Re: An All/Nothing multiverse model
An analysis I have made of my model: My model's foundation is not mathematics but the list of potential properties of things. The only mathematical like concepts I then use are power set, incompleteness, and inconsistency and these are derived from simply parsing the list. If my list is infinite and countable and its line items representable by finite bit strings then my starting point is just the natural numbers [including zero] along with an assignment of meaning to each. As I understand it the cardinality of the set of subsets of the natural numbers [i.e. the All and its kernels as power set] is the same as the cardinality of the reals i.e. c. One can therefore form a one to one correspondence between the kernels and the reals. In this pairing the real member of the pair can be thought of as representing the kernel half of the pair. Therefore the All is just the set of reals with an assigned meaning for each. Hal Ruhl
Re: An All/Nothing multiverse model
My analysis continued: Self awareness and consciousness: If the All is just the set of reals with an assigned meaning for each then undoubtedly some of these meanings would be kernels that contain sub kernels describing Self Aware Structures [SAS]. Given the random nature of the dynamic I derive in my model for the evolution of Somethings, the Instantation of Reality given to kernels as they are encompassed by the Somethings will have dwells of all durations. Some dwells for some kernels representing states of universes will have a duration that provides an apparent connection between states or flow of awareness [a flow of consciousness] for its SAS. Hal Ruhl
Re: An All/Nothing multiverse model
I have attached a revision to my model at (9) which makes the driver for the evolution of the Somethings more explicit. Definitions: The list of all possibilities: The list of all the possible properties and aspects of things. This list can not be empty since there is unlikely to be less than nothing and a nothing has at least one property - emptiness. The list is most likely at least countably infinite. Information: Information is the potential to establish a boundary on the list of all possibilities. Kernel of information: The information relevant to a specific boundary. The All: The complete ensemble of kernels. The Nothing: That which is empty of all kernels. The Everything: The boundary which establishes the All and separates it from the Nothing and thus it also establishes the Nothing. It could be said to contain both. A Something: A division [by a boundary] of the All into two subparts. True Noise: The inconsistency of the evolution of a Something reflected in the course of physical reality given to universes within it. Model Proposal: The Existence of our and other universes and their dynamics are the result of unavoidable definition and logical incompleteness. Justification: 1) Notice that Defining is the same as establishing a boundary - on the list of all possibilities [1def] - between what a thing is and what it is not. This defines a second thing: the is not. A thing can not be defined in isolation. 2) Given the definitions of the All, the Nothing, and the Everything: 3) These definitions are interdependent because you can not have one without the whole set. 4) These definitions are unavoidable because at least one of the [All, Nothing] pair must exist. Since they form an [is, is not] pair they bootstrap each other into existence via a single combined definition - the Everything. 5) The Nothing has a logical problem: since it is empty of kernels it can not answer any meaningful question about itself including the unavoidable one of its own stability [persistence]. 6) To answer this unavoidable question the Nothing must at some point penetrate the boundary between itself and the All [the only place information resides] in an attempt to complete itself. This could be viewed as a spontaneous symmetry breaking. 7) However, the boundary is permanent as required by the definitional [is, is not] pairing and a Nothing must be restored. 8) Thus the penetration process repeats in an always was and always will be manner. 9) The boundary penetration described above produces a shock wave [a boundary] that moves into the All as the old Nothing becomes a Something and tries to complete itself [perhaps like a Big Bang event]. This divides the All into two evolving Somethings - i.e. evolving multiverses. Evolving Somethings are unlikely to reach completeness short of encompassing the entire All. Notice that half the multiverses are contracting - i.e. losing kernels [but the cardinality of the number of kernels would be at least the cardinality of the list of all possibilities]. 10) Notice that the All also has a logical problem. Looking at the same meaningful question of its own stability it contains all possible answers because just one answer would constitute an exclusion of specific kernels which is contradictory to the definition of the All as the complete kernel ensemble. Thus the All is internally inconsistent. 11) Therefore the motion of a shock wave boundary in the All must echo this inconsistency. That is each step in the motion as it encompasses kernel after kernel [the evolution of a Something] can not be completely dependent on any past motion of that boundary. 12) Some kernels are states of universes and when the boundary of an evolving Something passes about a kernel, the kernel can have a moment of physical reality. [This moment can extend so that successor states can have a degree of overlapping physical reality resulting in a flow of consciousness for some sequences for universes that contain Self Aware Structures.] 13) From within any Something the future pattern of reality moments due to (11) would be non deterministic i.e. suffer True Noise. 14) The All of course contains a kernel re the founding definition and thus there is an infinitely nested potential to have All/Nothing pairs. This completes the system in that the origin of the dynamic basically destroys [Nothing, All] pairs but there is an infinite potential to form new Nothings. Hal Ruhl
Re: An All/Nothing multiverse model
Dear Hal, About this zero information feature, could it be due to a strict communitivity between any given subset of the All/Nothing? I ask this because it seems to me that the information content of any string follows from the existence of a difference between one ordering of the bits as compared to another. Commutativity would erase (bad choice of wording) the difference. In your theory, the distinction between what it *is* from what it *is not, when we chain it out to tuples, is obviously a non-commutativity property, at least. Kindest regards, Stephen - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Sunday, December 26, 2004 1:23 PM Subject: Re: An All/Nothing multiverse model Below is a background for my model and a rewrite of the original post. My concerns with a TOE which I am trying to resolve are: I would like to see the theory have a zero information content. I would like an origin for what we perceive as a changing reality - a dynamic. Postulating the existence of entities like an Everything or a Plenitude etc. seemed to me to leave residual information in the system because the definitional structure surrounding these concepts was like a label with an unfulfilled potential to distinguish another entity not in the system i.e. a Nothing. This eventually lead to the idea that definition was actually a boundary separating what a thing being defined is from what it is not and the is not is another thing. So definition simultaneously defines two entities - an [is, is not] pair. Another Idea I posted on awhile back was that a dynamic could be based on the incompleteness of the Nothing. It could resolve no meaningful questions about itself. Was there such a question? I proposed that it must resolve the question of its own stability - will it persist. Eventually the Nothing would have to spontaneously become something to try to resolve this question and this something would then evolve as it tried to complete itself and become an Everything. However if the Everything and the Nothing were a defintional [is, is not] pair which seemed reasonable what would give existence preference to one over the other and simultaneously put the system in a state of unused potential to divide i.e. contain information. The existence of at least one of the pair seemed assured so could the system work if both existed simultaneously? This eventually resulted in my post which is revised below. Definitions: 1) Information: Information is the potential to establish a boundary. 2) Kernel of information: The information required for the potential to establish a specific boundary. 3) The All: The complete kernel ensemble. 4) The Nothing: That which is empty of all kernels. 5) The Everything: The boundary which contains the All and separates it from the Nothing. Thus it also contains the Nothing. 6) A Something: A division [by a boundary] of the All into two subparts. 7) True noise: An inconsistency of the evolution of a Something reflected in the course of physical reality given to universes within it. Proposal: The Existence of our and other universes and their dynamics are the result of unavoidable definition and logical incompleteness. Justification: 1) Given definitions 3, 4, and 5: 2) These definitions are interdependent because you can not have one without the whole set. 3) Notice that Defining is the same as establishing a boundary between what a thing is and what it is not. This defines a second thing: the is not. A thing can not be defined in isolation. 4) These definitions are unavoidable because at least one of the [All, Nothing] pair must exist. Since they form an [is, is not] pair they bootstrap each other into existence. 5) The Nothing has a logical problem: since it is empty of kernels it can not answer any meaningful question about itself including the unavoidable one of its own stability [persistence]. 6) To answer this unavoidable question the Nothing must at some point penetrate the boundary between itself and the All [the only place information resides] in an attempt to complete itself. This could be viewed as a spontaneous symmetry breaking. 7) However, the boundary is permanent as required by the definitions and a Nothing must remain. 8) Thus the penetration process repeats in an always was and always will be manner. 9) The boundary penetration produces a shock wave [a boundary] that moves into the All as the old example of Nothing becomes a Something and tries to complete itself. This divides the All into two evolving Somethings - evolving multiverses. Notice that half the multiverses are contracting - losing kernels. 10) Notice that the All also has a logical problem. Looking at the same meaningful question of its own stability it contains all possible answers because just one would constitute a selection i.e. net internal information which is not an aspect of a complete
Re: An All/Nothing multiverse model
Hi Stephen: Since the Nothing has no information by definition and the boundary between them - the Everything - has no potential to divide further [i.e. no information] then the All must have no information if the system has no information. I do not think the latter part is controversial. For this to be so, somehow the kernels within the All sum to no net information. Like red, green, and blue can sum to white when viewed from a proper perspective. I used to call these complete sets of counterfactuals. To finish responding to a previous question in the thread if a complete set of counterfactuals was composed of just two kernels these kernels would be what I called pair wise inconsistent kernels. Hal At 02:45 PM 12/26/2004, you wrote: Dear Hal, About this zero information feature, could it be due to a strict communitivity between any given subset of the All/Nothing? I ask this because it seems to me that the information content of any string follows from the existence of a difference between one ordering of the bits as compared to another. Commutativity would erase (bad choice of wording) the difference. In your theory, the distinction between what it *is* from what it *is not, when we chain it out to tuples, is obviously a non-commutativity property, at least. Kindest regards, Stephen
Re: An All/Nothing multiverse model
Hi John: At 06:12 PM 12/26/2004, you wrote: Dear Hal, is there some draft seeable on the web? Not yet. If the idea still looks good at the end of this thread I intend to post something on my web page with visual aids etc. I thought I am comfortable with your terminology (whether I understand it or not) but now I wonder: Is Everything part of All, or All part of Everything? Then again it should be that Nothing is part of Everything, maybe not necessarily of All. You cannot say that everything except the nothing, but nothing cannot be part of All: it is per definitionem the entirety of somethings. I called the boundary between the Nothing and the All the Everything because it being the only boundary of both it contains them both. The All of course contains a kernel re the founding definition and thus there is an infinitely nested potential to have All/Nothing pairs. To the exchange with Stephen: (My) no-info Plenitude is so, because it contains the 'everything' in a timeless, dynamic(!!) total symmetry (=invariance of unlimited exchange), so no observables can be extracted in that atemporality. Then again THIS is information, so it is not true that it has none. I have a feeling that your no-info suffers from he same malaise. Unless you separate the information of the description from the info about the inner components only. The description of the All is one side of the definitional [is, is not] pair. The description of the Nothing is the other side. The simultaneous existence of both the All and the Nothing eliminates any residual potential to establish a boundary [information] that might have been inherent in the definition. Hal
Re: An All/Nothing multiverse model
Hi Jesse: I think some confusion took place surrounding the posts on or about 12/10. In my initial post I said: xx 9) Notice that the All also has a logical problem. Looking at the same meaningful question of its own stability it contains all possible answers because just one would constitute a selection i.e. net internal information which is not an aspect of the complete conceptual ensemble content of the All. Thus the All is internally inconsistent. 10) Thus the motion of a shock wave boundary in the All must be consistent with this inconsistency - That is the motion is at least partly random xx This has still not been commented on in the thread. Things got more confused when the internal was somehow lost and we got on to a discussion of specific possible internal components of the All and their consistency. As I said in an earlier post the All has no net information so any idea that it is itself - as an entity - is inconsistent has no basis. It can not be consistent in the true/false way either. I do not think that anyone has demonstrated that the All can not have internal components that are true/false inconsistent. Thus my point in the initial post: xx 10) Thus the motion of a shock wave boundary [an evolving Something] in the All must be consistent with this inconsistency - That is the motion is at least partly random. xx Today I would amend # 10 because random is not correct in my opinion because it has to pay attention to history to know it is indeed random. So the most recent motion must rather be inconsistent with its past or future - no accumulating info. Hal At 10:04 PM 12/20/2004, you wrote: Hal Ruhl wrote: I do not think the conversation re: I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises, has a valid place in this thread. Can you tell me why you do? Because you have said that your theory has this feature, and I was trying to understand if I might be misunderstanding you by asking you for other examples of theories that you think had this feature--I thought perhaps we might be understanding the idea of having to believe the premises in order to justify the premises differently, so that you might not actually be asking people to accept the tenets of your theory on blind faith. But if there is no misunderstanding, and you are indeed saying there is absolutely no justification for believing your theory in terms of any preexisting concepts we might have, then I suppose there is no further need to discuss this question. I still have the feeling that this is not quite the case though, since you are asking for comments/critiques of your theory, but what possible basis could comments/critiques have unless you believed we all had some shared standards for judging the merits of the theory? I think if you are able to figure out what standards you are using to judge the various elements of the theory, and what standards you expect others to judge it by in order to have useful comments about it, then if you can articulate these standards you may be able to give a clearer explanation of why you think it makes sense to accept your theory. For example, one of these standards may be the a theory of everything should have no arbitrary elements idea, which I think is shared by a lot of people on this list (I described this as the 'arbitrariness problem' in my post at http://www.escribe.com/science/theory/m2606.html ), and which you call the no information rule. Jesse
Re: An All/Nothing multiverse model
Hal Ruhl wrote: At 11:41 PM 12/18/2004, you wrote: Hal Ruhl wrote: 'The laws of logic need not be thought of as rules of discovery, they can be thought of purely as expressing Expressing seems to be a time dependent process. I don't think it needs to be. When we say a certain set of symbols expresses something, in the most abstract sense we're just saying there's a mapping between the symbols and some meaning. That would be static information within a kernel. So are you agreeing it makes sense to talk about the laws of logic expressing some truths without this being a time-dependent process? static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or discovered them. As are my kernels of information. For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.' Sure, That is a kernel. Observation does not make a kernel a kernel. OK, but this isn't really relevant to my question, namely, why does any of this require time? A kernel does not need a set of rules to make the informational relationships within it what they are. The very words rules, laws and the like carry the implication of a process where the rules and laws are consulted and followed. This is a hidden assumption of some ordered sequence - time. I do not know how to be clearer than that. I agree that world/kernels don't need to consult the laws of logic in order to avoid logical contradictions. I'm just saying that if you look at the facts of each world/kernel and translate these facts into propositions like all ducks have beaks (within this particular world/kernel), then you will find that no proposition or collection of propositions about a single world/kernel violate the laws of logic--for instance, you won't find that a proposition and its negation are *both* true of a single world/kernel, in exactly the same sense (ie applying to the same 'domain' like I talked about earlier). Likewise, you didn't address my point that I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises, I do not believe that Cantor would be sympathetic with that. I think you need to believe in infinity in order to justify working to understand it and thus justify it. Why do you say that? Cantor's ideas about infinity could be justified in terms of existing commonly-accepted mathematical notions. For example, mathematicians already thought the idea of sets made sense, so he defined the notion of special sets called ordinals, each of which was a set of smaller ordinals, with the smallest ordinal being the empty set. Then, since there seems to be no obvious contradiction in considering the set of all countable ordinals, it's easy to see that this set is itself an ordinal but cannot be a countable one, so its cardinality must be higher than the countable ordinals--he defined this cardinality as aleph-one. Then if you consider the set of all ordinals with cardinality aleph-one, this must be an ordinal with cardinality higher than aleph-one, which he called aleph-two, and so on. See my post at http://www.escribe.com/science/theory/m4919.html for a little more explanation. All this could be described in terms of preexisting ideas about set theory, he wasn't requiring anyone to already believe his ideas about infinities in order to prove them. I believe Bruno said that some information systems included a set of beliefs. As I recall the premises are these beliefs. Justification comes from emotions [based on other beliefs] surrounding the resulting system such as simplicity, elegance of apparent explanation etc. So it seems to me that justification is part of belief. My point is that if I want to demonstrate the truth of some statement X to you (without appealing to new empirical evidence), I look for some set of premises that we *already* share, and then try to show how these premises imply X. I can't think of any historical example where someone's new idea is accepted by other people without the person appealing to common premises they already share. Can you? See above re infinity. Well, see my comments above, I don't think that's a valid example. and you didn't address my question about whether you think there could be a world/kernel where a vehicle simultaneously Again time inserts itself as the notion of simultaneously. Simultaneously shouldn't be taken too literally, X and Y are simultaneously true is just a shorthand way of saying that X and Y are truths that both apply to exactly the same domain, whether same domain means same universe, same time, or whatever. For example, if I say Ronald Reagan was President of the U.S. in 1985 and Bill Clinton was President of the U.S. in 1995, these are two non-contradictory truths that apply to the domain of U.S.
