During the next few days, I do not have time to study exactly how you manage to tie together second-order logic, the symbol grounding problem, and qualia as Gödel sentences (or whatever that connection is). I am reminded of Hofstadter’s theory that consciousness has something to do with indirect self-reference in formal systems, so maybe you’re a kind of Hofstadterian eliminativist.
However, in response to this --
EN predicts that you will say that
-- I can tell you how a believer in the reality of intentional states, would go about explaining you and EN. The first step is to understand what the key propositions of EN are, the next step is to hypothesize about the cognitive process whereby the propositions of EN arose from more commonplace propositions, the final step is to conceive of that cognitive process in an intentional-realist way, i.e. as a series of thoughts that occurred in a mind, rather than just as a series of representational states in a brain.
You mention Penrose. Penrose had the idea that the human mind can reason about the semantics of higher-order logic because brain dynamics is governed by highly noncomputable physics (highly noncomputable in the sense of Turing degrees, I guess). It’s a very imaginative idea, and it’s intriguing that quantum gravity may actually contain a highly noncomputable component (because of the undecidability of many properties of 4-manifolds, that may appear in the gravitational path integral).
Nonetheless, it seems an avoidable hypothesis. A thinking system can derive the truth of Gödel sentences, so long as it can reason about the semantics of the initial axioms, so all you need is a capacity for semantic reflection (I believe Feferman has a formal theory of this under the name “logical reflection”). Penrose doesn’t address this because he doesn’t even tackle the question of how anything physical has intentionality, he sticks purely to mathematics, physics, and logic.
My approach to this is Husserlian realism about the mind. You don’t start with mindless matter and hope to see how mental ontology is implicit in it or emerges from it. You start with the phenomenological datum that the mind is real, and you build on that. At some point, you may wish to model mental dynamics purely as a state machine, neglecting semantics and qualia; and then you can look for relationships between that state machine, and the state machines that physics and biology tell you about.
But you should never forget the distinctive ontology of the mental, that supplies the actual “substance” of that mental state machine. You’re free to consider panpsychism and other identity theories, interactionism, even pure metaphysical idealism; but total eliminativism contradicts the most elementary facts we know, as Descartes and Rand could testify. Even you say that you feel the qualia, it’s just that you think “from a rational perspective, it must be otherwise”.
I’m truly grateful for the opportunity to engage meaningfully on this topic. You’ve brought up some important points:
“I do not have time” — Completely understandable. ”Symbol grounding” — This is inherently tied to the central issue we’re discussing. ”Qualia as Gödel sentences” — An important distinction here: it’s not that qualia are Gödel sentences, but rather, the absence of qualia functions analogously to a Gödel sentence — paradoxically. Consider this line of reasoning.
This paradox highlights the self-referential inconsistency — invoking Gödel’s incompleteness theorems:
To highlight expressivity: A. Lisa is a P-Zombie. B. Lisa asserts that she is a P-Zombie. C. A true P-Zombie cannot assert or hold beliefs. D. Therefore, Lisa cannot assert that she is a P-Zombie.
Cases:
A. Lisa is a P-Zombie. B. Lisa asserts that she is a P-Zombie. C. Lisa would be complete: Not Possible
A. Lisa is not a P-Zombie. B. Lisa asserts that she is a P-Zombie. C. Lisa would be not complete: Possible but irrelevant.
A. Lisa is a P-Zombie. B. Lisa asserts that she is a not P-Zombie. C. Lisa would be not complete: Possible
A. Lisa is not a P-Zombie. B. Lisa asserts that she is a not P-Zombie. C. Lisa would be complete: Not Possible
In order for Lisa to be internally consistent yet incomplete, she must maintain that she is not a P-Zombie. But if she maintains that she is not a P-Zombie AND IS NOT A P-Zombie, Lisa would be complete. AHA! Thus impossible.
This connects to Turing’s use of Modus Tollens in the halting problem — a kind of logical self-reference that breaks the system from within.
Regarding Hofstadter: My use of Gödel’s ideas is strictly arithmetic and formal — not metaphorical or analogical, as Hofstadter often approaches them. So while interesting, his theory diverges significantly from what I’m proposing.
You mentioned:
“I can tell you how a ‘believer’...” — Exactly. That’s the point. “Believer”
“You mention Penrose.” — Yes. Penrose is consequential. Though I believe his argument is flawed. His reasoning hinges on accepting qualia as a given. If he somehow manages to validate that assumption by proving second order logic in the quantum realm, I’ll tip my hat — but my framework challenges that very basis.
You said:
“My approach is Husserlian realism about the mind — you don’t start with mindless matter and hope...” — Right, but I’d like to clarify: this critique applies more to Eliminative Materialism than to Eliminative Nominalism. In EN, ‘matter’ itself is a symbol — not a foundational substance. So the problem isn’t starting with “mindless matter” — it’s assuming that “matter” has ontological priority at all. And finally, on the notion of substance — I’m not relying on that strawman. My position isn’t based on classical substance dualism
During the next few days, I do not have time to study exactly how you manage to tie together second-order logic, the symbol grounding problem, and qualia as Gödel sentences (or whatever that connection is). I am reminded of Hofstadter’s theory that consciousness has something to do with indirect self-reference in formal systems, so maybe you’re a kind of Hofstadterian eliminativist.
