Doesn’t address “the” hard problem. The problem that Penrose is trying to solve , how the mind grasps mathematical truth, isn’t much of a problem if you reject mathematical realism.
Their theory has two parts, a neurobiological hypothesis and a “physics of cognition” hypothesis. The neurobiological hypothesis is that neuronal microtubules are information processors that contribute substantially to cognition (Hameroff was advocating this long before he united with Penrose), and specifically that they are quantum information processors. The “physics of cognition” hypothesis is that the relevant quantum dynamics includes a non-Turing-computable quantum-gravitational selection of eigenstates, which in its deepest form manifests as the metamathematical ability to transcend any particular axiom system via conscious insight into the meanings of the axioms.
So from the perspective of consciousness studies, this is one more materialistic theory of consciousness which makes specific (and unusual) claims as to which material entities and processes are involved in consciousness. You have to add a philosophical gloss (such as a metaphysics) to make it address a philosophy-of-mind problem like the hard problem. Hameroff’s own interpretation is a kind of Tegmarkian panpsychism in which the physical world is made of Platonically real mathematics, but all those mathematical objects have a qualic aspect, and all qualia are some form of fundamental physics. This is not an outlook that he has developed systematically, in a way that would allow you to go through all the states of consciousness and identify the corresponding quantum states, or alternatively, to go through all quantum states and identify their conscious content and aspects.
Nonetheless, suppose that the theory (or any other “microphysical” theory of consciousness) had reached that level, presenting a comprehensive dictionary that allowed back-and-forth translation between physical and qualic descriptions of the fundamental states of the world. Would that provide an answer to the hard problem of consciousness? I think it would be progress, but the hard problem actually requires even more than that. The hard problem asks, why do physical states x, y, z have a conscious aspect? Even if we graduate to a neutral-monist theory-of-everything where every possible state can be interpreted “physically” or “qualically”, this duality might still look like a brute fact with no further explanation. Answering the hard problem would now require explaining why our world has a dual-aspect ontology in which one aspect is consciousness—and at that point you might be getting into: the theory of possible worlds in an ontological and not just logical sense; the anthropic principle as a constraint on the metaphysics, and not just the physics, that you can find yourself inhabiting; and perhaps Neoplatonic speculations about Leibnizian first causes and Hegelian metaphysical necessities (or some equally deep metaphysical thinking).
Along with the hard problem, you mention the problem of accounting for knowledge of mathematical truth. Penrose is indeed tackling an aspect of that problem, but with the very specific priority of explaining how mathematical knowledge is possible, given the constraints on knowledge implied by Gödelian theorems. The basic version of those theorems applies to Turing-equivalent computational systems working according to some set of axioms; but even if you add “oracle functions” as extra computational primitives, you can still Gödelize the resulting entity and construct undecidable propositions.
Penrose’s response has been to suppose that there is something transcendent about fundamental physical dynamics—transcendent in the way that Cantor’s Absolute Infinite transcends all the concrete notions of the transfinite—that is at work in the material processes underlying metamathematical cognition, and that specifically this occurs in a quantum gravitational process that is also responsible for “state vector reduction” or “collapsing the wavefunction”. It’s an idea that certainly wins points for imagination, it might be appealing to anyone who has an intuition of limitlessness or transcendence as being inherent in fundamental reality, and the world of 4-manifolds that one expects in quantum gravity does actually include undecidable propositions.
There aren’t many people who have embraced this approach to the challenge of Gödelian limits to physically based thought. The most common approach is to suppose that the human brain simply is genuinely finite in its capabilities and that there are mathematical facts that inherently transcend us. “Busy beaver numbers” are the main concretization of this, especially when used to rank the power of set-theory axioms.
