"The God of the Mathematicians"

[Anselm33]

The title for this thread is from an article by David P. Goldman in the August issue of First Things. It’s about the religious beliefs of Kurt Godel, the most famous and probably the greatest mathematician of the 20th century, whose “incompleteness theorem” showed that algorithms will never replace intuition, i.e. it will be impossible to construct thinking machines from hardware/software. Here’s a link to the article:
faqs.org/periodicals/201008/2080027241.html
I’ll quote from the article: “But Gödel’s God is not the well-behaved deity of the old natural theology, or the happy harmonizer of the intelligent-design subculture. Gödel’s God hides his countenance and can be glimpsed only in paradox and intuition. God is not an abstraction but “can act as a person,” as Gödel once wrote, confronting those who seek him with paradox, uplifting man through glorious insights while guarding his infinitude from human grasp. Gödel’s investigations in number theory and general relativity suggest a similar theological result: that God cannot be reduced to a mere principle of the natural world.” How great!
Godel was also working on a revision of Anselm’s ontological proof for God. He phrased his revision of Leibniz’s version of the ontological proof in logical notation. To quote again from the article: “I (Goldman) doubt Godel believed he had found the ultimate and irrefutable proof of the existence of God. His deep interest in the ontological proof, rather was one facet of his commitment to defend Leibniz’ theism against the new Spinozans of mathematics and physics.” (emphasis added).
Worth reading, particularly for those open-minded agnostics/atheists with a mathematical background/interest.
Anselm.

 

[Barbkw]

My proof of God the Father, is found in the amount of order upon Earth. And then how refined the order is. Allowing humanity to survive here upon it.

 

[Touchstone]

The title for this thread is from an article by David P. Goldman in the August issue of First Things. It’s about the religious beliefs of Kurt Godel, the most famous and probably the greatest mathematician of the 20th century, whose “incompleteness theorem” showed that algorithms will never replace intuition, i.e. it will be impossible to construct thinking machines from hardware/software. Here’s a link to the article:
faqs.org/periodicals/201008/2080027241.html
I’ll quote from the article: “But Gödel’s God is not the well-behaved deity of the old natural theology, or the happy harmonizer of the intelligent-design subculture. Gödel’s God hides his countenance and can be glimpsed only in paradox and intuition. God is not an abstraction but “can act as a person,” as Gödel once wrote, confronting those who seek him with paradox, uplifting man through glorious insights while guarding his infinitude from human grasp. Gödel’s investigations in number theory and general relativity suggest a similar theological result: that God cannot be reduced to a mere principle of the natural world.” How great!
Godel was also working on a revision of Anselm’s ontological proof for God. He phrased his revision of Leibniz’s version of the ontological proof in logical notation. To quote again from the article: “I (Goldman) doubt Godel believed he had found the ultimate and irrefutable proof of the existence of God. His deep interest in the ontological proof, rather was one facet of his commitment to defend Leibniz’ theism against the new Spinozans of mathematics and physics.” (emphasis added).
Worth reading, particularly for those open-minded agnostics/atheists with a mathematical background/interest.
Anselm.

Just a quick correction – maybe it was something mistyped by you? Gödel incompleteness is not problematic for artificial intelligence or thinking machines at all. Douglas Hofstadter’s Gödel, Escher, Bach has a good, deep section or two on just that mistake.

IIRC, it was Lucas who pioneered that goof, but it was identified long ago. The problem is the classic bugaboo – presuming one’s conclusion. Lucas supposed that the mind was complete, a direct negation Gödel’s discovery! Gödel’s work laid to waste Bertrand Russell’s dreams of a “complete math”, but in so doing, it also delivered the coup de grace to the notion that the mind as a logical system is any better, or any more complete. The mind, demonstrably, acts as a consistent formal system (e.g., “true” and “false” are consistently exclusive), and thus is subject to the Gödel’s limitations – a machine has as much claim of superiority over the mind in this regard as vice versa.

If one presumes upfront that the mind is ineffable, non-formal, magical, then one doesn’t need to bother with Gödel (who discredits the idea anyway) – it is presumed!

I realize your main point was something else, there, but somewhere along the line, someone got way confused about Gödel, minds, and machines.

-TS

 

[OrdinaryMelkite]

Just a quick correction – maybe it was something mistyped by you? Gödel incompleteness is not problematic for artificial intelligence or thinking machines at all. Douglas Hofstadter’s Gödel, Escher, Bach has a good, deep section or two on just that mistake.

