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Topic: Cosmogony, Holography and Causality
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Rex Kerr
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Member # 632
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posted 15. September 2003 21:28
But Russel, the universe is notorious for not quite matching our abstract rules for it. "Sort of matching" doesn't count as an isomorphism. If f=ma has abstract "real" existence, it has a funny way of showing it at v=0.99999c.
That we can find more complex mathematical descriptions of the behavior of the universe is a fine scientific assumption. I simply don't think we are justified in assuming that this must be the case in our metaphysics.
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chimp
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posted 16. September 2003 01:21
If a flying lab, out in space, free from gravitational forces, is traveling at a constant .999 c [inertial frame] and an experiment is done in that reference system, measuring "F = ma", it should agree exactly with the same experiment in a flying lab in interstellar space traveling at .001 c [inertial frame] , when an equivalent experiment is performed to measure "F = ma", when the two frames re-unite to compare their results. The laws of physics are the same for all inertial reference frames, according to Einstein, and ...falsification ![[Wink]](wink.gif) . An equilateral triangle has a rotational symmetry that is invariant for a Euclidean or non-Euclidian surface.
I agree that present mathematical formulations are only very close approximations. Yet, certain principles must hold for certain conditions. For example, in our perceptual universe, 1 cannot equal 0
Of course, under other conditions such as a "Bose Einstein Condensate", a collection of atoms all merge into the same "state" so in that regard, ...A equals ...not-A.
So, what holds everything together?
Abstract laws?
Where do these abstract laws come from?
The law of conservation of mass-energy is exact is it not? Sure, it could be violated during brief periods below the Planck time but it still will be impossible to build a perpetual motion machine, unless of course we could create a black hole in our garage
There is no escaping the fact, that this existence is bound by a collection of mathematical principles.
http://www.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences
quote:
The Unreasonable Effectiveness of Mathematics in the Natural Sciences, published by physicist Eugene Wigner in 1960 , argues that the capacity of mathematics to successfully predict events in physics cannot be a coincidence, but must reflect some larger or deeper or simpler truth in both.
This was a work of both physics and of the philosophy of mathematics , specifically it speculated on the relationship between the philosophy of science and the foundations of mathematics :
"It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them."
[ 16. September 2003, 02:34: Message edited by: Russell E. Rierson ]
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Christopher M. Langan
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Member # 264
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posted 16. September 2003 03:00
In response to David Garrett, Rex Kerr says that what David calls "the mental aspects of reality" may be ontologically secondary and "emergent".
No, they may not, at least insofar as emergence is an orderly process requiring coordination by general, abstract syntactic principles. That is, where emergence entails syntax, and syntax is abstract (mental or trans-physical) in nature, mental reality is critical to the emergence of physical reality and not vice versa. The fact that mind then achieves physical instantiation is beside the point; syntax is still more general than, and therefore logically prior to, the physical objects and states which instantiate it.
In response to a statement by Zachary, Rex then writes "there are multiple inconsistent sets of axioms of logic".
quote:
Here's a potential counterexample.
Let P(x) be a proof that x is true, and let LC be the statement that logic is internally consistent. Then:
System One: NOT P(LC) is true
System Two: P(LC) is true
System One is the subject of Godel's Incompleteness theorem, which basically says that NOT P(LC) for first order predicate logic (and it's been extended to other areas). System Two is the system that must be assumed if one can start with rationality and know that rationality is justified.
So, assuming we admit the Law of the Excluded Middle (i.e. A OR NOT A is a tautology), then one of the following holds:
(1) First order predicate logic is inconsistent.
(2) The process of rationally justifying rationality is impossible.
(3) There are multiple inconsistent sets of axioms of logic.
Godel never intended to show that logic must be either true or inconsistent; that would have been too obvious. Instead, he showed that a particular combination of logic and arithmetic is either complete or consistent, but not both. Because the consistency of logic has never been seriously in question, an undecidable (but logically correct) axiomatic system is merely incomplete, which means that certain true relationships cannot be verified within it.
The reason that logic cannot be inconsistent is that when all the inessential chicken-scratchings are stripped away to leave only the essential ones, consistency still equals truth, which equals the inclusion of the formal or factual image of an expression in a descriptive system or its universe. Because logic is tautological, i.e. universal and reflexive, that which is logically inconsistent is not only illogical but unreal. Any conceivable attack on the consistency of logic would effectively destroy its own logical integrity and thereby defeat itself, excluding itself from reality in the process. Because there inevitably comes a point at which any attempt to deny the consistency of logic undermines and invalidates itself, it can be taken for granted that logic is consistent. If it weren't, then all argumentation regarding it, along with the entirety of human thought, would be futile...and in that case, it would be pointless to argue for or against anything at all.
