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Author
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Topic: T-Duality Universe
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Zachary Aufdemberg
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Member # 335
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posted 31. May 2003 19:56
Parallel wrote:
quote:
If defining the undefined is not paradoxical, pray tell what is?
But you just defined it for yourself. Following this logic is not the concept of paradox a paradox? How can a logical inconsistency be described in a consistent way? If you believe it can't, then why even believe in paradox to start with?(Edit: If I wasn't clear I believe paradox can be described. I'm just pointing out that by Parallel's own logic it can't) I believe the CTMU clears this up by stratifying descriptions from what is described.
[ 31. May 2003, 23:29: Message edited by: Zachary Aufdemberg ]
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chimp
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posted 31. May 2003 23:18
Infinity is undefined but it is not paradoxical.
Georg Cantor discovered a mathematically rigorous treatment of infinity. Quantum mechanics explains that particles are really patterns in infinite dimensional "Hilbert space".
Likewise, UBT is undefined but it may not be paradoxical. Paradoxes are due to statements that end up as:
A = ~A
Thus, the CTMU cannot claim that infinite dimensional space, is paradoxical.
The Earth's 2-D surface is part of 3-D universe. The 3-D universe could be the hypersurface of a
4-D hypersphere. The 4-D hypersphere could be a cross section of a higher 5-dimensional curved space-time. The 5-D spacetime could be a planar layer in a stack of 6-D space-times. The alternate 6-D spacetimes could be a warpage of a higher 7-D space. The 7-D space could be on the surface of an 8-D mobius strip. The 8-D space could be evolving in a higher dimensional 9-D superspace-time ...etc. ...etc. This nesting of spaces could continue to infinity.
There needs to be a rigorous definition of the transformation of the state ...defined? as unbound-potential, to the state defined as actual. What is the "mechanics" of this transformation? How does unbound-potential map onto actual? Potential cannot recognize its actualization and the actualization can only "infer" its potential. How does unbound-potential make the transition to actual, when it does not have any mechanism to make the transition? It cannot be exclusively a one valued logic. Potential basically means ability to bring something into being. How can a one valued logic change if it is immutable? There will have to redefinition of *unbound-potential* as something other than a "one valued logic".
unbound-potential--->actual
This is a transition, a one way mapping. Potential is transformed into actual. Actual cannot create itself because this transition is *primary* i.e. before any type of *temporal* feedback can occur, or timeline is created.
[ 01. June 2003, 07:06: Message edited by: Russell E. Rierson ]
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chimp
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Member # 333
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posted 02. June 2003 13:30
The tautologies of classical 2v-logic have symmetry. Can the tautologies of "MV" logic be categorized as symmetry groups?
The Law of Excluded Middle:
X|~X|X V~X
T| F| T
F| T| T
(T|F) = (F|T) = T
Generalizing:
T = A
F = B
? = C
? = D
MV-logic = {A = T, B = F, C = ?, ...Z = ?, ...n = ? }
1valued logic
A = A
2valued logic
(A|B) = (B|A) = A
3valued logic
(A|B|C) = (B|C|A) = (C|A|B)
= (C|B|A) = (B|A|C) = (A|B|C) = A
4valued logic
[A|B|C|D]=[B|C|D|A]=[C|D|A|B]=[D|A|B|C]
=[D|C|B|A]=[C|B|A|D]=[B|A|D|C]=[A|D|C|D]
=[A|C|B|D]=[C|B|D|A]=[B|D|A|C]=[D|A|C|B]
=[B|A|C|D]=[A|C|D|B]=[C|D|B|A]=[D|B|A|C]
=[A|B|D|C]=[B|D|C|A]=[D|C|A|B]=[C|A|B|D]
=[D|B|C|A]=[B|C|A|D]=[C|A|D|B]=[A|D|B|C]
= A
Tautologies of *generalized* logic are "invariant" under choice of
truth value since they are always true.
Can these logical-tautology groups, be used in the mathematics of QM?
Does T*F = F*T ?
Does T+F = F+T ?
In this instance the symmetry is "T or F"
(T or F) = (F or T)
A logical tautology appears to be an invariance principle. So symmetry could be a higher level of generalization?
For every set A there is a choice function, f, such that for any non empty set B of A, f(B) is a member of B. There may be infinitely many sets B within A. Yet this axiom of choice is independent of the other axioms of "set theory". Are the other axioms of set theory independent of this "axiom of choice"?