IIRC, it was Lucas who pioneered that goof, but it was identified long ago. The problem is the classic bugaboo – presuming one’s conclusion. Lucas supposed that the mind was complete, a direct negation Gödel’s discovery! Gödel’s work laid to waste Bertrand Russell’s dreams of a “complete math”, but in so doing, it also delivered the coup de grace to the notion that the mind as a logical system is any better, or any more complete. The mind, demonstrably, acts as a consistent formal system (e.g., “true” and “false” are consistently exclusive), and thus is subject to the Gödel’s limitations – a machine has as much claim of superiority over the mind in this regard as vice versa.

If one presumes upfront that the mind is ineffable, non-formal, magical, then one doesn’t need to bother with Gödel (who discredits the idea anyway) – it is presumed!

I realize your main point was something else, there, but somewhere along the line, someone got way confused about Gödel, minds, and machines.

-TS

Great post------but isn’t it TRUE that Godel’s Theorem only wors for Axiomatic Systems, Not Higher Mathematical Systems like Astrophysicism? This was absilutely brought in the Larry King “Stephen Hawking denies God could have created the Universe” episode.

BTW-----------when the Theorem forst came out, it so devastated certain circles that a College Professor allegedly committed suicide over it.

There goes Genius for you.

 

[Anselm33]

Just a quick correction – maybe it was something mistyped by you? Gödel incompleteness is not problematic for artificial intelligence or thinking machines at all. Douglas Hofstadter’s Gödel, Escher, Bach has a good, deep section or two on just that mistake.

IIRC, it was Lucas who pioneered that goof, but it was identified long ago. The problem is the classic bugaboo – presuming one’s conclusion. Lucas supposed that the mind was complete, a direct negation Gödel’s discovery! Gödel’s work laid to waste Bertrand Russell’s dreams of a “complete math”, but in so doing, it also delivered the coup de grace to the notion that the mind as a logical system is any better, or any more complete. The mind, demonstrably, acts as a consistent formal system (e.g., “true” and “false” are consistently exclusive)(emphasis added), and thus is subject to the Gödel’s limitations – a machine has as much claim of superiority over the mind in this regard as vice versa.

If one presumes upfront that the mind is ineffable, non-formal, magical, then one doesn’t need to bother with Gödel (who discredits the idea anyway) – it is presumed!
(emphasis added)
I realize your main point was something else, there, but somewhere along the line, someone got way confused about Gödel, minds, and machines.

-TS

You’re correct, I was sloppy in my characterization of Godel’s theorem. Actually, it was Turing who showed that algorithmic procedures could not solve every arithmetic problem (i.e. the Halting problem)…and Roger Penrose (“The Emperor’s New Clothes” and “Shadows of the Mind”) who has connected this with the impossibility of AI (algorithmic intelligence). The relevance of Godel’s theorem to Artificial Intelligence is also pointed out by John Searle (“The Mystery of Consciousness”). I’m not sure your statements in boldface are true; I don’t really understand the second one.
Oh, by the way, I don’t put any credence in Hofstadter’s opinions about mind or consciousness. GEB is a fun book for the Escher pictures and interesting for his comments about Bach, but that’s as far as it goes. Fr. Stanley Jaki has some devastating criticisms of Hofstadter, but I’ll have to look up the reference.

 

[Fr_of_Jazz]

You’re correct, I was sloppy in my characterization of Godel’s theorem. Actually, it was Turing who showed that algorithmic procedures could not solve every arithmetic problem (i.e. the Halting problem)…and Roger Penrose (“The Emperor’s New Clothes” and “Shadows of the Mind”) who has connected this with the impossibility of AI (algorithmic intelligence). The relevance of Godel’s theorem to Artificial Intelligence is also pointed out by John Searle (“The Mystery of Consciousness”). I’m not sure your statements in boldface are true; I don’t really understand the second one.
Oh, by the way, I don’t put any credence in Hofstadter’s opinions about mind or consciousness. GEB is a fun book for the Escher pictures and interesting for his comments about Bach, but that’s as far as it goes. Fr. Stanley Jaki has some devastating criticisms of Hofstadter, but I’ll have to look up the reference.

One book by Jaki that addresses the issue is Brain, Mind and Computers. Hofstadter references it in the bib. of Gödel, Escher, Bach p. 750 with the comment that “every page exudes contempt for the computational paradigm for understanding the human mind.”

Also Ernest Nagel and James R. Newman, Gödel’s Proof chap. VIII covers the question of the adequacy of the computational machine model of the human mind in the light of Gödel’s work and answers in the negative.