Because the laws of nature exist independently of concrete instances and are therefore abstract, reality must conform to a self-consistent logical syntax consisting of valid rules of sentential and semantic abstraction. The rules of perception must be isomorphically consistent with the rules of logic; otherwise, perceptions could not be mentally acquired, i.e. isomorphically mapped from the natural world into the mind of the perceiver. The same applies to cognition itself; if there were no consistent cognition-to-cognition identity mapping, then cognition could not acquire its own products, and what some have characterized as the "many-valued logic" of human mentation would infiltrate cognition at the syntactic level. Cognitive-perceptual reality would then disintegrate for lack of a stable syntactic identity in terms of which its rules of structure, evolution and recognition could be formulated.
Rex continues: "However, if you can't use logic to prove that logic is valid, then it may matter how you happened across it. For example, suppose you find a box and you point it at the sentence, "NOT (A AND B) IFF (NOT A OR NOT B))". It says "true". You do this a whole bunch and it always gets the right answer. Then you write down, "This box always gives me the truth value of a sentence." You point the box at it. It says "true". But are you justified in believing this answer?"
Actually, you are. This is because of another (related) kind of box called a "truth table", which effectively defines logical connectives and functors on truth and consistency and vice versa. A little reflection reveals that these functors (not, and, or, implication and biconditionality), along with the synonymy of truth and descriptive inclusion, are utterly basic to human thought. Try to avoid them, and you forsake any possibility of being able to think straight. The mental operatons they represent are simply too elementary and too universal. Try to define alternates, and you'll be forced to do so in terms of the originals.
The looplike tautological axioms of logic will always be consistent because, in order to implicate them in any sort of contradiction, one must add on a particular instance of LSAT in which expressions are no longer isolated. Instead, they are linked in common variables to which truth values are to be assigned. These tentative linkages and assignments do not occur in the system of propositional logic per se; compound expressions admitted to the formal system of logic must previously have been proven true under all possible truth value assignments, and thus identified as tautologies. In contrast, an arbitrary instance of LSAT has not been proven tautological or even solvable; its internal consistency depends on the logical evaluation of its (likely) non-tautological structure under all possible "test assumptions", or compound truth functions assigning truth values to all of its sentential variables in all possible models. When all possible predicative test assumptions fail, it is the particular LSAT configuration and not logic which collapses.
As we have already noted with regard to the equivalence of truth and inclusion, this kind of inconsistency can mean one of just two things: either something that was assumed to be a part of the inconsistent LSAT system is not really a part of the system, in which case the system can be surgically altered and restored to logical consistency ("the theory only appeared to be logically inconsistent and can be saved"), or the system is irremediably inconsistent and cannot be surgically rehabilitated, in which case it is fundamentally illogical and all argumentation based on it is futile ("the theory must be discarded"). But in neither case is the truth of logic at stake, for logic stands above the illogical or extralogical structure responsible for the failure. It distributes over the formal sentential (syntactic) structures of individual expressions, independently of the attributive (semantic) links distinguishing the structure as a whole.
Although inferences depend on models - this is something which scientists and mathematicians must always consider - logic is a truly basic, syntax-level self-model that defines its own functions and connectives on its own consistency, and therein lies its tautological integrity. It defines truth on its own terms, and its terms on its own kind of truth. Ultimately, the only kind of consistency that matters is consistency with the tautological definitions of sentential functors - everything else is "to be determined" - and this is what logic is by definition. Tautology, as based on the universal descriptivity and cognitive-perceptual necessity of logical functors, is its characteristic attribute, and this makes it unconditionally correct. Where predicate logic and model theory are properly regarded as extensions of propositional logic accommodating semantic and interpretative operations respectively, they are subject to the rules of propositional logic and do not support violations of it.