My own view is that the finitist approach is the sensible one, but Cantorian infinitism is not totally out of the question; but also that both sides of this debate are un-rigorous when it comes to the nature of knowledge. Philosophical rigor requires more precision about the nature of intentionality than either side employs. The wellspring of the debate is a confrontation between phenomenology—the phenomena of mathematical reasoning and mathematical knowledge—and natural science—the apparent finitude of the information processing that can occur in the human brain. But neither side can anchor its intuitions in a clear picture of how mathematical thinking is related to neuronal processes, or even a principled answer to the general Searlean question of how brain states “represent” or manage to “be about” mathematics. Rigorous mathematical results about the capabilities of formal systems or computer programs, are then mapped onto the brain/consciousness/math situation in vague or speculative ways.
This isn’t just a quibble, because knowledge of what axioms are about—access to semantic and not just syntactic information, so to speak—actually allows one to transcend Gödelian limits. Penrose cites the work of Solomon Feferman, e.g. his “completeness theorem” which says that everything in arithmetic is decidable if, along with the Peano axioms, you allow transfinitely iterated “reflection” on them. This shouldn’t be surprising, because Gödel theorems and Gödel propositions are constructed precisely by appealing to metamathematical knowledge of what a formal system is actually about.
You could say that the Feferman completeness of human thought, is what allows us to prove the Gödel incompleteness of a formal system; and the debate between Penrose and cog-sci common sense, is a debate over whether human thought isn’t literally Feferman-complete, but only extends some basic axiom system by a few rounds of reflection; or whether we have a physical ontology which really does allow a thinking system to be, in principle, fully Feferman-complete.
Let me round this out with some miscellaneous final thoughts.
I said Hameroff espouses a Tegmarkian panpsychism; Penrose on the other hand, is known for suggesting a vague circular relationship between three worlds of mathematics, physics, and consciousness. One might say that Hameroff asserts the identity of the three worlds and thereby collapses them into one, whereas Penrose maintains an agnostic attitude that the truth about it may be subtle and elusive. Regarding how all this is still not yet a solution to the hard problem per se, I think Chalmers writes about this in some of the more esoteric sections of his work.
My own interest in quantum mind theories derives especially from the belief that physical theories of mind have a severe sorites problem (one dimension of which you can see in this ongoing discussion), and that quantum entanglement, and fundamental physics in general, offer a way out in the form of entities which are “wholes” with complex internal structure and non-arbitrary boundaries. And my interest in microtubule-based theories of quantum mind, is because they are still the best candidate I’ve seen for how this quantum holism could actually be a part of conscious cognition (since the movement of quanta around the cylinder of the microtubule, could produce topological quantum states robust against room-temperature decoherence). I’m able to draw a line between the bare idea of quantum states in the microtubule, and the more elaborate theorizings of Hameroff and Penrose. But I still like to understand their ideas in detail.
Weinstein’s idea has been devastatingly critiqued.
The observations in that paper, while technically valid, are only the tip of the iceberg. They are not proofs that Weinstein’s theory is untenable, they are simply questions to which the theory must have an answer. The most famous critique from the paper is usually presented as a proof that Weinstein’s shiab operator cannot exist. What is actually the case, is that the existence of the operator requires the complex form of his gauge group; and a complex gauge group, because non-compact, is argued to have physically untenable consequences. However, Weinstein is happy to bite the bullet and embrace the non-compact gauge group, because he thinks he has a mechanism that will de facto reduce it to a compact subgroup. A variety of such mechanisms are already used in other theories.
Weinstein hasn’t helped himself by refusing to answer those questions (or at least, by refusing to respond to that author). Between his public relations strategy, and all the usual reasons why new ideas have an uphill struggle, even in theoretical physics, the public discussion of his theory is in a dismal state. However, there’s enough information and insight out there, that a much deeper assessment is now possible. But rather than go on about it here, I’ll just link to the blog I created in order to work through it all.
The “physics of cognition” hypothesis is that the relevant quantum dynamics includes a non-Turing-computable quantum-gravitational selection of eigenstates, which in its deepest form manifests as the metamathematical ability to transcend any particular axiom system via conscious insight into the meanings of the axioms.
OK, but that’s another unnecessary problem, because you don’t have to regard the mind as a (consistent) axiomatic system.