 

[Touchstone]

You’re correct, I was sloppy in my characterization of Godel’s theorem. Actually, it was Turing who showed that algorithmic procedures could not solve every arithmetic problem (i.e. the Halting problem)…and Roger Penrose (“The Emperor’s New Clothes” and “Shadows of the Mind”) who has connected this with the impossibility of AI (algorithmic intelligence). The relevance of Godel’s theorem to Artificial Intelligence is also pointed out by John Searle (“The Mystery of Consciousness”). I’m not sure your statements in boldface are true; I don’t really understand the second one.

OK, gotcha. Searle makes a variation of the same problem (not familiar with Penrose’s take on this), but I suppose that would be a topic for a different thread.

On the second quote, it’s just noting that per Lucas, and I think the other proponent was Storrs McCall, the argument reduces to something like this.

1. The mind is not a consistent formal system
2. Consistent formal systems are necessarily incomplete
3. Ergo, the mind is not necessarily incomplete (i.e. subject to Godel’s theorem).

All the probitive work is assumed in the premise (1). And as I said, we can watch the mind at work chugging along as a consistent formal system, discrediting (1) anyway. It’s an easy mistake to make; readers of Gödel take the idea that we can see the truth of some sentences outside their provability to be indicative of the mind’s magical abilities, or worse, its self-completeness. That is to completely miss the force of Gödel’s idea – the mind is just one formal system interacting with another, and that it can affirm sentences that are unprovable within system X just establishes the mind as an external context to X. The mind still exists as its own system, subject to the very same limitations as X, in its own frame.

Oh, by the way, I don’t put any credence in Hofstadter’s opinions about mind or consciousness. GEB is a fun book for the Escher pictures and interesting for his comments about Bach, but that’s as far as it goes. Fr. Stanley Jaki has some devastating criticisms of Hofstadter, but I’ll have to look up the reference.

Maybe you just didn’t understand Hofstadter? That’s not such a knock from me, who’s read it six or seven times now, and really only started to get some of the deeper stuff after multiple passes. I’m always intereste in critiques of Hofstadter… I’ll Google that up. I suspect Jaki (or others) may be battling a later book by Hofstadter, I am a Strange Loop, but I’ll see what comes up.

-TS

 

[Touchstone]

Great post------but isn’t it TRUE that Godel’s Theorem only wors for Axiomatic Systems, Not Higher Mathematical Systems like Astrophysicism? This was absilutely brought in the Larry King “Stephen Hawking denies God could have created the Universe” episode.

Insofar as you have math – a formal system that deterministically proceeds to proofs – the force of Gödel incompleteness applies. But much of science, although heavily reliant on math, is inductive, not deductive, which I think is the basic distinction you and/or the crew on the Larry King show are getting at. Wherever you have a deterministic calculus, though, you will have some sentences that are formally undecidable, and this applies just as much to the human mind as any computer.

BTW-----------when the Theorem forst came out, it so devastated certain circles that a College Professor allegedly committed suicide over it.

There goes Genius for you.

Yeah, that’s one of the reasons Gödel is a thinker of extraordinary interest for me. His idea was a huge sledgehammer.

-TS

 

[Anselm33]

OK, gotcha. Searle makes a variation of the same problem (not familiar with Penrose’s take on this), but I suppose that would be a topic for a different thread.

On the second quote, it’s just noting that per Lucas, and I think the other proponent was Storrs McCall, the argument reduces to something like this.

1. The mind is not a consistent formal system
2. Consistent formal systems are necessarily incomplete
3. Ergo, the mind is not necessarily incomplete (i.e. subject to Godel’s theorem).

All the probitive work is assumed in the premise (1). And as I said, we can watch the mind at work chugging along as a consistent formal system, discrediting (1) anyway. It’s an easy mistake to make; readers of Gödel take the idea that we can see the truth of some sentences outside their provability to be indicative of the mind’s magical abilities, or worse, its self-completeness. That is to completely miss the force of Gödel’s idea – the mind is just one formal system interacting with another, and that it can affirm sentences that are unprovable within system X just establishes the mind as an external context to X. The mind still exists as its own system, subject to the very same limitations as X, in its own frame.

Maybe you just didn’t understand Hofstadter? That’s not such a knock from me, who’s read it six or seven times now, and really only started to get some of the deeper stuff after multiple passes. I’m always intereste in critiques of Hofstadter… I’ll Google that up. I suspect Jaki (or others) may be battling a later book by Hofstadter, I am a Strange Loop, but I’ll see what comes up.