The premises on which Rex bases his arguments are closely related. That cognitive and perceptual reality can be separated even on the logical level, that one can use logical functors and tautologies to show that logic can be inconsistent or that there can be "alternatives" to logic, and that the truth of a logical tautology is somehow subject to empirical confirmation all lean on each other. Because none of these premises stands up, the three of them fall as one. Such argumentation is utterly indebted to logical functors and tautologies for any claim it might have to validity, and logic by definition will not permit these functors and tautologies to be used to subvert it. Only a theory of reality reflecting this incontrovertible fact can yield any amount of certainty.
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Aliet Jacob
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posted 16. September 2003 08:53
Langan argues that "mental reality is critical to the emergence of physical reality and not vice versa". I understand syntax to be "a set of structural and functional rules which determine how a transducer behaves on a given input".
From Langan's statement, and I stand to be corrected, I think when he uses the word "syntax", he has in mind software-like commands and he sees the physical as hardware whose "emergence" is an orderly process whose "coordination" is guided by the syntax. Thus anything that results from the physical is dictated by the syntax/hardware. In other words, the physical exists (in the form that it does) because the hardware "said so" (not to be compared with Stone Cold Steve Austin's punchline).
I think this is a flawed view because syntax (the abstract/mental) alone cannot give rise to the physical. It would involve a degree of indeterminacy (at least with respect to the emergence of the physical from the non-physical/mental). And indeterminacy is one thing the CTMU sets out to eliminate.
Besides, the mental alone has no causative powers on the physical without something physical. They must be causaly related for the mental to affect the physical.
About syntax being logically prior to the physical, it would be good to see what "logically prior" means because I do not find logic to be a temporal entity. I find the expression "logically prior" incongruous and I can only compare it to a phrase like "logically red" or "physically false".
[ 16. September 2003, 08:57: Message edited by: Aliet Jacob ]
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Rex Kerr
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posted 16. September 2003 09:02
I agree with Russel that mathematics is unreasonably effective at explaining the physical sciences (esp. physics). However, I think it's important to avoid drawing too strong of a conclusion from this.
Certainly one possbility is that "this existence is bound by a collection of mathematical principles". This makes it sound as though existence is somehow in the power of or subordinate to mathematical principles. And while this may be the case, there are other possible explanations where the mathematical principles sort of match the universe through less certain means. For example, the universe could be a giant lookup table with an infinite number of states, and we can percieve only the infinitesimal fraction of them that are (accidentally) regular. Or, the universe may be horribly simple, but we may be unable to see the real simplicity, and instead use mathematics to describe the asymptotic behavior of the underlying ultra-simple system.
-------------------
Christopher Langan makes a number of good points. In particular, I've been rather sloppy about distinguishing between models and theories (sets of axioms) and predicate logic itself, and in making explicit the limitations in the form of arguments I can use based on the fact that I am (hopefully) using logic.
With respect to Godel's Incompleteness Theorem, I glossed over that it applies to a set of axiomatic systems; as far as I know, axiom sets containing Peano's Arithmetic are incomplete. (I am unsure of the status of proofs both in higher-order logic and extended axiom sets, although I know at least a fair number of each have been completed.)
The reason I glossed it over was that it doesn't affect my conclusions if we believe that logic is supposed to help us understand the world.
First, note that axiom-free logic can't validate itself because it can't talk about "logic". It's just a bunch of tautologies; there is no way whatsoever to actually reference the concept of "logic" from within logic. So we must adopt an axiom system in order to get anywhere.
I do agree that logic alone isn't inconsistent for exactly the reasons Chris described. It may, however, be useless.
Once you adopt axioms so that you can talk about logic, Godel's incompleteness theorem applies, and you get the trichotomy I presented before.
One can come up with other sets of rules besides "logic", and without axioms or models they too will be utterly self-consistent, but perhaps not useful. For example:
A=A
A=!!!A
A*B=B*(B*A)
(A*A)*A=!!A
A:B:C=C:!B:!!A
A:B*C:D = C*B:A:D = B:A:D*C
Is this good for anything? Probably not. Is it self-consistent? Incontrovertibly!
It is precisely the axomatization that makes logic useful. It is precisely the observation that logic and axioms describe a model that is a good fit to our observations that underlies rationality.
To assume that it must be this way is weird. Why logic instead of the system I invented above, except that logic is useful and the six axioms above are (on first glance) not?
I'm not entirely clear on what Chris means by cognitive and perceptual reality, and in any case, I hope I've explained my position more clearly and rigorusly in ways that partially circumvent what Chris says in his last paragraph. Therefore, although I have a strong suspicion that if I fully understood Chris's meaning that I would disagree, I'm going to stop here and see if the issue comes up again.