Re: An All/Nothing multiverse model
John M wrote: Dear Jesse, ashamed for breaking my decision NOT to babble into this discussion with my personal common sense, here is something to your position from my problems: (First a bit of nitpicking, as an appetizer) For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.' how can an unnoticed truth be included into noticed (mutual) truth? * Time. I tackle a timeless (atemporal) system. The problem is change. What does a timeless change mean? One has to eliminate 'sequence', the result of a change, or: Hal's All is static and includes both ends of all changes. Hi John--I would say the idea of timeless changes makes a kind of sense, like how the value of f(x)=x^2 changes as x increases. Basically it just means that as you vary one thing, another thing varies along with it. And if you have a t coordinate marked time, you can say that the state of physical systems in 3D space varies as t varies, while at the same time believing spacetime as a whole is a timeless entity. See this article by physicist Paul Davies on this subject: http://www.american-buddha.com/myster.flow.physics.htm You used the 'static' cop-out: static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or discovered them. * Of course a 'change' is meaningless in this case. We speculated a lot about Process, where change is involved between the endpoints of process. If All is not static, change is there (time?) if it is static, it is meaningless as a world. In that case it is a nirvana, static timelessness = eternity for nothing. I disagree--if you have a movie film laid out before you, you can see all the different frames in a timeless way, but the people on the film seem to be perceiving the world in a sequential way. Of course the idea of distinguishing first-person perception vs. third-person objective reality brings up a whole 'nother set of tricky philosophical questions surrounding the nature of consciousness, but without getting into that right now, I think my view would be that time exists on a first-person level but not at the level of an objective description of the All. I am afraid, although I never studied formal logic, I have an inherent sense of 'human' logic in my speculations and cannot get over it. Human logic (formal or formless) is one aspect of nature, not necessarily the one covering All (of it). (The 1 = 0 case?) * Your discussions reached Taoistic levels, the format where not even the contrary or other variants of a statement may be true. Well, note that I don't actually believe contradictory statements can both be true, I was just arguing that *if* Hal Ruhl does not believe that the laws of logic apply to reality as a whole, then he has no reason to deny they could be. It was meant as more of a reductio ad absurdum than anything else. I do have some interest in mysticism and in particular the Buddhist notion of relative and absolute truth, described at http://tinyurl.com/5eaco , but I don't think this notion of two truths expresses an actual logical contradiction (two opposite statements which are both true in *exactly the same sense*), my feeling is it's something more like the philosophy complementarity in quantum physics, two different descriptions of the same reality. But what do I know, I'm not a mystic... Jesse
Re: An All/Nothing multiverse model
Hi Jesse: I do not think the conversation re: I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises, has a valid place in this thread. Can you tell me why you do? Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: I do not think the conversation re: I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises, has a valid place in this thread. Can you tell me why you do? Because you have said that your theory has this feature, and I was trying to understand if I might be misunderstanding you by asking you for other examples of theories that you think had this feature--I thought perhaps we might be understanding the idea of having to believe the premises in order to justify the premises differently, so that you might not actually be asking people to accept the tenets of your theory on blind faith. But if there is no misunderstanding, and you are indeed saying there is absolutely no justification for believing your theory in terms of any preexisting concepts we might have, then I suppose there is no further need to discuss this question. I still have the feeling that this is not quite the case though, since you are asking for comments/critiques of your theory, but what possible basis could comments/critiques have unless you believed we all had some shared standards for judging the merits of the theory? I think if you are able to figure out what standards you are using to judge the various elements of the theory, and what standards you expect others to judge it by in order to have useful comments about it, then if you can articulate these standards you may be able to give a clearer explanation of why you think it makes sense to accept your theory. For example, one of these standards may be the a theory of everything should have no arbitrary elements idea, which I think is shared by a lot of people on this list (I described this as the 'arbitrariness problem' in my post at http://www.escribe.com/science/theory/m2606.html ), and which you call the no information rule. Jesse
Re: An All/Nothing multiverse model
Dear Jesse, ashamed for breaking my decision NOT to babble into this discussion with my personal common sense, here is something to your position from my problems: (First a bit of nitpicking, as an appetizer) For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.' how can an unnoticed truth be included into noticed (mutual) truth? * Time. I tackle a timeless (atemporal) system. The problem is change. What does a timeless change mean? One has to eliminate 'sequence', the result of a change, or: Hal's All is static and includes both ends of all changes. You used the 'static' cop-out: static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or discovered them. * Of course a 'change' is meaningless in this case. We speculated a lot about Process, where change is involved between the endpoints of process. If All is not static, change is there (time?) if it is static, it is meaningless as a world. In that case it is a nirvana, static timelessness = eternity for nothing. I am afraid, although I never studied formal logic, I have an inherent sense of 'human' logic in my speculations and cannot get over it. Human logic (formal or formless) is one aspect of nature, not necessarily the one covering All (of it). (The 1 = 0 case?) * Your discussions reached Taoistic levels, the format where not even the contrary or other variants of a statement may be true. The opposite end of conventional physical thinking and I doubt whether there is a way to combine the two (maybe more than twoG?) ends of the spectrum into one way (of thinking)? Which end would you choose? You underwent a young-age brainwashing for the (conventional) physicist end and have an open enough mind for the other end. Can you compensate? can anybody? I am neither a physicist, nor a philosopher. I got my natural science brainwashing and try to deregulate my mind (with questionable success). Regards John Mikes - Original Message - From: Jesse Mazer [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, December 18, 2004 11:41 PM Subject: Re: An All/Nothing multiverse model Hal Ruhl wrote: Snip, 2 quotes above included
Re: An All/Nothing multiverse model
Hi Bruno and Jesse: At 10:23 AM 12/18/2004, you wrote: At 21:48 17/12/04 -0500, Hal Ruhl wrote: Can a kernel of information be self inconsistent? From Bruno's last post I think it is possible to impose this idea on the All. I'm afraid I said the contrary (unless I misunderstand what you are pointing at through the expression kernel of information). If you agree that a kernel of information is like a theory or any finitely describable machine, then only such a thing can be said inconsistent. At this point I have talked myself into the position that since the All is absent information then we have no way to describe it as consistent or inconsistent in the usual logic meaning that I understand. It may contain self inconsistent kernels or pair wise inconsistent kernels but this seems to sum to a neutral position. Pair wise [or better group wise] inconsistent kernels would differ in the truth value assigned to the same internal component but sum to a neutral position to maintain the overall nature of the All. I am not saying they exist but allow for it. The All, I put it on the semantical side, I don't see how that can be made inconsistent in any interesting way. It is *our* attempts to manage the All which can lead to our inconsistencies. In case we discover some of those inconsistencies we better should backtrack. I think. No? I now agree with this as above. Next post: At 11:28 AM 12/18/2004, you wrote: At 20:39 17/12/04 -0800, Pete Carlton wrote: As usual when I ask a question like this, if the answer is available in a text on logic or elsewhere, please just tell me where to look. ..I'm also interested in the implicit use of time, or sequence, in many of the ideas discussed here. For instance you might say that some of your Somethings are 'bitstrings' that could make up one of Bruno's or Jürgen's worlds/observers. Remember that comp, as I present it, make worlds non computable. It is a consequence of of the self-duplicability, when distinguishing 1 and 3 person points of view. Do you mind then a little more non computability re the third person point of view as per my dynamic? Part of our idea of a string is the convention that one element comes first, then the second, then the third, et cetera. However, the information that accounts for that convention is not contained in the string itself. 'Taking' a Something as a bitstring involves some degree of external convention. Indeed, it needs a universal machine, and even an infinity of them. But all that exists and describes by the set of (sigma1) true arithmetical propositions. See Podniek's page http://www.ltn.lv/~podnieks/gt.html I may not have time left for yet another schooling but I intend to take a much closer look at your material after I resolve my issues with residual information and the origin of the dynamic which this thread might accomplish. So my question is, what do you mean when you say a universe that has a sequence of successive states that follow a set of fixed rules? What could make one state give rise to the next state?Citing causality just gives a name the problem; it doesn't explain it. I completely agree with you. The primitive causality of the comp platonist is just the implication of classical propositionnal logic. Most of the time (sorry for the pun) time of a computation can be described using no more than the axioms of Peano Arithmetic, including especially the induction axioms: that if P(0) is true and if for all x (P(x) -P(x+1) ) then for all x we have P(x). (Witten B(0) Ax(B(x)-B(Sx)) - AxB(x) in http://www.ltn.lv/~podnieks/gt3.html#BM3 (S x) is x + 1 As I said in another post I think the idea of one state giving rise to the next creates issues with accumulating algorithmic complexity. However, a sequence in which each state is independent of any other state could look causal for long strings of states. And I don't think introducing a Turing machine helps with this basic problem, since in any automaton you have rules that say e.g. state X at time T begets state Y at time T+1, again placing a convention of sequence (time, here) external to the system itself. But that time can be substituted by natural numbers, enumerating for exemple the states of some universal machine (itself described in arithmetic). This sounds like kernels to me. This question doesn't engage with your schema head-on; it's more of a side detour I've thought of asking about many times on the list; I thought it might get explained at some point. Well, now I'm asking. Now, if you ask where natural numbers comes from, that's a real mystery. But then I can explain you why no Lobian Machine can solve that mystery, and why, if we want to talk about all the natural numbers, we are obliged to postulate them at the start. My kernels would be describable by natural numbers so are they actually natural numbers? Next post: At 11:45 AM 12/18/2004, you wrote: At 03:31 18/12/04 -0500, Jesse Mazer wrote: I
Re: An All/Nothing multiverse model
Hal Ruhl wrote: As to the Laws of Logic with respect to information [and I think I said this earlier] the information in a kernel is indeed static. The laws of Logic are just our locally grown [and apparently sequential] way of revealing it. The question I raise is the implicit inclusion of time in this process. I think it would be simpler if you responded directly to quotes from my previous post, rather than just making general statements about issues raised in that post. For example, here you continue to *assert* that there is something inherently time-based about logical statements, but you don't in any way explain what is wrong with my counterargument from that post: 'The laws of logic need not be thought of as rules of discovery, they can be thought of purely as expressing static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or discovered them. For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.' Likewise, you didn't address my point that I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises, and you didn't address my question about whether you think there could be a world/kernel where a vehicle simultaneously had different numbers of wheels, or my question about whether, when you make statements about your theory as a whole like the information re the Nothing is in the All so they are infinitely nested you are assuming that the negation of these statements (in this case, 'the information re the Nothing is not in the All so they are not infinitely nested') is false. Should we have the hubris to impose this somewhat questioned concept on all other universes? In my view the states of all universes preexist in the All [as some of the kernels] and Physical Reality washes over them in some sequentially inconsistent way. So do believe the statement the states of all universes don't preexist in the All, and 'Physical Reality' does not wash over them in any sequentially inconsistent way would be false? If so, it seems that you yourself have the hubris to apply the logical law of noncontradiction to statements about reality as a whole. I do not agree with your rather based cancelation of the residual information issue since I see it as an unnecessary complication of my own method. I'm not sure what you mean by rather based cancellation. If you're talking about my point that every statement could be simultaneously true and false if you throw out the laws of logic, obviously *I* don't believe this is a good way to solve the residual information issue, since I think it's nonsensical to allow logical contradictions. But since you seem to be saying the laws of logic aren't absolute, I was just pointing out that you would have no basis for denying that statements about reality can be simultaneously true and false. If you say that it is an unnecessary complication to allow statements about reality as a whole to be both true and false, then you are in effect saying it would be an unnecessary complication to claim that the laws of logic don't apply to reality as a whole! Can a kernel of information be self inconsistent? From Bruno's last post I think it is possible to impose this idea on the All. I don't think Bruno's last post was really implying that everything would be inconsistent, I thought his point was more that you can't consider things like the collection of all possible sets to itself be a set. My current view is that each state of that dynamic has to be completely independent of the current state. Does that mean you say the statement each state of the dynamic is completely dependent on the current state is false? The way I describe this is to say that the dynamic is inconsistent. It helps this idea if there are kernels that are pairwise inconsistent. I don't understand what this means--can you give a concrete example of two kernels that are pairwise inconsistent? I think that is straight forward enough. If there are kernels that are self inconsistent then all the better. Why should they be selected out? Then why did you earlier say I am not ready to include a two wheeled tricycle that is simultaneously a one, three, or four wheeled tricycle? As to does mathematics contain information, mathematics has the potential to erect boundaries so by my definition it is information. But doesn't *any* statement you make about reality as a whole, like each state of that dynamic has to be completely independent of the current state, erect a boundary between itself and its negation, in this case each state of the dynamic is completely dependent on the current state? Jesse
Re: An All/Nothing multiverse model
At 21:48 17/12/04 -0500, Hal Ruhl wrote: Can a kernel of information be self inconsistent? From Bruno's last post I think it is possible to impose this idea on the All. I'm afraid I said the contrary (unless I misunderstand what you are pointing at through the expression kernel of information). If you agree that a kernel of information is like a theory or any finitely describable machine, then only such a thing can be said inconsistent. The All, I put it on the semantical side, I don't see how that can be made inconsistent in any interesting way. It is *our* attempts to manage the All which can lead to our inconsistencies. In case we discover some of those inconsistencies we better should backtrack. I think. No? Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
At 20:39 17/12/04 -0800, Pete Carlton wrote: As usual when I ask a question like this, if the answer is available in a text on logic or elsewhere, please just tell me where to look. ..I'm also interested in the implicit use of time, or sequence, in many of the ideas discussed here. For instance you might say that some of your Somethings are 'bitstrings' that could make up one of Bruno's or Jürgen's worlds/observers. Remember that comp, as I present it, make worlds non computable. It is a consequence of of the self-duplicability, when distinguishing 1 and 3 person points of view. Part of our idea of a string is the convention that one element comes first, then the second, then the third, et cetera. However, the information that accounts for that convention is not contained in the string itself. 'Taking' a Something as a bitstring involves some degree of external convention. Indeed, it needs a universal machine, and even an infinity of them. But all that exists and describes by the set of (sigma1) true arithmetical propositions. See Podniek's page http://www.ltn.lv/~podnieks/gt.html So my question is, what do you mean when you say a universe that has a sequence of successive states that follow a set of fixed rules? What could make one state give rise to the next state?Citing causality just gives a name the problem; it doesn't explain it. I completely agree with you. The primitive causality of the comp platonist is just the implication of classical propositionnal logic. Most of the time (sorry for the pun) time of a computation can be described using no more than the axioms of Peano Arithmetic, including especially the induction axioms: that if P(0) is true and if for all x (P(x) -P(x+1) ) then for all x we have P(x). (Witten B(0) Ax(B(x)-B(Sx)) - AxB(x) in http://www.ltn.lv/~podnieks/gt3.html#BM3 (S x) is x + 1 And I don't think introducing a Turing machine helps with this basic problem, since in any automaton you have rules that say e.g. state X at time T begets state Y at time T+1, again placing a convention of sequence (time, here) external to the system itself. But that time can be substituted by natural numbers, enumerating for exemple the states of some universal machine (itself described in arithmetic). This question doesn't engage with your schema head-on; it's more of a side detour I've thought of asking about many times on the list; I thought it might get explained at some point. Well, now I'm asking. Now, if you ask where natural numbers comes from, that's a real mystery. But then I can explain you why no Lobian Machine can solve that mystery, and why, if we want to talk about all the natural numbers, we are obliged to postulate them at the start. Kind Regards Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
At 03:31 18/12/04 -0500, Jesse Mazer wrote: I don't think Bruno's last post was really implying that everything would be inconsistent, I thought his point was more that you can't consider things like the collection of all possible sets to itself be a set. Exactly. It is the machine which gives a name to something too big which will take the risk of being inconsistent. The big all is not made inconsistent by allowing the possibility of inconsistent machines. Remark. Actually it is already consistent for a consistent loebian machine to be inconsistent, and this is not only true *about* any consistent Lobian machine, but it is communicable by any of them (provable by G* but already by G). Cf FU. It is again the second incompleteness theorem: (t = true or p_p) CONSISTENT t - NOT(PROVABLE(CONSISTENT t)), or by the duality between CONSISTENT and PROVABLE: CONSISTENT t - CONSISTENT (NOT (CONSISTENT t)) Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
Hi Jesse: At 03:31 AM 12/18/2004, you wrote: I think it would be simpler if you responded directly to quotes from my previous post, rather than just making general statements about issues raised in that post. For example, here you continue to *assert* that there is something inherently time-based about logical statements, but you don't in any way explain what is wrong with my counterargument from that post: I was still having reading difficulties with my new lenses so this was easier for me. 'The laws of logic need not be thought of as rules of discovery, they can be thought of purely as expressing Expressing seems to be a time dependent process. static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or discovered them. As are my kernels of information. For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.' Sure, That is a kernel. Observation does not make a kernel a kernel. Likewise, you didn't address my point that I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises, I believe Bruno said that some information systems included a set of beliefs. As I recall the premises are these beliefs. Justification comes from emotions [based on other beliefs] surrounding the resulting system such as simplicity, elegance of apparent explanation etc. So it seems to me that justification is part of belief. and you didn't address my question about whether you think there could be a world/kernel where a vehicle simultaneously Again time inserts itself as the notion of simultaneously. had different numbers of wheels, If the world was a CA and half the applicable cells were in a two wheel state and half in a three wheel state what would that be? What would be the concept of number in such a place? or my question about whether, when you make statements about your theory as a whole like the information re the Nothing is in the All so they are infinitely nested you are assuming that the negation of these statements (in this case, 'the information re the Nothing is not in the All so they are not infinitely nested') is false. See below Should we have the hubris to impose this somewhat questioned concept on all other universes? In my view the states of all universes preexist in the All [as some of the kernels] and Physical Reality washes over them in some sequentially inconsistent way. So do believe the statement the states of all universes don't preexist in the All, and 'Physical Reality' does not wash over them in any sequentially inconsistent way would be false? If so, it seems that you yourself have the hubris to apply the logical law of noncontradiction to statements about reality as a whole. I am just try to think of the simplest system that contains no information and yet has a dynamic that could support what might be the universe some may believe they inhabit. But then is there really a process like think? The All as I defined it [my current proposed belief] contains a kernel for the Nothing as well as a kernel for the All thus the nesting. From the inside perspective we are forced to be in, all we have to justify such a belief system is our own beliefs re efficiency, beauty, etc. etc. so our beliefs justify our beliefs. Is this not self referential? I do not intend to impose that on the system as a whole. I do not agree with your rather based cancelation of the residual information issue since I see it as an unnecessary complication of my own method. I'm not sure what you mean by rather based cancellation. If you're talking about my point that every statement could be simultaneously true and false if you throw out the laws of logic, obviously *I* don't believe this is a good way to solve the residual information issue, since I think it's nonsensical to allow logical contradictions. But since you seem to be saying the laws of logic aren't absolute, I was just pointing out that you would have no basis for denying that statements about reality can be simultaneously true and false. If you say that it is an unnecessary complication to allow statements about reality as a whole to be both true and false, then you are in effect saying it would be an unnecessary complication to claim that the laws of logic don't apply to reality as a whole! I just believe in my own sense of neatness. You gave two apparently contradictory statements which when put in the same pot seem to sum to what I propose for the whole system absent the rather. I wish to avoid including our laws of logic as a necessary component of a kernel. Further a kernel contains information but the whole system does not so how does logic apply to the whole system in the first place. Can a kernel of information be self inconsistent? From
Re: An All/Nothing multiverse model
