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Retelling the Story of Science by Stephen M. Barr in Copyright (c) 2003 First Things 131 (March 2003): 16-25. The Atheism of the Gaps by Stephen M. Barr in Copyright (c) 1995 First Things 57 (November 1995): 50-53.
GODEL'S THEOREMS AND TRUTH by By Daniel Graves, MSL Where Does Truth Come From? by David Delk Einstein's Search & The Illusion of Reality
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Don't forget this one.  | ||||
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OK, guys, I think I follow, but how about one or both of you give us the "skinny" on this and why it has relevance in a forum on Christianity Today.  | ||||
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You got me, Phil. I guess he's trying to stipulate that the human mind is not a formal axiomatic model. Anyone who is married can already appreciate that. | ||||
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give us the "skinny" on this and why it has relevance in a forum on Christianity Today Do you want a consistent answer that is incomplete? Or, do you want a complete answer that is inconsistent? This is a hard problem . | ||||
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Thus any scientific cosmology, which is necessarily expressed in mathematical terms must fall short of being a theory that shows that the world must necessarily be what it is. There is always the possibility of the surprising, the unexpected, that points beyond this world for those who have eyes to see. OK, so math can't explain everything, and Godel shows why that's so. Is that it? Cool!  Now, JB, have you informed Stephen Hawking?  (Good one, Craig! ) | ||||
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Seriously, I've used the phrase, you can model the rules but you can't explain them , so many times that I thought I owed Godel a citation or two. | ||||
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Godelian thought has its application in Catholic moral theology, especially in the manuals that priests used to decide on penances for use in the confessional: Aristotelian kiss a kiss performed using techniques gained solely from theoretical speculation untainted by any experiential data by one who feels that the latter is irrelevant anyway Hegelian kiss dialiptical technique in which the kiss incorporates its own antithikiss, forming a synthekiss Wittgensteinian kiss the important thing about this type of kiss is that it refers only to the symbol (our internal mental representation we associate with the experience of the kiss--which must necessarilly also be differentiated from the act itself for obvious reasons and which need not be by any means the same or even similar for the different people experiencing the act) rather than the act itself and, as such, one must be careful not to make unwarranted generalizations about the act itself or the experience thereof based merely on our manipulation of the symbology therefor Godelian kiss a kiss that takes an extraordinarilly long time, yet leaves you unable to decide whether you've been kissed or not Socratic kiss really a Platonic kiss, but it's claimed to be the Socratic technique so it'll sound more authoritative; however, compared to most strictly Platonic kisses, Socratic kisses wander around a lot more and cover more ground. Kantian kiss a kiss that, eschewing inferior "phenomenal" contact, is performed entirely on the superior "noumenal" plane; though you don't actually feel it at all, you are, nonetheless, free to declare it the best kiss you've ever given or received. Kafkaesque kiss a kiss that starts out feeling like it's about to transform you but ends up just bugging you. Sartrean kiss a kiss that you worry yourself to death about even though it really doesn't matter anyway. Russell-Whiteheadian kiss a formal kiss in which each lip and tongue movement is rigorously and completely defined, even though it ends up seeming incomplete somehow. Hertzsprung-Russellian kiss Oh, Be A Fine Girl/Guy, Kiss Me. Pythagorean kiss a kiss given by someone who has developed some new and wonderful techniques but refuses to use them on anyone for fear that others would find out about them and copy them. Cartesian kiss a particularly well-planned and coordinated movement: "I think, therefore, I aim." In general, a kiss does not count as Cartesian unless it is applied with enough force to remove all doubt that one has been kissed. (cf. Polar kiss, a more well-rounded movement involving greater nose-to-nose contact, but colder overall.) Heisenbergian kiss a hard-to-define kiss--the more it moves you, the less sure you are of where the kiss was; the more energy it has, the more trouble you have figuring out how long it lasted. Extreme versions of this type of kiss are known as "virtual kisses" because the level of uncertainty is so high that you're not quite sure if you were kissed or not. Virtual kisses have the advantage, however, that you need not have anyone else in the room with you to enjoy them. Nietzscheian kiss "she/he who does not kiss you, makes your lust stronger." Epimenidian kiss a kiss given by someone who does not kiss. Grouchoic kiss a kiss given by someone who will only kiss those who would not kiss him or her. Harpoic kiss shut up and kiss me. Zenoian kiss your lips approach, closer and closer, but never actually touch. Procrustean kiss suffice it to say that it is a technique that, once you've experienced it, you'll never forget it, especially when applied to areas of the anatomy other than the lips. All of the above are only venial sins. There is one kiss that was a mortal sin and that was the French Kiss, now known as the Freedom Kiss. | ||||