[ 16. September 2003, 09:02: Message edited by: Rex Kerr ]
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gedanken
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posted 16. September 2003 09:17
One of the first mathematics that I learned that was more abstract than the "algebra" aspects as described in early arithmetic is the following:
Euclidean Geometry -- and specifically the concept of the straight line. Russel already mentioned an "equilateral triangle", though discussing it in terms of non-euclidean geometry.
So where in physical reality do we find the straight line? (One that obeys euclidean geometry? And of course I don't mean approximations--as that would be a mental concept trying imperfectly to describe some relationship in the real world.)
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chimp
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posted 17. September 2003 03:40
Rex and Gedankin, you seem to be saying that because we can observe a phenomena repeatedly, for example, the sun rising and setting every day, and from the various observations, we can generalize deterministic rules that predict future events, but we can't say that those rules are the "absolute truth"...?
The world must have rules. Matter-energy is really abstract rules interacting?
Quantities relate to other quantities according to certain rules. The rules cannot be assumptions. The rules may not be completely defined, but their existence[identity] must be accepted as inviolate and absolute...?
Einstein did away with the "ether", so light can appear to propagate through the vacuum of empty space without a medium. Certain waves, such as water waves, sound waves, etc, need a medium to propagate through. Other waves that travel at "c", the speed of light in vacuum, have no medium of propagation but they do have a real measurable existence. These types of wave can be described by abstract mathematical formulas. If total spacetime is explained as a constant, where, successive spacetimes are nested within previous iterations, the photons are carried along with the iterated spacetime itself. This agrees with Einstein It explains why no medium is required for light waves.
A first principle must be that the world operates according to logically consistent rules.
Or can we only say that the world just appears to operate that way, since we can only know incomplete truth, and not the total, complete, truth?
[ 17. September 2003, 06:42: Message edited by: Russell E. Rierson ]
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Rex Kerr
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posted 17. September 2003 09:36
I think it is not a principle but an observation that the universe operates, in some areas, in close approximation to logically consistent rules.
Speaking as a scientist, that's all I need to use said rules to describe the universe, and I will say that "the universe behaves this way" (to good approximation / high degree of certainty).
However, speaking as a metaphysicist, I have to consider the implications of my premises. If I assume that (1) the universe is governed by logically consistent rules and (2) we can know this with absolute certainty, there will be various consequences. I think these premises are unjustified, though; at the metaphysical level, they are wishful thinking, given that we could have a universe that was identical in appearance where (2) was false and (1) was true, or both were false.
Therefore, I view any statements that assume (2) as inviolably true to be (not very well supported) conjecture. Statements that assume only (1) but not (2) are less uncertain, but should still be taken as tentative given that if we have (1) but not (2), we can't know (1) and hence we cannot rule out that (1) is not entirely accurate.
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gedanken
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posted 17. September 2003 10:24
Russel said:
quote:
A first principle must be that the world operates according to logically consistent rules.
Or can we only say that the world just appears to operate that way, since we can only know incomplete truth, and not the total, complete, truth?
Rex did better at answering this than I most likely will, but let me put in some comments anyway.
If you ask people around the world whether they think the world operates according to “logically consistent rules” I’ll bet that you get an awfully large number of negative answers. And that certainly has not been the perception of people as of several hundred years ago. The assumptions of that time were that even the motions of the apparent objects in the “heavens” was according to the will of God (or Gods) and not specifically “consistent rules”—even if given by those Gods. And today, Dr. William Dembski suggests that biological systems are modified by “unembodied designers,” who are not operating by any “logically consistent rules” that we seem to be able to nail down. So there certainly is no agreement on that subject. (Not that I give his opinion any weight with respect to “science”.)
I like the concept of a “useful fiction”. Classical mechanics “rules” form a very very useful fiction for explaining motion of planets and many other mechanical movements here on Earth and in space. But remember that rather than following those rules like F=M*A (or was it F=DP/Dt?), they are probably more accurately described as some sort of curved space-time coordinate system, such that the planet is actually moving in a “straight line” in its particularly described curved space-time system in some sense. So which view is right? The latter predicts more observable phenomena more accurately. The former is more easily calculated for the vast majority of planetary (and space shot) cases. We use the one that is most relevant for our task, and don’t worry about its “absolute truth”. We recognize the latter will have its own domain of accuracy and failures—so how does it differ from the “truth” of classical mechanics?
