Penrose, Godel and Consciousness

I discuss Roger Penrose's argument that human thought cannot be represented on a digital computer, based on Kurt Godel's incompleteness theorem. I argue against it. My website: http://www.tobypereira.co.uk

Category:

People & Blogs

Tags:

• roger
• penrose
• kurt
• godel
• emperor's
• new
• shadows
• of
• the
• mind
• incompleteness
• theorem
• philosophy
• mathematics
• consciousness
• thought
• digital
• computer
• algorithm
• algorithmic
• quantum
• mechanics
• AI
• artificial
• intelligence
• toby
• pereira

[dirtydonki]

Pointless

[philosophertoby]

@dirtydonki The self-reference is quite Godelian itself. Nice.

[drunkagnostic]

Why, exactly, couldn't we find our own algorithm? Because then the algorithm would have to contain itself? The Godel sentence is held to contain itself in a self-referencing sense. Reject 'thing containing itself' and you reject Godel's proof. Admit 'thing containing itself' and your anti-Penrose argument collapses.

[FinisReflectatOpus]

@philosophertoby @philosophertoby First, about Godel sentences: you say "such statements are known as Godel sentences", but they generally are not (Godel sentences are a trivial case--merely used to prove general incompleteness). For instance, an unprovable truth in Euclidean geometry is the parallel lines postulate. This is clearly not a Godel statement and not generated (or generatable)! Nor would it matter if we had never recognized it. Second pt. follows...

[FinisReflectatOpus]

@philosophertoby Second, Penrose does not make this statement. He merely needs to show 1. there exists ANY EXAMPLE of Godel sentence that we can see, and 2. there exists no Godel sentence that any Turing-type process can see (which was Godel's very point). The extraordinary claim is that AI hosted by a Turing machine could recognize one, i.e. to disprove Godel! Do you see that an infinitude of other Godel-type sentences that we can't recognize can exist without harming Penrose's points at all?

[philosophertoby]

@FinisReflectatOpus Thanks for the like. Godel's proof says any algorithmic system that can prove theorems won't be able to prove all statements expressable in the system. We humans can just see that such Godel sentences are true, so our thought isn't algorithmic, according to Penrose. This is fallacious because it assumes without argument that we'll recognise a Godel sentence. My further arguments aren't required - the burden is on Penrose to present a coherent case first.

[FinisReflectatOpus]

@philosophertoby I need clarification on where self-awareness, particularly self-descriptiveness (or being able to perceive or express one's own code, or algorithm, or ways and means in any sense whatever) enters in to it at all. These seem like extremely strong armaments deployed upon an unrelated battlefield. One can bootstrap Turing-based arguments from any Turing-based basis set, but isn't this Penrose's point? Fundamentally, Godel proves INCOMPLETENESS. Penrose need not re-prove this?

[FinisReflectatOpus]

@philosophertoby Great video, which I "liked" as these talks are just what is needed, but Godel does not state that his sentences are the only non-provable truths. He offers them as an example (= proof that at least one CLASS of such islands exist) nor does he imply that any of these in particular need or can ever be perceived or illustrated in order to still be there. Rather, he says, they can only be discovered (i.e. in general may never be derived). It may be a huge miss to rest on algorithm.

[JayGatsbyOdysseus]

I suppose this gentleman is talking about Singularity. If a microchip can reach human brain computation levels then will the computer have consciousness? Isn't this the question? It is the same idea put forth in the movie 2001: Space Odyssey. It will not happen because the chip will not have Planck's Constant.

[leeeejohnson]

im distracted by all the dishes