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JB: Is all this Godel stuff a fancy schmancy way of saying that it's not just a case of the more we know the more we don't know? It's that there are important things we CAN'T know and thus God is not only possible but that something supernatural is probable. | ||||
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Let me suggest this. If there is a God as conceived by the Thomistic Metaphysic, then Godel's Theorem would be expected. Godel's Theorem does seem to suggest that, in addition to space-time, mass and charge, consciousness could be fundamental. It does seem to suggest that our brains have more than computational capability and could not be emulated by artificial intelligence. For all of the exception that a philosopher like Dennett might take regarding these ideas, to me, he hasn't satisfactorily overcome the more rigorous analyses of consciousness by David Chalmers . There does seem to be an ontological discontinuity occupying the epistemic gap. It all makes for some rather compelling inferences. However, as we move from math to philosophy to metaphysics, we shouldn't over-reach in our conclusions. So while we would expect Godel's Theorem to be operative from a theistic view, the fact that it exists doesn't, at the same time, lead only to theism. Bertrand Russell might have eaten a little crow though. pax, jb | ||||
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From Retelling the Story of Science: Its adherents see science as having a mission that goes beyond the mere investigation of nature or the discovery of physical laws. That mission is to free mankind from superstition in all its forms, and especially in the form of religious belief. I don't know about the rest of you, but this was a major revelation for me and one of the most important things I've learned here at SP. Part of it I may have indeed suspected, but I never knew how to put it into words. The world is usually painted as a divide between the "rational" and the "religious", meaning those who believe in scientific facts and those who believe in fantasy. But as I've delved deeper into this issue I've found that this type of reasoning is just another attempt to win the debate by phrasing the argument in highly prejudicial ways (and thus my liberal "Spider Senses" instinctively were tingling at this familiar tactic). It's not a matter of one being either strictly beholden to science or else one is therefore a raving evangelist. In fact, the strangest of realizations has occurred to me - the reverse seems truer: those who profess a strict adherence to materialism are perhaps engaging in as much if not more of a leap of faith as any Christian. And while in my own mind I'm not sure about the details of any religion, I'm quite sure that in principle those who are religious have as good, if not better, a rationale for believing in things other than materialism than those who believe only in materialism. This whole issue has flip-flopped for me. I didn't plan this. I'm not particularly religious. It just seems the logic, at least for me, is inescapable. | ||||
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So while we would expect Godel's Theorem to be operative from a theistic view, the fact that it exists doesn't, at the same time, lead only to theism. What is theism but our attempt to express in necessarily imprecise language and ideas that which is inherently outside of our realm but is necessary to it? So I would say that by definition Godel's Theorem leads to theism in the broadest sense. Looking at the Big Picture it should come as no surprise that there are so many religions that have vast differences but that also have much in common. And if consciousness is fundamental but not material then perhaps we have a bridge to whatever is outside the material world. Therefore it should come as no surprise that imprecise descriptions of it are so different and yet have so many themes in common. | ||||