Physics joke: What is the capacitance of a chicken?
Physicist starts his answer: “Assume a spherical chicken. ...”
The more accurately one models the real world, usually the greater accuracy one gets in predictions. By “accuracy” I mean completeness of covering all the physical factors involved, how accurately the details put into the model agree with the physical world’s case, and the like. Then after all that, sometimes that turns out to not be correct. So we have quantum mechanics, general and special relativity, and a plethora modern physics theories—just in one discipline!
Who is going to try to find the “capacitance” of a chicken by constructing a finite element model of a chicken’s form, including the resistivity of elements of the feather stems, beak? Believe it or not, there is some importance to questions like this. There are (rather simple) “human body” models for estimating damage to electronic components by static discharge from a human handling the parts. These are very useful “fictions” which do a pretty good job of predicting how the real world operates.
But what do they say about our world as viewed from some sort of omniscient viewpoint? We simply don’t know from the direct study of science, in my opinion. One can’t even construct a model of what that question means, using the tools of science.
In fact I am convinced that the misunderstanding of the relationship of science to “absolute truth” drives much of the interest ID claims. Many ID enthusiasts are worried that science is making some sort of claim about “truth” of our origins, rather than statements of the physical relationships of the real world. The difference is subtle, but very important. For example if “God” wanted our world to operate according to relationships that we could understand in large part, would “He” not create the world to have consistency? (And do we not observe this fair degree of consistency—as many have remarked?) You see if one uses certain assumptions one can find various implications that go quite beyond what science can provide. That does not mean that scientific observation can distinguish the truth of those implications.
But the result of science is that there are beautiful simple relationships in nature, but that finding all the details is very difficult, and none of them seem to hold without requiring modification at some point, at some degree of accuracy or change of circumstance.
--- [ADDED in Edit]
Also there is this confusion between relationship and rule. In part it comes about due to the common use of the term “law” in science.
But a scientific “law” is a relationship that holds with substantial universality, accuracy, and certainty. There was no intention that “law” be considered like human “laws” that are declared first, then followed. In science, the order is in fact the exact opposite—we would not call a principle a “law” until we already observed that the relationship was commonly “followed” in nature. Science thus makes no statement about whether there was some external representation of the “law” outside of nature itself.
This confusion shows itself here. One should not conclude that the relationships in science have any necessity of external representation, just because we find that we as humans can describe the relationships as consistently holding in what we observe. Remember the degree of art in applying the relationships of science properly to make predictions, and the degree to which these relationships have inherent inaccuracies which are also a known aspect of the science itself.
AND a second irony: The greater degree to which the “law” can be given an external meaning—say as having been held by (a, the) god as a concept under which physical reality regularly and with considerable certainty operates by way of having been intended to operate in such a way with consistency—then the less that an ID perspective is relevant in terms of problems for Darwinian evolutionary processes. The reason is simple, for the “law” to be externally held and consistently applied, it must be “consistently” applied. Therefore we expect to be able to consistently observe those “laws” and relationships that might relate to those “laws”. Therefore there is no reason to find fault with Darwinian results being expected, for example, based on some principle that there is a philosophical bias against “design”. Because “design” is never a consistent relationship, certainly not a relationship that has consistent regularity across the entire universe, precisely because “design” is considered novel.
[ 17. September 2003, 14:57: Message edited by: gedanken ]
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chimp
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posted 17. September 2003 14:53
Yes, truth is incomplete. Given the existence of undecidability, how can the ultimate truth be known unless the total complete truth is known? So the ultimate truths can never be known, because larger truths are continually being discovered, which open our eyes a little with each new discovery. All of the sudden we discover that the earth revolves around the sun. So to say what the ultimate truth is, would be short changing our future knowledge about ...truth.
A CTMU ace up the sleeve, still cannot say what the ultimate truths ...are ...?
[ 17. September 2003, 14:54: Message edited by: Russell E. Rierson ]
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gedanken
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posted 18. September 2003 00:17
quote:
All of the sudden we discover that the earth revolves around the sun. So to say what the ultimate truth is, would be short changing our future knowledge about ...truth.
But of course in the case of quantum theory, and relativity theory, there are "correspondence" principles that say that the older classical mechanics relationships must hold in those very large number of cases in which they are observed to be so accurate.