It is difficult finding a correspondence between abstract mathematics and the real world, but any given "set?" of abstract relations could sit on the shelf until a correspondence between them and the real world is discovered.
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David M. Garrett
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Member # 438
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posted 02. June 2003 22:38
I have thought quite a bit through the arguments and I would like to say that Russ and I are both wrong. I retract my statement about 1VL and eat my delicious crow. But, in some form of satisfaction I can say that Russ is wrong as well.
UBT is no type of "valued logic". It is non constrained. Any initial actualization would automatically yield a dualization out of a common underlying syntax. Read 2VL emerging out of sameness (syndiffeonesis). UBT does have an aspect of non-comparativeness as well as an infinite potential. Russ and I were right about those aspects. But to call UBT by any type of 1VL or mVL is constraining the unconstrained.
And that is the way I see it now.
Dave
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chimp
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posted 03. June 2003 03:52
Yes, an "unbound potential" would not be a finite valued logic, but rather an infinite valued logic. "MV" logic where M = infinity. It would be an undefined or infinite freedom. Freedom is the complement of constraint, but can freedom be truly independent of its complement?
What is the mechanics of the UBT--->BT transformation? Unbound potential has no cognitive machinery(defining constraints) to initialize a bound form of itself and the bound form called "actualization" can only infer its ontological groundstate(UBT).
So anything that can exist and support its own existence DOES exist in the ...UBT? Magic?
PRESTO! instant reality complete with temporal feedback?
Therefore UBT cannot be ...exclusively, a one valued, or finite valued logic. Or can it? It is undefinable, the mysterious ..."beyond". It is a type of ontological multiverse groundstate(infinite potential?), yet, the other universes are forever disjoint from this one ...???
Pass the crow please ![[Wink]](wink.gif)
Russ
[ 03. June 2003, 05:56: Message edited by: Russell E. Rierson ]
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Rex Kerr
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Member # 632
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posted 03. June 2003 21:42
Now I am going to worry too much about which infinite cardinality we are using, if any.
If we restrict ourselves to an omega_0 of values (i.e. 1-1 correspondence with the natural numbers), aren't we constricted relative to |R|, the cardinality of the reals? And that is restricted relative to omega_omega, clearly. And so on. So I'm not sure that "unbound potential" neatly maps to an infinite valued logic.
Thus, I'm inclined to agree with David that inasmuch as it is sensible to say anything about UBT, it's more accurate to not ascribe any type of valued logic to UBT.
But I simultaneously agree with Russ (if this is what he's saying) that unbound potential can't get off the ground to develop bounds and constraints.
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David M. Garrett
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posted 03. June 2003 21:47
quote:
Pass the crow please
Yes Russ, it appears we're both eating a little crow on this one!
quote:
Yes, an "unbound potential" would not be a finite valued logic, but rather an infinite valued logic. "MV" logic where M = infinity. It would be an undefined or infinite freedom. Freedom is the complement of constraint, but can freedom be truly independent of its complement?
An infinite valued "logic"? No, I think this is even off the mark. UBT would not be any type of "valued logic". Logical bindings would be out. But the thing is, Freedom would not be the compliment of Constraint in reference to UBT but it would be its compliment once a dualization has occurred. That is why Freedom takes priority over constraint.
quote:
So anything that can exist and support its own existence DOES exist in the ...UBT? Magic?
In a sense you are right. As long as you keep in mind that this "inside" and "outside" is not a geometrical inside or outside, but a logical inside and outside.
quote:
yet, the other universes are forever disjoint from this one ...???
Illogical or unbound universes, yes! Actual universes, No!
Now let's enjoy our crow together, shall we?
Dave
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chimp
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posted 04. June 2003 01:11
Rex Kerr:
quote:
Now I am going to worry too much about which infinite cardinality we are using, if any.
If we restrict ourselves to an omega_0 of values (i.e. 1-1 correspondence with the natural numbers), aren't we constricted relative to |R|, the cardinality of the reals? And that is restricted relative to omega_omega, clearly. And so on. So I'm not sure that "unbound potential" neatly maps to an infinite valued logic.
Thus, I'm inclined to agree with David that inasmuch as it is sensible to say anything about UBT, it's more accurate to not ascribe any type of valued logic to UBT.
But I simultaneously agree with Russ (if this is what he's saying) that unbound potential can't get off the ground to develop bounds and constraints.