Hi Pete: At 11:39 PM 12/17/2004, you wrote: As usual when I ask a question like this, if the answer is available in a text on logic or elsewhere, please just tell me where to look. ..I'm also interested in the implicit use of time, or sequence, in many of the ideas discussed here. For instance you might say that some of your Somethings are 'bitstrings' that could make up one of Bruno's or Jürgen's worlds/observers. Part of our idea of a string is the convention that one element comes first, then the second, then the third, et cetera. However, the information that accounts for that convention is not contained in the string itself. 'Taking' a Something as a bitstring involves some degree of external convention. One could argue that the rules for decoding a string are in the string itself. So a given string would represent all structures that are such a parsing of the string. So my question is, what do you mean when you say a universe that has a sequence of successive states that follow a set of fixed rules? What could make one state give rise to the next state? The rules contained in the string read the string and generate the next string. In my view this can cause problems [or point to explanations] re accumulating algorithmic complexity. Citing causality just gives a name the problem; it doesn't explain it. And I don't think introducing a Turing machine helps with this basic problem, since in any automaton you have rules that say e.g. state X at time T begets state Y at time T+1, again placing a convention of sequence (time, here) external to the system itself. Yes a dynamic [why that], and who ordered the computer [residual information] in the first place. I try to give a base for a dynamic and allow that some sequences could look computer generated but there seems to me to be a need [as payment for the dynamic] to also allow input to the computer that is inconsistent with any of its prior states. I think Bruno might call it a little third person indeterminacy if I sufficiently remember and understand his material. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: I think it would be simpler if you responded directly to quotes from my previous post, rather than just making general statements about issues raised in that post. For example, here you continue to *assert* that there is something inherently time-based about logical statements, but you don't in any way explain what is wrong with my counterargument from that post: I was still having reading difficulties with my new lenses so this was easier for me. OK, no problem. 'The laws of logic need not be thought of as rules of discovery, they can be thought of purely as expressing Expressing seems to be a time dependent process. I don't think it needs to be. When we say a certain set of symbols expresses something, in the most abstract sense we're just saying there's a mapping between the symbols and some meaning. static relationships between static truths, relationships that would exist regardless of whether anyone contemplated or discovered them. As are my kernels of information. For example, in every world where X and Y are simultaneously true, it is also true that X is true, even if no one notices this.' Sure, That is a kernel. Observation does not make a kernel a kernel. OK, but this isn't really relevant to my question, namely, why does any of this require time? Likewise, you didn't address my point that I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises, I believe Bruno said that some information systems included a set of beliefs. As I recall the premises are these beliefs. Justification comes from emotions [based on other beliefs] surrounding the resulting system such as simplicity, elegance of apparent explanation etc. So it seems to me that justification is part of belief. My point is that if I want to demonstrate the truth of some statement X to you (without appealing to new empirical evidence), I look for some set of premises that we *already* share, and then try to show how these premises imply X. I can't think of any historical example where someone's new idea is accepted by other people without the person appealing to common premises they already share. Can you? and you didn't address my question about whether you think there could be a world/kernel where a vehicle simultaneously Again time inserts itself as the notion of simultaneously. Simultaneously shouldn't be taken too literally, X and Y are simultaneously true is just a shorthand way of saying that X and Y are truths that both apply to exactly the same domain, whether same domain means same universe, same time, or whatever. For example, if I say Ronald Reagan was President of the U.S. in 1985 and Bill Clinton was President of the U.S. in 1995, these are two non-contradictory truths that apply to the domain of U.S. history in our universe, so in that sense they are simultaneous truths about this domain even though they refer to different dates. On the other hand, if I said Ronald Reagan was President of the U.S. in 1985 and Lex Luthor was President of the U.S. in 1985, and both applied to the domain of U.S. history in our universe, then this would be a contradiction. But if I made clear that the first statement applied to the domain of U.S. history in our universe and the second applied to the domain of U.S. history in an alternate universe then there would no longer be any contradiction in these statements. had different numbers of wheels, If the world was a CA and half the applicable cells were in a two wheel state and half in a three wheel state what would that be? I can't really picture a CA where the state of a cell specified a number of wheels, but never mind--this would clearly involve no contradiction, because the statements the cell is in a 2-wheel state and the cell is in a 3-wheel state would not apply to the same domain, since they refer to two *different* cells. There is only a logical contradiction here if both apply to exactly the same domain--in this case, the same cell in the same world at a single time. Do you think it could be possible for two contradictory statements about the state of a single cell at a single moment in a single world to *both* be true? Should we have the hubris to impose this somewhat questioned concept on all other universes? In my view the states of all universes preexist in the All [as some of the kernels] and Physical Reality washes over them in some sequentially inconsistent way. So do believe the statement the states of all universes don't preexist in the All, and 'Physical Reality' does not wash over them in any sequentially inconsistent way would be false? If so, it seems that you yourself have the hubris to apply the logical law of noncontradiction to statements about reality as a whole. I am just try to think of the simplest system that contains no information and yet has a dynamic
Re: An All/Nothing multiverse model
Hi Jesse: I think I respond to most earlier questions and comments below: As to the Laws of Logic with respect to information [and I think I said this earlier] the information in a kernel is indeed static. The laws of Logic are just our locally grown [and apparently sequential] way of revealing it. The question I raise is the implicit inclusion of time in this process. Should we have the hubris to impose this somewhat questioned concept on all other universes? In my view the states of all universes preexist in the All [as some of the kernels] and Physical Reality washes over them in some sequentially inconsistent way. Just like being in Bruno's transporter etc. we would never notice. My approach is designed to address the residual information problem and provide a basis for a dynamic. I do not agree with your rather based cancelation of the residual information issue since I see it as an unnecessary complication of my own method. Can a kernel of information be self inconsistent? From Bruno's last post I think it is possible to impose this idea on the All. My interest was to have a dynamic which did not impose any residual information on the All. My current view is that each state of that dynamic has to be completely independent of the current state. The way I describe this is to say that the dynamic is inconsistent. It helps this idea if there are kernels that are pairwise inconsistent. I think that is straight forward enough. If there are kernels that are self inconsistent then all the better. Why should they be selected out? Can any of this exclude a universe that has a sequence of successive states that follow a set of fixed rules? I think that one must insist that the inconsistency permeate every corner of the dynamic i.e. some level of external noise impressed on all state sequences. As to does mathematics contain information, mathematics has the potential to erect boundaries so by my definition it is information. It also seems possible that there is room for what might be called bifurcated boundaries - inconsistencies. Hal
Re: An All/Nothing multiverse model
As usual when I ask a question like this, if the answer is available in a text on logic or elsewhere, please just tell me where to look. ..I'm also interested in the implicit use of time, or sequence, in many of the ideas discussed here. For instance you might say that some of your Somethings are 'bitstrings' that could make up one of Bruno's or Jürgen's worlds/observers. Part of our idea of a string is the convention that one element comes first, then the second, then the third, et cetera. However, the information that accounts for that convention is not contained in the string itself. 'Taking' a Something as a bitstring involves some degree of external convention. So my question is, what do you mean when you say a universe that has a sequence of successive states that follow a set of fixed rules? What could make one state give rise to the next state?Citing causality just gives a name the problem; it doesn't explain it. And I don't think introducing a Turing machine helps with this basic problem, since in any automaton you have rules that say e.g. state X at time T begets state Y at time T+1, again placing a convention of sequence (time, here) external to the system itself. This question doesn't engage with your schema head-on; it's more of a side detour I've thought of asking about many times on the list; I thought it might get explained at some point. Well, now I'm asking. Best regards Pete On Dec 17, 2004, at 6:48 PM, Hal Ruhl wrote: snip My interest was to have a dynamic which did not impose any residual information on the All. My current view is that each state of that dynamic has to be completely independent of the current state. The way I describe this is to say that the dynamic is inconsistent. It helps this idea if there are kernels that are pairwise inconsistent. I think that is straight forward enough. If there are kernels that are self inconsistent then all the better. Why should they be selected out? Can any of this exclude a universe that has a sequence of successive states that follow a set of fixed rules? I think that one must insist that the inconsistency permeate every corner of the dynamic i.e. some level of external noise impressed on all state sequences. As to does mathematics contain information, mathematics has the potential to erect boundaries so by my definition it is information. It also seems possible that there is room for what might be called bifurcated boundaries - inconsistencies. Hal
Re: An All/Nothing multiverse model
At 23:12 12/12/04 -0500, Jesse Mazer wrote: Hal Ruhl wrote: At 09:35 PM 12/12/2004, you wrote: Godel's theorem would also apply to infinite axiomatic systems whose axioms are recursively enumerable (computable). But sure, if you allow non-computable axiomatic systems, you could have one that was both complete and consistent. A complete axiomatized arithmetic would be I believe be inconsistent as supported by to Bruno' post. http://www.escribe.com/science/theory/m5812.html No, I'm sure Bruno was only talking about recursively enumerable axiomatic systems. He said himself that the set of all true statements about arithmetic would be both complete and consistent, so if you allow non-computable sets of axioms you could just have every true statement about arithmetic be an axiom. Yes indeed. Most books give different definition of axiomatic and recursively enumerable, but there is a theorem by Craig which shows that for (most) theories, the notion are equivalent. (See Boolos and Jeffrey for a proof of Craig's theorem). Also, consistency is a pure syntactical notion, at least for theories having a symbol for falsity or having a negation connective. A theory (or a theorem proving machine) is consistent iff there is no derivation in it of the falsity (or of a proposition and its negation). Now, for the important class of first order logical theories (like Peano Arithmetics, Zermelo Fraenkel Set theory, etc.) the completeness theorem of Godel (note: the completeness, not the incompleteness one!) gives that being consistent is equivalent with having a model. But I do think, and perhaps that's related with Hal intuition (I'm not sure), that any theory which try to capture too big things will be inconsistent. Classical example is the naive idea of set which leads to Frege theory and this one was shown inconsistent by Russell. Church's logical theory based on his Lambda calculus was inconsistent, etc. What is a little bit amazing is Hal insistence that the ALL should be inconsistent. This is not an uninteresting idea, but it is a risky idea which is in need of handling with care (like in the paraconsistent logic perhaps?). I agree also with Jesse that to explain something to someone else there is a need to find common grounds. Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
Hi Jesse and Bruno: To consolidate my response: Yes indeed. Most books give different definition of axiomatic and recursively enumerable, but there is a theorem by Craig which shows that for (most) theories, the notion are equivalent. (See Boolos and Jeffrey for a proof of Craig's theorem). Also, consistency is a pure syntactical notion, at least for theories having a symbol for falsity or having a negation connective. A theory (or a theorem proving machine) is consistent iff there is no derivation in it of the falsity (or of a proposition and its negation). Now, for the important class of first order logical theories (like Peano Arithmetics, Zermelo Fraenkel Set theory, etc.) the completeness theorem of Godel (note: the completeness, not the incompleteness one!) gives that being consistent is equivalent with having a model. The All contains all information [is this controversial?] but that must add up to no net information content if my total system is to have no information. The small amount of external information necessary to define the All is balanced to zero net information by the other components of the system. I do not think that all information adding up to no net information is controversial. Further there is a dynamic within the All [computer simulations etc.] in the majority of positions I am aware of on this list - including my own - resulting in evolving universes. I give a justification for that dynamic based in the incompleteness of one of the components of my system - the Nothing. Now to maintain a zero net information within the All this dynamic must be devoid of selection and plan. I used to think that the solution was to say the dynamic was random. I now think that this is not correct. Random after all is a selection in its own right and pays attention to past behavior. But to say that the dynamic is inconsistent with its past seems to retire the problem. To me to say that the All is inconsistent carries benefits when explaining our universe not disadvantages. I am not a mathematician by formal training but it seems to me that there may be additional justification for my position in what Bruno says below. But I do think, and perhaps that's related with Hal intuition (I'm not sure), that any theory which try to capture too big things will be inconsistent. Classical example is the naive idea of set which leads to Frege theory and this one was shown inconsistent by Russell. Church's logical theory based on his Lambda calculus was inconsistent, etc. What is a little bit amazing is Hal insistence that the ALL should be inconsistent. This is not an uninteresting idea, but it is a risky idea which is in need of handling with care (like in the paraconsistent logic perhaps?). As to the Laws of Logic I do not see that each kernel of information as I call them requires the presence of anything of the sort to be. The laws of Logic [in my opinion] are rather a way to progressively decompress the information in such a kernel. Turing said that to prove is the same as to compute. So I seem to be in good company. To us compute is a process and thus assumes that time exists. This assumption is today suspect. Why should we impose it on other universes? Hal
Re: An All/Nothing multiverse model
Hi Jesse: I will go over the thread and try to clear things up but I am having eye surgery in the morning and ran out of time. Why would mathematics be the only thing in the All? Is that not a selection? At 07:38 PM 12/13/2004, you wrote: It is controversial that mathematics contains any information in the first place--by the most commonly-accepted definition of information in information theory, I don't think it would, simply because there is no room for multiple possible answers to a given question. Then does not all information include multiple possible answers? Later Hal
Re: An All/Nothing multiverse model
At 07:28 PM 12/11/2004, you wrote: Hal Ruhl wrote: You wrote: Well, what I get from your answer is that you're justifying the idea that the All is inconsistent in terms of your own concept of evolving Somethings, not in terms of inconsistent axiomatic systems. Just the reverse. The evolving Somethings inevitably encompass the inconsistencies within the All [all those inconsistent systems [self or pairwise] each with their full spectrum of unselected meaning. That is why the Somethings evolve randomly and inconsistently. OK, since I don't really understand your system I should have said something more general, like you're justifying the idea that the All is inconsistent in terms of your own theoretical framework, not in terms of inconsistent axiomatic systems. Do you grant that the All which contains all information contains a completed axiomatized arithmetic? So, again, you don't have any way of showing to a person who doesn't share your theoretical framework in the first place that everything, i.e. the All, need be inconsistent. I expect that this is a common problem for anyone's ideas. I do not believe in TOE's that start with the natural numbers - where did that info come from? I don't consider that to be information because it seems logically impossible that a statement such as one plus one equals two could be false. Why? Is there no universe [state] wherein the transitory meaning assigned to these symbols makes the sentence false? You might as well ask, where do the laws of logic come from? Do you consider the laws of logic to be information? The Laws of Logic [at least as we have assembled them in our little corner of our multiverse] establish a process designed to discover the information compressed into a system. A process takes place in a dimension we call time. Thus time is a hidden assumption in the Laws of Logic. This assumption is suspect. What is the justification for this ordered sequence called time? So the Laws of Logic are not only just a locally grown way of finding preexisting potential to divide [information] and not such a potential themselves but they are also highly suspect. What is the justification for imposing them on all the other universes and multiverses? If you don't think the laws of logic can be taken for granted, you could just solve the information problem by saying it is simultaneously true that there is something rather than nothing and also nothing rather than something, even though these facts are contradictory. There would still be the information contained in the existence of the contradiction which divides it from systems that are not contradictory. If you grant that the laws of logic and mathematics contain no information because there is no possible world in which they could be otherwise, then you could always adopt a theory like Tegmark's which just says that the everything consists of all possible mathematical structures, although you might still have a problem with picking a measure on these structures if you want a notion of probability (to solve things like the 'white rabbit problem'), and if there is any element of choice in picking the measure that would be form of arbitrariness or information (see my post at http://www.escribe.com/science/theory/m2606.html ). See above re the Laws of Logic. Hal
Re: An All/Nothing multiverse model
Hi Jesse: At 04:46 PM 12/12/2004, you wrote: Hal Ruhl wrote: OK, since I don't really understand your system I should have said something more general, like you're justifying the idea that the All is inconsistent in terms of your own theoretical framework, not in terms of inconsistent axiomatic systems. Do you grant that the All which contains all information contains a completed axiomatized arithmetic? No, because Godel proved that no axiomatic system can generate the set of all statements that would be true of our model of arithmetic (at least not without also generating false statements). Except an infinite one. So, again, you don't have any way of showing to a person who doesn't share your theoretical framework in the first place that everything, i.e. the All, need be inconsistent. I expect that this is a common problem for anyone's ideas. Not really, usually when people try to convince others of new ideas they appeal to some common framework of beliefs or common understanding they already share--that's why people are capable of changing each other's mind through reasoned arguments, rather than everyone just making arguments like if you grant that the Bible is the word of God, I can use passages from the Bible to show that it is indeed the word of God. Well ideas of this nature then where the framework shifts. I do not believe in TOE's that start with the natural numbers - where did that info come from? I don't consider that to be information because it seems logically impossible that a statement such as one plus one equals two could be false. Why? Is there no universe [state] wherein the transitory meaning assigned to these symbols makes the sentence false? I intentionally wrote the statement out in english words to convey the notion that I was making a meaningful statement about our model of arithmetic, rather than quoting a string of arbitrary symbols which can be mapped to the model in a certain way but don't have to be. There is no logically possible universe where the *idea* I am expressing in english when I say one plus one equals two is false, although of course we can imagine a universe where a non-english-speaker might use that particular string of letters to mean something different, like my thorax is on fire (as we would translate the meaning of his statement in english). Again we deal with logically possible - see below. You might as well ask, where do the laws of logic come from? Do you consider the laws of logic to be information? The Laws of Logic [at least as we have assembled them in our little corner of our multiverse] establish a process designed to discover the information compressed into a system. A process takes place in a dimension we call time. Thus time is a hidden assumption in the Laws of Logic. I disagree. X AND Y - X does not imply that first you have X AND Y and then it somehow transforms into X at a later date, it just means if it is true that statements X and Y are both true, then statement X must be true. You miss my point. As I said in earlier posts the information is static, the process of uncovering it is not. Try to stop thinking and reach a decision or uncover a truth. But what keeps thinking and deciding from being local illusions. If you don't think the laws of logic can be taken for granted, you could just solve the information problem by saying it is simultaneously true that there is something rather than nothing and also nothing rather than something, even though these facts are contradictory. There would still be the information contained in the existence of the contradiction which divides it from systems that are not contradictory. No it wouldn't, because if you abandon the laws of logic you can say that it is also true that this system is not contradictory--in other words, although it's true that both these contradictory statements are true (so the 'system' containing both is contradictory), it's also true that one is true and one is false (so the system containing both is not contradictory). Of course, you can now say the meta-system containing both the statements I just made is contradictory, but I can apply the exact same anti-logic to show this meta-system is not contradictory. And you can also use anti-logic to show that every statement I have made in this paragraph about the implications of anti-logic is false, including this one. Once you abandon the principle that if a statement is true, its negation must be false and vice-versa, then anything goes. And why is anything goes a problem? Anything goes includes universes such as ours. Hal
Re: An All/Nothing multiverse model
Hi Jesse: At 09:35 PM 12/12/2004, you wrote: Hal Ruhl: Hi Jesse: At 04:46 PM 12/12/2004, you wrote: Hal Ruhl wrote: OK, since I don't really understand your system I should have said something more general, like you're justifying the idea that the All is inconsistent in terms of your own theoretical framework, not in terms of inconsistent axiomatic systems. Do you grant that the All which contains all information contains a completed axiomatized arithmetic? No, because Godel proved that no axiomatic system can generate the set of all statements that would be true of our model of arithmetic (at least not without also generating false statements). Except an infinite one. Godel's theorem would also apply to infinite axiomatic systems whose axioms are recursively enumerable (computable). But sure, if you allow non-computable axiomatic systems, you could have one that was both complete and consistent. A complete axiomatized arithmetic would be I believe be inconsistent as supported by to Bruno' post. http://www.escribe.com/science/theory/m5812.html So, again, you don't have any way of showing to a person who doesn't share your theoretical framework in the first place that everything, i.e. the All, need be inconsistent. I expect that this is a common problem for anyone's ideas. Not really, usually when people try to convince others of new ideas they appeal to some common framework of beliefs or common understanding they already share--that's why people are capable of changing each other's mind through reasoned arguments, rather than everyone just making arguments like if you grant that the Bible is the word of God, I can use passages from the Bible to show that it is indeed the word of God. Well ideas of this nature then where the framework shifts. Since I don't understand your ideas I can't really comment. But I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises. But you do not understand my ideas so how does this apply? You might as well ask, where do the laws of logic come from? Do you consider the laws of logic to be information? The Laws of Logic [at least as we have assembled them in our little corner of our multiverse] establish a process designed to discover the information compressed into a system. A process takes place in a dimension we call time. Thus time is a hidden assumption in the Laws of Logic. I disagree. X AND Y - X does not imply that first you have X AND Y and then it somehow transforms into X at a later date, it just means if it is true that statements X and Y are both true, then statement X must be true. You miss my point. As I said in earlier posts the information is static, the process of uncovering it is not. So why couldn't the static ideas expressed by the laws of logic be timelessly true, even if we can only see the relationships between these truths in a sequential way? You still miss what I am saying. The laws of logic are designed to discover preexisting information. The preexisting information is static. Discovery is a time dependent process. It assumes time exists. Why that? How is it justified? Try to stop thinking and reach a decision or uncover a truth. But what keeps thinking and deciding from being local illusions. I don't know, the justification of beliefs is a part of the field of epistemology, and I don't have any good theory of epistemology. But I generally trust my thought-processes nevertheless. I trust mine as well, but on reflection I can not verify that my thought-processes even take place. If you don't think the laws of logic can be taken for granted, you could just solve the information problem by saying it is simultaneously true that there is something rather than nothing and also nothing rather than something, even though these facts are contradictory. There would still be the information contained in the existence of the contradiction which divides it from systems that are not contradictory. No it wouldn't, because if you abandon the laws of logic you can say that it is also true that this system is not contradictory--in other words, although it's true that both these contradictory statements are true (so the 'system' containing both is contradictory), it's also true that one is true and one is false (so the system containing both is not contradictory). Of course, you can now say the meta-system containing both the statements I just made is contradictory, but I can apply the exact same anti-logic to show this meta-system is not contradictory. And you can also use anti-logic to show that every statement I have made in this paragraph about the implications of anti-logic is false, including this one. Once you abandon the principle that if a statement is true, its negation must be false and vice-versa, then anything goes. And why is anything goes a problem? Anything