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It's not a matter of one being either strictly beholden to science or else one is therefore a raving evangelist. In fact, the strangest of realizations has occurred to me - the reverse seems truer: those who profess a strict adherence to materialism are perhaps engaging in as much if not more of a leap of faith as any Christian. And while in my own mind I'm not sure about the details of any religion, I'm quite sure that in principle those who are religious have as good, if not better, a rationale for believing in things other than materialism than those who believe only in materialism. This whole issue has flip-flopped for me. I didn't plan this. I'm not particularly religious. It just seems the logic, at least for me, is inescapable. Brad, that is really a very profound statement there. Though I am religious, I come to the same logical conclusion. To me, to deny the "beyond" science realm is to deny a part of ourselves because WE are beyond science. To deny the mystical (or I suppose the strict science crowd would call it superstition) is to deny the very thing that makes us above animals or plants...the soul. Thanks....that was a great statement to read this morning .JB always seems to bring out the deeper part of thinking in us...lol...this is a great board! Blessings, Terri | ||||
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Curiously, Roger Penrose, renowned physicist, makes a very strong case against artificial intelligence using Godel, but he still clings to a non-algorithmic explanation for consciousness that is rooted in quantum physics. While most folks find Penrose's arguments against strong AI very compelling, I don't think many scientists think that he does a very good job at all in his attempt to rescue consciousness a la materialism using quantum physics. He gets rather far out. My personal feelings are that, as far as neurobiology and neurochemistry go, we pretty much have all the science we need to understand basic brain biology and the "easy problems" of consciousness. What Penrose has done, brilliant mathematician and physicist that he is, is paint himself and other materialists in a corner that not even Daniel Dennett can get them out of. As it is, Dennett only substantively addresses the easy problem of consciousness - sensation, awareness, perception, etc - but doesn't satisfactorily address the hard problem, which is subjective experience, though he claims he has by reducing same to its function, which doesn't cut it for most people. In a nutshell, Dennett well addresses syntactical consciousness but no one has truly addressed semantical consciousness. So, yes, Godel's Theorem does make for some rather compelling theistic inferences, which become even more compelling when taken together with all the other inferences that Thomism presents: causal, cosmological, ontological, teleological, impossible being, possible being, necessary being and on and on. For materialism, so far, it seems to present more problems than it solves as far as materialism goes. Penrose's quantum gymnastics perhaps reveal how silly some very intelligent people can become when married a priori to a worldview. | ||||
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this is a great board! Dear Yoko, The Fab Four would not be the same without YOU! Love, John | ||||
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I'm quite sure that in principle those who are religious have as good, if not better, a rationale for believing in things other than materialism than those who believe only in materialism. Setting the metanarratives of religion aside, because of quantum weirdness, simultaneity, synchronicity, anomalous phenomena, nonlocality, superluminality, possible implicate order, nonalgorithmic consciousness, possible morphic resonance, subtle energy phenomena, the causal inferences of possible and necessary being, the design inferences of possible irreducible complexity, epistemological inferences from our fundamental trust of uncertain reality, etc etc etc all pointing toward a possible nonenergetic causation that very much involves informational dynamics ---- it seems to me that openness to nonspatial, atemporal, immaterial and nonenergetic phenomena is the safer bet, that in addition to space-time, mass and charge, there is another fundamental that is unknown and, in a Godelian sense, unknowable, EXCEPT through inference (which is how we know MOST of what we know, not uncritically and not without good methodology). As we all know, to pooh-pooh what can be known through inference not only flushes metaphysics but much of modern science, too, especially physics and medicine. This other influence, this other fundamental, be it consciousness or otherwise, I don't suppose necessarily implies the supernatural but does suggest an otherwise non-natural causality. Enter Aristotle with his system of causation: material, efficient, formal and final causation. As Yoko cut to the chase, enter the soul. I would suppose it is not non-natural causality per se that would put materialists off but the spectre of what might follow the non-natural camel's head into their materialist tent! Truly, the door to the plausibility of the supenatural would be flung wide open (this notwithstanding the windows have been open all along and the breeze blowing in at that!) So, as I said before, I'd be Catholic, after critical analysis and sober reflection, even if not for its dogmatic theology, for its coherent metaphysic and such a natural theology as leads one to the threshold of revealed theology. Then, once considering how Thomas Aquinas