Along with the hard problem, you mention the problem of accounting for knowledge of mathematical truth. Penrose is indeed tackling an aspect of that problem, but with the very specific priority of explaining how mathematical knowledge is possible, given the constraints on knowledge implied by Gödelian theorems.
There’s no way of confirming that we have a kind of knowledge that goes beyond “proveable from unfounded axioms” and “seems to work in practice”.
Perhaps we aren’t as limited as a single formal system, but then we might be using cheap tricks like switching between systems, using intuition, or tolerating inconsistency.
There aren’t many people who have embraced this approach to the challenge of Gödelian limits to physically based thought. The most common approach is to suppose that the human brain simply is genuinely finite in its capabilities and that there are mathematical facts that inherently transcend us.
From the anti realist point of views, If there are facts that transcend everyone, they aren’t facts. They aren’t sitting somewhere gathering dust for eternity, they just aren’t there at all.
My own view is that the finitist approach is the sensible one,
Which finitist approach? An anti realist can regard infinties as suitable objects of study, no less real than other numbers.
The wellspring of the debate is a confrontation between phenomenology—the phenomena of mathematical reasoning and mathematical knowledge—and natural science—the apparent finitude of the information processing that can occur in the human brain.
Perhaps, but the phenomenological argument is really weak. Phenomenology is strong evidence of phenomenality..if it things seems to you to be certain way,then that is evidence that somethings seems so some way to you...but weak evidence of anything else.
But neither side can anchor its intuitions in a clear picture of how mathematical thinking is related to neuronal processes,
There isn’t the slightest evidence that mathematical thinking is non neuronal or otherwise unusual … from.neuroscience.
or even a principled answer to the general Searlean question of how brain states “represent” or manage to “be about” mathematics.
Under the form of anti realism known as fictionalism , there is no problem...the brain simply conjures up mathematical objects like dragons and werewolves.
It is the form of realism known as Platonism that causes the problems, since it needs to explain how immaterial entities affect thought, and therefore neural activity.
You could say that the Feferman completeness of human thought, is what allows us to prove the Gödel incompleteness of a formal system;
I wouldn’t:understanding GIT might require some leveling meanness, but doesnt require transfinite levels....
and the debate between Penrose and cog-sci common sense, is a debate over whether human thought isn’t literally Feferman-complete, but only extends some basic axiom system by a few rounds of reflection;
...as you say.
My own interest in quantum mind theories derives especially from the belief that physical theories of mind have a severe sorites problem (one dimension of which you can see in this ongoing discussion)
That’s another unnecessary problem. There’s actually lots of evidence that consciousness is non binary.
* Drowsiness, states between sleep.and waking.
* Autopilot and flow states , where the sense of a self deciding actions isn absent.
More rarely there are forms of heightened consciousness: peak experiences, meditations jñanas, psychedelic enhanced perceptions , etc.
, and that quantum entanglement, and fundamental physics in general, offer a way out in the form of entities which are “wholes” with complex internal structure and non-arbitrary boundaries.
Like Chalmers , I don’t see why any mathematical structure would have associated qualia.
Their theory has two parts, a neurobiological hypothesis and a “physics of cognition” hypothesis. The neurobiological hypothesis is that neuronal microtubules are information processors that contribute substantially to cognition (Hameroff was advocating this long before he united with Penrose), and specifically that they are quantum information processors. The “physics of cognition” hypothesis is that the relevant quantum dynamics includes a non-Turing-computable quantum-gravitational selection of eigenstates, which in its deepest form manifests as the metamathematical ability to transcend any particular axiom system via conscious insight into the meanings of the axioms.
So from the perspective of consciousness studies, this is one more materialistic theory of consciousness which makes specific (and unusual) claims as to which material entities and processes are involved in consciousness. You have to add a philosophical gloss (such as a metaphysics) to make it address a philosophy-of-mind problem like the hard problem. Hameroff’s own interpretation is a kind of Tegmarkian panpsychism in which the physical world is made of Platonically real mathematics, but all those mathematical objects have a qualic aspect, and all qualia are some form of fundamental physics. This is not an outlook that he has developed systematically, in a way that would allow you to go through all the states of consciousness and identify the corresponding quantum states, or alternatively, to go through all quantum states and identify their conscious content and aspects.
