Hi Jesse Mazer I admire Penrose and what he is courageously trying to do (pointing out the deficiiencies of materialism, although he still protects himself by calling himself a humanist and an atheist).
But both Penrose and Chalmers are still stuck with the intractable cartesian mind/body dichotomy adopted by modern science, who simply ignore that the dichotomy exists. There is some hiope that they might see the virtues of quantum monadology, which adopts Leibniz's Idealism. Too much to ask, I suppose, but I see no other way. My only wishful consolution is Max Planck's quip that science advances one funeral at a time. But at the same time its stagnation (not moving ahead) lies not in conservatism, whose fundamental criteria are logic, truth and facts, but because of liberal's clever tactic of stigmatizing any mention of God or employing any philosophy but materialism. So our culture is gradually IMHO degenerating into materialism and atheism. Roger Clough, rclo...@verizon.net 8/24/2012 Leibniz would say, "If there's no God, we'd have to invent him so everything could function." ----- Receiving the following content ----- From: Jesse Mazer Receiver: everything-list Time: 2012-08-23, 21:09:46 Subject: Re: A remark on Richard's paper On Thu, Aug 23, 2012 at 8:41 PM, Richard Ruquist <yann...@gmail.com> wrote: Jesse, This is what Chalmers says in the 95 paper you link about the second Penrose argument, the one in my paper: " 3.5 As far as I can determine, this argument is free of the obvious flaws that plague other G?elian arguments, such as Lucas's argument and Penrose's earlier arguments. If it is flawed, the flaws lie deeper. It is true that the argument has a feeling of achieving its conclusion as if by magic. One is tempted to say: "why couldn't F itself engage in just the same reasoning?". But although there are various directions in which one might try to attack the argument, no knockdown refutation immediately presents itself. For this reason, the argument is quite challenging. Compared to previous versions, this argument is much more worthy of attention from supporters of AI.?" Chalmers finally concludes that the flaw for Godel, which Penrose also assumed, is the assumption that we can know we are sound. So the other way around, if Godel is correct, so is the Penrose second argument, which Chalmers confirmed. However, Chalmers seems to be saying the Godel is incorrect, hardly a basis for my paper. What do you mean "the flaw for Godel"? There is no doubt that Godel's mathematical proof is correct, and if you think Chalmers is suggesting any such doubt in his paper you are misreading him. The argument he's talking about is one specifically concerning human intelligence, which Godel's mathematical proof says nothing about (Godel did offer some brief comments about the implications of his mathematical proof for human intelligence, but they were very brief and somewhat ambiguous, see http://www.iep.utm.edu/lp-argue/#H4 ). And I already quoted his conclusions about the second argument, after the section you quote above: that although Chalmers agrees that Penrose's second argument does show that *either* our reasoning cannot be captured by a formal system *or* that we cannot be sure our reasoning is sound, Chalmers thinks Penrose is wrong to prefer the first option rather than the second. ? Personally, when I am sound, I know I am sound. When I am unsound I usually know that I am unsound. However, psychosis runs in my family, and many times I have watched a relative lapse into psychosis without him realizing it. Chalmers/Penrose aren't talking about "sound" in the ordinary colloquial sense of sanity or anything like that, they're talking about soundness in the sense of perfect mathematical certainty that there is absolutely no chance--not even a chance of 1 in 10^1000000000 or smaller, say--that they might have made an error in their judgement about the truth or falsity of some (potentially very complicated) proposition about arithmetic. Besides I sent the paper to Chalmers and he had no problem with. But he did wish me luck getting it published. He knew something I had not yet learned. Richard Did Chalmers offer any detailed commentary suggesting he had read through the whole thing carefully? If not it's possible he skimmed it and missed that sentence, or just read the abstract and decided it didn't interest him, but sent the note out of politeness. Jesse ? On Thu, Aug 23, 2012 at 8:19 PM, Jesse Mazer <laserma...@gmail.com> wrote: A quibble with the beginning of Richard's paper. On the first page it says: 'It is beyond the scope of this paper and admittedly beyond my understanding to delve into G?elian logic, which seems to be self-referential proof by contradiction, except to mention that Penrose in Shadows of the Mind(1994), as confirmed by David Chalmers(1995), arrived at a seemingly valid 7 step proof that human ?easoning powers cannot be captured by any formal system?.' If you actually read Chalmers' paper at?http://web.archive.org/web/20090204164739/http://psyche.cs.monash.edu.au/v2/psyche-2-09-chalmers.html he definitely does *not* "confirm" Penrose's argument! He says in the paper that Penrose has two basic arguments for his conclusions about consciousness, and at the end of the section titled "the first argument" he concludes that the first one fails: "2.16 It is section 3.3 that carries the burden of this strand of Penrose's argument, but unfortunately it seems to be one of the least convincing sections in the book. By his assumption that the relevant class of computational systems are all straightforward axiom-and-rules system, Penrose is not taking AI seriously, and certainly is not doing enough to establish his conclusion that physics is uncomputable. I conclude that none of Penrose's argument up to this point put a dent in the natural