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> Maybe someone can elucidate. Godel's theorems apply to tightly-controlled formal systems Turing machine is a tightly-controlled formal system. Either the bra

> Maybe someone can elucidate. Godel's theorems apply to tightly-controlled formal systems Turing machine is a tightly-controlled formal system. Either the brain is a Turing machine, which means it can be accurately simulated on our computers and it is a subject of the limitations of the Godel theorem, or it is not a Turing machine, which Penrose argues for, in which case it can't be accurately simulated on Turing machines.

dvt 9y ago
As a trained philosopher and logician, I completely understand how a Turing machine relates to Godel's Theorems, but I think you're passing the buck here. You can make all kinds of claims: - Either the brain is a V12 engine or it's not - Either the brain is a perfect circle or it's not - Either the brain is X or it's not All these statements are trivially true, but it's not like I look at a V12 engine thinking "hmm, I wonder if it's conscious" (some pan-psychists do but that's still weird to me). Similarly, looking at the property of a formal system and jumping to consciousness makes (to me) little sense. Besides, my knock-down argument goes something like this: I can concede that our brains are machines, but suppose I believe they are Presburger counting machines, where Godel's incompleteness does not apply. What then? There is no insight in that claim. I just think Turing machines and Godel are used as a bait and switch. Because, really, any theory of consciousness will not have anything to do with either.
- mixedbit 9y ago
  In the context of the Penrose hypothesis, the question if the brain is a Turing machine is key, because if it is, the hypothesis is false.
  - qubex 9y ago
    The point posed by Penrose isn't (quite) whether the human brain is a Universal Turing Machine or not: it clearly is, in the sense that we can sit down with pencil and paper and emulate a Turing Machine of our choosing (infinite storage excepted, of course). Penrose's statement is that we are a superset of Turing Machines that can both emulate any Turing Machine and do non-computable things, too.
maiklasvegas 9y ago
Well I like to think of it this way. We know that the brain is at least a Turing machine since we can perform the same calculations. If the brain is more powerful than a Turing machine than any attempts to replicate it in a general sense will not work. A pushdown automaton can solve certain problems that a finite state machine can't. Finite state machines can't solve the general palindrome problem, but they can be designed to solve palindromes of a bounded length / alphabet. The complexity explodes with the length of the string and number of characters, but it can be done. To me our attempts at creating a general AI with a turing machine is starting to take a similar shape. We know we can generate an algorithm (machine learning) that can solve a contained problem.

dvt 9y ago

As a trained philosopher and logician, I completely understand how a Turing machine relates to Godel's Theorems, but I think you're passing the buck here. You can make all kinds of claims: - Either the brain is a V12 engine or it's not - Either the brain is a perfect circle or it's not - Either the brain is X or it's not All these statements are trivially true, but it's not like I look at a V12 engine thinking "hmm, I wonder if it's conscious" (some pan-psychists do but that's still weird to me). Similarly, looking at the property of a formal system and jumping to consciousness makes (to me) little sense. Besides, my knock-down argument goes something like this: I can concede that our brains are machines, but suppose I believe they are Presburger counting machines, where Godel's incompleteness does not apply. What then? There is no insight in that claim. I just think Turing machines and Godel are used as a bait and switch. Because, really, any theory of consciousness will not have anything to do with either.

mixedbit 9y ago
In the context of the Penrose hypothesis, the question if the brain is a Turing machine is key, because if it is, the hypothesis is false.
- qubex 9y ago
  The point posed by Penrose isn't (quite) whether the human brain is a Universal Turing Machine or not: it clearly is, in the sense that we can sit down with pencil and paper and emulate a Turing Machine of our choosing (infinite storage excepted, of course). Penrose's statement is that we are a superset of Turing Machines that can both emulate any Turing Machine and do non-computable things, too.

maiklasvegas 9y ago

Well I like to think of it this way. We know that the brain is at least a Turing machine since we can perform the same calculations. If the brain is more powerful than a Turing machine than any attempts to replicate it in a general sense will not work. A pushdown automaton can solve certain problems that a finite state machine can't. Finite state machines can't solve the general palindrome problem, but they can be designed to solve palindromes of a bounded length / alphabet. The complexity explodes with the length of the string and number of characters, but it can be done. To me our attempts at creating a general AI with a turing machine is starting to take a similar shape. We know we can generate an algorithm (machine learning) that can solve a contained problem.