The mathematician Georg Cantor came to the conclusion, that ultimately, there was an "Absolute", a quantity that cannot be analyzed or comprehended within mathematics. He identified this Absolute with God, "Ein Sof", an infinity that lies outside what we humans can comprehend.
This unattainable Absolute agrees with Goedel's incompleteness theorems, because there is always something larger than any given system.
The Unbound Potential must be this "Absolute". Yes, it would be more than just an infinite valued logic. More than any language-words uttered by "self aware life forms" within this universe, *attempting* to describe ...IT.
It would be incorrect to define this Absolute-UBT-TAO, as freedom *only*. Can this Absolute or UBT or TAO, be explained *only* as being totally without constraint?
No. *UBT-TAO-Absolute* is incomprehensible.
Russ
[ 04. June 2003, 01:12: Message edited by: Russell E. Rierson ]
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Rex Kerr
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posted 04. June 2003 05:06
As part of being "incomprehensible", demonstrating existence is probably not possible, let alone uniqueness. So using the singular "it" to refer to Tao-UBT should be taken as a linguistic convenience only and not indicative of anything about Tao-UBT.
I'd guess the structure is more like that of a filamentous mold-like spot of comprehensibility, which by analogy one could imagine being imbedded in an infinite sea of incomprehensible cheese. (Ah, but is it Tao-UBT-cheese, or Tao-UBT-bread?)
These discussions always amuse me since for the most part postulating extra incomprehensible stuff has no impact on anything we do or experience, since you could replace it with different stuff (or no stuff) and we'd never know the difference.
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Christopher M. Langan
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posted 04. June 2003 13:16
Some of the posts in this thread touch on the concept of "physical infinity". Aside from the question of whether infinite space is paradoxical a priori, physical counting processes are finitely limited. (To understand why, just ask yourself how long it would take you to count an infinite number of small physical objects.) Physics is constructive by nature; that which is logical but cannot be finitely constructed is metaphysical in the analytical sense. Thus, although infinite nestings of sets and spaces are sometimes assumed to exist in the realm of pure mathematics as products of transfinite induction, it has never been shown that this abstraction possesses a physical analogue.
Transfinite geometry preceded transfinite arithmetic by millennia. Long before Georg Cantor discovered transfinite arithmetic, the ancient Greeks were wondering about an infinite cosmos and the flight of arrows along infinitesimally converging series of intervals. General solutions for these problems (if not their corresponding notations) were offered considerably before Cantor, and Cantor's work arguably adds no physical or philosophical, as opposed to algebraic, insight. In any case, certain problems that existed before Cantor made the scene remain controversial to this day, and the physical sciences still lack anything resembling a blanket justification for the physical application of transfinite algebra (a criticism that does not necessarily apply to the CTMU). Therefore, it seems questionable to single out anybody's theory in particular, especially the CTMU, for special criticism because some particular person feels that he or she has not been satisfactorily edified regarding the troublesome problem of infinity.
To some extent, the situation can be viewed in terms of the distinction between perceptual reality, consisting of that which can be perceived or experienced, and cognitive reality, i.e. that which can be conceived. Perceptual reality is finite (constructive) with respect to perceptions involving countable processes and the spatial or objective components thereby enumerated. Physical constraints or laws, on the other hand, can be infinitary, involving infinite series, differential equations and renormalizations. But the whole point of non-finite quantities and processes is that they cannot be actualized in any completely finite, physically countable way. Thus, infinitary laws of nature are just what any decent logician knows they are: metaphysical ingredients of a cognitive metalanguage of perceptual reality. The CTMU merely develops the implications of this distinction.
In a qualified sense, I agree that we need a rigorous definition of the relationship between unbound and bound (actualized) potential. To some extent, there already is one; for example, the CTMU rigorously applies a strong self-containment criterion of which other theories fall abysmally short. However, the idea that everything can be reduced to "mechanics" is highly dubious, especially insofar as it seems to preclude any explanation of the genesis of mechanics itself. It is also highly dubious to speak of a "transformation" or temporal "transition" from unbound to bound "states", since prior to binding, nothing is well-enough bound to coherently serve as a "state" or any other kind of transformational argument. A major point of CTMU cosmogony is to let the logical SCSPL universe serve as its own transformational argument, and to eliminate the need for an initial "transition" in the usual simplistic sense. The ontological potential described as UBT brings nothing into being that was not in a way "already there"; in the sense adumbrated by John Wheeler, it is pregeometric = pre-spatiotemporal = pre-temporal and not itself subject to temporal ordering operations, all of which presuppose syntactic coherence and are necessarily intrinsic to SCSPL systems. A salient feature of CTMU cosmogony is that the pre-temporal cosmic potential of any particular SCSPL universe fails to coherently distribute over UBT, and is therefore not distributively identifiable with UBT.