My point above was that even though it is only accurate in some circumstances, that classical mechanics has some sort of basic "truth" about it. Just not in an absolute sense, meaning all-encompassing. It can be fundamental with out being all-encompassing. The "useful fiction" is not so because it will be displaced tomorrow, but because greater detail has, well, greater detail. In learning more we learn how to bound previous knowledge, not necessarily rejecting it. Classical mechanics has in a very real sense not been “rejected” or replaced.
Many seem to retreat (with regard to their arguments) into the uncertainty of science. But science has not provided such uncertainty, just because it does provide an expected pathway to discovering more complexity. Classical mechanics will be useful in another 200 years.
---
For Chris, and others, on subject symbolic and syntactic reasoning:
The Symbol Grounding Problem by Stevan Harnad
Actually here is a series of interesting papres.
[ 18. September 2003, 01:36: Message edited by: gedanken ]
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Mark
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posted 19. September 2003 12:31
I come to this thread a little late in the day, but a couple of Langan's comments in his most recent post caught my eye, and I think they go to the heart of the matter.
quote:
Because logic is tautological, ie, universal and reflexive, that which is logically inconsistent is not only illogical but unreal.
And:
quote:
The rules of perception must be isomorphically consistent with the rules of logic; otherwise perceptions could not be mentally acquired, ie, isomorphically mapped from the natural world to the mind of the perceiver. The same applies to cognition itself; . . . [In the absence of this mapping] cognitive-perceptual reality would then disintegrate. . . .
Among other things, I think Langan is making two points relevant to empirical science. He is explaining, first, why empirical or observational science "works." If not for the logic inherent in reality, and the mapping between the natural world and the mental world of the perceiver (and in particular, the capacity of the perceiver to distinguish the logical from the non-logical -- that is, the real from the not-real), there would be no empirical or observational science in the first instance, or, if there was, it would be a fool's errand.
He is also explaining the assumptions (or at least one of the assumptions) of the empirical or observational sciences, and in the process demonstrating that this assumption is not an assumption at all, but a tautology, that is, that empirical observations are valuable, because first, the above-mentioned mapping exists, and secondly, the facts or events that are observed either bear a consistent (read logical) relation to other events, or are in themselves part of a larger order or process that is itself regular, consistent, and (given the correct theoretical model) predictable (that is, they are logical, or rather, they are themselves expressions of the property of the logical that inheres in all of the natural world).
As I understand the CMTU, logic is not a skill set, nor an abstract construction of the human mind, nor a method or rule book for argumentation, nor an arbitrary construct of otherwise bored philosophers; rather -- and I think this is one of the claims made by Langan that deserves some thought -- logic is inherent in, and an essential property of, the universe itself (Langan goes so far as to claim that the non-logical is not real, and conversely all that is real not only is, but must be, logical). In other words, human minds have not invented or constructed logic for their own convenience or amusement; on the contrary, we have discovered it, and we have discovered it in the "real," that is, within the natural world, or as much of the natural world to which we are presently privy. And having discovered it, we have also discovered that it works in the natural sciences, because it inheres within the natural world itself (including our own brains).
Thus, as I understand Langan, logic is part of the "syntax" of the real, and if we wish to either perceive, know, or participate in the real, we must speak its syntax, and absent logic we cannot do that. In other words, we cannot communicate with, perceive, or know the real (or even communicate with or know ourselves within our own minds) in the absence of logic. The absence of logic indicates the not-real.
I'm sure Langan will correct me if I misrepresent his claims, and I certainly don't claim to be an expert on the CMTU. But I do think Langan is making an important point that attempts to answer a question about the emprical or observational sciences, a question that some might think is too obvious to even ask: Why should it work at all? Why should observational or experimental science hope to discover or explain anything about the real, other than some isolated, otherewise disconnected events or observations which we choose to call "facts"?
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gedanken
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posted 19. September 2003 13:23
In commenting that they “go to the heart of the matter”, I assume that Mark is not just pointing out what Langhan was saying, but also signaling agreement.
This seems to ignore the presentations of several noting the derivation of “logic” from experience—making logic “empirical” in its own verification at a level not requiring “logic” per se for its verification.
Part of the problem is that this presentation contained a simple short loop, assume certain logic, thus logic demonstrates that very logic by consistency with logic. Then consider why empirical observational science really “works”. It does so because its results appear to have a certain “reliability”, that they are consistently (though not perfectly) applicable to the natural world. We can repeat observations which have been determined to be consistent (e.g. “scientifically verifiable”) and they remain consistently verifiable.