However, in response to this --
-- I can tell you how a believer in the reality of intentional states, would go about explaining you and EN. The first step is to understand what the key propositions of EN are, the next step is to hypothesize about the cognitive process whereby the propositions of EN arose from more commonplace propositions, the final step is to conceive of that cognitive process in an intentional-realist way, i.e. as a series of thoughts that occurred in a mind, rather than just as a series of representational states in a brain.
You mention Penrose. Penrose had the idea that the human mind can reason about the semantics of higher-order logic because brain dynamics is governed by highly noncomputable physics (highly noncomputable in the sense of Turing degrees, I guess). It’s a very imaginative idea, and it’s intriguing that quantum gravity may actually contain a highly noncomputable component (because of the undecidability of many properties of 4-manifolds, that may appear in the gravitational path integral).
Nonetheless, it seems an avoidable hypothesis. A thinking system can derive the truth of Gödel sentences, so long as it can reason about the semantics of the initial axioms, so all you need is a capacity for semantic reflection (I believe Feferman has a formal theory of this under the name “logical reflection”). Penrose doesn’t address this because he doesn’t even tackle the question of how anything physical has intentionality, he sticks purely to mathematics, physics, and logic.
My approach to this is Husserlian realism about the mind. You don’t start with mindless matter and hope to see how mental ontology is implicit in it or emerges from it. You start with the phenomenological datum that the mind is real, and you build on that. At some point, you may wish to model mental dynamics purely as a state machine, neglecting semantics and qualia; and then you can look for relationships between that state machine, and the state machines that physics and biology tell you about.
But you should never forget the distinctive ontology of the mental, that supplies the actual “substance” of that mental state machine. You’re free to consider panpsychism and other identity theories, interactionism, even pure metaphysical idealism; but total eliminativism contradicts the most elementary facts we know, as Descartes and Rand could testify. Even you say that you feel the qualia, it’s just that you think “from a rational perspective, it must be otherwise”.
I’m truly grateful for the opportunity to engage meaningfully on this topic. You’ve brought up some important points:
“I do not have time” — Completely understandable.
”Symbol grounding” — This is inherently tied to the central issue we’re discussing.
”Qualia as Gödel sentences” — An important distinction here: it’s not that qualia are Gödel sentences, but rather, the absence of qualia functions analogously to a Gödel sentence — paradoxically.
Consider this line of reasoning.
This paradox highlights the self-referential inconsistency — invoking Gödel’s incompleteness theorems:
To highlight expressivity:
A. Lisa is a P-Zombie.
B. Lisa asserts that she is a P-Zombie.
C. A true P-Zombie cannot assert or hold beliefs.
D. Therefore, Lisa cannot assert that she is a P-Zombie.
Cases:
A. Lisa is a P-Zombie.
B. Lisa asserts that she is a P-Zombie.
C. Lisa would be complete: Not Possible
A. Lisa is not a P-Zombie.
B. Lisa asserts that she is a P-Zombie.
C. Lisa would be not complete: Possible but irrelevant.
A. Lisa is a P-Zombie.
B. Lisa asserts that she is a not P-Zombie.
C. Lisa would be not complete: Possible
A. Lisa is not a P-Zombie.
B. Lisa asserts that she is a not P-Zombie.
C. Lisa would be complete: Not Possible
In order for Lisa to be internally consistent yet incomplete, she must maintain that she is not a P-Zombie. But if she maintains that she is not a P-Zombie AND IS NOT A P-Zombie, Lisa would be complete. AHA! Thus impossible.
This connects to Turing’s use of Modus Tollens in the halting problem — a kind of logical self-reference that breaks the system from within.
Regarding Hofstadter: My use of Gödel’s ideas is strictly arithmetic and formal — not metaphorical or analogical, as Hofstadter often approaches them. So while interesting, his theory diverges significantly from what I’m proposing.
You mentioned:
“I can tell you how a ‘believer’...”
— Exactly. That’s the point. “Believer”
“You mention Penrose.”
— Yes. Penrose is consequential. Though I believe his argument is flawed. His reasoning hinges on accepting qualia as a given. If he somehow manages to validate that assumption by proving second order logic in the quantum realm, I’ll tip my hat — but my framework challenges that very basis.
You said:
“My approach is Husserlian realism about the mind — you don’t start with mindless matter and hope...”
— Right, but I’d like to clarify: this critique applies more to Eliminative Materialism than to Eliminative Nominalism. In EN, ‘matter’ itself is a symbol — not a foundational substance. So the problem isn’t starting with “mindless matter” — it’s assuming that “matter” has ontological priority at all.
And finally, on the notion of substance — I’m not relying on that strawman. My position isn’t based on classical substance dualism