Regarding the assertion that the actual "cannot create itself because this transition is *primary* i.e. before any type of *temporal* feedback can occur, or timeline is created," this would seem to be a profoundly unwarranted statement. By definition, a primary transformation (in a sequence of evolutionary transformations) is merely a self-contained transformation that does not require external prompting or an external antecedent, and this criterion is satisfied by a reflexive transformation in 3-way coincidence with its domain and codomain. If the point of coincidence "was always there" in the form of an externally unactualized, unevolved atemporal potential, then no external transformation is required. With anyone who fails to see this, I really don't know what more there is to discuss. Suffice it to say that any such person is stuck with a set of intractable paradoxes that he can neither resolve nor constructively circumvent, and that such a person is obviously in no position to criticize anybody else's means of circumvention.
That being said, I couldn't help but notice the ongoing disagreement regarding UBT and n-valued logic. UBT is not a logic; that is, it lacks any distributed syndiffeonic structure. It makes no difference how many values one tries to pin on it; nonlogic is nonlogic. Instead of a syndiffeonic interplay of freedom and constraint, there is only freedom. (We can, of course, define "nonlogic" by applying the negation functor of logic to logic itself, something that is logically necessary due to the self-referentiality of logic. Deny this, and logic becomes non-self-referential even in principle, and thus cannot be used to explain itself or anything that it characterizes.)
What about logical systems? For the expression of structure, 2-valued logic (2VL) is a necessary and sufficient criterion. In any structured (syndiffeonic) system, everything finally comes down to 2VL. We can come at this fact from below and from above. From below, we merely observe that because 0VL and 1VL do not permit nontrivial distinctions to be made among syntactic components, they do not admit of nontrivial, nonunary expressive syntax and have no power to differentially express structure. From above, on the other hand, we note that any many-valued logic, including infinite-valued logic, is a 2-valued theory - it must be for its formal ingredients and their referents to be distinguished from their complements and from each other - and thus boils down to 2VL. So 2VL is a necessary and sufficient element of logical syntax for systems with distributed internal structure. Infinite-valued logics can add nothing in the way of scope, but can only increase statistical resolution within the range of 2VL itself (and not individual resolution except in a probabilistically inductive sense).
For those unfamiliar with the CTMU concept of syndiffeonesis - and it has already been explained at some length - it captures the interplay of freedom and constraint in a relational context. Synesis is distributive, deterministic sameness with respect to a coherent antecedent constraint such as a definite combination of law and state (and corresponds to an algebraic identity), while diffeonesis comprises differences among possible consequential constraints. This reflects the fact that bound telesis is bound freedom, and that imposing a constraint on freedom, i.e. logically binding it and conspansively bounding it, cannot destroy the essential nature of that which is bound. This is why the wave function is the fundamental unit of reality in quantum mechanics; the multiplexing of possibilities in the wave function is just absolute freedom expressing itself (through symmetric diffeonesis) within the bounds of synetic constraints consisting of laws and states. The wave function expresses the freedom of UBT within a distributed mathematical constraint consisting of 2VL and Hilbertian operator algebra. It is by virtue of syndiffeonesis that we can speak of the intrinsic structure of a medium. UBT lacks syndiffeonesis because it admits of no coherent distributed (syntactic) constraint; from the viewpoint of 2VL systems which take "singular" form with respect to it, freedom is all that it has in any distributive sense.
I can't help but be a bit taken aback when people who talk authoritatively about quantum mechanics, uncertainty, infinite-dimensional Hilbert spaces, infinitely-nested spacetimes and other clear manifestations of absolute freedom rail against UBT. Where do they think all of that freedom comes from? From constraint? Constraint is deterministic. Even if we posit the existence of a primal constraint which drives a deterministic many-worlds (relative-state) multiplexing of state and thus "creates freedom", what accounts for the nondeterministic (telic or aleatory) mapping of our consciousness into one particular history among the infinite possible histories thereby "created"? Again, we are forced to confront an inevitable fact: freedom is built into the microscopic structure of reality, and because the wave function is a stratified affair ultimately embracing the entire cosmos (regardless of the number of ulterior spaces in which our immediate reality is nested), it is built into the macroscopic structure of reality as well. Quantum mechanics, syndiffeonesis and UBT go together; remove any one of them, and all that finally remains is a teetering pile of paradoxes waiting to collapse.
