Talk:Shadows of the Mind
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Why was the mathematical criticism of the Godelian argument removed? That criticism was essentially a simpler restatement of Solomon Feferman's criticsm, and I certainly think that an award-winning Stanford mathematician qualifies as a reliable source on Godel's Incompleteness Theorem.
I'm going to go ahead and add it back if I do not hear the justification for its removal. Tarcieri 00:59, 31 July 2006 (UTC)
- As I wrote in the edit summary, it was just a slab of critique which came from a site that didnt seem to be classed as a reliable source. It is very important with these sorts of controversial academic topics not to paste in text that isnt considered reliable, especially when they make blatant statements like "Penrose claims that the mathematician already knows G(G) is non-terminating, because they understand the Gödelian argument. This is not the case." The content you put in however seems quite reasonably sourced, and links back to the original text rather than just copy/pasting. Remy B 08:19, 31 July 2006 (UTC)
When I type "Shadows of the Mind" (without the quotes) in the main wikipedia search bar and hit search it does not find the "Shadows of the Mind" topic. This, despite the fact that there is text in the source that matches that. I guess this is a general question...how could we fix that for this topic ? Thanks.Rlbyrne 14:12, 13 September 2006 (UTC)
- It works for me? Remy B 03:59, 14 September 2006 (UTC)
Error in "Interpreting F as a robot mathematician"
There is trivial error in the mentioned section. WE DON'T KNOW THAT G(G) is not terminating. We know that G(G) is not terminating IF AND ONLY IF we have information that the robot mathematician F is consistent. Human mathematician MUST know that the robot mathematician F is consistent in order to make the conclusion that G(G) is not terminating. And yes, now there is big difference - we don't know something else that the robot mathematician does not know. The Goedel's first theorem is provable by the robot F, so he can also say "If I am consistent, then (G) is not terminating". Of course the robot mathematician is algorithm, and if the robot is consistent, he cannot prove its own consistency - this is what second Goedel theorem says. So emerges the question "Can a human determine whether arbitrary robot algorithm F is consistent?" and similarly if Penrose's thesis is true, it implies that the human "directly sees that G(G) is not terminating" and therefore "directly sees that the robot F is consistent" !!! No need to say that neither me, nor any mathematician on this Earth can "see" for all possible algorithms whether they are consistent or not. Therefore Penrose's thesis is flawed. And this is proved not only by me in this post, but in the perfect textbook by Karlis Podnieks here What is Mathematics: Goedel theorem and around (hypertextbook for students). The relevant proof is in section 6.1 Regards, Danko Georgiev MD 14:00, 24 November 2006 (UTC)
Comment re Penrose
Anyone who has done any computer programming knows that it can be difficult to impossible to comprehend the purpose of a sophisticated program written in a higher-level language based on an analysis of what you see happening on the machine-language level.
IMHO (& no doubt someone else's) the "mind" may be similar to a much higher-level program "running" on brain "hardware" which is *much* more complex than computer hardware. To an extent we're all born with similar hardware, but unique life experiences, insights and epiphanies, along with hardware differences (like those of savants) make improbable any demonstration that creativity arises from a "mere" machine. This does *not* rule out the possibility of creativity in machines, but it may take an evolutionary time-scale to see it. Twang 00:30, 28 December 2006 (UTC)
As with the article about Penrose himself, there is very little detail about his arguments here and much more about peoples' negative criticisms of them. SHADOWS OF THE MIND is an extraordinarily complex book taking in everything from Relativity to Plato, but precious little of that is discussed here. All we get is statements about who doesn't agree with him. It would be helpful to know what isn't being agreed with. Articles about famous novels on Wikipedia are more detailed about their contents than this one is on a science book. ThePeg (talk)
The text relating to John Searle reads - "(He) criticizes Penrose's appeal to Gödel as resting on the fallacy that all computational algorithms must be capable of mathematical description". If this were Searles argument it would be faulty as Penrose argues that from Godel we can see that not all mathematical truths can be derived using computational algorithms, which is an altogether different proposition. However Searles argument has been misrepresented here and this section should be removed. His actual argument in "The Mystery of Consciousness" uses the vehicle plate example but is along somewhat different lines to those stated here. However I believe his actual argument is also flawed and quite unsatisfying, so I am not inclined to add it to this wiki entry. — Preceding unsigned comment added by Gyan Gralinski (talk • contribs) 05:20, 13 March 2012 (UTC)