AI position: that our reasoning powers may be captured by a sound formal system F, where we cannot determine that F is sound." Then when dealing with Penrose's "second argument", he says that Penrose draws the wrong conclusions; where Penrose concludes that our reasoning cannot be the product of any formal system, Chalmers concludes that the actual issue is that we cannot be 100% sure our reasoning is "sound" (which I understand to mean we can never be 100% sure that we have not made a false conclusion about whether all the propositions we have proved true or false actually have that truth-value in "true arithmetic"): "3.12 We can see, then, that the assumption that we know we are sound leads to a contradiction. One might try to pin the blame on one of the other assumptions, but all these seem quite straightforward. Indeed, these include the sort of implicit assumptions that Penrose appeals to in his arguments all the time. Indeed, one could make the case that all of premises (1)-(4) are implicitly appealed to in Penrose's main argument. For the purposes of the argument against Penrose, it does not really matter which we blame for the contradiction, but I think it is fairly clear that it is the assumption that the system knows that it is sound that causes most of the damage. It is this assumption, then, that should be withdrawn. "3.13 Penrose has therefore pointed to a false culprit. When the contradiction is reached, he pins the blame on the assumption that our reasoning powers are captured by a formal system F. But the argument above shows that this assumption is inessential in reaching the contradiction: A similar contradiction, via a not dissimilar sort of argument, can be reached even in the absence of that assumption. It follows that the responsibility for the contradiction lies elsewhere than in the assumption of computability. It is the assumption about knowledge of soundness that should be withdrawn. "3.14 Still, Penrose's argument has succeeded in clarifying some issues. In a sense, it shows where the deepest flaw in G?elian arguments lies. One might have thought that the deepest flaw lay in the unjustified claim that one can see the soundness of certain formal systems that underlie our own reasoning. But in fact, if the above analysis is correct, the deepest flaw lies in the assumption that we know that we are sound. All G?elian arguments appeal to this premise somewhere, but in fact the premise generates a contradiction. Perhaps we are sound, but we cannot know unassailably that we are sound." So it seems Chalmers would have no problem with the "natural AI" position he discussed earlier, that our reasoning could be adequately captured by a computer simulation that did not come to its top-level conclusions about mathematics via a strict axiom/proof method involving the mathematical questions themselves, but rather by some underlying fallible structure like a neural network. The bottom-level behavior of the simulated neurons themselves would be deducible given the initial state of the system using the axiom/proof method, but that doesn't mean the system as a whole might not make errors in mathematical calculations; see Douglas Hofstadter's discussion of this issue starting on p. 571 of "Godel Escher Bach", the section titled "Irrational and Rational Can Coexist on Different Levels", where he writes: "Another way to gain perspective on this is to remember that a brain, too, is a collection of faultlessly functioning element-neurons. Whenever a neuron's threshold is surpassed by the sum of the incoming signals, BANG!-it fires. It never happens that a neuron forgets its arithmetical knowledge-carelessly adding its inputs and getting a wrong answer. Even when a neuron dies, it continues to function correctly, in the sense that its components continue to obey the laws of mathematics and physics. Yet as we all know, neurons are perfectly capable of supporting high-level behavior that is wrong, on its own level, in the most amazing ways. Figure 109 is meant to illustrate such a class of levels: an incorrect belief held in the software of a mind, supported by the hardware of a faultlessly functioning brain." Figure 109 depicts the outline of a person's head with "2+2=5" appearing inside it, but the symbols in "2+2=5" are actually made up of large collections of smaller mathematical equations, like "7+7=14", which are all correct. A nice way of illustrating the idea, I think.? I came up with my own thought-experiment to show where Penrose's argument goes wrong, based on the same conclusion that Chalmers reached: a community of "realistic" AIs whose simulated brains work similarly to real human brains would never be able to be 100% certain that they had not reached a false conclusion about arithmetic, and the very act of stating confidently in mathematical that they would never reach a wrong conclusion would ensure that they were endorsing a false proposition about arithmetic. See my discussion with LauLuna on the "Penrose and algorithms" thread here: http://groups.google.com/group/everything-list/browse_thread/thread/c92723e0ef1a480c/429e70be57d2940b?#429e70be57d2940b Jesse? On Thu, Aug 23, 2012 at 6:38 PM, Stephen P. King <stephe...@charter.net> wrote: Dear Richard, ?? Your paper is very interesting. It reminds me a lot of Stephen Wolfram's cellular automaton theory. I only have one big problem with it. The 10d manifold would be a single fixed structure that, while conceivably capable of running the computations and/or implementing the Peano arithmetic, has a problem with the role of time in it. You might have a solution to this problem that I see that I did not deduce as I read your paper. How do you define time for your model? -- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com. 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