The bottom line, I suppose, is that insofar as mainstream theorists can't even come close to explaining cosmogony or difficult related concepts like infinity, they and their supporters have no business specifically targeting theorists who have chosen not to be limited by their scientifically obstructive conceptual handicaps. In a word, people in theoretical glass houses shouldn't throw stones, or delude themselves (or others) that the CTMU fails to shed light on problems that more popular theories fail to even address. The only way that someone could possibly make such a claim is if he understands virtually nothing about the CTMU.
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Christopher M. Langan
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posted 04. June 2003 13:20
Rex Kerr opines that since demonstrating the unique existence of the incomprehensible is probably not possible, "using the singular 'it' to refer to Tao-UBT should be taken as a linguistic convenience only and not indicative of anything about Tao-UBT."
How true. Mathematically, it is indeed convenient that variables can be defined regardless of multiplicity of content, and can thus be referred to as “it”. But on a deeper level, the UBT issue is all about whether the negation functor of logic can be applied to logic itself to yield non-logic, which together with logic would approximate UBT. If not, then logic has no complement and must be taken as a primitive constraint. This pretty well captures the falsificationist viewpoint, according to which logic is tautological and therefore trivial, in light of which some people may find it shocking that (e.g.) their digital computers and all of the symbolic reasoning that went into their development and everything that they can be used to calculate and simulate are “trivial”.
But Rex's viewpoint leads to a couple of even more dire problems. (1) That which has no complement is indistinguishable from its complement and therefore contains zero information. But if logic has no informational value, then neither does logical consistency. And if logical consistency has no informational value, then consistent and inconsistent theories are of equal validity. Oops...goodbye, math & science! [Don’t you think that maybe it would be better to take something else other than logic as "that (primitive entity) which has no complement", and that maybe this trans-logical, pre-logical something should be taken as a mathematical criterion of meaningful scientific theorization?] (2) If logical functors cannot be applied to logic as a whole, then logic cannot serve as a metalanguage of logic. But then logic is in no way self-explanatory, and we’ve run into an explanatory brick wall due to which certain urgent questions, including questions at the very heart of the ID/neo-Darwinism controversy, may be unanswerable. After all, if logic cannot in any sense be logically explained, then neither can that which is necessarily formulated in terms of logic...e.g., everything of interest to science.
Rex then guesses that the structure (of UBT) is more like that of a filamentous mold-like spot of comprehensibility, which by analogy one could imagine being imbedded in an infinite sea of incomprehensible cheese. “Ah”, he asks, “but is it Tao-UBT-cheese, or Tao-UBT-bread?” All that one need add to this colorful and witty metaphor is a bottle of vino and a few paintings, and one has an art gallery buffet!
Rex then owns to being amused by these discussions “since for the most part postulating extra incomprehensible stuff has no impact on anything we do or experience, since you could replace it with different stuff (or no stuff) and we'd never know the difference.” But of course, this says more about the limitations of current scientific inquiry than it does about the logical structure of scientific theories. In fact, the question of whether the universe is free or deterministically constrained is clearly relevant to questions like biological evolution and free will, and the relationship between freedom and constraint ultimately comes down to that between UBT and logic.
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Rex Kerr
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posted 04. June 2003 22:17
I'm not sure that my viewpoint is the same one that Christopher Langan is arguing against. However, I am not averse to playing the role of logician's advocate, so I will to some extent adopt the positions he ascribes to me even though I have (other) disagreements with them.
First, I would note that some questions may be unanswerable. Although people wonder about biological evolution and free will, it does not follow that the structure of the universe admits an easy (or any) answer to those questions.
Second, my mold-metaphor was supposed to describe the structure of comprehensibility. UBT would be the cheese, which may exist, or not exist, or exist and not exist, or neither exist nor not exist (according to Buddhists, anyway).
Third, logic may not be completely explicable by logic. This would be unfortunate, but as comforting as global and universal applicability of logic is, it isn't necessary for doing science. Practically everything we use science for can be done with systems that are locally consistent and/or locally logical.