-TS

As far as Hofstadter goes, my problem with believers in strong AI (i.e. those who believe “Data” from Star Trek, or Asimov’s robots are a real possibility) is that there is so much evidence to the contrary that I don’t really try to go through their arguments in depth to pick out the fallacies–so little time, so much to learn.
Fr. Jaki has some trenchant points to make (he said in one essay that Hofstadter wrote him that his ideas were interesting, but didn’t bother to rebut them explicitly in his book),
but his idee fixe about Godel’s theorem applied to a “Theory of Everything” does not, I believe, hold water. Godel’s theorem would apply to a mathematical system. (e.g number theory, topology, etc.) In my experience in theoretical applications, you lift equations out and apply them to physical systems–e.g density matrix theory (using matrices, exponential operators, etc.) is not a mathematical system in itself. The situation may be different for the more mathematically abstruse stuff, as in M- theory (M standing variously for Membrane, Mystery or Muddle) which may have whole mathematical systems, but that’s not really science, since it isn’t empirically falsifiable.
(at least not yet, although there are some proposed qubit experiments that are supposed to show it will give the same entanglement results as predicted by QM).
One more point in this rambling discourse. I would tend to agree that the mind is not a consistent (logically) formal system. How would logic explain poetry, music, art and all that good stuff?
Anselm

 

[Touchstone]

As far as Hofstadter goes, my problem with believers in strong AI (i.e. those who believe “Data” from Star Trek, or Asimov’s robots are a real possibility) is that there is so much evidence to the contrary that I don’t really try to go through their arguments in depth to pick out the fallacies–so little time, so much to learn.

Fair enough. I’m a software developer by profession (or was for 20 plus years prior to more recent moves into managing tech teams, with, lamentably, not much actually coding, day to day), and one that has focused on evolutionary algorithms and machine learning (sometimes both together, even), so that has been an area I’m obviously fine with ‘sweating the details’ on. But admittedly, it’s a very deep and complex problem domain.

Fr. Jaki has some trenchant points to make (he said in one essay that Hofstadter wrote him that his ideas were interesting, but didn’t bother to rebut them explicitly in his book),
but his idee fixe about Godel’s theorem applied to a “Theory of Everything” does not, I believe, hold water. Godel’s theorem would apply to a mathematical system. (e.g number theory, topology, etc.) In my experience in theoretical applications, you lift equations out and apply them to physical systems–e.g density matrix theory (using matrices, exponential operators, etc.) is not a mathematical system in itself. The situation may be different for the more mathematically abstruse stuff, as in M- theory (M standing variously for Membrane, Mystery or Muddle) which may have whole mathematical systems, but that’s not really science, since it isn’t empirically falsifiable.

The ramifications of Gödel apply to mathematical systems, but maths are just a subset of the formal systems that the Incompleteness Theorem addresses. That means that any system which provides “deterministic finite automata” (i.e. a computable answer) is going to be subject to the paradox; some of its well-formed sentences in the system will be formally undecidable.

This does not mean that Gödel’s idea somehow has an empirical impact; nature is what it is, regardless. But per Gödel, our models are cannot hope to be complete as comprehensive models. They may fit empirically with observations perfectly, but they will still be incomplete in admitting, necessarily, non-computable computations in the system’s own calculus.

It’s worth pointing out that we are overloading on “completeness” and “everything” here. A physical “grand unified theory” or “theory of everything” in physics does NOT purport to provide all possible physical explanations – that’s not even a coherent challenge. Rather, the “theory of everything” coalesces the currently disparate spheres of physics – QM and GR. “Everything” is a bit casual, in that sense, and really for accuracy should use a word like “unified”.

No physicist supposes that even the most robust “theory of everything” would provide all answers to all questions.

(at least not yet, although there are some proposed qubit experiments that are supposed to show it will give the same entanglement results as predicted by QM).
One more point in this rambling discourse. I would tend to agree that the mind is not a consistent (logically) formal system. How would logic explain poetry, music, art and all that good stuff?
Anselm

Gödel’s ideas only apply to formal systems, and insofar as the things you mention are subjective valuations, I think those are also subject to scientific modeling (why do we like this poetry and not that?, for example), but that is beside the major point which is that once you move your focus to “good” and “like”, you have left the domain of knowledge altogether. This is the mind just engaging in something different and unrelated. But wherever one proposes to use a term like “true” or “false” as meaningful, one has necessarily placed oneself in back in “human logic system” mode, and thus subject to the problems Gödel identified.

