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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
by dvt 10y 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 10y agoIn 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 10y agoThe 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.