Nonetheless, suppose that the theory (or any other “microphysical” theory of consciousness) had reached that level, presenting a comprehensive dictionary that allowed back-and-forth translation between physical and qualic descriptions of the fundamental states of the world. Would that provide an answer to the hard problem of consciousness? I think it would be progress, but the hard problem actually requires even more than that. The hard problem asks, why do physical states x, y, z have a conscious aspect? Even if we graduate to a neutral-monist theory-of-everything where every possible state can be interpreted “physically” or “qualically”, this duality might still look like a brute fact with no further explanation. Answering the hard problem would now require explaining why our world has a dual-aspect ontology in which one aspect is consciousness—and at that point you might be getting into: the theory of possible worlds in an ontological and not just logical sense; the anthropic principle as a constraint on the metaphysics, and not just the physics, that you can find yourself inhabiting; and perhaps Neoplatonic speculations about Leibnizian first causes and Hegelian metaphysical necessities (or some equally deep metaphysical thinking).
Along with the hard problem, you mention the problem of accounting for knowledge of mathematical truth. Penrose is indeed tackling an aspect of that problem, but with the very specific priority of explaining how mathematical knowledge is possible, given the constraints on knowledge implied by Gödelian theorems. The basic version of those theorems applies to Turing-equivalent computational systems working according to some set of axioms; but even if you add “oracle functions” as extra computational primitives, you can still Gödelize the resulting entity and construct undecidable propositions.
Penrose’s response has been to suppose that there is something transcendent about fundamental physical dynamics—transcendent in the way that Cantor’s Absolute Infinite transcends all the concrete notions of the transfinite—that is at work in the material processes underlying metamathematical cognition, and that specifically this occurs in a quantum gravitational process that is also responsible for “state vector reduction” or “collapsing the wavefunction”. It’s an idea that certainly wins points for imagination, it might be appealing to anyone who has an intuition of limitlessness or transcendence as being inherent in fundamental reality, and the world of 4-manifolds that one expects in quantum gravity does actually include undecidable propositions.
There aren’t many people who have embraced this approach to the challenge of Gödelian limits to physically based thought. The most common approach is to suppose that the human brain simply is genuinely finite in its capabilities and that there are mathematical facts that inherently transcend us. “Busy beaver numbers” are the main concretization of this, especially when used to rank the power of set-theory axioms.
My own view is that the finitist approach is the sensible one, but Cantorian infinitism is not totally out of the question; but also that both sides of this debate are un-rigorous when it comes to the nature of knowledge. Philosophical rigor requires more precision about the nature of intentionality than either side employs. The wellspring of the debate is a confrontation between phenomenology—the phenomena of mathematical reasoning and mathematical knowledge—and natural science—the apparent finitude of the information processing that can occur in the human brain. But neither side can anchor its intuitions in a clear picture of how mathematical thinking is related to neuronal processes, or even a principled answer to the general Searlean question of how brain states “represent” or manage to “be about” mathematics. Rigorous mathematical results about the capabilities of formal systems or computer programs, are then mapped onto the brain/consciousness/math situation in vague or speculative ways.
This isn’t just a quibble, because knowledge of what axioms are about—access to semantic and not just syntactic information, so to speak—actually allows one to transcend Gödelian limits. Penrose cites the work of Solomon Feferman, e.g. his “completeness theorem” which says that everything in arithmetic is decidable if, along with the Peano axioms, you allow transfinitely iterated “reflection” on them. This shouldn’t be surprising, because Gödel theorems and Gödel propositions are constructed precisely by appealing to metamathematical knowledge of what a formal system is actually about.
You could say that the Feferman completeness of human thought, is what allows us to prove the Gödel incompleteness of a formal system; and the debate between Penrose and cog-sci common sense, is a debate over whether human thought isn’t literally Feferman-complete, but only extends some basic axiom system by a few rounds of reflection; or whether we have a physical ontology which really does allow a thinking system to be, in principle, fully Feferman-complete.