-TS

 

[Anselm33]

Fair enough. I’m a software developer by profession (or was for 20 plus years prior to more recent moves into managing tech teams, with, lamentably, not much actually coding, day to day), and one that has focused on evolutionary algorithms and machine learning (sometimes both together, even), so that has been an area I’m obviously fine with ‘sweating the details’ on. But admittedly, it’s a very deep and complex problem domain.

Thanks for your comments… interesting ideas to chew on.

 

[Touchstone]

There are, I admit, applications of neural network learning that would almost convince me that AI is a possibility, for example, diagnosis of mammographies that beat radiology residents and are on a par with expert radiologists on a ROC curve.

One of the areas I’ve been deeply immersed in is network intrusion detection and anamolous/fraudulent network detection. There’ve been a handful of times when the algorithms my team and I wrote found interesting things it alerted us to, and thoroughly creeped me out in doing so. At some point the runtime reconfigurability of the learning engine figures things out in ways that are both way different than where we pointed, so to speak, and eerily close to the way a human might pick out subtle, odd patterns and cues.

But even so, that’s really a measure of the sophistication of our current technology, isn’t it? Gödel’s reminder stands nevertheless, for humans and any other formally consistent system: The universe of well-formed sentences within it will necessary contain (externally verifiable) truths that are formally undecidable within the system. Which means, more casually, there are true propositions in the human logic system that cannot be logically deduced. This, from reading lots of Gödel over the years, was the kernel of an idea that Kurt thought made some room for God – God as a truth that obtained independently, yet was not derivable within the system.

I’m not clear on the distinction you’re making here. You have a system of axioms and theorems, and can show (using the Cantor diagonalization technique and self-referential labelling) that one or another theorem may be true but is unprovable within the system. I’m not sure how that fits in with physics, where you lift equations and mathematical techniques to correspond to presumed real physical quantities (real in some ad hoc sense, such as quarks or strings). However, if what you say is true, that would vindicate Fr. Jaki’s assertion about a theory of everything not being possible.

I think Father Jaki is certainly correct on his understanding – there can be no theory of everything where such a theory is both self-consistent and complete. But this is either just a misunderstanding or an equivocation on what pshyicists mean by the term “theory of everything”. As above, it’s a much more practical, and physical “everything” being referred to by physicists, a unified theory that harmonize the sub atomic with the macroscaled, meaning a theory that can describe, predict and explain phenomena from bosons all the way up to galaxy clusters and beyond. A coherent, single model for space/time/energy/matter (STEM).

the bold-face stuff really threw me

OK, I said “[our models] may fit empirically with observations perfectly, but they will still be incomplete in admitting, necessarily, non-computable computations in the system’s own calculus”. I still like the conciseness of that, but I grant it may be confusing.

To put that another way, so long as we build a rule-based system (Gödel’s test was that the system be at least able to describe integer arithmetic, IIRC), that system will permit propositions which are formally undecidable based on the axioms of that system. The rules applied, so long as there are degrees of freedom in recombination that are at least sufficient to enable integer math, will necessarily produce hypotheses that cannot be judged by the set of rules that produced it.

I know that risks reiteration. But when we attach this to the real world, by matching our rules with empirical observations, so long as we have a formal calculus, no matter how successful that math may be in modeling and predicting in the real world, that same system cannot possibly “fill in the gaps”, analytically, providing answers for the propostions that are not directly mappable to empirical tests. SOME of them will remain formally undecidable. That’s the bummer Gödel launched upon Bertrand Russell and the rest of the world for ever and ever, who were thinking that if we could just get serious about mapping out our formal systems in a rigorous and complete way, we’d have all the answers. We cannot, even in principle. This is the nature of formal systems, as Gödel shows.

-TS

 

[Touchstone]

Anselm33:

I had thought that really devoutly physicalist scientists, like Steven Weinberg, would have the TOE predict the numerical values of physical constants, and everything, as in…"…we catch glimpses of a final theory, one that would be of unlimited validity and entirely satisfying in its completeness and consistency." (from Weinberg’s “Dreams of a Final Theory”, p, 6, as quoted by Fr. Stanley Jaki in “The Limits of a Limitless Science”)

This is just an historical artifact now, a marker on the timeline for M-Theory, and for Steven Weinberg and everyone else. Back in the early 1990s, when this quote came from Weinberg, physicists were in one of the heady periods of anticipation of an underlying mathematical rationale that indicated and predicted the cosmological constants. Witten, Susskind, Greene, and many other brilliant but lesser known minds were feverish chasing The Solution™, and it was thought that the breakthrough was imminent, upon them, ushering in a golden new era of physics where we had now mathematical modeled the fine tuning constants of the universe.

