where our perceptual-cognitive systems intersect with perceptual reality a diffeonic relation exists, and this implies that they are both reducible to a common self-consistent and homogenous ontological medium with differential extension. The most general ontological medium distributes over all of the diffeonic relands contained within 'reality', securing covariance and eliminating the source of the problem of induction.
[ 14. November 2003, 21:24: Message edited by: jasonyoung ]
IP: Logged
|
|
Rex Kerr
Member
Member # 632
|
posted 14. November 2003 23:18
Well, this is going to take more space than it is worth, given its marginal relevence. But:
Apparently my paradox wasn't understood the first time. This has nothing to do with incompleteness, and everything to do with broken definitions. (Russel's links to Abstract State Machines could be interpreted as an understanding of the problem and its solution, but he didn't actually identify the problem, so I won't assume that.)
Note that there are no more than 120^256 possible strings in ASCII of length 120 or less. This is an upper bound on the number of integers that can (uniquely) be defined in a 120-character string of English.
Thus, between 0 and 120^256 + 1 there is at least one integer that cannot be defined in an English string of 120 characters or less.
Let S be the set of all such integers. The integers are well-ordered and we have a finite nonempty set, so we can find a minimal element s in S.
Therefore:
There exists a smallest positive integer that cannot be defined by an English string of 120 characters or less.
We'll call this statement A. We have proven it above, using a counting argument plus set theory.
Let N be the smallest positive integer that cannot be defined by an English string of 120 characters or less.
This definition has fewer than 120 characters, and defines N if it exists. But if N exists, it fails to meet the requirements its own definition, generating a contradiction. So N must not exist. Therefore:
There does not exist a smallest positive integer that cannot be defined by an English string of 120 characters or less.
We'll call this statement ~A, because it is the negation of statement A.
A & ~A.
Something is going wrong here, and it's not incompleteness, but rather unsoundness. Incompleteness states, roughly, that not all necessarily true statements have proofs. Unsoundness states that a proof is no guarantee of truth!
So I ask again: what is going on above? Where is the flaw in the analysis?
IP: Logged
|
|
jasonyoung
Member
Member # 432
|
posted 15. November 2003 00:43
Rex, for clarificatory purposes, I need to ask a few questions:
How is a character defined in English? With a natural language I can just create new characters to denote complex relationships between more basic characters.
With ASCII we're stuck using the basic characters. We cannot create new characters with composite referents to reduce the number of 'total characters' in strings.
So, my second question is, then, why can we equate the number of integers able to be defined by a 120 character string in ASCII with the number of integers able to be defined by a 120 character string in English (I'd say we can define any number at all using exactly 1 English character, in fact)?
If my question is ignorant, that's fine, you can tell me so and I'll shut up. I know nothing about the subject aside from what I've deduced from your post. If you want a clarification of my point, don't hesitate to ask.
If this is a sly way of getting us to examine the very definition of 'definition', kudos, but I'd like you to tell me so before I submit my opinion on that subject.
[ 15. November 2003, 00:45: Message edited by: jasonyoung ]
IP: Logged
|
|
Aliet Jacob
Member
Member # 908
|
posted 15. November 2003 02:06
quote:
That's relational holism, and, a self reference is not a fallacy of composition.
Strawman. I did not say that self-reference is a fallacy of composition.
You omitted the context of my statements.
quote:
FOPC is complete, "therefore" the three metalogical axioms endow predicate logical and model theoretic levels with closure also...?
If FOPC is sufficiently strong to allow one to do basic arithmetic, then it is incomplete.
quote:
Therefore the tautology [X or not-X] correspondes exactly to [Real or not-Real]
It yields absurdities, like "unreality is real" or "nonexuistence exists".
This is, to borrow Rex's use of the word, UNSOUNDNESS.
If you think thats immaterial, well, have fun!
quote:
Where our perceptual-cognitive systems intersect with perceptual reality a diffeonic relation exists, and this implies that they are both reducible to a common self-consistent and homogenous ontological medium with differential extension.
Incorrect. The link between a syndiffeonic relation and 'common syntax' is still spurious.
Me and a mountain do no have a common syntax. I can imagine, have sex, die and go to school. The mountain cannot.