Let me round this out with some miscellaneous final thoughts.
I said Hameroff espouses a Tegmarkian panpsychism; Penrose on the other hand, is known for suggesting a vague circular relationship between three worlds of mathematics, physics, and consciousness. One might say that Hameroff asserts the identity of the three worlds and thereby collapses them into one, whereas Penrose maintains an agnostic attitude that the truth about it may be subtle and elusive. Regarding how all this is still not yet a solution to the hard problem per se, I think Chalmers writes about this in some of the more esoteric sections of his work.
My own interest in quantum mind theories derives especially from the belief that physical theories of mind have a severe sorites problem (one dimension of which you can see in this ongoing discussion), and that quantum entanglement, and fundamental physics in general, offer a way out in the form of entities which are “wholes” with complex internal structure and non-arbitrary boundaries. And my interest in microtubule-based theories of quantum mind, is because they are still the best candidate I’ve seen for how this quantum holism could actually be a part of conscious cognition (since the movement of quanta around the cylinder of the microtubule, could produce topological quantum states robust against room-temperature decoherence). I’m able to draw a line between the bare idea of quantum states in the microtubule, and the more elaborate theorizings of Hameroff and Penrose. But I still like to understand their ideas in detail.
The observations in that paper, while technically valid, are only the tip of the iceberg. They are not proofs that Weinstein’s theory is untenable, they are simply questions to which the theory must have an answer. The most famous critique from the paper is usually presented as a proof that Weinstein’s shiab operator cannot exist. What is actually the case, is that the existence of the operator requires the complex form of his gauge group; and a complex gauge group, because non-compact, is argued to have physically untenable consequences. However, Weinstein is happy to bite the bullet and embrace the non-compact gauge group, because he thinks he has a mechanism that will de facto reduce it to a compact subgroup. A variety of such mechanisms are already used in other theories.
Weinstein hasn’t helped himself by refusing to answer those questions (or at least, by refusing to respond to that author). Between his public relations strategy, and all the usual reasons why new ideas have an uphill struggle, even in theoretical physics, the public discussion of his theory is in a dismal state. However, there’s enough information and insight out there, that a much deeper assessment is now possible. But rather than go on about it here, I’ll just link to the blog I created in order to work through it all.
OK, but that’s another unnecessary problem, because you don’t have to regard the mind as a (consistent) axiomatic system.
There’s no way of confirming that we have a kind of knowledge that goes beyond “proveable from unfounded axioms” and “seems to work in practice”.
Perhaps we aren’t as limited as a single formal system, but then we might be using cheap tricks like switching between systems, using intuition, or tolerating inconsistency.
From the anti realist point of views, If there are facts that transcend everyone, they aren’t facts. They aren’t sitting somewhere gathering dust for eternity, they just aren’t there at all.
Which finitist approach? An anti realist can regard infinties as suitable objects of study, no less real than other numbers.
Perhaps, but the phenomenological argument is really weak. Phenomenology is strong evidence of phenomenality..if it things seems to you to be certain way,then that is evidence that somethings seems so some way to you...but weak evidence of anything else.
There isn’t the slightest evidence that mathematical thinking is non neuronal or otherwise unusual … from.neuroscience.
Under the form of anti realism known as fictionalism , there is no problem...the brain simply conjures up mathematical objects like dragons and werewolves.
It is the form of realism known as Platonism that causes the problems, since it needs to explain how immaterial entities affect thought, and therefore neural activity.
I wouldn’t:understanding GIT might require some leveling meanness, but doesnt require transfinite levels....
...as you say.
That’s another unnecessary problem. There’s actually lots of evidence that consciousness is non binary.
* Drowsiness, states between sleep.and waking.
* Autopilot and flow states , where the sense of a self deciding actions isn absent.
More rarely there are forms of heightened consciousness: peak experiences, meditations jñanas, psychedelic enhanced perceptions , etc.
Like Chalmers , I don’t see why any mathematical structure would have associated qualia.