The breakthrough never came. After more than a decade of grueling, agonizing, painstaking work to resolve it, the various investigators came to rest on the conclusion that there was no one solution that uniquely predicted the observed parameters of the universe, but instead, the maths produced a landscape of available configurations, innumerable discrete configurations that resolved.

So those glimpses were an illusion (at least as a view to a theory that produced a unique set of constants that match our universe), and that idea has become obsolete, abandoned, and have given way to what Susskind calls “the cosmic landscape”, and to which Hawking, long dubious about Susskind’s ideas, has finally and famously capitulated.

That said, even if the world had been otherwise and physicists really did find the formula that predicted and demanded just the parameters we had, that still would not have been a ‘theory of everything’ in the sense Father Jaki is apparently resisting.

Referring to the bold-face part–but it’s still the mind working. Is there a part of the mind that is irrational, to which Godel’s theorem applies, and a part that’s logical, to which it does?

I’m not comfortable with using “rational/irrational” as the distinction. It’s axiomatic formalisms that Gödel Incompleteness applies to. Where the mind is not operating in a formal logic mode (and much of our cognition is NOT this), Gödel just doesn’t apply. Maybe the distinction would be the mind operating in “formal/informal” mode.

The mind serves many functions. But where it does invoke logical produce necessary conclusions (“if P, then Q; P; thus Q”), the mind is just as subject to the ramifcations of Gödelian Incompleteness as any other formal system. That the mind is a “wet machine” as opposed a silicon-based “dry machine” is immaterial to the nature of incompleteness in formal systems.

Thanks for your comments… interesting ideas to chew on.

Same to you, thanks for the thought invested, here.

-TS

 

[Anselm33]

This, from reading lots of Gödel over the years, was the kernel of an idea that Kurt thought made some room for God – God as a truth that obtained independently, yet was not derivable within the system.

That’s what really hits home for me!

I understand the rest of your explanations now and am disposed to agree with them (to the extent that my understanding is real). As a purely gut feeling, I don’t have a high regard for M-theory; I wouldn’t understand the math at that high a level, but reading Peter Voit’s book, “Not Even Wrong” (the title is after Pauli’s comment on a very bad paper he was reviewing “it’s so bad it’s not even wrong!”) my feeling is that M-theory is off into metaphysics, not empirically verifiable science.

Thanks again.

 

[Touchstone]

That’s what really hits home for me!

I understand the rest of your explanations now and am disposed to agree with them (to the extent that my understanding is real). As a purely gut feeling, I don’t have a high regard for M-theory; I wouldn’t understand the math at that high a level, but reading Peter Voit’s book, “Not Even Wrong” (the title is after Pauli’s comment on a very bad paper he was reviewing “it’s so bad it’s not even wrong!”) my feeling is that M-theory is off into metaphysics, not empirically verifiable science.

Thanks again.

Ok, fair enough. M-Theory is, at this point, not substantially distinguishable from theology. It’s likely not going to stay that way, as M-Theory does have ways, at least in principle, that can test it and falsify it, which Catholic theology, by contrast doesn’t. But in practice now, it’s not falsifiable and that is what should be clear and agreed upon as the primary consideration. I agree with the “not even even wrong” epithet for M-Theory for now, even as I expect this won’t always be the case. But remember the epithet obtains by lowering M-Theory to something like theology.

The ironic thing about Lucas, McCall and others who presuppose a mind that is “consistent and complete” in defiance of Gödel’s discovery about formal systems is that if they are right, they have put their theism further in the whole. For this is what you and I can understand about Gödel, per above, that incompleteness provides room for the “ghost in the machine”, so to speak. For McCall, the ramifications of his presupposition of the Gödel-defying mind are that there are no hidden, inaccessible pockets where God may abide. On McCall’s view, God is now “out in the open” if he obtains at all, and this is not good for theism, given theism’s challenges in demonstrating God in such ways.

-TS

 

[Charlemagne_II]

On Godel’s religion.

oidatherapy.org/articles/part_07f.htm

 

[sinnerdexter]

Quanta are contextual which means no classical computer can come close to simulating their behavior in real world situations.