Re: An All/Nothing multiverse model
Hal Ruhl wrote: OK, since I don't really understand your system I should have said something more general, like you're justifying the idea that the All is inconsistent in terms of your own theoretical framework, not in terms of inconsistent axiomatic systems. Do you grant that the All which contains all information contains a completed axiomatized arithmetic? No, because Godel proved that no axiomatic system can generate the set of all statements that would be true of our model of arithmetic (at least not without also generating false statements). So, again, you don't have any way of showing to a person who doesn't share your theoretical framework in the first place that everything, i.e. the All, need be inconsistent. I expect that this is a common problem for anyone's ideas. Not really, usually when people try to convince others of new ideas they appeal to some common framework of beliefs or common understanding they already share--that's why people are capable of changing each other's mind through reasoned arguments, rather than everyone just making arguments like if you grant that the Bible is the word of God, I can use passages from the Bible to show that it is indeed the word of God. I do not believe in TOE's that start with the natural numbers - where did that info come from? I don't consider that to be information because it seems logically impossible that a statement such as one plus one equals two could be false. Why? Is there no universe [state] wherein the transitory meaning assigned to these symbols makes the sentence false? I intentionally wrote the statement out in english words to convey the notion that I was making a meaningful statement about our model of arithmetic, rather than quoting a string of arbitrary symbols which can be mapped to the model in a certain way but don't have to be. There is no logically possible universe where the *idea* I am expressing in english when I say one plus one equals two is false, although of course we can imagine a universe where a non-english-speaker might use that particular string of letters to mean something different, like my thorax is on fire (as we would translate the meaning of his statement in english). You might as well ask, where do the laws of logic come from? Do you consider the laws of logic to be information? The Laws of Logic [at least as we have assembled them in our little corner of our multiverse] establish a process designed to discover the information compressed into a system. A process takes place in a dimension we call time. Thus time is a hidden assumption in the Laws of Logic. I disagree. X AND Y - X does not imply that first you have X AND Y and then it somehow transforms into X at a later date, it just means if it is true that statements X and Y are both true, then statement X must be true. If you don't think the laws of logic can be taken for granted, you could just solve the information problem by saying it is simultaneously true that there is something rather than nothing and also nothing rather than something, even though these facts are contradictory. There would still be the information contained in the existence of the contradiction which divides it from systems that are not contradictory. No it wouldn't, because if you abandon the laws of logic you can say that it is also true that this system is not contradictory--in other words, although it's true that both these contradictory statements are true (so the 'system' containing both is contradictory), it's also true that one is true and one is false (so the system containing both is not contradictory). Of course, you can now say the meta-system containing both the statements I just made is contradictory, but I can apply the exact same anti-logic to show this meta-system is not contradictory. And you can also use anti-logic to show that every statement I have made in this paragraph about the implications of anti-logic is false, including this one. Once you abandon the principle that if a statement is true, its negation must be false and vice-versa, then anything goes. Jesse
Re: An All/Nothing multiverse model
Hal Ruhl: Hi Jesse: At 04:46 PM 12/12/2004, you wrote: Hal Ruhl wrote: OK, since I don't really understand your system I should have said something more general, like you're justifying the idea that the All is inconsistent in terms of your own theoretical framework, not in terms of inconsistent axiomatic systems. Do you grant that the All which contains all information contains a completed axiomatized arithmetic? No, because Godel proved that no axiomatic system can generate the set of all statements that would be true of our model of arithmetic (at least not without also generating false statements). Except an infinite one. Godel's theorem would also apply to infinite axiomatic systems whose axioms are recursively enumerable (computable). But sure, if you allow non-computable axiomatic systems, you could have one that was both complete and consistent. So, again, you don't have any way of showing to a person who doesn't share your theoretical framework in the first place that everything, i.e. the All, need be inconsistent. I expect that this is a common problem for anyone's ideas. Not really, usually when people try to convince others of new ideas they appeal to some common framework of beliefs or common understanding they already share--that's why people are capable of changing each other's mind through reasoned arguments, rather than everyone just making arguments like if you grant that the Bible is the word of God, I can use passages from the Bible to show that it is indeed the word of God. Well ideas of this nature then where the framework shifts. Since I don't understand your ideas I can't really comment. But I can't think of any historical examples of new mathematical/scientific/philosophical ideas that require you to already believe their premises in order to justify these premises. You might as well ask, where do the laws of logic come from? Do you consider the laws of logic to be information? The Laws of Logic [at least as we have assembled them in our little corner of our multiverse] establish a process designed to discover the information compressed into a system. A process takes place in a dimension we call time. Thus time is a hidden assumption in the Laws of Logic. I disagree. X AND Y - X does not imply that first you have X AND Y and then it somehow transforms into X at a later date, it just means if it is true that statements X and Y are both true, then statement X must be true. You miss my point. As I said in earlier posts the information is static, the process of uncovering it is not. So why couldn't the static ideas expressed by the laws of logic be timelessly true, even if we can only see the relationships between these truths in a sequential way? Try to stop thinking and reach a decision or uncover a truth. But what keeps thinking and deciding from being local illusions. I don't know, the justification of beliefs is a part of the field of epistemology, and I don't have any good theory of epistemology. But I generally trust my thought-processes nevertheless. If you don't think the laws of logic can be taken for granted, you could just solve the information problem by saying it is simultaneously true that there is something rather than nothing and also nothing rather than something, even though these facts are contradictory. There would still be the information contained in the existence of the contradiction which divides it from systems that are not contradictory. No it wouldn't, because if you abandon the laws of logic you can say that it is also true that this system is not contradictory--in other words, although it's true that both these contradictory statements are true (so the 'system' containing both is contradictory), it's also true that one is true and one is false (so the system containing both is not contradictory). Of course, you can now say the meta-system containing both the statements I just made is contradictory, but I can apply the exact same anti-logic to show this meta-system is not contradictory. And you can also use anti-logic to show that every statement I have made in this paragraph about the implications of anti-logic is false, including this one. Once you abandon the principle that if a statement is true, its negation must be false and vice-versa, then anything goes. And why is anything goes a problem? Anything goes includes universes such as ours. The contradictory truths aren't truths about different domains, like different universes--then they really wouldn't be contradictory, since there's no contradiction involved in saying X is true in universe #1 but false in universe #2. I am talking about contradictory truths in a single domain, like it being simultaneously true that *our* universe contains stars and true that our universe does not contain stars. Anyway, are you now agreeing that if you abandon the laws of logic, you can solve the information problem by saying it is both true that
Re: An All/Nothing multiverse model
Hi Jesse You wrote: Well, what I get from your answer is that you're justifying the idea that the All is inconsistent in terms of your own concept of evolving Somethings, not in terms of inconsistent axiomatic systems. Just the reverse. The evolving Somethings inevitably encompass the inconsistencies within the All [all those inconsistent systems [self or pairwise] each with their full spectrum of unselected meaning. That is why the Somethings evolve randomly and inconsistently. But in this case, someone who doesn't believe (or understand) your own theory in the first place need not agree that there's any reason to think a theory of everything would involve everything being inconsistent. I do not believe in TOE's that assume structures such as just an Everything thus yielding a theory with that assumption as irreducible information. After all where did that come from? I do not believe in TOE's that assume a dynamic such as computers simulating universes without a justification for a dynamic. I do not believe in TOE's that start with the natural numbers - where did that info come from? If you select a particular meaning out of its spectrum of possible meanings and assign it to a system is that not even more information in any such TOE? My approach solves these issues for me and has only few small prices to pay: Computer simulations or other dynamics will suffer random input. But so what? For example a CA that tends to an attractor can be stabilized in a reasonably self similar behavior off the attractor with the right amount of random input. Such an input to a universe is a decent explanation for an accelerating expansion of that universe given a max info storage and a fixed or increasing susceptibility to such input per unit volume. One could not do a statistical extract of information [there is none] say re why we find ourselves in this particular kind of universe. But again so what? Why would that be a believable expectation of a TOE in the first place? All universes over and over is in my belief system more satisfying and may be able to put some handle on ideas such as self aware and free will etc. at least for me. As to the individual beliefs, understandings, or needs of others I can not speak. Hal
Re: An All/Nothing multiverse model
Hal, With reference to your inconsistent TOE model (which I do not claim to understand), you state My approach solves these issues for ME . . . You also state All universes over and over is in my belief system more satisfying and may be able to put some handle on ideas such as self aware and free will etc. at least for ME. As to the individual beliefs, understandings, or needs of others I can not speak. (My capitalizations.) Are you implying that your model is NOT universal? Are you saying that reality is subjective? Norman - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, December 11, 2004 11:56 AM Subject: Re: An All/Nothing multiverse model Hi Jesse You wrote: Well, what I get from your answer is that you're justifying the idea that the All is inconsistent in terms of your own concept of evolving Somethings, not in terms of inconsistent axiomatic systems. Just the reverse. The evolving Somethings inevitably encompass the inconsistencies within the All [all those inconsistent systems [self or pairwise] each with their full spectrum of unselected meaning. That is why the Somethings evolve randomly and inconsistently. But in this case, someone who doesn't believe (or understand) your own theory in the first place need not agree that there's any reason to think a theory of everything would involve everything being inconsistent. I do not believe in TOE's that assume structures such as just an Everything thus yielding a theory with that assumption as irreducible information. After all where did that come from? I do not believe in TOE's that assume a dynamic such as computers simulating universes without a justification for a dynamic. I do not believe in TOE's that start with the natural numbers - where did that info come from? If you select a particular meaning out of its spectrum of possible meanings and assign it to a system is that not even more information in any such TOE? My approach solves these issues for me and has only few small prices to pay: Computer simulations or other dynamics will suffer random input. But so what? For example a CA that tends to an attractor can be stabilized in a reasonably self similar behavior off the attractor with the right amount of random input. Such an input to a universe is a decent explanation for an accelerating expansion of that universe given a max info storage and a fixed or increasing susceptibility to such input per unit volume. One could not do a statistical extract of information [there is none] say re why we find ourselves in this particular kind of universe. But again so what? Why would that be a believable expectation of a TOE in the first place? All universes over and over is in my belief system more satisfying and may be able to put some handle on ideas such as self aware and free will etc. at least for me. As to the individual beliefs, understandings, or needs of others I can not speak. Hal
Re: An All/Nothing multiverse model
Hi Norman: I suppose a person would hope that a theory they propose is in some way global but I was talking about the idea that belief is a factor in mathematical as well as other discourse. Bruno said in an earlier post in this thread: A proposition P is logically possible, relatively to 1) a consistent set of beliefs A 2) the choice of a deduction system D (and then consistent means does not derive 0=1). Most mathematical proofs are too complex to be judged by other than the belief of the majority of mathematicians. Hal At 03:44 PM 12/11/2004, you wrote: Hal, With reference to your inconsistent TOE model (which I do not claim to understand), you state My approach solves these issues for ME . . . You also state All universes over and over is in my belief system more satisfying and may be able to put some handle on ideas such as self aware and free will etc. at least for ME. As to the individual beliefs, understandings, or needs of others I can not speak. (My capitalizations.) Are you implying that your model is NOT universal? Are you saying that reality is subjective? Norman - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, December 11, 2004 11:56 AM Subject: Re: An All/Nothing multiverse model Hi Jesse You wrote: Well, what I get from your answer is that you're justifying the idea that the All is inconsistent in terms of your own concept of evolving Somethings, not in terms of inconsistent axiomatic systems. Just the reverse. The evolving Somethings inevitably encompass the inconsistencies within the All [all those inconsistent systems [self or pairwise] each with their full spectrum of unselected meaning. That is why the Somethings evolve randomly and inconsistently. But in this case, someone who doesn't believe (or understand) your own theory in the first place need not agree that there's any reason to think a theory of everything would involve everything being inconsistent. I do not believe in TOE's that assume structures such as just an Everything thus yielding a theory with that assumption as irreducible information. After all where did that come from? I do not believe in TOE's that assume a dynamic such as computers simulating universes without a justification for a dynamic. I do not believe in TOE's that start with the natural numbers - where did that info come from? If you select a particular meaning out of its spectrum of possible meanings and assign it to a system is that not even more information in any such TOE? My approach solves these issues for me and has only few small prices to pay: Computer simulations or other dynamics will suffer random input. But so what? For example a CA that tends to an attractor can be stabilized in a reasonably self similar behavior off the attractor with the right amount of random input. Such an input to a universe is a decent explanation for an accelerating expansion of that universe given a max info storage and a fixed or increasing susceptibility to such input per unit volume. One could not do a statistical extract of information [there is none] say re why we find ourselves in this particular kind of universe. But again so what? Why would that be a believable expectation of a TOE in the first place? All universes over and over is in my belief system more satisfying and may be able to put some handle on ideas such as self aware and free will etc. at least for me. As to the individual beliefs, understandings, or needs of others I can not speak. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: You wrote: Well, what I get from your answer is that you're justifying the idea that the All is inconsistent in terms of your own concept of evolving Somethings, not in terms of inconsistent axiomatic systems. Just the reverse. The evolving Somethings inevitably encompass the inconsistencies within the All [all those inconsistent systems [self or pairwise] each with their full spectrum of unselected meaning. That is why the Somethings evolve randomly and inconsistently. OK, since I don't really understand your system I should have said something more general, like you're justifying the idea that the All is inconsistent in terms of your own theoretical framework, not in terms of inconsistent axiomatic systems. So, again, you don't have any way of showing to a person who doesn't share your theoretical framework in the first place that everything, i.e. the All, need be inconsistent. I do not believe in TOE's that start with the natural numbers - where did that info come from? I don't consider that to be information because it seems logically impossible that a statement such as one plus one equals two could be false. You might as well ask, where do the laws of logic come from? Do you consider the laws of logic to be information? If you don't think the laws of logic can be taken for granted, you could just solve the information problem by saying it is simultaneously true that there is something rather than nothing and also nothing rather than something, even though these facts are contradictory. If you grant that the laws of logic and mathematics contain no information because there is no possible world in which they could be otherwise, then you could always adopt a theory like Tegmark's which just says that the everything consists of all possible mathematical structures, although you might still have a problem with picking a measure on these structures if you want a notion of probability (to solve things like the 'white rabbit problem'), and if there is any element of choice in picking the measure that would be form of arbitrariness or information (see my post at http://www.escribe.com/science/theory/m2606.html ). Jesse
Re: An All/Nothing multiverse model
To continue: As I said attach no significance to the little thought pictures I am using to illustrate various aspects of my system. They illustrate little chunks and then break down. The system has no net information. The Nothing has no internal information. The Everything is the boundary of both erected by the unavoidable definition and has no further ability to divide so it has no information. Thus the All must have no net internal information. Neither the All nor the Nothing can stand alone because they are a definitional pair and their simultaneity allows the boundary [the definition also called the Everything] to have no net information other wise it would only contain one of the pair and thus have a residual potential to divide. A kernel of information is the that information constituting a particular potential to divide. The All contains all such kernels. The All is internally inconsistent because it contains for example a complete axiomatized arithmetic as well as an infinity of other such kernels of information. Further the system can not have a fixed structure because that is a possible selection [a potential to divide] and that is not allowed in the system so at this point drop most of the original All as sphere picture. It was meant to illustrate just a few aspects of the system. Now pick things up with the original post with the Nothing bring incomplete re having to resolve the meaningful question of its own persistence. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: A kernel of information is the that information constituting a particular potential to divide. The All contains all such kernels. The All is internally inconsistent because it contains for example a complete axiomatized arithmetic as well as an infinity of other such kernels of information. So a set of all statements generated by an axiomatic system would qualify as a kernel of information? Even if you allow inconsistent axiomatic systems (as opposed to just consistent but incomplete ones), I still don't see why this makes the All inconsistent. After all, an axiomatic system is just a rule for generating strings of symbols which have no inherent meaning, such as TBc3\. It is only when we make a mapping between the symbols and a *model* in our head (like 'in terms of my model of arithmetic, let T represent the number two, B represent addition, c represent the number three, 3 represent equality, and \ represent the number five') that we can judge whether any pair of symbol-strings is inconsistent. Without such a mapping between symbols and models there can be no notion of inconsistency, because two meaningless strings of symbols cannot possibly be inconsistent. And if we do assign symbol-strings a meaning in terms of a model, then if we find that two strings *are* inconsistent, that doesn't mean the symbols represent an inconsistent model, it just means that one of the statements must be *false* when applied to the model (for example, the symbol-string 7+1=9 is false when applied to our model of arithmetic). The model itself is always consistent. So unless you believe that inconsistent axiomatic systems represent true facts about inconsistent models, I don't think you can say the All must be inconsistent based on the fact that it contains rules which generate false statements about models as well as true ones. Jesse
Re: An All/Nothing multiverse model
Hi Jesse: Meaning can not be assigned as an inherent component of the All. That would be a selection. Meaning can only be assigned if at all within the wave of physical reality associated with an evolving Something. Evolving Somethings will eventually encompass pairs of counterfactual and self counterfactual kernels of information thus making their future evolution which is an individual journey to completeness inconsistent with their past evolution. Thus the All is filled with inconsistent and non selected [random] activity. Its internal dynamic is random and inconsistent. Are these both not required for a global non selected activity? Random could still be consistent which would be a selection. Hal At 09:10 PM 12/10/2004, you wrote: Hal Ruhl wrote: A kernel of information is the that information constituting a particular potential to divide. The All contains all such kernels. The All is internally inconsistent because it contains for example a complete axiomatized arithmetic as well as an infinity of other such kernels of information. So a set of all statements generated by an axiomatic system would qualify as a kernel of information? Even if you allow inconsistent axiomatic systems (as opposed to just consistent but incomplete ones), I still don't see why this makes the All inconsistent. After all, an axiomatic system is just a rule for generating strings of symbols which have no inherent meaning, such as TBc3\. It is only when we make a mapping between the symbols and a *model* in our head (like 'in terms of my model of arithmetic, let T represent the number two, B represent addition, c represent the number three, 3 represent equality, and \ represent the number five') that we can judge whether any pair of symbol-strings is inconsistent. Without such a mapping between symbols and models there can be no notion of inconsistency, because two meaningless strings of symbols cannot possibly be inconsistent. And if we do assign symbol-strings a meaning in terms of a model, then if we find that two strings *are* inconsistent, that doesn't mean the symbols represent an inconsistent model, it just means that one of the statements must be *false* when applied to the model (for example, the symbol-string 7+1=9 is false when applied to our model of arithmetic). The model itself is always consistent. So unless you believe that inconsistent axiomatic systems represent true facts about inconsistent models, I don't think you can say the All must be inconsistent based on the fact that it contains rules which generate false statements about models as well as true ones. Jesse
Re: An All/Nothing multiverse model
At 20:08 07/12/04 -0500, Hal Ruhl wrote: I believe we discussed this and you agreed that a complete arithmetic would be inconsistent. I have not found the applicable posts. If by arithmetic you mean an axiomatizable theory, then indeed, by incompleteness it follows that such an arithmetic, if complete, must be inconsistent. If by arithmetic you mean a (not necessarily axiomatizable, and actually: necessarily not axiomatizable) model, then incompleteness does not apply. A model (identified with some set of sentences) can be both complete and consistent. Sometimes people use arithmetic (with a little a) for an axiomatizable presentation of arithmetic, and Arithmetic for the set of sentence true in the standard model of arithmetic. We have reached too many levels of nesting. I have been of on my own excavations. Is not all true arithmetical sentences a part of comp? Comp just asks for the truth of those sentences not depending of me or you. My problem is that I have not a clear idea of what you mean by nothing, dynamic, boundary, all. About the inconsistency of the ALL I could imagine a resemblance with my critics of Tegmark, which is that if you take a too bigger mathematical ontology you take the risk of being inconsistent (i.e. that your theory is inconsistent). It is like giving a name to the unnameable. Before axiomatic set theories like Zermelo-Fraenkel, ... Cantor called the collection of all sets the Inconsistent. But this does make sense for me. Only a theory, or a machine, or a person can be inconsistent, not a set, or a realm, or a model. Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