Common medium does not entail common syntax. My existence is not based on tectonic activity, the mountain's is.
The fact that I can see the mountain does not mean me an the mountain operate in a similar manner. The mountain cannot see me.
I think Rex is moving to algorithmic complexity and entropy. I think that is a bit of a drift from the 2VL in CTMU and the common syntax argument.
IP: Logged
|
|
jasonyoung
Member
Member # 432
|
posted 15. November 2003 02:55
For those with eyes and egos bigger than their brains I can offer nothing but my commiseration and a friendly pat on the back. My time is of course too precious to squandor disabusing philosophical naifs of their terribly obstructive notions concerning the universe and language, especially when they've yet to display a willingness or an ability to understand what others are saying. In all seriousness, I don't think anyone who has read and digested the paper can construe your comments as anything more than a feeble attempt at diverting attention away from the apposite features of the theory under discussion.
quote:
Me and a mountain do no have a common syntax. I can imagine, have sex, die and go to school. The mountain cannot
A syndiffeonic relation must still hold between sub-syntaxes within reality. Covered directly in the paper.
Re-read the paper and get back to me on your next point.
[ 15. November 2003, 02:58: Message edited by: jasonyoung ]
IP: Logged
|
|
chimp
Member
Member # 333
|
posted 15. November 2003 03:12
quote:
Rex:
Something is going wrong here, and it's not incompleteness, but rather unsoundness. Incompleteness states, roughly, that not all necessarily true statements have proofs. Unsoundness states that a proof is no guarantee of truth!
http://www.chaos.org.uk/~eddy/math/Godel.html
quote:
Gödel's Theorem
Gödel's contribution to the study of logic revolves around the discovery of a limitation on what one can sensibly seek from a logical system. Prior to his work, a great many mathematicians, vaguely headed by the likes of Bertrand Russel, were hard at work trying to prove consistency and completeness of the Zermelo-Fränkel formalism for set theory and logic, together with Peano's axioms for the natural numbers. In so far as they were able to believe that this might fail, they expected the failure to show them how to replace their formalism with one which would be consistent and complete. Gödel derailed this project in the most spectacular manner possible: he showed that any logical system capable of supporting Peano's axioms
could not be both consistent and complete; and
could not prove itself consistent without proving itself inconsistent.
Unsoundness is an inconsistency, in that a proposition A, and its negation ~A are both true. Goedel's incompleteness theorem DOES apply to Rex's problem. Wake up and smell the logic Rex ![[Wink]](wink.gif)
I already provided a link to the ASM machine
quote:
Aliet:
Strawman. I did not say that self-reference is a fallacy of composition.
You omitted the context of my statements.
Repeat quote:
quote:
Aliet:
Rational Holism is NOT M=R. M=R and statements like "self-referencing" as a description of reality are based on the fallacy of composition.
First you called relational holism "rational holism"? A typo? Then you said: " Statements like 'self-referencing' as a description of reality are based on the fallacy of composition". Aliet, holism expains that the whole is more than the sum of its parts, or properties. Since [M=R] is based on the holistic "hology" principle, it is not a fallacy of composition... OK. I directly answered your direct quote, therefore, my rebuttle is not a "strawman"...
quote:
If FOPC is sufficiently strong to allow one to do basic arithmetic, then it is incomplete.
Yes, but it is complete within itself.
http://mathworld.wolfram.com/First-OrderLogic.html
quote:
Gödel's completeness theorem established equivalence between valid formulas of first-order predicate calculus and formal theorems of first-order predicate calculus. In contrast to propositional calculus , use of truth tables does not work for finding valid sentential formulas in first-order predicate calculus because its truth tables are infinite. However, Gödel's completeness theorem opens a way to determine validity, namely by proof.
Aliet, I concede that you make a good point about incompleteness, and the complexity of logical systems. All logical systems of any complexity are, by definition, incomplete.
quote:
Aliet:
This is, to borrow Rex's use of the word, UNSOUNDNESS.
Unsoundness is an inconsistency. Goedel's incompleteness theorem explains that some statements of mathematics will always be either inconsistent or incomplete.
IP: Logged
|
|
|
Printer-friendly view of this topic