and the brethren got all of the metaphysical and scientific stuff right, I might concede to Catholicism no small measure of reliability, credibility and authoritativeness. Then, not oblivious to what they have clearly gotten wrong over the years, I might consider how they have mostly gotten everything pretty much right, metaphysically and scientifically. Then, once presented with the intransigent historical record vis a vis dogmatic theology and revelatory claims of the New Testament, as explicated by rigorous exegetical analysis, historical/literary and form criticisms, coupled with the most coherent and consistent and congruent and consilient and consonant metaphysic around (read ROBUST) and as further bolstered by the signs and wonders (read MIRACLES) as have occurred even in modern times (see Miracle A Day -- as updated every two weeks) --- this sentence is so long, I forgot where I was headed. pax, jb | ||||
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So, yes, Godel's Theorem does make for some rather compelling theistic inferences, which become even more compelling when taken together with all the other inferences that Thomism presents: I realize you're only being as cautious and precise as you can, JB, so as to not make some of the same mistakes others have made. That's good and I have no wish to degrade the discussion with rants that are similar but opposite to those of the materialists. But the difference is that I do not deny the existence of the material world even though there is more than ample evidence to put it into question. I'm just giving them a little of their own medicine. Hardly surprising considering the source. | ||||
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...it seems to me that openness to nonspatial, atemporal, immaterial and nonenergetic phenomena is the safer bet, that in addition to space-time, mass and charge, there is another fundamental that is unknown and, in a Godelian sense, unknowable, EXCEPT through inference Let us topple that statue, or at least put it a little of kilter, as well. | ||||
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So, playing this out a little more, Godel's Theorem expresses the Incompleteness Principle of representation or description stipulating that nothing can ever be described finally and exhaustively. There is a perpetual tradeoff of completeness and consistency. Godel proved that some things can neither be proven to be nor be proven not to be. This is saying that any symbolic system based on deriving truth from axioms is incomplete. It is difficult to draw a distinction between the symbolic representations of the universe in our minds and the universe itself, between any supposedly complete system and reality. Any model of reality that we can contrive is contained within reality and will therefore necessarily always be smaller than reality or, conversely, reality would have to be larger than itself. It is important to remember that there are statements that are true within a system but that they simply cannot be proven true within the system. In math, such statements can be proven true once we Jump Outside The System [JOTS] but then we inhabit a new system based on axioms that can never be proven within the system itself until we JOTS. brb | ||||
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Ahaha...nothing to add, but I just had to comment that I've never seen a "brb" on a bulletin board...LOL! *Yoko, huh? Don't I have an apartment in NY or something?!?* | ||||
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Oh, Yoko, I'm just now getting to the juicy part It seems to me that one of the lessons of JOTS is beginner's mind ! | ||||
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So, let's keep running at the virtual mouth here in free association mode Jumping Outside of the System, Beginner's Mind and Thinking Outside of the Box, in light of Godel's Theorem, involve more than just moving back and forth between right and left brain hemispheres, alternating between cognition and intuition. It involves moving from the realm of the coding and indexing of information according to syntax and algorithm to the realm of the semantical and the meaningful. To some extent, it appears to me that the line of demarcation between the easy problem of consciousness (sensation, perception, objective awareness) and the hard problem (subjective awareness, awareness of awareness) is clearly the line between the syntactical and the semantical, the computational/algorithmic and noncomputational/nonalgorithmic. One consciousness thus seems to dwell in the space-time-matter-energy plenum while the other seems to transcend it. When you get right down to it, I suppose I am suggesting that the nondual awareness seems like Zen while the dual awareness (awareness of awareness, in one manner of speaking) seems like classical western philosophy (Aristotle, Plato, Aquinas et al). One way to separate Zen from other awareness, then, might be to think of it in terms of simply being there, might be in that act of awareness that precedes judgment, that moment between stimulus