At 16:29 08/12/04 +0100, I wrote: Before axiomatic set theories like Zermelo-Fraenkel, ... Cantor called the collection of all sets the Inconsistent. But this does make sense for me. Only a theory, or a machine, or a person can be inconsistent, not a set, or a realm, or a model. Read instead: But this does NOT make sense for me. (sorry) Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
Hi Hal, In my questions about truth etc I was not really looking for a response but was rather trying to demonstrate the need for additional information in your theory. I don't have a theory. Just an argument showing that if we are machine then eventually physics is derivable from machine psychology/computer science. Your responses made my point I think. It is this issue I struggle with. I seek a TOE that has no net information. Though its components individually may have any amount of information the sum of all the information in all the components is no information. Why the down select re descriptions vs the All. I don't understand. My theory almost [However see below] includes yours as a sub component. My only spin is that my theory necessarily has all dynamics in it subject to external random input. Why down select to just your theory and as a result add all that extra required info? How is the set of such sentences known to be consistent? It is never known to be consistent. We can just hope it is. That is what I thought. (Smullyan makes a different case for arithmetical truth, but this would be in contradiction with the comp hyp). Please give me a URL or reference for his work. I deduce this from many readings of Smullyan. But I think Smullyan is just afraid that people takes Godel's second incompleteness theorem as an argument showing that Peano Arithmetic cannot been known to be consistent. And I agree with Smullyan on that point. But with comp I cannot know my own consistency and I can only show (to myself) that IF I am consistent then Peano Arithmetic is consistent. Look at the Forever Undecided book (on the net or in the list archive). To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - ... Right. This indeed follows from Goedel's incompleteness. Here you appear to me to be saying that your theory is indeed subject to random external input. Not the theory, but the possible observers described by theory. This is just a consequence of comp: we belongs' to an uncountable infinity of (infinite) computations. Cf our talk on the white rabbits. We don't need to inject randomness: a priori we have too much (first person) randomness. With comp it is the *lack* of randomness which is in need to be explained. Random because we do not know if the set of sentences is consistent in its current state and if incomplete it can be added to. How can it be added to in a manner that is consistent with the existing state? This is not relevant. See Jesse's post. So it would seem that your theory is indeed a sub component of my theory so as I said why down select and be burdened with all that net info? But which theory? COMP ? COMP is mainly the hope that it is possible to survive some treatment in a hospital. ...and where did all that info come from and why allow any in a base level system for worlds? Concerning just natural numbers this is a mystery. With comp it is necessarily mysterious. Perhaps it is mysterious because it is unnecessary. But then you should explain why we believe in natural numbers. (You did give plenty evidence that you believe in natural numbers). Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
Hi Bruno: At 06:40 AM 12/7/2004, you wrote: Hi Hal, In my questions about truth etc I was not really looking for a response but was rather trying to demonstrate the need for additional information in your theory. I don't have a theory. Just an argument showing that if we are machine then eventually physics is derivable from machine psychology/computer science. I have almost no current opposition to this. It sounds to me that it is in the All with my adder of a random input to the machine. Your responses made my point I think. It is this issue I struggle with. I seek a TOE that has no net information. Though its components individually may have any amount of information the sum of all the information in all the components is no information. Why the down select re descriptions vs the All. I don't understand. My theory almost [However see below] includes yours as a sub component. My only spin is that my theory necessarily has all dynamics in it subject to external random input. Why down select to just your theory and as a result add all that extra required info? How is the set of such sentences known to be consistent? It is never known to be consistent. We can just hope it is. That is what I thought. (Smullyan makes a different case for arithmetical truth, but this would be in contradiction with the comp hyp). Please give me a URL or reference for his work. I deduce this from many readings of Smullyan. But I think Smullyan is just afraid that people takes Godel's second incompleteness theorem as an argument showing that Peano Arithmetic cannot been known to be consistent. And I agree with Smullyan on that point. I believe we discussed this and you agreed that a complete arithmetic would be inconsistent. I have not found the applicable posts. But with comp I cannot know my own consistency and I can only show (to myself) that IF I am consistent then Peano Arithmetic is consistent. Look at the Forever Undecided book (on the net or in the list archive). There seems to be many ways to establish the necessary and sufficient properties of my All and the above seems to be one of them. To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - ... Right. This indeed follows from Goedel's incompleteness. Here you appear to me to be saying that your theory is indeed subject to random external input. Not the theory, but the possible observers described by theory. This is just a consequence of comp: we belongs' to an uncountable infinity of (infinite) computations. Cf our talk on the white rabbits. We don't need to inject randomness: a priori we have too much (first person) randomness. With comp it is the *lack* of randomness which is in need to be explained. The randomness injected at each event can be quite small. Also it is injected into each Something which itself is a multiverse so it is spread over all the universes in that multiverse. Seldom would it parse so as to inject large deltas into individual universes. Random because we do not know if the set of sentences is consistent in its current state and if incomplete it can be added to. How can it be added to in a manner that is consistent with the existing state? This is not relevant. See Jesse's post. But not wrong? See my previous post which is a clearer statement of what I mean. The above is a contribuitor to the random evolution dynamic of the Somethings. Two identical Somethings may not take the same next step. So it would seem that your theory is indeed a sub component of my theory so as I said why down select and be burdened with all that net info? But which theory? COMP ? COMP is mainly the hope that it is possible to survive some treatment in a hospital. We have reached too many levels of nesting. I have been of on my own excavations. Is not all true arithmetical sentences a part of comp? ...and where did all that info come from and why allow any in a base level system for worlds? Concerning just natural numbers this is a mystery. With comp it is necessarily mysterious. Perhaps it is mysterious because it is unnecessary. But then you should explain why we believe in natural numbers. (You did give plenty evidence that you believe in natural numbers). They would be in the All. Hal
Re: An All/Nothing multiverse model
At 06:37 PM 12/7/2004, you wrote: To clarify - the All contains all information simultaneously [see the definition in the original post] - including ALL Truing machines with ALL possible output tapes - so it contains simultaneously both output tapes re your comment below. But if there is a fact which is true in one world being simulated by a given Turing machine, but false in a different Turing machine simulation, that doesn't mean that the All is contradictory. After all, the statement this planet contains life is true of Earth but not true of Pluto, but that doesn't mean the solar system is contradictory, it just means that different facts are true of different planets. This really misses my meaning. That is not how Somethings evolve in the All. The Somethings incorporate preexisting information such as states of universes in a random dynamic. Similarly, if the All contains all possible worlds in some sense (all possible Turing machine programs, for example), then different facts could be true of different worlds, without this meaning the All itself is inconsistent. If Turing machine program #2334 simulates a 3-dimensional universe while Turing machine program #716482 simulates a 2-dimensional universe, that doesn't mean the inconsistent statements the universe is 3-dimensional and the universe is 2-dimensional are simultaneously true in the All--rather, it just means the statements the universe described by program #2334 is 3-dimensional and the universe described by program #716482 is 2-dimensional are simultaneously true in the All, and there is no contradiction between these statements. See above. As long as you always describe the *context* of any statement, I don't see any reason why we should describe the All as inconsistent. So if you think the All is inconsistent somehow, you need to explain in more detail why you think this is. I already have. Would you agree that Turing's result says that some subset of FAS are inconsistent? Also, you didn't answer my earlier question about whether your idea of the All only includes worlds that could be simulated on a Turing machine, or if it also includes worlds that could be simulated by a hypercomputer which is capable of performing uncomputable operations (like instantly deciding if a given Turing machine program will halt or not). The All is all information without restriction. All the information is in there all the time. The boundaries of the Somethings wash across the inherent counterfactuals counterfactually. Hal
Re: An All/Nothing multiverse model
Hi Jesse: At 09:23 PM 12/7/2004, you wrote: Hal Ruhl wrote: To clarify - the All contains all information simultaneously [see the definition in the original post] - including ALL Truing machines with ALL possible output tapes - so it contains simultaneously both output tapes re your comment below. But if there is a fact which is true in one world being simulated by a given Turing machine, but false in a different Turing machine simulation, that doesn't mean that the All is contradictory. After all, the statement this planet contains life is true of Earth but not true of Pluto, but that doesn't mean the solar system is contradictory, it just means that different facts are true of different planets. This really misses my meaning. That is not how Somethings evolve in the All. The Somethings incorporate preexisting information such as states of universes in a random dynamic. I am not asking about how Somethings evolve in your theory, I'm asking what's your justification for claiming that the All is inconsistent. You are giving examples of machines simulating worlds. That is not how my approach works. Thus my response. For the other see below. As long as you always describe the *context* of any statement, I don't see any reason why we should describe the All as inconsistent. So if you think the All is inconsistent somehow, you need to explain in more detail why you think this is. I already have. Would you agree that Turing's result says that some subset of FAS are inconsistent? You don't need Turing's results to show that, Its one of many ways of showing that the All contains kernels of information that are inconsistent with each other. The kernels are always there. No computers are running in my All it only may look that way here and there from time to time. it is quite trivial to construct an axiomatic system with two contradictory axioms, or with different subsets of axioms that can be used to prove inconsistent theorems. However, there is a distinction between saying an axiomatic system is inconsistent, and saying there is something inconsistent in the behavior of the Turing machine simulating that system. There will always be a single definite truth about what symbol the Turing machine prints out at what time--it is only when you try to interpret the *meaning* of different strings of symbols that it prints out that you will see an inconsistency. As an analogy, suppose I am running a complex simulation of a human being sitting at a writing desk, and he writes two sentences on a simulated piece of paper: I have a beard and I do not have a beard. If we interpret these sentences in terms of their english meaning, obviously they represent inconsistent statements, but that doesn't mean the simulation itself is somehow inconsistent, does it? One of the statements will be true and one will be false, so there's no problem. Get rid of the machine. Your argument would only show the All to be inconsistent if you believe that for every axiomatic system a Turing machine can simulate, there must be a corresponding world within the All where all the axioms and theorems represent simultaneously true statements about that world. But if you believe that, then you are saying the All must contain not only all possible worlds, but logically impossible worlds as well. Is that what you're saying? All states of all worlds are logically within the venue and visited with physical reality over and over. Also, you didn't answer my earlier question about whether your idea of the All only includes worlds that could be simulated on a Turing machine, or if it also includes worlds that could be simulated by a hypercomputer which is capable of performing uncomputable operations (like instantly deciding if a given Turing machine program will halt or not). The All is all information without restriction. All the information is in there all the time. The boundaries of the Somethings wash across the inherent counterfactuals counterfactually. I don't understand what these words are supposed to mean, or how they address my question above. Can you just answer yes or no? Again get rid of the machine. The dynamic is not a simulation generating states in any way. Hal
Re: An All/Nothing multiverse model
Maybe this will help: The All contains all possible output states of all Turing machines [among all manner of other info such as states of really messy universes] simultaneously. These states are given Physical reality by evolving Somethings in random order over and over. Some such sequences can arbitrarily closely approach or even exactly match those that would be output by a Turing machine for long runs of states [but not infinite runs of states due to the random input factor - no selection allowed]. All other sequences of all kinds of states also take place. Hal
Re: An All/Nothing multiverse model
From: Hal Ruhl [EMAIL PROTECTED] To: Jesse Mazer [EMAIL PROTECTED] Subject: Re: An All/Nothing multiverse model Date: Tue, 07 Dec 2004 22:19:02 -0500 Hi Jesse: At 09:23 PM 12/7/2004, you wrote: Hal Ruhl wrote: To clarify - the All contains all information simultaneously [see the definition in the original post] - including ALL Truing machines with ALL possible output tapes - so it contains simultaneously both output tapes re your comment below. But if there is a fact which is true in one world being simulated by a given Turing machine, but false in a different Turing machine simulation, that doesn't mean that the All is contradictory. After all, the statement this planet contains life is true of Earth but not true of Pluto, but that doesn't mean the solar system is contradictory, it just means that different facts are true of different planets. This really misses my meaning. That is not how Somethings evolve in the All. The Somethings incorporate preexisting information such as states of universes in a random dynamic. I am not asking about how Somethings evolve in your theory, I'm asking what's your justification for claiming that the All is inconsistent. You are giving examples of machines simulating worlds. That is not how my approach works. Thus my response. For the other see below. As long as you always describe the *context* of any statement, I don't see any reason why we should describe the All as inconsistent. So if you think the All is inconsistent somehow, you need to explain in more detail why you think this is. I already have. Would you agree that Turing's result says that some subset of FAS are inconsistent? You don't need Turing's results to show that, Its one of many ways of showing that the All contains kernels of information that are inconsistent with each other. The kernels are always there. No computers are running in my All it only may look that way here and there from time to time. What is a kernel of information? Can you give a concrete example of two kernels of information within the All that are inconsistent with each other? However, there is a distinction between saying an axiomatic system is inconsistent, and saying there is something inconsistent in the behavior of the Turing machine simulating that system. There will always be a single definite truth about what symbol the Turing machine prints out at what time--it is only when you try to interpret the *meaning* of different strings of symbols that it prints out that you will see an inconsistency. As an analogy, suppose I am running a complex simulation of a human being sitting at a writing desk, and he writes two sentences on a simulated piece of paper: I have a beard and I do not have a beard. If we interpret these sentences in terms of their english meaning, obviously they represent inconsistent statements, but that doesn't mean the simulation itself is somehow inconsistent, does it? One of the statements will be true and one will be false, so there's no problem. Get rid of the machine. OK, instead of talking about a simulated person running on a machine, let's just talk about a real person like you or me, whatever you think real people are. If I write the words I have a beard and then write the words I do not have a beard, does this show the All is inconsistent? If not, then why does the fact that we can write down (or conceive of) inconsistent axiomatic systems show that the All is inconsistent? Your argument would only show the All to be inconsistent if you believe that for every axiomatic system a Turing machine can simulate, there must be a corresponding world within the All where all the axioms and theorems represent simultaneously true statements about that world. But if you believe that, then you are saying the All must contain not only all possible worlds, but logically impossible worlds as well. Is that what you're saying? All states of all worlds are logically within the venue and visited with physical reality over and over. What is the venue? Can you give an example of what you mean by a state of a world? Can you explain why the fact that there are inconsistent axiomatic systems shows that All is inconsistent? Also, you didn't answer my earlier question about whether your idea of the All only includes worlds that could be simulated on a Turing machine, or if it also includes worlds that could be simulated by a hypercomputer which is capable of performing uncomputable operations (like instantly deciding if a given Turing machine program will halt or not). The All is all information without restriction. All the information is in there all the time. The boundaries of the Somethings wash across the inherent counterfactuals counterfactually. I don't understand what these words are supposed to mean, or how they address my question above. Can you just answer yes or no? Again get rid of the machine. The dynamic is not a simulation generating states
Re: An All/Nothing multiverse model
Hi Jesse: The All contains inconsistent FAS [we have no issue here as far as I can tell] and thus all of the theorems of such FAS as some of the kernels of information simultaneously. [Do we have an issue here?] This content makes the All inconsistent. [OK?] The All does not output anything - it is internally inconsistent. [OK?]. A Something [see the original post] can not evolve [its boundary moving through the All in an attempt to complete itself ] consistent with its prior evolution because each new kernel encompassed by its boundary changes the Something and further some such kernels may be inconsistent with those kernels already encompassed. [OK?] Further the consistent evolution of a Something would be a selection [evolution according to some plan] which is not allowed [see original post] [OK?] This in no way prevents any kind of string of states from being encompassed. [OK?] Hal
Re: An All/Nothing multiverse model
From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: Re: An All/Nothing multiverse model Date: Tue, 07 Dec 2004 22:41:45 -0500 Maybe this will help: The All contains all possible output states of all Turing machines [among all manner of other info such as states of really messy universes] simultaneously. These states are given Physical reality by evolving Somethings in random order over and over. Some such sequences can arbitrarily closely approach or even exactly match those that would be output by a Turing machine for long runs of states [but not infinite runs of states due to the random input factor - no selection allowed]. All other sequences of all kinds of states also take place. Hal OK, that is helpful in making your ideas a little more concrete. But in this case, what would it mean for two possible states to be inconsistent with one another? Can you give an example of two Turing machine states that are inconsistent? Also, when you talk about Turing machine states, are you talking about different possible strings of numbers on the tape that will be seen *after* a given Turing machine's computation has halted, or are you talking about the state of a Turing machine during a single step in its computation, like the tape reads 100011010, the Turing machine's read/write head is on the second zero, and the machine is in internal state #14? Jesse
Re: An All/Nothing multiverse model
At 17:15 03/12/04 -0500, Hal Ruhl wrote: Hi Bruno: I assume your theory is intended to give the range of descriptions of worlds. The All in my model contains - well - ALL so it includes systems to which Godel's theorem applies. Your theory has problems for me. What is truth? Truth is a queen who wins all the wars without any army. You can guess it by reading a newspaper. But you can better guess it by reading two independent newspaper, and still better by reading three independent newspapers, etc. What is a sentence? An informal sentence is a ordered set of words having hopefully some meaning. A formal sentence is the same but with a decidable grammar, and sometimes a mathematical notion of meaning in the form of a mathematical structure satisfying the sentence. This can be find in any textbook in logic. What is arithmetical? A sentence is arithmetical, roughly, if it bears on (natural) numbers. As Stephen Paul King asked: How is truth resolved for a given sentence? It is resolved partially by proof. Why the down select re descriptions vs the All. I don't understand. How is the set of such sentences known to be consistent? It is never known to be consistent. We can just hope it is. (Smullyan makes a different case for arithmetical truth, but this would be in contradiction with the comp hyp). To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - ... Right. This indeed follows from Goedel's incompleteness. ...and where did all that info come from and why allow any in a base level system for worlds? Concerning just natural numbers this is a mystery. With comp it is necessarily mysterious. Best regards, Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
Hi Bruno: In my questions about truth etc I was not really looking for a response but was rather trying to demonstrate the need for additional information in your theory. Your responses made my point I think. It is this issue I struggle with. I seek a TOE that has no net information. Though its components individually may have any amount of information the sum of all the information in all the components is no information. At 08:13 AM 12/6/2004, you wrote: At 17:15 03/12/04 -0500, Hal Ruhl wrote: Hi Bruno: I assume your theory is intended to give the range of descriptions of worlds. The All in my model contains - well - ALL so it includes systems to which Godel's theorem applies. Your theory has problems for me. What is truth? Truth is a queen who wins all the wars without any army. You can guess it by reading a newspaper. But you can better guess it by reading two independent newspaper, and still better by reading three independent newspapers, etc. What is a sentence? An informal sentence is a ordered set of words having hopefully some meaning. A formal sentence is the same but with a decidable grammar, and sometimes a mathematical notion of meaning in the form of a mathematical structure satisfying the sentence. This can be find in any textbook in logic. What is arithmetical? A sentence is arithmetical, roughly, if it bears on (natural) numbers. As Stephen Paul King asked: How is truth resolved for a given sentence? It is resolved partially by proof. Why the down select re descriptions vs the All. I don't understand. My theory almost [However see below] includes yours as a sub component. My only spin is that my theory necessarily has all dynamics in it subject to external random input. Why down select to just your theory and as a result add all that extra required info? How is the set of such sentences known to be consistent? It is never known to be consistent. We can just hope it is. That is what I thought. (Smullyan makes a different case for arithmetical truth, but this would be in contradiction with the comp hyp). Please give me a URL or reference for his work. To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - ... Right. This indeed follows from Goedel's incompleteness. Here you appear to me to be saying that your theory is indeed subject to random external input. Random because we do not know if the set of sentences is consistent in its current state and if incomplete it can be added to. How can it be added to in a manner that is consistent with the existing state? . So it would seem that your theory is indeed a sub component of my theory so as I said why down select and be burdened with all that net info? ...and where did all that info come from and why allow any in a base level system for worlds? Concerning just natural numbers this is a mystery. With comp it is necessarily mysterious. Perhaps it is mysterious because it is unnecessary. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - ... Right. This indeed follows from Goedel's incompleteness. Here you appear to me to be saying that your theory is indeed subject to random external input. Random because we do not know if the set of sentences is consistent in its current state and if incomplete it can be added to. How can it be added to in a manner that is consistent with the existing state? . We can choose whether a Godel statement should be judged true or false by consulting our model of arithmetic. See this post of mine on the use of models in mathematics from the thread Something for Platonists (you can see the other posts in the thread by clicking 'View This Thread' at the top): http://www.escribe.com/science/theory/m4584.html Jesse
Re: An All/Nothing multiverse model
