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.
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.