Finally, I am not entirely sure I understand why not having a complement is the same as being indistinguishable from it. For example, wavelength doesn't have a complement, but it's a perfectly usable quantity. Additionally, "logic" and "not-logic" is a contradiction, under logic, so if logic admits both "logic" and "not-logic" then logic is self-contradictory. (There's no problem with having non-logical statements, just allowing the entire theory of logic and the theory of not-logic to simultaneously exist in the same model.)
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Christopher M. Langan
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posted 05. June 2003 02:08
Rex Kerr notes that some questions may be unanswerable, including questions involving biological evolution and free will. While this may be a reasonable starting hypothesis - we do, after all, have undecidability, uncertainty and various kinds of model-theoretic ambiguity to consider - it requires rational or empirical support with respect to any given question. Until such support is given, it implies nothing about the structure of the universe, particularly with regard to which questions can or cannot be answered, easily or otherwise, by rational or empirical means. It is probably more constructive to concentrate on what the universe, broadly including logic and mathematics, can tell us, at least until we have the means to define hard epistemological limitations of the kind that Rex seems to anticipate. This, I think, is more in keeping with the pursuit of knowledge and the spirit of scientific inquiry.
Regarding Rex’s mold metaphor, he is in a better position than I to affix the mold labels, the cheese labels and the bread labels. It is, after all, his metaphor. However, since UBT and SCSPL are my concepts, I’m probably the one to say whether or not his metaphor holds water relative to their relationship. Unfortunately, I’m afraid that while I find the metaphor droll, I just don’t see much illustrative value in it. Nor, I daresay, would many Buddhists.
Rex conjectures that logic may not be completely explicable by logic, and that as comforting as the putative global and universal applicability of logic might be, it unnecessary for doing science. As I’ve already pointed out, this merely sets a limit on the kind of science that Rex is content to do. Although Rex states that “practically everything we use science for can be done with systems that are locally consistent and/or locally logical”, local logic and local consistency, even if they can be coherently defined, are inadequate with respect to answering questions of a global or fundamental nature, e.g. questions regarding existence, origins and causality. Thus, according to the limits that Rex has imposed on science, ordinary scientists would have no business attempting to address such questions, and should leave questions about the true nature of biological origins and evolution to theorists who are less limited in their approach. (Then again, I suspect that many scientists would prefer to question their limitative assumptions rather than suffer the epistemological consequences of failing to do so.)
Rex professes a lack of understanding as to why not having a complement is the same as being indistinguishable. The standard answer, of course, is that since information always restricts (or constrains) a potential by eliminating its alternatives therein, nothing to which informational value can be attached lacks a complement (in some probability space). For example, since observing that something exists is to rule out its nonexistence - existence and nonexistence are complementary states, provided that we conveniently classify nonexistence as a "state" - such observations distinguish existence from nonexistence and thus have positive informational value. On the other hand, that to which no information at all can be attached cannot be said to exist, and is thus indistinguishable. Because this applies to consistency and inconsistency, it also applies to logic and nonlogic.
Rex then presents the example of wavelength, saying that while it “doesn't have a complement, it's a perfectly usable quantity.” However, wavelength, like any other quantity, has meaning only with respect to a perceptual and cognitive syntax according to which it is defined and measured. First, it is not clear that the predicate “wavelength” cannot be considered to have a complement in this syntax, e.g. a complement consisting of all other predicates in that syntax (and so on). Secondly, what we’re really talking about here is the complement not merely of a predicate, but of an entire syntax, and we’ve already explained why such a complement is necessary. Specifically, we explained that if the syntax of logic were to have no complement, then consistency and inconsistency would be impossible to distinguish either locally or globally, and concepts like “truth” and “science” would be meaningless. Because the truth predicate is global by nature and cannot be locally confined, it gives way not to “localized truth” when cut off from global criteria, but merely to uncertainty. Conversely, anything about which an observer can be locally certain relies on global syntax, i.e. on mental syntactic structures that he or she cognitively and perceptually distributes over everything that he or she thinks and experiences.
Rex then states that "'logic' and 'not-logic' is a contradiction, under logic, so if logic admits both 'logic' and 'not-logic' then logic is self-contradictory." Not if it treats nonlogic as something which is excluded by logic in any given model, for example a nondistributive lattice. He then observes that “there's no problem with having non-logical statements, just allowing the entire theory of logic and the theory of not-logic to simultaneously exist in the same model.” Although I see where Rex is coming from, logic and nonlogic can in fact exist in the same model, e.g. a nondistributive lattice, provided that nonlogic does not interfere with logic in that part of the model over which logical syntax in fact distributes, e.g. the Boolean parts of the lattice. That the non-Boolean parts of the lattice approximate poorly-understood relationships among Boolean domains is irrelevant to the value of such "non-logical" models, as we see from the fact that nondistributive lattices permit the representation of real noncommutative relationships in quantum mechanics.