Hi Jesse: My originating post appeals only to the result of Turing to the effect that there is in general no decision procedure. As a result FAS in general can not be both complete and consistent. Since my All contains all FAS including the complete ones then the All is inconsistent. That is the simplicity of it. As to any confusion over the concept of model I can call just as well call it a theory. Hal At 02:40 PM 12/6/2004, you wrote: Hal Ruhl wrote: To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - ... Right. This indeed follows from Goedel's incompleteness. Here you appear to me to be saying that your theory is indeed subject to random external input. Random because we do not know if the set of sentences is consistent in its current state and if incomplete it can be added to. How can it be added to in a manner that is consistent with the existing state? . We can choose whether a Godel statement should be judged true or false by consulting our model of arithmetic. See this post of mine on the use of models in mathematics from the thread Something for Platonists (you can see the other posts in the thread by clicking 'View This Thread' at the top): http://www.escribe.com/science/theory/m4584.html Jesse
Re: An All/Nothing multiverse model
Hal Ruhl wrote: Hi Jesse: My originating post appeals only to the result of Turing to the effect that there is in general no decision procedure. There's no single decision procedure for a Turing machine, but if you consider more general kinds of machines, like a hypercomputer that can check an infinite number of cases in a finite time, then there may be a single decision procedure for such a machine to decide if any possible statement about arithmetic is true or false. If your everything includes only computable universes, then such hypercomputers wouldn't exist in any universe, but if you believe in an everything more like Tegmark's collection of all conceivable mathematical structures, then there should be universes where it would be possible to construct such a hypercomputer, even if they can't be constructed in ours. By the way, do you understand that Godel's proof is based on the idea that, if we have an axiomatic system A, we can always find a statement G that we can understand to mean axiomatic system A will not prove statement G to be true? Surely it is not simply a matter of random choice whether G is true or false--we can see that as long as axiomatic system A is consistent, it cannot prove G to be false (because that would mean axiomatic system A [i]will[/i] prove G to be true), nor can it prove it is true (because that would mean it was proving true the statement that it would never prove it true). But this means that A will never prove G true, which means we know G *is* true, provided A is consistent. I would say that we can *know* that the Peano axioms are consistent by consulting our model of arithmetic, in the same way we can *know* the axiomatic system discussed in my post at http://www.escribe.com/science/theory/m4584.html is consistent, by realizing those axioms describe the edges and vertices of a triangle. Do you disagree that these model-based proofs of consistency are valid? Jesse
Re: An All/Nothing multiverse model
Hi Jesse: I think you miss my point. The All contains ALL including Turing machines that model complete FAS and other inconsistent systems. The All is inconsistent - that is all that is required. Godel's theorem is a corollary of Turing's. As you say a key element of Godel's approach to incompleteness is to assume consistency of the system in question. The only way I see to falsify my theory at this location is to show that all contents of the All are consistent. Hal At 11:46 PM 12/6/2004, you wrote: Hal Ruhl wrote: Hi Jesse: My originating post appeals only to the result of Turing to the effect that there is in general no decision procedure. There's no single decision procedure for a Turing machine, but if you consider more general kinds of machines, like a hypercomputer that can check an infinite number of cases in a finite time, then there may be a single decision procedure for such a machine to decide if any possible statement about arithmetic is true or false. If your everything includes only computable universes, then such hypercomputers wouldn't exist in any universe, but if you believe in an everything more like Tegmark's collection of all conceivable mathematical structures, then there should be universes where it would be possible to construct such a hypercomputer, even if they can't be constructed in ours. By the way, do you understand that Godel's proof is based on the idea that, if we have an axiomatic system A, we can always find a statement G that we can understand to mean axiomatic system A will not prove statement G to be true? Surely it is not simply a matter of random choice whether G is true or false--we can see that as long as axiomatic system A is consistent, it cannot prove G to be false (because that would mean axiomatic system A [i]will[/i] prove G to be true), nor can it prove it is true (because that would mean it was proving true the statement that it would never prove it true). But this means that A will never prove G true, which means we know G *is* true, provided A is consistent. I would say that we can *know* that the Peano axioms are consistent by consulting our model of arithmetic, in the same way we can *know* the axiomatic system discussed in my post at http://www.escribe.com/science/theory/m4584.html is consistent, by realizing those axioms describe the edges and vertices of a triangle. Do you disagree that these model-based proofs of consistency are valid? Jesse
Re: An All/Nothing multiverse model
Hal Ruhl wrote: Hi Jesse: I think you miss my point. The All contains ALL including Turing machines that model complete FAS and other inconsistent systems. The All is inconsistent - that is all that is required. You mean because the All contains Turing machines which model axiomatic systems that are provably inconsistent (like a system that contains the axiom all A have property B as well as the axiom there exists an A that does not have property B), that proves the All itself is inconsistent? If that's your argument, I don't think it makes sense--the Turing machine itself won't behave in a contradictory way as it prints out symbols, there will always be a single definite truth about which single it prints at a given time, it's only when we interpret the *meaning* of those symbols that we may see the machine has printed out two symbol-strings with opposite meaning. But we are free to simply believe that the machine has printed out a false statement, there is no need to believe that every axiomatic system describes an actual world within the All, even a logically impossible world where two contradictory statements are simultaneously true. Godel's theorem is a corollary of Turing's. As you say a key element of Godel's approach to incompleteness is to assume consistency of the system in question. But do you agree it is possible for us to *prove* the consistency of a system like the Peano arithmetic or the axiomatic system describing the edges and points of a triangle, by finding a model for the axioms? The only way I see to falsify my theory at this location is to show that all contents of the All are consistent. Hal I think you need to give a more clear definition of what is encompassed by the All before we can decide if it is consistent or inconsistent. For example, does the All represent the set of all logically possible worlds, or do you demand that it contains logically impossible worlds too? Does the All contain sets of truths that cannot be printed out by a single Turing machine, but which could be printed out by a program written for some type of hypercomputer, like the set of all true statements about arithmetic (a set which is both complete and consistent)? Jesse
Re: An All/Nothing multiverse model
Hi John: At 02:29 PM 12/3/2004, you wrote: Dear Hal, here are some stupid remarks (I call them stupid, because - they really are - I cannot follow the theoretical logic of your discussion with Bruno, and base my remarks on feeling while reading your text - which is not the most scientific way of dicussion. Nevertheless I submit them FYI: I quote and reply below.- Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, December 01, 2004 3:49 PM Subject: Re: An All/Nothing multiverse model (Hal: BrunoJM: blank lines) Hi Bruno: In the following call an individual [Ai,Dj] pair logic system Ln where i, j, and n can go from 1 to an uncountable infinity and all possible [Ai,D,j] pairings are considered. What if i or j are '0'? do you take it out from 'all possible,' if the pair is a single logic item? i and j are just used as an index. You can start at 0 if you want, you still run over all A and D. (That would be no valid description of Worlds? restrictions on 'valid'?) In Nothing both are '0', (I suppose). Is this an exception from your model? BTW All and Nothing cannot have a model in the usual sense. (Common sense, that is). I call a 'model' an informational (topical, etc.) restricted view. Such possibility would violate the impossibility of 0 = 1 (- in the consistency). I see no reason to exclude the Ln which have such an Ai from being a valid description of a World. It is just an explicit expression of incompleteness rather than an implicit one. Thus there could be two subsets of Ai in W. I deny the argument I see no reason to exclude... (Nescio non est argumentum). Such as: this is the only way it can be... is appealing to ignorance of the other ways. My statement was not an argument that no such reason exists just an indication that I personally have not been able to think of one. Absence of evidence is not evidence of absence. However I do give an argument in favor of not excluding such Ln: It is just an explicit expression of incompleteness rather than an implicit one. Thus induction would fail for all worlds in W because the logical foundation for all worlds would be constantly shifting from one Ln to another. Concerning many theories, to say that a proposition (or a set of propositions) A is logically possible is the same as saying that A is consistent (i.e you cannot derive 0 = 1 from it), No matter what, the unlimited Multiverse cannot be based on a possibility WITHIN A N Y of the logical systems derivable in our mind. Our descriptive talent can have limits but not the W. Even the 0=1 impossibility postulate is human logic, see above my Latin phrase. Exactly my point. One can not - I believe - build a valid theory of descriptions of worlds based on a down selection from the All. When talking of descriptions of worlds - in such a venue consistency would only be applicable to individual states [if at all] and not to successions of states. The question then is can the All [which contains W] contain self inconsistent states such as one with a correctly and completely assembled two wheeled tricycle or a cat that is both alive and dead or the same thing having two valid sets of coordinates? Now the All is complete so it is internally inconsistent so I see no way to argue against the presence of such states founded on inconsistent Ai. That sounds better, (including the i=0 above case as well?) If you meant 1 = 0, Yes. This could be a rather odd world, but degree of oddity is not relevant. I advise reflection on the opinion of the dung beetle when considering what constitutes and suitable world. or saying that A has a model (a reality, a mathematical structure) satisfying it. Human logic again. Is A modeled with the unmodelable ALL or Nothing? It seems that the idea that mathematical structures are actually consistent is nice but lacks any basis. ! Was that a sign of agreement? To help place my model in context with the above: A core idea is the definitional pair relationship. The [All,Nothing] pair is unique in being inherently unavoidable but still summing to no information. Thus it has no initiation and no end. Amen Another core idea is: Is there a meaningful question the Nothing must resolve? The answer to this is: Yes there is: The Nothing either continues [persists], or it does not. The answer must be inherent in the information within the Nothing but there is none in there by definition. Therefore the Nothing is incomplete - it can not resolve any meaningful question. But in this case it must do so. The only reservoir of information is the All. Therefore it must breach the barrier between itself and the All. In doing so it losses contact with what it was [an Ln shift] and becomes an evolving [including successive Ln shifts] - a multiverse - within the All. And so on...The 'partners of yours (All Nothing) get a task, MUST DO
Fw: An All/Nothing multiverse model
Dear Bruno, How is the trueness of members of this theory (of all true arithmetical sentences) given? By fiat? Kindest regards, Stephen - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, December 03, 2004 8:03 AM Subject: Re: An All/Nothing multiverse model At 15:49 01/12/04 -0500, Hal Ruhl wrote: the All is internally inconsistent since it is complete. I have a counter-example: take the following theory: All true arithmetical sentences. This is complete and yet consistent. Gödel's theorem applies only on axiomatizable (or mechanically generable) theory. Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
Hi Bruno: I assume your theory is intended to give the range of descriptions of worlds. The All in my model contains - well - ALL so it includes systems to which Godel's theorem applies. Your theory has problems for me. What is truth? What is a sentence? What is arithmetical? As Stephen Paul King asked: How is truth resolved for a given sentence? Why the down select re descriptions vs the All. How is the set of such sentences known to be consistent? To answer these questions it seems necessary to inject information into your theory beyond what may already be there - the sentences - and where did all that info come from and why allow any in a base level system for worlds? Yours Hal At 08:03 AM 12/3/2004, you wrote: At 15:49 01/12/04 -0500, Hal Ruhl wrote: the All is internally inconsistent since it is complete. I have a counter-example: take the following theory: All true arithmetical sentences. This is complete and yet consistent. Gödel's theorem applies only on axiomatizable (or mechanically generable) theory. Bruno http://iridia.ulb.ac.be/~marchal/
Re: An All/Nothing multiverse model
Hi Bruno: At 09:38 AM 11/30/2004, you wrote: At 13:40 26/11/04 -0500, Hal Ruhl wrote: What does logically possible mean? In the above I meant in the context of the larger phrase of: logically possible worlds. In the following call an individual [Ai,Dj] pair logic system Ln where i, j, and n can go from 1 to an uncountable infinity and all possible [Ai,D,j] pairings are considered. A proposition P is logically possible, relatively to 1) a consistent set of beliefs A 2) the choice of a deduction system D (and then consistent means does not derive 0=1). if the negation of P is not deductible (in D) from A. So in the larger phrase rather than dealing with a proposition P in relation to Ln I am exploring the range of [Ai,Dj] pairs that would be valid descriptions of worlds. Call this sort after ensemble W. The further issue is induction and whether or not it fails for a particular Ln. Now suppose that belief set Ai includes the belief that Ai, and Dj for j over some range are both subject to random input from outside the system. I see no reason to exclude the Ln which have such an Ai from being a valid description of a World. It is just an explicit expression of incompleteness rather than an implicit one. Thus there could be two subsets of Ai in W. Is there any reason why the ensemble W can not for reasons of its own structure include Ai from both subsets and also insist that the incompletenesses both implicit and explicit be progressively resolved? I know of none and to avoid a selection within the W it would seem that this arrangement is unavoidable. Thus induction would fail for all worlds in W because the logical foundation for all worlds would be constantly shifting from one Ln to another. Concerning many theories, to say that a proposition (or a set of propositions) A is logically possible is the same as saying that A is consistent (i.e you cannot derive 0 = 1 from it), When talking of descriptions of worlds - in such a venue consistency would only be applicable to individual states [if at all] and not to successions of states. The question then is can the All [which contains W] contain self inconsistent states such as one with a correctly and completely assembled two wheeled tricycle or a cat that is both alive and dead or the same thing having two valid sets of coordinates? Now the All is complete so it is internally inconsistent so I see no way to argue against the presence of such states founded on inconsistent Ai. or saying that A has a model (a reality, a mathematical structure) satisfying it. It seems that the idea that mathematical structures are actually consistent is nice but lacks any basis. To help place my model in context with the above: A core idea is the definitional pair relationship. The [All,Nothing] pair is unique in being inherently unavoidable but still summing to no information. Thus it has no initiation and no end. Another core idea is: Is there a meaningful question the Nothing must resolve? The answer to this is: Yes there is: The Nothing either continues [persists], or it does not. The answer must be inherent in the information within the Nothing but there is none in there by definition. Therefore the Nothing is incomplete - it can not resolve any meaningful question. But in this case it must do so. The only reservoir of information is the All. Therefore it must breach the barrier between itself and the All. In doing so it losses contact with what it was [an Ln shift] and becomes an evolving [including successive Ln shifts] - a multiverse - within the All. Since the [All,Nothing] is as above an unavoidable definitional pair a new Nothing simultaneously replaces the old one. The cycle repeats. The cycle always was and always will be and the All contains an infinite number of these Somethings all evolving towards completeness. This produces waves of physical reality passing through a random sequence of states [including Ln shifts as per above]. The Somethings evolve because of their own incompleteness and the need for no selection no net information within the All. The evolution must be random because of no selection and the All is internally inconsistent since it is complete. Hal
Re: An All/Nothing multiverse model
Hi, Hal, I feel we have a semantic dichotomy: using model in diverse meanings. As I guess yours is a 'metaphoric compendium some simulation of a 'total' into usable terms from other sources, while I use the word as a cut-off from totality, focussing on the characteristics (content?) relevant to the study (observation, discussion), omitting the 'not involved' connotations. 'Yours' is more comprehensive, 'mine' is incomplete, reductionistic. John Mikes - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, November 21, 2004 4:36 PM Subject: Re: An All/Nothing multiverse model Hi John: I am trying to make the model independent of what might be the detail structure of individual universes within it. Hal At 10:41 AM 11/21/2004, you wrote: Hal: how about this: a 'concept' is THE part of ALL cut (limited?) by topical boundaries into a (topical) model disregarding other connections and e/affects. Our reductionist science uses such restrictions because of our incapability to encompass a wider domain of ALL into our mental function. (I am not the best in formulating). John Mikes - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, November 20, 2004 11:32 PM Subject: Re: An All/Nothing multiverse model I was asked about concepts. I would define concept as any division of the All into two sub components, each of the sub components is a concept. Usefullness of a concept as judged by a SAS [if they exist] is not an issue. Hal
Re: An All/Nothing multiverse model
Hal: how about this: a 'concept' is THE part of ALL cut (limited?) by topical boundaries into a (topical) model disregarding other connections and e/affects. Our reductionist science uses such restrictions because of our incapability to encompass a wider domain of ALL into our mental function. (I am not the best in formulating). John Mikes - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, November 20, 2004 11:32 PM Subject: Re: An All/Nothing multiverse model I was asked about concepts. I would define concept as any division of the All into two sub components, each of the sub components is a concept. Usefullness of a concept as judged by a SAS [if they exist] is not an issue. Hal
Re: An All/Nothing multiverse model
Hi John: I am trying to make the model independent of what might be the detail structure of individual universes within it. Hal At 10:41 AM 11/21/2004, you wrote: Hal: how about this: a 'concept' is THE part of ALL cut (limited?) by topical boundaries into a (topical) model disregarding other connections and e/affects. Our reductionist science uses such restrictions because of our incapability to encompass a wider domain of ALL into our mental function. (I am not the best in formulating). John Mikes - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Saturday, November 20, 2004 11:32 PM Subject: Re: An All/Nothing multiverse model I was asked about concepts. I would define concept as any division of the All into two sub components, each of the sub components is a concept. Usefullness of a concept as judged by a SAS [if they exist] is not an issue. Hal
Re: An All/Nothing multiverse model
I was asked about concepts. I would define concept as any division of the All into two sub components, each of the sub components is a concept. Usefullness of a concept as judged by a SAS [if they exist] is not an issue. Hal
Re: An All/Nothing multiverse model
Hal: makes sense to me - with one question: I take: ALL stands for the totality (wholeness as I say) and your -- is is confined to whatever we do, or are capable (theoretically) to know - whether already discovered or not. In that case the 'definitional pair' wouold be anthropocentric? (It would not make sense, if you consider it as the 'infinite computer' rather than us). * That would really equate ALL and NOTHING, because in the nothing the is not component includes all. Not a pair? John Mikes - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, November 17, 2004 7:29 PM Subject: Re: An All/Nothing multiverse model In my [is, is not] definitional pair the is not component is the All minus the is component. Thus the is not member is not simply unwinged horses or the like. In most of these pairs I suspect the is not component has no apparent usefulness [to most SAS [if they exist]]. Be that as it may both members of the [All, Nothing] pair seem to have usefulness. Hal
Re: An All/Nothing multiverse model
Hi John: At 11:27 AM 11/18/2004, you wrote: Hal: makes sense to me - with one question: I take: ALL stands for the totality (wholeness as I say) and your -- is is confined to whatever we do, or are capable (theoretically) to know - whether already discovered or not. It is more than that. The All is all information. In that case the 'definitional pair' wouold be anthropocentric? I try to make it as generalized as I can but there is the limits of an unavoidable inside perspective. (It would not make sense, if you consider it as the 'infinite computer' rather than us). * That would really equate ALL and NOTHING, because in the nothing the is not component includes all. Not a pair? The All and the Nothing are nearly identical in that they both contain no information since all information is equivalent to having no information. The only left over issue is the defining information for each and this is the same [they are a definitional pair] and so it too sums to no information. The result is a zero information system that allows computer simulations [noisy ones] of some multiverses and a rationale for a dynamic i.e. the computers run. Hal
Re: An All/Nothing multiverse model
I forgot to point out that the definitional information for the [All,Nothing] pair cancels because the inverse definition i.e. the [Nothing, All] pair is the same system. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote:
Hi George:
Hi Hal,
At 09:13 PM 11/16/2004, you wrote:
Hal Ruhl wrote:
My use of these words is convenience only but my point is why should
existence be so anemic as to prohibit the simultaneous presence of an
All and a Nothing.
The prohibition does not come from an anemia of existence
(as you suggest) but rather from the strength of nothing(ness),
at least in my view of things.
I am not sure I understand where we disagree (and even if we
really disagree) on this question of the {something, nothing,
concept, existence} question.
Even if we consider that defining something automatically
defines (a complementary) something else, this happens at the
concept level. It might well be that both defined concepts
simultaneously exists (say at least in the mind/brain of a
few humans beings) but this says noting about whether either
one or the other actually gets at something that would exist.
Even if the *concepts of* something (or all) and nothing do
need to exist simultaneously for any of them to exist, it
(obviously ?) does not follows that something (or all) and
nothing also needs to exist simultaneously (or even simply
makes sense in any absolute way).
Last but not least, what is the complementary concept of a
given concept is not that obvious. Let's consider the concept
of a winged horse. Regardless of whether it actually gets
at something or not, it can be considered to be opposed to
non winged horses or to winged things that are not horses
rather that to anything that is not a winged horses. In
set theory, a complementary of a set is always considered
only within a given larger set and never in any fully open
way (and there are well known and very good reasons for that
whatever common sense may say). Similarly, defining an all
or something in a fully open way is likely to be inconsistent.
The situation is different here from the case of the winged
horse and probably from all other cases and there is no reason
that common sense be still relevant (like in the set of all
sets paradox). This might be a case (possibly the only one)
in which defining/considering something does not automatically
make appear a complementary something (even simply at the
concept level).
This would be an arbitrary truncation without reasonable justification.
Just as the opposite.
I provided a justification - a simple basis for evolving universes -
which does not yet seem to have toppled.
It might be not so simple. I went through it and I still can't
figure what evolving universes might get at. Up to this point,
I did not find something that would sound to me as a (more)
reasonable justification. This may well comme from me.
What appears reasonable or not or what appears as an actual
justification or not is certainly very relative. Currently, I am
still in the process of trying to find some sense (in my view of
things) in what you are talking about (and/or of trying to
figure out what your view of things might be). *Not* to say it
necessarily hasn't.
Georges.
Re: An All/Nothing multiverse model
There do exist consistent approaches to set theory where you do have a
universal set and can therefore consider taking complements to be a
sinle-argument operation. to bypass the obvious paradox (that any set can be
used to make a necessarily larger powerset) you need to concoct a map from
the universal set onto its own powerset. The easiest way to do this is to
have lots of 'urelements' or' indivisible but somehow different sets, which
can then be mapped to larger sets in the powerset. If you find urelements
philosophically objectionable (which most computationally-minded people do)
then there exist other more difficult approaches: Try a google search for
Alonzo Church, Willard Quine or Thomas Forster to see some people who
have tried...