and the processing that occurs prior to response. It is, from this analysis, not so much a deconstructive moment as it is a preconstructive moment, though for a person who dwells in a dualistic mindset, inhabiting their symbolic world rather than the real world, it would clearly seem deconstructive. What gets deconstructed, however, is not reality but our model of reality, a model which is necessarily incomplete because of the perpetual self-referentiality involved in Godel's Theorem, the proof of the model's correspondence to reality collapsing as a consequence of the system itself. What happens, then, in the case of the dual vs nondual, for instance, is not so much that one system must be true and the other false, but that as competing systems they both could appear true and neither could be proven false. Godel's Theorem doesn't so much prove materialism is false but rather says that its presupposition cannot be proven to be true or not true from within the system. Same, however, for immaterialism. Materialists can thus proceed with their inference that a materialist monism may be true but just not provable, but so can ontological dualists. Hence the stalemate we've witnessed for centuries. The problem with a strict atheistic materialism, therefore, is that it seems to be invoking some type of epistemological superiority by claiming that it does not Jump Outside of the System, does not attempt, iow, to transcend the space-time plenum. Their ontology and epistemology could well be true and they feel that it is at the level of inference, what they feel is compelling inference. They haven't proven, however, and cannot, ever, prove their metaphysic from within the system because their model of reality is as self-referential as anyone else's, is incomplete. To the extent they invoke completeness they sacrifice consistency (recall their paradoxical and nowhere anchored unjustified trust in uncertain reality vis a vis Kung). The JOTS who invoke transcendence aren't any better off, proof-wise. So, it comes back down to inferences and what people find compelling with the built-in Godelian constraints on our symbolic reasoning. This is why the problem of consciousness and the question of artificial intelligence is pivotal for choosing a worldview that is compelling. Notwithstanding that Godel's Theorem makes choosing between materialism and immaterialism a priori impossible, still there is that matter of practical proof or inference. To the extent that consciousness is a product of emergence, reductionistically resulting from a something more from nothing but process, then it would be expected that consciousness is computational and algorithmic. Artificial Intelligence could, in principle, emulate human consciousness. Our own subjective experience reveals semantical processes, though, that are not computational and not algorithmic. Even Penrose holds this to be true, while Dennett just ignores it. A computer cannot be set up, in principle, to have a self-reflexive awareness whereby the axioms that guide its algorithms can be proven within the system. You cannot get the something more of an axiom from a computer when you start with the nothing but of an algorithm. From this we can infer the immateriality of that aspect of consciousness, if the implications of Godel's math hold up in metaphysics and engineering systems design. This implies ontological discontinuity, dualism. It is what drives our inferences regarding the distinction between necessary being and possible being, a distinction that could be quite true but which cannot, in principle, be proven, from within our models of reality. Out of space, time, mass, charge and consciousness, since it is consciousness that most eludes us, one might surmise that it is going to be the most fundamental of all. Even this consciousness would only be an analog, however, to any supernatural consciousness, though I'd have to think we are approaching that nexus where information enters the system as formal causation, as soul. I'm a soul man, dah dut dah duh dah dut dah duh | ||||
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God does not play dice. Einstein The good Lord is subtle, but He is not malicious. Einstein Stop telling God what to do. Bohr God not only plays dice, but sometimes he throws them where they cannot be seen. Hawking As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to the reality. Einstein As the island of our knowledge grows, so does the shore of our ignorance. John Wheeler As we have discovered more and more fundamental physical principles they seem to have less and less to do with us. Steven Weinberg Dennett seemed to doubt whether even superintelligent machines would ever fully comprehend themselves. Trying to know themselves, the machines would have to become still more complicated; they would thus be caught in a spiral of ever-increasing complexity, chasing their own tails for all eternity. John Horgan More Quotes in this Book Review: John Horgan, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age by John L. Roeder | ||||
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