Suppose that the world was not that way in that certain apparent “miracles” of physical causal relationships were regularly observed to occur—meaning that regularly observable breaking of physical causal relationships occurred on a regular and observable basis, though not universally or everywhere. In that case, would not “logic” still be consistently observable? “Logic” could still be found to be usable language methodology, without the empirical method being reliable. This unreliability of the empirical method would not depend on the correctness of logic per se, and thus empirical method is not derived from “logic”. I agree that the methods of empirical method and aspects of “logic” share common mappings of language to experience. But those mappings are precisely the demonstration of the empirical derivation of logic itself, not a demonstration of the opposite.
I think that all the discussions that assume that logic is somehow inherent in the human all ignore our growing up experience. Which of us did not grow up from a baby, and learn language and thought patterns from our environment? The one who can demonstrate that is one whom I will listen to in terms of the inherent qualities of “logic”.
quote:
... In other words, human minds have not invented or constructed logic for their own convenience or amusement; on the contrary, we have discovered it, and we have discovered it in the "real," that is, within the natural world, or as much of the natural world to which we are presently privy. And having discovered it, we have also discovered that it works in the natural sciences, because it inheres within the natural world itself (including our own brains).
Thus, as I understand Langan, logic is part of the "syntax" of the real, and if we wish to either perceive, know, or participate in the real, we must speak its syntax, and absent logic we cannot do that. In other words, we cannot communicate with, perceive, or know the real (or even communicate with or know ourselves within our own minds) in the absence of logic. The absence of logic indicates the not-real.
Sorry for long quote, but I disagree with the implication from first to second quoted paragraph fragments.
Now I do agree that humans have “discovered” logic—but I don’t necessarily agree that they therefore did not “constructed logic for their own convenience”. The issue is one of degree of consistency of mapping, and I think this may come through in what follows. One can construct the description of logical rules for one’s convenience, though there is a fairly reliable consistency of the mapping of those rules to experience of the real world. (In other words it is not “logic” as described in human language that is the essence of the consistent relationship property of the physical world.)
I agree that apparent “logical” consistency of physical reality must be an aspect of physical reality itself. In other words that the mapping of language aspects of “logic” and some properties of consistency of physical world must exist. But I in fact have disagreements with some aspects of “logic” per se. For example the boolean or two-valued truth level that is assumed in logical statements. In fact we use many shades of gradation of our meanings of “truth value” in our arguments, even layering truth in conceptual tiers within description of “logic” itself! (Note the class schemes needed to avoid logical inconsistencies like sets containing themselves as subsets.)
Consider a simple statement “he is in the room”. If he is outside the door, this is “false”. If he is inside the door, this is “true”. But if he is standing in the doorway—is it “true” or “false”? It is somewhere in between! Similarly for classification of organisms in species. Since these notions of logic seem to break down in terms of strictly obeying the “logical rules”, and we have to use our judgment in order to adjudicate those problems, I claim that logic per se is not nearly as certain and direct a mapping to the physical world as is claimed.
[ 19. September 2003, 13:44: Message edited by: gedanken ]
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Rex Kerr
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posted 19. September 2003 16:47
Let me answer Mark with an analogy.
In physics, it is common to use Green's functions to solve various mathematical problems. Basically, it involves considering how a system responds to an "impulse function", e.g. an infinitely short application of infinite force.
This is a very useful tool for predicting the behavior of systems, but it does not follow that it is an essential property of the universe. In fact, everything we know about the physical universe suggests that it is impossible for an impulse function to exist.
Impulse functions are a way to break down a process into somewhat arbitrary but easily computed pieces. One has to consider that logic may play a similar role.
[ 19. September 2003, 16:48: Message edited by: Rex Kerr ]
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Mark
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posted 20. September 2003 00:25
Thank you for your comments. You conjectured that I agreed with the two statements I quoted from Langan. With respect to the second, I think I agree. With respect to the first, I'm agnostic -- I neither agree nor disagree (I suppose I'm part of the excluded middle on that one), but I'm intrigued.
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This seems to ignore the presentations of several noting the derivation of "logic" from experience - making logic "empirical" in its own verification at a level not requiring "logic" per se for its verification.