--Chris Collins
- Original Message -
From: Georges Quenot [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Wednesday, November 17, 2004 10:36 AM
Subject: Re: An All/Nothing multiverse model
Hal Ruhl wrote:
Hi George:
Hi Hal,
At 09:13 PM 11/16/2004, you wrote:
Hal Ruhl wrote:
My use of these words is convenience only but my point is why should
existence be so anemic as to prohibit the simultaneous presence of an
All and a Nothing.
The prohibition does not come from an anemia of existence
(as you suggest) but rather from the strength of nothing(ness),
at least in my view of things.
I am not sure I understand where we disagree (and even if we
really disagree) on this question of the {something, nothing,
concept, existence} question.
Even if we consider that defining something automatically
defines (a complementary) something else, this happens at the
concept level. It might well be that both defined concepts
simultaneously exists (say at least in the mind/brain of a
few humans beings) but this says noting about whether either
one or the other actually gets at something that would exist.
Even if the *concepts of* something (or all) and nothing do
need to exist simultaneously for any of them to exist, it
(obviously ?) does not follows that something (or all) and
nothing also needs to exist simultaneously (or even simply
makes sense in any absolute way).
Last but not least, what is the complementary concept of a
given concept is not that obvious. Let's consider the concept
of a winged horse. Regardless of whether it actually gets
at something or not, it can be considered to be opposed to
non winged horses or to winged things that are not horses
rather that to anything that is not a winged horses. In
set theory, a complementary of a set is always considered
only within a given larger set and never in any fully open
way (and there are well known and very good reasons for that
whatever common sense may say). Similarly, defining an all
or something in a fully open way is likely to be inconsistent.
The situation is different here from the case of the winged
horse and probably from all other cases and there is no reason
that common sense be still relevant (like in the set of all
sets paradox). This might be a case (possibly the only one)
in which defining/considering something does not automatically
make appear a complementary something (even simply at the
concept level).
This would be an arbitrary truncation without reasonable
justification.
Just as the opposite.
I provided a justification - a simple basis for evolving universes -
which does not yet seem to have toppled.
It might be not so simple. I went through it and I still can't
figure what evolving universes might get at. Up to this point,
I did not find something that would sound to me as a (more)
reasonable justification. This may well comme from me.
What appears reasonable or not or what appears as an actual
justification or not is certainly very relative. Currently, I am
still in the process of trying to find some sense (in my view of
things) in what you are talking about (and/or of trying to
figure out what your view of things might be). *Not* to say it
necessarily hasn't.
Georges.
Re: Fw: An All/Nothing multiverse model
All members of [is,is not] definitional pairs including the [All, Nothing] pair have a conceptual foundation within the All. Why would the [All, Nothing} pair be the only one denied a mutual and concurrent physical expression? Hal
Re: Fw: An All/Nothing multiverse model
Hal Ruhl wrote:
All members of [is,is not] definitional pairs including the [All,
Nothing] pair have a conceptual foundation within the All. Why would
the [All, Nothing} pair be the only one denied a mutual and concurrent
physical expression?
Well... It seems that we do not share the same conception of
what nothing(ness) might be. It seems that I am even unable to
figure out what your conception of it might be. I see no problem
with that. I suppose that this just means that we are different
human beings.
I feel that the {all, nothing} pair requires a kind of frame
it would have to fit into while the {something, nothingness}
do not. The best image I can get of our two views would be
that in yours nothing would be the empty set while in mine
nothingness would be the absence or inexistence of any set.
But I am probably still out.
I do not see either why the [All, Nothing] pair should have a
conceptual foundation within the All and I can't even figure
what that might mean.
Still, when you write Why would the [All, Nothing} pair be the
only one denied a mutual and concurrent physical expression?,
I suspect (though that does not truly follows) that you mean the
[All, Nothing} pair would be denied something that would be
granted to some other pairs. This implies that the all have
some internal structure from which one couls identify strict
and non empty subparts. Therefore, nothing would not remain
the one and only thing that coud be opposed to the all.
Last, I am not sure we need to involve anything physical here,
even between quotes. Physicality might well just be how things
appear (to SASs for instance) from within the all.
Quite frustrating. I guess on your side, too.
Georges.
Re: An All/Nothing multiverse model
rmiller wrote: This is starting to sound like discussion Hume must have had with himself. Might be. And was Hume finally able to conclude something ? Georges.
Re: An All/Nothing multiverse model
John Collins wrote: There do exist consistent approaches to set theory where you do have a universal set and can therefore consider taking complements to be a sinle-argument operation. to bypass the obvious paradox (that any set can be used to make a necessarily larger powerset) you need to concoct a map from the universal set onto its own powerset. I was not thinking of that one but rather to the inconsistency that appears when one wants to consider things like the set of all sets that do not containe themselves. The easiest way to do this is to have lots of 'urelements' or' indivisible but somehow different sets, which can then be mapped to larger sets in the powerset. If you find urelements philosophically objectionable (which most computationally-minded people do) This is the first time I heard of such things as 'urelements' and I haven't that faintest idea of what that might be but, for sure, I must be severely computationally-minded. then there exist other more difficult approaches: Try a google search for Alonzo Church, Willard Quine or Thomas Forster to see some people who have tried... I have heard of the first two but not on that topic. Georges.
Re: An All/Nothing multiverse model
In my [is, is not] definitional pair the is not component is the All minus the is component. Thus the is not member is not simply unwinged horses or the like. In most of these pairs I suspect the is not component has no apparent usefulness [to most SAS [if they exist]]. Be that as it may both members of the [All, Nothing] pair seem to have usefulness. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: [...] The idea that defining a thing actually defines two things seems self evident [once you notice it]. At least one case of unavoidable definition also seems self evident [once you notice it]. The problem with evidence is that on one side there is no other known basis to build certainties and on the other it appears to be very relative [once you notice it]. :-) Also, (self) evidence that seems so sounds like a pleonasm to me. Georges.
Fw: An All/Nothing multiverse model
- Original Message - From: John M [EMAIL PROTECTED] To: Hal Ruhl [EMAIL PROTECTED] Sent: Tuesday, November 16, 2004 4:26 PM Subject: Re: An All/Nothing multiverse model Hi, Hall, (to your post below and many preceding that): I feel there is a semantic game going on. ALL we know of (or: can know of), or ALL that 'exists' (another restriction) or ALL just undefined to 'everything? In most minds the restrictions in thinking is considering this (our) universe- world. Even expanded into thinking in terms of a Multiverse sticks of similar universes. A BIG restriction. My Multiverse consists of universes unlimited in number and qualia (process capability, whatever). ALL in my mind is an invariant multitude of processes (sorry, I am not on ontological is bases, rather in 'changes' (whatever does change) resulting in the final infinite i.e. invariant symmetry of total multitude. I never used this 'ALL' term. I used as a beginning the nothingness which, by identifying ITSELF as such, became a somethingness as realizing the nothingness. What meant a difference which I call: existence. Acknowledged difference is the information and here we are: a system. The details come in unlimitedly. Concepts: I cannot blame you for not 'believeing' in such things: they are limited views of topically restricted 'parts' of the total (I call it wholeness) and such 'models' can be formulated as we wish. Arithmetic in my mind is ONE plane of the views: based on the quale of quantizability. I still did not develop my idea of mathematics without quantitative connotations, nobody showed the way to such understanding (although I asked many plavces - many times). The qualia, however, of the totality, consist of unlimited such planes and all interfere in so far very scantily discovered ways. So arithmetic is a limited model, the reason for Goedel (even Turing, as you wrote). (Maybe I should use 'math'? it might stand in the broader way for human logic and I don't want to overextend what I say). Decision is also a model-based conclusion. Within the observed boundaries of the restricet view. I would not be able to anticipate a conclusion which the infinite computer may produce. BTW to call it (the infinite) a computer is an oxymoron: unless we allow the functions in unlimited nature/fashion, which is not really 'computer-wise'. To call a qualitatively infinite result-churning system a 'computer' seems to me as a pars pro toto. (A reverse: totum pro parte is AI, which is indeed a contraption for the Artificial Machine Intelligence - not a device for Artificial Human Intelligence as many regard it). Sorry for the long winded writing. I don't want to persuade anybody to accept my ideas, just wanted to add my tuppence. John Mikes - Original Message - From: Hal Ruhl [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, November 15, 2004 10:33 PM Subject: Re: An All/Nothing multiverse model Hi Eric: At 09:46 PM 11/15/2004, you wrote: On Tue, 2004-11-16 at 10:13, Hal Ruhl wrote: To respond to comments on consistency. I see no reason why components of the system need to be internally consistent. And I have indicated that the All is not internally consistent. Generally speaking evolving Somethings are also not consistent. Actually evolving Somethings are a sequence of Somethings in that each new quantum of information incorporated into a Something makes it a new system. Arithmetic and any system that incorporates it can not prove its [their] own consistency. Not to be able to prove its consistency doesn't mean it's inconsistent, does it? Going a little further Turing showed that there is in general no decision procedure. Godel's proof is a corollary of this. So if arithmetic ever became complete it would have to be inconsistent. The All contains all arithmetics including the complete and inconsistent one. So the All is internally inconsistent. Also if you did add an axiom to arithmetic how could this be done so it was known to be consistent with the previous axioms? I'm thinking about an inconsistent system as one that can prove both a statement and its negation. That is right What exactly do you mean by your All? All systems of representations, or All that 'exists'? If the latter, what does it mean 'to exist'? If the former, do these systems necessarily have a one-to-one correspondence to something that 'exists', and in what sense? As I said in an earlier post the information within the All may have a separate physical existence. I left open for now what that might be. I do believe this to be in any way essential as part of the description of worlds. The All since it contains all information sums to no net information. Concepts would be packets of associated information. All this points to the first of the above which is a position I have
Re: An All/Nothing multiverse model
Hal Ruhl wrote: Boundaries: I have as I said in one post of this thread and as I recall in some earlier related threads defined information as a potential to erect a boundary. So the All is chuck full of this potential. Actual boundaries are the Everything and any evolving Something. This is unclear to me. To take a practical and simple example, from which wavelength a monochromatic radiation ceases to be red ? The All and the Nothing are not mutually exclusive. I understand that one can have a view differing from mine on this question. In any sound sense of these concepts for me, they are exclusive however. Perhaps the exclusive idea is based on a hidden assumption of some sort of space that can only be filled with or somehow contain one or the other but not both. This is intersting. I have exactly the opposite feeling. In my view, there cannot be anything like space or time (and therefore no other time/place for any something to hide or coexist) if there is(*) nothing. (*) is must be considered here in an intemporel mode and not in the present one. Somehow like equals in 2 and 2 equals 4 Georges.
Re: An All/Nothing multiverse model
On Wed, 2004-11-17 at 08:39, Georges Quenot wrote: Hal Ruhl wrote: [...] The idea that defining a thing actually defines two things seems self evident [once you notice it]. At least one case of unavoidable definition also seems self evident [once you notice it]. The problem with evidence is that on one side there is no other known basis to build certainties and on the other it appears to be very relative [once you notice it]. :-) But that's inevitable, or isn't it? Can we have any certainty other than those logically derived from assumed principles? And in this case, isn't it desirable that at least the assumed principles are self-evident? Could we have something better? Also, (self) evidence that seems so sounds like a pleonasm to me. Yes, I think I agree with you, but that's the common usage. A'self-evident' means evident without proof. But can something be 'evident' only after proof? It seems to me that an 'evident' proposition doesn't need proof either. Eric.
Re: An All/Nothing multiverse model
At 05:39 PM 11/16/2004, you wrote: Hal Ruhl wrote: [...] The idea that defining a thing actually defines two things seems self evident [once you notice it]. At least one case of unavoidable definition also seems self evident [once you notice it]. The problem with evidence is that on one side there is no other known basis to build certainties and on the other it appears to be very relative [once you notice it]. :-) Here I was not trying to support the idea that Self-evident is necessarily a positive characteristic of an idea but rather that Monday morning quarterbacking can make it appear so. This was in response to the comment I received. I suppose that many ideas originally considered to be self evident after near term reflection were ultimately rejected. Also, (self) evidence that seems so sounds like a pleonasm to me. To me self evident is a belief. The validity assigned to most mathematical proofs appears - as has been said by others - to be dependent on the belief of the majority who examine the proof. In most cases this belief is all that is available so it is not redundant but it is no more than majority opinion. Hal
Re: An All/Nothing multiverse model
Eric Cavalcanti wrote: On Wed, 2004-11-17 at 08:39, Georges Quenot wrote: Hal Ruhl wrote: [...] The idea that defining a thing actually defines two things seems self evident [once you notice it]. At least one case of unavoidable definition also seems self evident [once you notice it]. The problem with evidence is that on one side there is no other known basis to build certainties and on the other it appears to be very relative [once you notice it]. :-) But that's inevitable, or isn't it? Can we have any certainty other than those logically derived from assumed principles? That's part of the problem, yes. And in this case, isn't it desirable that at least the assumed principles are self-evident? Oh, lots of things appear desirable. That does not make them true (unfortunately in many cases). And when desirableness comes in as a cause (if not a reason) things turns even more relative. Could we have something better? That's another part of the problem. Also, (self) evidence that seems so sounds like a pleonasm to me. Yes, I think I agree with you, but that's the common usage. Yes and no. I don't feel it is neutral, even if frequent. A'self-evident' means evident without proof. But can something be 'evident' only after proof? It seems to me that an 'evident' proposition doesn't need proof either. I meant: did anyone ever encounter such a thing as an evidence that did not seem to be so ? How can one discriminate between an evidence and something that would just seem to be an evidence ? Georges.
Re: An All/Nothing multiverse model
At 05:58 PM 11/16/2004, you wrote: Hal Ruhl wrote: Boundaries: I have as I said in one post of this thread and as I recall in some earlier related threads defined information as a potential to erect a boundary. So the All is chuck full of this potential. Actual boundaries are the Everything and any evolving Something. This is unclear to me. To take a practical and simple example, from which wavelength a monochromatic radiation ceases to be red ? Color is a complex and local system reaction to the collision between a small system - a photon to temporarily stay with a particle view - and a larger system - a photo receptor etc. The information in the photon [its energy] and the information in the chemistry of the photo receptor determine the initial path of this response in a given large system and create a boundary between this initiation and the initiation that would have been if the information differed. [By the way I do not support this description of such systems but that is another discussion.] The All and the Nothing are not mutually exclusive. I understand that one can have a view differing from mine on this question. In any sound sense of these concepts for me, they are exclusive however. Perhaps the exclusive idea is based on a hidden assumption of some sort of space that can only be filled with or somehow contain one or the other but not both. This is intersting. I have exactly the opposite feeling. In my view, there cannot be anything like space or time (and therefore no other time/place for any something to hide or coexist) if there is(*) nothing. As I said my approach to physics differs from the standard one re space and time etc. My use of these words is convenience only but my point is why should existence be so anemic as to prohibit the simultaneous presence of an All and a Nothing. This would be an arbitrary truncation without reasonable justification. (*) is must be considered here in an intemporel mode and not in the present one. Somehow like equals in 2 and 2 equals 4 See above. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: At 05:39 PM 11/16/2004, you wrote: Hal Ruhl wrote: [...] The idea that defining a thing actually defines two things seems self evident [once you notice it]. At least one case of unavoidable definition also seems self evident [once you notice it]. The problem with evidence is that on one side there is no other known basis to build certainties and on the other it appears to be very relative [once you notice it]. :-) Here I was not trying to support the idea that Self-evident is necessarily a positive characteristic of an idea but rather that Monday morning quarterbacking can make it appear so. Do you mean that for the particular idea that defining a thing actually defines two things ? This was in response to the comment I received. I suppose that many ideas originally considered to be self evident after near term reflection were ultimately rejected. Do you consider that this could be the case for this particular idea ? Also, (self) evidence that seems so sounds like a pleonasm to me. To me self evident is a belief. OK. Fine. The validity assigned to most mathematical proofs appears - as has been said by others - to be dependent on the belief of the majority who examine the proof. In most cases this belief is all that is available so it is not redundant but it is no more than majority opinion. I agree here. And sometimes, even unanimity fails (there is a famous example: Cauchy produced a false theorem about the continuity of a series of continuous functions, he taught it and it was in class books for years whithout anyone finding any problem until some day someone noticed that it fails for the Fourier series of f(x) = x; of course, he saved the theorem by adding an additional premise but the false theorem had been recognized/believed as true in the mean time). Georges.
Re: An All/Nothing multiverse model
Hal Ruhl wrote: At 05:58 PM 11/16/2004, you wrote: Hal Ruhl wrote: Boundaries: I have as I said in one post of this thread and as I recall in some earlier related threads defined information as a potential to erect a boundary. So the All is chuck full of this potential. Actual boundaries are the Everything and any evolving Something. This is unclear to me. To take a practical and simple example, from which wavelength a monochromatic radiation ceases to be red ? Color is a complex and local system reaction to the collision between a small system - a photon to temporarily stay with a particle view - and a larger system - a photo receptor etc. The information in the photon [its energy] and the information in the chemistry of the photo receptor determine the initial path of this response in a given large system and create a boundary between this initiation and the initiation that would have been if the information differed. [By the way I do not support this description of such systems but that is another discussion.] Do you mean that it is a nonsense to say that a monochromatic radiation of 700 nm is red if it does not actually hit and activate some photoreceptors of the appropriate type ? The All and the Nothing are not mutually exclusive. I understand that one can have a view differing from mine on this question. In any sound sense of these concepts for me, they are exclusive however. Perhaps the exclusive idea is based on a hidden assumption of some sort of space that can only be filled with or somehow contain one or the other but not both. This is interesting. I have exactly the opposite feeling. In my view, there cannot be anything like space or time (and therefore no other time/place for any something to hide or coexist) if there is(*) nothing. As I said my approach to physics differs from the standard one re space and time etc. I meant here something similar to the standard space and time as considered in physics and common sense. I could consider other possible senses but I currently can't figure any. My use of these words is convenience only but my point is why should existence be so anemic as to prohibit the simultaneous presence of an All and a Nothing. The prohibition does not come from an anemia of existence (as you suggest) but rather from the strength of nothing(ness), at least in my view of things. This would be an arbitrary truncation without reasonable justification. Just as the opposite. Georges.
Re: An All/Nothing multiverse model
At 08:48 PM 11/16/2004, you wrote: Hal Ruhl wrote: At 05:39 PM 11/16/2004, you wrote: Hal Ruhl wrote: [...] The idea that defining a thing actually defines two things seems self evident [once you notice it]. At least one case of unavoidable definition also seems self evident [once you notice it]. The problem with evidence is that on one side there is no other known basis to build certainties and on the other it appears to be very relative [once you notice it]. :-) Here I was not trying to support the idea that Self-evident is necessarily a positive characteristic of an idea but rather that Monday morning quarterbacking can make it appear so. Do you mean that for the particular idea that defining a thing actually defines two things ? I mean it in a universal way - it is always the situation. This was in response to the comment I received. I suppose that many ideas originally considered to be self evident after near term reflection were ultimately rejected. Do you consider that this could be the case for this particular idea ? Darwin seems to have felt this way about Origins [Stephen Gould's The Structure of Evolutionary Theory, page 2] so why should my ideas be special? Also, (self) evidence that seems so sounds like a pleonasm to me. To me self evident is a belief. OK. Fine. The validity assigned to most mathematical proofs appears - as has been said by others - to be dependent on the belief of the majority who examine the proof. In most cases this belief is all that is available so it is not redundant but it is no more than majority opinion. I agree here. And sometimes, even unanimity fails (there is a famous example: Cauchy produced a false theorem about the continuity of a series of continuous functions, he taught it and it was in class books for years whithout anyone finding any problem until some day someone noticed that it fails for the Fourier series of f(x) = x; of course, he saved the theorem by adding an additional premise but the false theorem had been recognized/believed as true in the mean time). Georges. Hal
Re: An All/Nothing multiverse model
Hal Ruhl wrote: At 08:48 PM 11/16/2004, you wrote: Darwin seems to have felt this way about Origins [Stephen Gould's The Structure of Evolutionary Theory, page 2] so why should my ideas be special? We agree here. Interesting reference. Georges.