[ 05. June 2003, 03:08: Message edited by: Christopher M. Langan ]
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chimp
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posted 05. June 2003 14:43
This infinite freedom(UBT-TAO-POTENTIAL?) implies that anything that can exist DOES exist, where the generic universe in question, refines itself FROM the UBT.
The potential has no cognitive machinery to recognize its refinement from ..."itself" and the refinement can only infer the existence of this most fundamental *ontological grounstate* quantity. We know from discussion that the unbound potential is not equal to bound potential because they are defined as two separate things, yet the unbound potential is described as the "ontological ground state" of bound potential.
It is also a transformation?:
(unbound potential)-->(potential-->actualization)
If reality is X and UBT is "not-X" there is a transformation:
not-X--->X
not-X implies X ???
incomprehensible implies comprehensible ?
Logic says that not-X is equivalent to itself i.e. (not-X) = (not-X)
Then the question becomes:
Does (UBT) = (UBT) ?
Does (UBT) = (not-UBT) ?
Does (UBT) = (not-UBT) AND (UBT) ?
Does UBT = freedom ?
Of course from a general language syntax perspective, (freedom) = (freedom)
Does UBT = (freedom)?
Is UBT infinite freedom?
Potential infinity?
Cantor's transfinite completed infinities?
Totally unknown?
There must be a solution to these simple equations for a most necessary and sufficient clarification of this enigmatic (incomprehensible?) to (comprehensible?) relationship?
Russ
[ 05. June 2003, 14:45: Message edited by: Russell E. Rierson ]
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Christopher M. Langan
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posted 05. June 2003 15:36
Russell Rierson says that "The (UBT) potential has no cognitive machinery to recognize its refinement from ... ‘itself’,..."
Since UBT is not to any extent refined except within an SCSPL domain, it needs cognitive machinery to recognize itself only within that domain. And that’s where the cognitive machinery is in fact present, right there in the self-refining SCSPL domain. Because SCSPL syntax fails to distribute over UBT, neither does the associated machinery, but it doesn’t have to. It need only coincide with the SCSPL which is undergoing self-configuration. Since I don’t know how I can make this any clearer, I request that if you still don’t understand it, you think harder about what has already been explained regarding it (including a bit more that I’ll write below).
Russell continues: "...and the refinement can only infer the existence of this most fundamental *ontological groundstate* quantity. We know from discussion that the unbound potential is not equal to bound potential because they are defined as two separate things,..."
No, UBT and SCSPL are not defined as "two separate things", any more than a chunk of ice floating in a pond is a "separate thing" from the water in the pond. The water in the pond is where the chunk of ice came from and what it is essentially composed of, but the crystalline lattice structure of the ice does not distribute over the pond, and the water in the pond is not distributively bound by this structure. The molecules in the liquid-phase H20 have more degrees of freedom than those in the ice; they are less constrained, and less bound. All that you need do in order to apply this analogy is to take it to its logical conclusion while generalizing your usual idea of containment, replacing ice with SCSPL, the pond and its molecules of liquid water with UBT, and the crystalline molecular lattice of the ice with an SCSPL logic lattice, and to relax your grip on the tidy little picture of a chunk of ice with extrinsic measure bobbing around "in" the water. Any metric imputed to UBT must be intrinsically derivable within SCSPL domains (e.g., by intrinsic mutual exclusion).
Russell concludes: "...yet the unbound potential is described as the "ontological ground state" of bound potential."
Yes, just as a pond full of water in which a chunk of ice forms by an intrinsic phase change can be regarded as the "ontological groundstate" of the chunk of ice. Other than the need for and the implications of intrinsic metrization, this is a very straightforward concept, and it is absolutely central to the development of a logical model spanning the existence of logic itself. Because this is as simple as it gets at the level of concreteness you seem to desire, your only choices are to reject the CTMU on what I've already shown to be illogical grounds, or surrender a little concreteness. It’s your choice.
[ 05. June 2003, 15:41: Message edited by: Christopher M. Langan ]
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