My apologies. When Chalmers used the words "godelian argument" I thought he was referring to Godel. Now I can see I misread it.
On Thu, Aug 23, 2012 at 9:09 PM, Jesse Mazer <[email protected]> wrote: > > > On Thu, Aug 23, 2012 at 8:41 PM, Richard Ruquist <[email protected]>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 Gödelian 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 <[email protected]>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 Gödelian 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 “reasoning 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.htmlhe >>> 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 Gödelian 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 Gödelian >>> 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 >>> <[email protected]>wrote: >>> >>>> Dear Richard, >>>> >>>> Your paper <http://vixra.org/pdf/1101.0044v1.pdf> 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 [email protected]. >>>> To unsubscribe from this group, send email to >>>> [email protected]. >>>> 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 protected]. >>> To unsubscribe from this group, send email to >>> [email protected]. >>> 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 protected]. >> To unsubscribe from this group, send email to >> [email protected]. >> 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 protected]. > To unsubscribe from this group, send email to > [email protected]. > 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. 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