Re: An All/Nothing multiverse model
Hi George: At 09:13 PM 11/16/2004, you wrote: Hal Ruhl wrote: At 05:58 PM 11/16/2004, you wrote: Hal Ruhl wrote: Boundaries: I have as I said in one post of this thread and as I recall in some earlier related threads defined information as a potential to erect a boundary. So the All is chuck full of this potential. Actual boundaries are the Everything and any evolving Something. This is unclear to me. To take a practical and simple example, from which wavelength a monochromatic radiation ceases to be red ? Color is a complex and local system reaction to the collision between a small system - a photon to temporarily stay with a particle view - and a larger system - a photo receptor etc. The information in the photon [its energy] and the information in the chemistry of the photo receptor determine the initial path of this response in a given large system and create a boundary between this initiation and the initiation that would have been if the information differed. [By the way I do not support this description of such systems but that is another discussion.] Do you mean that it is a nonsense to say that a monochromatic radiation of 700 nm is red if it does not actually hit and activate some photoreceptors of the appropriate type ? Such a photon has only part of the information required for the parsing of red from other color responses of a particular large system. Further you and I may both indicate red when colliding with such a photon but this is a learned designation for who knows what different sensations [change] we our respective large systems have. Not that I believe in observers or in the isolation of systems. The All and the Nothing are not mutually exclusive. I understand that one can have a view differing from mine on this question. In any sound sense of these concepts for me, they are exclusive however. Perhaps the exclusive idea is based on a hidden assumption of some sort of space that can only be filled with or somehow contain one or the other but not both. This is interesting. I have exactly the opposite feeling. In my view, there cannot be anything like space or time (and therefore no other time/place for any something to hide or coexist) if there is(*) nothing. As I said my approach to physics differs from the standard one re space and time etc. I meant here something similar to the standard space and time as considered in physics and common sense. I could consider other possible senses but I currently can't figure any. My use of these words is convenience only but my point is why should existence be so anemic as to prohibit the simultaneous presence of an All and a Nothing. The prohibition does not come from an anemia of existence (as you suggest) but rather from the strength of nothing(ness), at least in my view of things. This would be an arbitrary truncation without reasonable justification. Just as the opposite. I provided a justification - a simple basis for evolving universes - which does not yet seem to have toppled. Hal
Re: Fw: An All/Nothing multiverse model
Hi John: At 05:46 PM 11/16/2004, you wrote: snip My Multiverse consists of universes unlimited in number and qualia (process capability, whatever). My All would be infinite and could contain multiple multiverses - multiple Somethings - evolving all at once. I see no restriction on the nature of these Somethings except that they all are subject to information injection from an external random oracle i.e. the current but momentary remainder [relative to that individual multiverse] of the All. snip Hal
Re: An All/Nothing multiverse model
This is starting to sound like discussion Hume must have had with himself. RM
Re: Who believe in Concepts ? (Was: An All/Nothing multiverse model)
Hal Ruhl wrote: At 07:56 AM 11/14/2004, you wrote: Hal Ruhl wrote: I would appreciate comments on the following. I placed the definitions at the end for easy group reference. Proposal: The Existence of our and other universes and their dynamics are the result of unavoidable definition and logical incompleteness. Justification: 1) Given definitions 1, 2, and 3: [see original post] I have already a problem here. It might not be specific to this proposal but this is a good opportunity to raise the question. Defintion 1 and everything that follows depends in a strong way of the concept of concept and on strong properties of that concept (like the possibilty to discrimate what is a concept from what is not and to gather all concepts in a set/ensemble/collection with a consistent meaning). Perhaps I could find a more neutral word or define what I mean by concept. Please note however that the complete ensemble can not be consistent - after all it contains a completed arithmetic. Generally smaller sets can not prove their own consistency. snip It des not sound consistent to me for various reasons. Is seems not to be consistent for you either. Yet you mean to draw something from it ? Let's assume nothingness exists. Therefore something (nothingness) exists. That is one of my points if one replaces your nothingness with my nothing and your something with my All. Indeed I inserted that because I perceived a similarity between this and what you said. But this was rather an illustration for the question of whether words used in this utterance actually get at something and whether their combination can make sense. Put in such an extreme form, it appears to me as a mere game of word or a sophism and I wonder if anyone can get convinced by such reasonning. Any definition defines two entities simultaneously. Generally but not necessarily the smaller of the two entities is the one about which the definition says: This entity is:. The definition creates a boundary between this entity and a second entity which is all that the first is not. Most of the second entities may have no apparent usefulness but usefulness of an entity is not relevant. Therefore nothingness doesn't exist. Do you mean to cite the first instance or the second instance here ? Therefore nothingness doesn't exist (because something exists) or Therefore nothingness doesn't exist (because assuming it exists leads to the assertion of both a proposition and its negation) ? Not at all. One can not define a something without simultaneously defining a nothing and vice versa. This is not obvious to me. Defining a property that would always be true does not imply that it have to or even it just could be false sometimes. But this is not the point. My first therefore (and therefore the second one) holds even though because this is the minimum property that one would expect of any solid sense of nothingness. In case you insist to define simultaneously a something and a nothing, you would just have demonstrated the inconsistency of any sound (nothing,something) theory. I think that (at least) Heidegger seriously claimed that. That is the usually unnoticed aspect of the definitional process. This leads you to the exclusionary statement below. That's why there's something rather than noting. To the contrary both exist if either does. You insist to claim that. Yet they are also exclusive since by its very nature, nothingness excludes the existence of any something. Georges. I disappear when I am named. Who am I ?
Re: An All/Nothing multiverse model
Hal Ruhl wrote: At 08:16 AM 11/14/2004, you wrote: Hal Ruhl wrote: 4) A Something: A division of the All into two subparts. That too, sounds bad to me. It might well be that the only something that deserve the title of Something would be the All itself. Everything else might appear so only in our minds (and/or in other types of minds). I believe my use of the term Something in the text of the justification is consistent with my definition. One must allow for the case that the All could have internal boundaries of some sort. Hi Hal, I would say that this is a matter of faith. Indeed, It *could*. But no one has the ability to prove either It has or It hasn't any such boundary (in an absolute sense, of course). From this point of view, I am at best agnostic and I seriously doubt It actually has. That's why I would also like to say : One must allow for the case that the All could have no (true) internal boundaries of any sort. Georges.
Who believes in Boundaries ? (Was: An All/Nothing multiverse model)
Georges Quenot wrote: Hal Ruhl wrote: At 08:16 AM 11/14/2004, you wrote: Hal Ruhl wrote: 4) A Something: A division of the All into two subparts. That too, sounds bad to me. It might well be that the only something that deserve the title of Something would be the All itself. Everything else might appear so only in our minds (and/or in other types of minds). I believe my use of the term Something in the text of the justification is consistent with my definition. One must allow for the case that the All could have internal boundaries of some sort. Hi Hal, I would say that this is a matter of faith. Indeed, It *could*. But no one has the ability to prove either It has or It hasn't any such boundary (in an absolute sense, of course). From this point of view, I am at best agnostic and I seriously doubt It actually has. That's why I would also like to say : One must allow for the case that the All could have no (true) internal boundaries of any sort. In a previous post, I asked TOE participants their opinion about the existence of Concepts. What I meant might not be clear. It is in fact equivalent to the (hopefully) clearer idea of Boundary mentionned here. Again, using the upper case for Boundary, I mean here something that would exist in an absolute sense and not just the relative, contingent and fuzzy boundaries we use in everday life. A Concept would be something tht would be on one side of a Boundary ande vices versa. Do some TOE participants believe in such Boundaries, even at least in some particular cases ? If yes, which ones and on whice bases ? To take a particular example. It is often considered in this group the concept od Self-Aware Structure (SAS). Who believes that Boundaries can be drawn around individuals SASs and/or around the category ? Georges.
Re: An All/Nothing multiverse model
I received the following comments from Eric Cavalcanti but did not see them post on the Everything list. It is the same idea as Godel's approach to showing the incompleteness of arithmetic. The structure of arithmetic was asked a question [the truth or falseness of a grammatically valid statement] it could not answer [resolve]. The Nothing can not escape being asked if it is stable or not and has no ability to resolve the question. But it's not as wave-handing as you make it sound. Godel's theorem has a precise meaning and proof given the axioms of Mathematics. It works within those axioms, and has no meaning outside that scope. If you want to use a similar argument, you need to carefully define what you mean by It's the same idea as Godel's approach. Godel's theorem was about arithmetic but the idea behind the theorem was to ask a system a question meaningful to that system which it could not in its present state resolve. That is what is happening in my model. My Nothing can not avoid determining its stability [i.e. its persistence] but can not make this determination without changing. It may sound pedantic, but the problem is that you are trying to create a theory that describes everything, and therefore it's desirable that its constructs are self-evident and certainly required that they are self-consistent. The idea that defining a thing actually defines two things seems self evident [once you notice it]. At least one case of unavoidable definition also seems self evident [once you notice it]. The All is not internally consistent because it is complete. What do you mean by self-consistent in this case. In my view there is no need for universes to be consistent. See #10 and #11 of the original post. What sense does it make to say that the Nothing must answer a question if no question is actually asked? As Pete Carlton said, I believe that you are using a metaphor for something else, but then you need to carefully explain what it is, without the metaphor. See above for the unavoidable meaningful question. I also don't understand why the Nothing should be the kind of thing that penetrates boundaries, attempts to complete itself, etc. It seems that your Nothing gets up to quite a lot of action considering that it's Nothing. Are these actions metaphors for something else, and if so, what? The Nothing can not escape answering the stability question so it must try to add structure [information] to itself until it has an answer. The only source of this structure is the ALL . Thus the Everything boundary must be breached. What is the stability question? Why is it that the Nothing cannot escape answering it? See above What does it mean for the Nothing to penetrate the boundary, There are three components in the system: The All The Nothing Boundaries The only component that may be capable of answering the question is the All. Thus the Nothing must breach the boundary between them [the Everything]. It can not avoid this because it persists or it does not. When this happens an evolving multiverse [a Something] and a renewed Nothing are formed and the cycle starts again. and in what sense does the Nothing complete itself in this process? It adds information that resides in the All. What is information? I have else where defined information as: The potential to divide as with a boundary. An Example: The information in a Formal Axiomatic System [FAS] divides true statements from not true statements [relevant to that FAS]. How does Nothing know when it has found an answer? A Something pays no active attention to what it was. In fact it can not because each new added bit of information creates a new system. This continues until it is a one for one with the All. How can a Nothing become something else? It must do so by filling itself with information. - see above - What does it become if it does? A different Nothing? It becomes a Something i.e. an evolving multiverse as outlined in the original post. How can you distinguish between the former and the latter? It will no longer meet the definition of Nothing. Hal
Re: An All/Nothing multiverse model
Hal, I'm way out of my depth, but if I'm correctly interpreting what you are saying, it looks to me that your multiverse model cannot be valid. This is because it answers the question Why does anything exist? with the answer Because it's not possible to conceive of Nothing, since the concept of Nothing is Something. However, this answer requires Something that conceptualizes. Suppose that Something is not there? If there were Nothing, there could be no Something. Norman
Re: An All/Nothing multiverse model
Hi Norman: My model has both a Nothing, the All, and a set of Somethings simultaneously. Hal At 06:10 PM 11/15/2004, you wrote: Hal, I'm way out of my depth, but if I'm correctly interpreting what you are saying, it looks to me that your multiverse model cannot be valid. This is because it answers the question Why does anything exist? with the answer Because it's not possible to conceive of Nothing, since the concept of Nothing is Something. However, this answer requires Something that conceptualizes. Suppose that Something is not there? If there were Nothing, there could be no Something. Norman
Re: An All/Nothing multiverse model
Norman's answer sounds pretty good to me. I also checked http://www.nothing.com/ found maybe or maybe not nothing there. Something's also at http://www.something.com - Ben Udell. - Original Message - From: Norman Samish [EMAIL PROTECTED] To: Hal Ruhl [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Monday, November 15, 2004 6:10 PM Subject: Re: An All/Nothing multiverse model Hal, I'm way out of my depth, but if I'm correctly interpreting what you are saying, it looks to me that your multiverse model cannot be valid. This is because it answers the question Why does anything exist? with the answer Because it's not possible to conceive of Nothing, since the concept of Nothing is Something. However, this answer requires Something that conceptualizes. Suppose that Something is not there? If there were Nothing, there could be no Something. Norman
Re: An All/Nothing multiverse model
Hi Benjamin: Norman's comments as I indicated in a response completely miss the essence of my model. Hal At 06:25 PM 11/15/2004, you wrote: Norman's answer sounds pretty good to me. I also checked http://www.nothing.com/ found maybe or maybe not nothing there. Something's also at http://www.something.com - Ben Udell. - Original Message - From: Norman Samish [EMAIL PROTECTED] To: Hal Ruhl [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Monday, November 15, 2004 6:10 PM Subject: Re: An All/Nothing multiverse model Hal, I'm way out of my depth, but if I'm correctly interpreting what you are saying, it looks to me that your multiverse model cannot be valid. This is because it answers the question Why does anything exist? with the answer Because it's not possible to conceive of Nothing, since the concept of Nothing is Something. However, this answer requires Something that conceptualizes. Suppose that Something is not there? If there were Nothing, there could be no Something. Norman
Re: An All/Nothing multiverse model
To answer a few other comments/questions: Boundaries: I have as I said in one post of this thread and as I recall in some earlier related threads defined information as a potential to erect a boundary. So the All is chuck full of this potential. Actual boundaries are the Everything and any evolving Something. Something(s): In my model these are evolving universes and not anti Nothings. The All is the anti Nothing. Definitions: The only definitions for which I identify both members of the [is, is not] pair are the [All,Nothing] pair and the complementary Somethings pairs. [Is, is not] pairs are not alternates or true/false comparisons but are rather information/content complements. The Everything is a boundary and its complement is all other boundaries. True noise is a concept re information flow and its complement is all other concepts. The All and the Nothing are not mutually exclusive. Perhaps the exclusive idea is based on a hidden assumption of some sort of space that can only be filled with or somehow contain one or the other but not both. Hal
Re: An All/Nothing multiverse model
To respond to comments on consistency. I see no reason why components of the system need to be internally consistent. And I have indicated that the All is not internally consistent. Generally speaking evolving Somethings are also not consistent. Actually evolving Somethings are a sequence of Somethings in that each new quantum of information incorporated into a Something makes it a new system. Arithmetic and any system that incorporates it can not prove its [their] own consistency. Hal
Re: An All/Nothing multiverse model
Hi Eric: At 09:46 PM 11/15/2004, you wrote: On Tue, 2004-11-16 at 10:13, Hal Ruhl wrote: To respond to comments on consistency. I see no reason why components of the system need to be internally consistent. And I have indicated that the All is not internally consistent. Generally speaking evolving Somethings are also not consistent. Actually evolving Somethings are a sequence of Somethings in that each new quantum of information incorporated into a Something makes it a new system. Arithmetic and any system that incorporates it can not prove its [their] own consistency. Not to be able to prove its consistency doesn't mean it's inconsistent, does it? Going a little further Turing showed that there is in general no decision procedure. Godel's proof is a corollary of this. So if arithmetic ever became complete it would have to be inconsistent. The All contains all arithmetics including the complete and inconsistent one. So the All is internally inconsistent. Also if you did add an axiom to arithmetic how could this be done so it was known to be consistent with the previous axioms? I'm thinking about an inconsistent system as one that can prove both a statement and its negation. That is right What exactly do you mean by your All? All systems of representations, or All that 'exists'? If the latter, what does it mean 'to exist'? If the former, do these systems necessarily have a one-to-one correspondence to something that 'exists', and in what sense? As I said in an earlier post the information within the All may have a separate physical existence. I left open for now what that might be. I do believe this to be in any way essential as part of the description of worlds. The All since it contains all information sums to no net information. Concepts would be packets of associated information. All this points to the first of the above which is a position I have preferred for awhile. I just can't grasp what you could possibly mean by an inconsistent All. And therefore I can't see what use this model could possibly have, and how can it possibly represent Anything. :) See above. If our world is indeed subject to true noise as I state in my model it would be a sequence of new systems - how does prove which is a step by step process within a given system have any relevance? Hal
Who believe in Concepts ? (Was: An All/Nothing multiverse model)
Hal Ruhl wrote: I would appreciate comments on the following. I placed the definitions at the end for easy group reference. Proposal: The Existence of our and other universes and their dynamics are the result of unavoidable definition and logical incompleteness. Justification: 1) Given definitions 1, 2, and 3: [see original post] I have already a problem here. It might not be specific to this proposal but this is a good opportunity to raise the question. Defintion 1 and everything that follows depends in a strong way of the concept of concept and on strong properties of that concept (like the possibilty to discrimate what is a concept from what is not and to gather all concepts in a set/ensemble/collection with a consistent meaning). Though we make such assumptions everyday and it work perfectly well in practice for most current affairs, it is far from obvious (at least for me) that it follows that things are really so (just think of the concept of dog in an evolutionary and/or universe-wide perspective for instance). Personnally, I do not believe in Concepts (the upper case denotes here a solid sense for the concept of concept, for instance, a sense strong enough to make correct assumptions such as: concepts cae be isolated concepts can be discriminaed from things that aren't concepts and/or one from another, concepts actually get (or not) at things in the real worlds and, last but not least, concepts can be arranged in utterances that says true or false things about the real world). This has quite frustrating consequences, including the one of not being able to apropriately comment your proposal and, more generallly, to consistently take part in many interesting discussions. I find puzzling that many people, especially among those that are not very religious and/or those that shares many of my views, believes in Concepts. Or do they ? Or up to what ? This is why I would like to ask participants of the TOE group what they believ or not about Concepts as well as about their handling in natural language reasonning. I am also interested in opinions about the impact of this in discussions in the TOE group. Indeed, many questions seem relative to the senses that should/could be given to sepcific concepts (existence, reality, physical, universes, ...). Examples (positive or nengative) would certainly help. Thanks, Georges. Let's assume nothingness exists. Therefore something (nothingness) exists. Therefore nothingness doesn't exist. Therefore nothingness doesn't exist. That's why there's something rather than noting.
Re: An All/Nothing multiverse model
Hal Ruhl wrote: 4) A Something: A division of the All into two subparts. That too, sounds bad to me. It might well be that the only something that deserve the title of Something would be the All itself. Everything else might appear so only in our minds (and/or in other types of minds). Georges.
Re: Who believe in Concepts ? (Was: An All/Nothing multiverse model)
At 07:56 AM 11/14/2004, you wrote: Hal Ruhl wrote: I would appreciate comments on the following. I placed the definitions at the end for easy group reference. Proposal: The Existence of our and other universes and their dynamics are the result of unavoidable definition and logical incompleteness. Justification: 1) Given definitions 1, 2, and 3: [see original post] I have already a problem here. It might not be specific to this proposal but this is a good opportunity to raise the question. Defintion 1 and everything that follows depends in a strong way of the concept of concept and on strong properties of that concept (like the possibilty to discrimate what is a concept from what is not and to gather all concepts in a set/ensemble/collection with a consistent meaning). Perhaps I could find a more neutral word or define what I mean by concept. Please note however that the complete ensemble can not be consistent - after all it contains a completed arithmetic. Generally smaller sets can not prove their own consistency. snip Let's assume nothingness exists. Therefore something (nothingness) exists. That is one of my points if one replaces your nothingness with my nothing and your something with my All. Any definition defines two entities simultaneously. Generally but not necessarily the smaller of the two entities is the one about which the definition says: This entity is:. The definition creates a boundary between this entity and a second entity which is all that the first is not. Most of the second entities may have no apparent usefulness but usefulness of an entity is not relevant. Therefore nothingness doesn't exist. Not at all. One can not define a something without simultaneously defining a nothing and vice versa. That is the usually unnoticed aspect of the definitional process. This leads you to the exclusionary statement below. That's why there's something rather than noting. To the contrary both exist if either does. Hal