I have no objection to an empirical verification of logic. That would seem to be perfectly legitimate. And, I think that if logic is a fundamental property of the real, as Langan claims, that empirical confirmation would not only be legitimate but that such confirmation would be invited by the claim itself. As noted, I'm agnostic as to that particular claim.
And I have no objection to the notion that logic cannot be used to verify itself. I'm not sure that logic can verify anything, nor do I think that it makes such a claim. Logic does not deal in the truth or falsity of propositions (including the proposition that "logic is true," or "logic is valid"). My understanding of logic is that it does not deal with the content (the truth values) of propositions, but only with the relations between propositions. Logic can be employed to pass on the truth value of a proposition, but only in relation to other propositions (and premises) known or granted to be true (or false).
Thus, the capacity of logic to pass on the truth value of a proposition depends entirely upon, for want of a better word, the "information" currently available. Given faulty premises, or "bad" information, logic can, and will, yield an incorrect result (although, given such available premises and information, the result would be, in a strictly logical sense, perfectly valid).
An example is offered of so-called gradients or gray areas: "He is in the room," (or, alternatively, the classification of species).
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Since these notions of logic seem to break down in strictly obeying the logical rules, and we have to use our judgment in adjudicating these problems, I claim that logic per se is not nearly so certain and direct a mapping to the physical world as is claimed.
I intuit two issues here. The first is the "mapping" issue. Correct me if I'm wrong, but I think you are proposing that, because the natural world presents what we consider gradients or gray areas, this suggests that the natural world is in some sense not strictly logical, and hence this fact requires scientists to use their judgment to discern the true state of affairs, or alternatively, just admit (at least tentatively) that there are insoluble gray areas.
I don't view this as a problem of logic. I see it as an issue of information. The propositions we have at hand may present a gray area; they may even present a contradiction or a paradox. If science confronts such a situation, I suggest that historically it seeks more or better information (or better models) to resolve the contradiction (but you can be sure that science is keenly aware that an apparent contradiction exists, and that such contradictions create discomfort).
I think Langan's point about "mapping" is an intelligibility issue. The mapping makes it possible for science to discern a gradient, a gray area, blind spots, apparent paradoxes, and the like. I don't necessarily agree that the presence of such gray areas invalidates the mapping as much as it suggests that all relevant information may not be on the table.
The second issue arises, I think, from your apparent contention that gray areas, gradients, apparent contradictions, and the like, pose a problem for logic, and therefore the mapping, though more or less reliable, is inconsistent and at times patchy. I think I disagree, if I understand you correctly. If there is a gray area, an unknown, a gradient, or the like, logic would treat such a state of affairs like any other proposition, and govern it like any other proposition in relation to other propositions that are known to be true. In fact, it is just this relation between propositions that alerts us to and permits us to discern apparent contradictions or gray areas.
Consider your thought experiment: "he is in the room." You are apparently asking logic to pass on the truth value of this statement, and, given that "he" is standing in the doorway, it cannot do this, since, in your opinion, logic has only two choices: in the room or outside the room. Since "he" is in the doorway, partly in the room and partly outside the room, logic provides no assistance in evaluating the validity of either proposition.
Actually, logic does not have to, and in fact cannot, make this choice. It can determine the truth value of the statement "he is in the room" only in relation to the given premises and other propositions it knows to be true. If the premises and other true propositions present a contradiction, then it is logic that discloses the contradiction.
Finally, you posed a thought experiment involving miracles, the random eruption of discontinuity in the universe, and suggest that logic (in some form) would survive the collapse of the empirical method. You then conclude that the empirical method is not derived from logic, but quite the contrary, that logic is derived from the empirical.
I'm not sure the issue is one of derivation, or if one is, or is not, derived from the other. I think Langan's point is one of dependence rather than derivation. In any case, we may debating what came first, the chicken or the egg. I'm willing to grant your point, but I can't help observing that if logic is derived from the empirical (by which I assume you mean observation of or confrontation with the natural world), this would seem to confirm Langan's thesis that logic is a fundamental property of the world (or the universe, or the real, or whatever we choose to call it).
With respect to Rex's post:
quote:
Impulse functions are a way to break down a process into somewhat arbitrary but easily computed pieces. One has to consider that logic may play a similar role.
I don't disagree. I assume you are referring to logic as computation. I will have to think about that. I'm sure there are participants on this board who are more literate than I concerning the relation between and/or identity of computation and logic.
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