`Chalmers followed my talk on the UD Argument at ASSC 4 and leaved the`

`room at step 3, saying that there is no indeterminacy as he will feel`

`to be at both places.`

`This made perhaps some sense in his dualist interpretation of Everett,`

`(if *that* makes sense), but makes no sense at all in comp. I guess`

`that like John Clark he confused the 1-view of the 1-view, with some 3-`

`view on the 1-view.`

## Advertising

`I know only two people stopping at step 3. But if you know others, let`

`me know. (I don't count the person who stop at step 3 because they`

`have something else to do).`

Bruno On 24 Aug 2012, at 02:41, Richard Ruquist wrote:

Jesse,This is what Chalmers says in the 95 paper you link about the secondPenrose argument, the one in my paper:" 3.5 As far as I can determine, this argument is free of theobvious flaws that plague other Gödelian arguments, such as Lucas'sargument and Penrose's earlier arguments. If it is flawed, the flawslie deeper. It is true that the argument has a feeling of achievingits conclusion as if by magic. One is tempted to say: "why couldn'tF itself engage in just the same reasoning?". But although there arevarious directions in which one might try to attack the argument, noknockdown 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 ofAI. "Chalmers finally concludes that the flaw for Godel, which Penrosealso assumed, is the assumption that we can know we are sound. Sothe other way around, if Godel is correct, so is the Penrose secondargument, which Chalmers confirmed. However, Chalmers seems to besaying the Godel is incorrect, hardly a basis for my paper.Personally, when I am sound, I know I am sound. When I am unsound Iusually know that I am unsound. However, psychosis runs in myfamily, and many times I have watched a relative lapse intopsychosis without him realizing it.Besides I sent the paper to Chalmers and he had no problem with. Buthe did wish me luck getting it published. He knew something I hadnot yet learned.RichardOn 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 pageit says:'It is beyond the scope of this paper and admittedly beyond myunderstanding to delve into Gödelian logic, which seems to be self-referential proof by contradiction, except to mention that Penrosein Shadows of the Mind(1994), as confirmed by David Chalmers(1995),arrived at a seemingly valid 7 step proof that human “reasoningpowers 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 inthe paper that Penrose has two basic arguments for his conclusionsabout consciousness, and at the end of the section titled "the firstargument" he concludes that the first one fails:"2.16 It is section 3.3 that carries the burden of this strand ofPenrose's argument, but unfortunately it seems to be one of theleast convincing sections in the book. By his assumption that therelevant class of computational systems are all straightforwardaxiom-and-rules system, Penrose is not taking AI seriously, andcertainly is not doing enough to establish his conclusion thatphysics is uncomputable. I conclude that none of Penrose's argumentup to this point put a dent in the natural AI position: that ourreasoning powers may be captured by a sound formal system F, wherewe cannot determine that F is sound."Then when dealing with Penrose's "second argument", he says thatPenrose draws the wrong conclusions; where Penrose concludes thatour reasoning cannot be the product of any formal system, Chalmersconcludes that the actual issue is that we cannot be 100% sure ourreasoning is "sound" (which I understand to mean we can never be100% sure that we have not made a false conclusion about whether allthe propositions we have proved true or false actually have thattruth-value in "true arithmetic"):"3.12 We can see, then, that the assumption that we know we aresound leads to a contradiction. One might try to pin the blame onone of the other assumptions, but all these seem quitestraightforward. Indeed, these include the sort of implicitassumptions that Penrose appeals to in his arguments all the time.Indeed, one could make the case that all of premises (1)-(4) areimplicitly appealed to in Penrose's main argument. For the purposesof the argument against Penrose, it does not really matter which weblame for the contradiction, but I think it is fairly clear that itis the assumption that the system knows that it is sound that causesmost of the damage. It is this assumption, then, that should bewithdrawn."3.13 Penrose has therefore pointed to a false culprit. When thecontradiction is reached, he pins the blame on the assumption thatour reasoning powers are captured by a formal system F. But theargument above shows that this assumption is inessential in reachingthe contradiction: A similar contradiction, via a not dissimilarsort of argument, can be reached even in the absence of thatassumption. It follows that the responsibility for the contradictionlies elsewhere than in the assumption of computability. It is theassumption about knowledge of soundness that should be withdrawn."3.14 Still, Penrose's argument has succeeded in clarifying someissues. In a sense, it shows where the deepest flaw in Gödelianarguments lies. One might have thought that the deepest flaw lay inthe unjustified claim that one can see the soundness of certainformal systems that underlie our own reasoning. But in fact, if theabove analysis is correct, the deepest flaw lies in the assumptionthat we know that we are sound. All Gödelian arguments appeal tothis premise somewhere, but in fact the premise generates acontradiction. Perhaps we are sound, but we cannot know unassailablythat we are sound."So it seems Chalmers would have no problem with the "natural AI"position he discussed earlier, that our reasoning could beadequately captured by a computer simulation that did not come toits top-level conclusions about mathematics via a strict axiom/proofmethod involving the mathematical questions themselves, but ratherby some underlying fallible structure like a neural network. Thebottom-level behavior of the simulated neurons themselves would bededucible given the initial state of the system using the axiom/proof method, but that doesn't mean the system as a whole might notmake errors in mathematical calculations; see Douglas Hofstadter'sdiscussion of this issue starting on p. 571 of "Godel Escher Bach",the section titled "Irrational and Rational Can Coexist on DifferentLevels", where he writes:"Another way to gain perspective on this is to remember that abrain, too, is a collection of faultlessly functioning element-neurons. Whenever a neuron's threshold is surpassed by the sum ofthe incoming signals, BANG!-it fires. It never happens that a neuronforgets its arithmetical knowledge-carelessly adding its inputs andgetting a wrong answer. Even when a neuron dies, it continues tofunction correctly, in the sense that its components continue toobey the laws of mathematics and physics. Yet as we all know,neurons are perfectly capable of supporting high-level behavior thatis wrong, on its own level, in the most amazing ways. Figure 109 ismeant to illustrate such a class of levels: an incorrect belief heldin the software of a mind, supported by the hardware of afaultlessly 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 upof large collections of smaller mathematical equations, like"7+7=14", which are all correct. A nice way of illustrating theidea, I think.I came up with my own thought-experiment to show where Penrose'sargument goes wrong, based on the same conclusion that Chalmersreached: a community of "realistic" AIs whose simulated brains worksimilarly to real human brains would never be able to be 100%certain that they had not reached a false conclusion aboutarithmetic, and the very act of stating confidently in mathematicalthat they would never reach a wrong conclusion would ensure thatthey were endorsing a false proposition about arithmetic. See mydiscussion with LauLuna on the "Penrose and algorithms" thread here: http://groups.google.com/group/everything-list/browse_thread/thread/c92723e0ef1a480c/429e70be57d2940b?#429e70be57d2940bJesseOn 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 StephenWolfram's cellular automaton theory. I only have one big problemwith it. The 10d manifold would be a single fixed structure that,while conceivably capable of running the computations and/orimplementing the Peano arithmetic, has a problem with the role oftime in it. You might have a solution to this problem that I seethat I did not deduce as I read your paper. How do you define timefor your model?-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.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 GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.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 GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.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.

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