MindPapers: 6.1b. Godelian arguments

Benacerraf, Paul (1967). God, the devil, and Godel. The Monist 51 (January):9-32. (Annotation | Google | Edit)

Bojadziev, Damjan (1997). Mind versus Godel. In Matjaz Gams & M. Wu Paprzycki (eds.), Mind Versus Computer. IOS Press. (Cited by 1 | Google | More links | Edit)

Bowie, G. Lee (1982). Lucas' number is finally up. Journal of Philosophy Logic 11 (August):279-85. (Cited by 10 | Annotation | Google | More links | Edit)

Boyer, David L. (1983). R. Lucas, Kurt Godel, and Fred astaire. Philosophical Quarterly 33 (April):147-59. (Annotation | Google | Edit)

Bringsjord, Selmer & Xiao, H. (2000). A refutation of Penrose's new Godelian case against the computational conception of mind. Journal of Experimental and Theoretical Artificial Intelligence 12. (Google | Edit)

Chari, C. T. K. (1963). Further comments on minds, machines and Godel. Philosophy 38 (April):175-8. (Annotation | Google | Edit)

Chalmers, David J. (1996). Minds, machines, and mathematics. Psyche 2:11-20. (Cited by 17 | Google | More links | Edit)

Abstract: In his stimulating book SHADOWS OF THE MIND, Roger Penrose presents arguments, based on Gödel's theorem, for the conclusion that human thought is uncomputable. There are actually two separate arguments in Penrose's book. The second has been widely ignored, but seems to me to be much more interesting and novel than the first. I will address both forms of the argument in some detail. Toward the end, I will also comment on Penrose's proposals for a "new science of consciousness"

Chihara, C. (1972). On alleged refutations of mechanism using Godel's incompleteness results. Journal of Philosophy 69 (September):507-26. (Cited by 9 | Annotation | Google | More links | Edit)

Coder, David (1969). Godel's theorem and mechanism. Philosophy 44 (September):234-7. (Annotation | Google | Edit)

Copeland, Jack (1998). Turing's o-machines, Searle, Penrose, and the brain. Analysis 58 (2):128-138. (Cited by 15 | Google | More links | Edit)

Abstract: In his PhD thesis (1938) Turing introduced what he described as 'a new kind of machine'. He called these 'O-machines'. The present paper employs Turing's concept against a number of currently fashionable positions in the philosophy of mind

Dennett, Daniel C. (1989). Murmurs in the cathedral: Review of R. Penrose, The Emperor's New Mind. Times Literary Supplement (September) 29. (Cited by 5 | Google | Edit)

Abstract: The idea that a computer could be conscious--or equivalently, that human consciousness is the effect of some complex computation mechanically performed by our brains--strikes some scientists and philosophers as a beautiful idea. They find it initially surprising and unsettling, as all beautiful ideas are, but the inevitable culmination of the scientific advances that have gradually demystified and unified the material world. The ideologues of Artificial Intelligence (AI) have been its most articulate supporters. To others, this idea is deeply repellent: philistine, reductionistic (in some bad sense), as incredible as it is offensive. John Searle's attack on "strong AI" is the best known expression of this view, but others in the same camp, liking Searle's destination better than his route, would dearly love to see a principled, scientific argument showing that strong AI is impossible. Roger Penrose has set out to provide just such an argument

Dennett, Daniel C. (1978). The abilities of men and machines. In Brainstorms. MIT Press. (Cited by 3 | Annotation | Google | Edit)

Edis, Taner (1998). How Godel's theorem supports the possibility of machine intelligence. Minds and Machines 8 (2):251-262. (Google | More links | Edit)

Abstract: Gödel's Theorem is often used in arguments against machine intelligence, suggesting humans are not bound by the rules of any formal system. However, Gödelian arguments can be used to support AI, provided we extend our notion of computation to include devices incorporating random number generators. A complete description scheme can be given for integer functions, by which nonalgorithmic functions are shown to be partly random. Not being restricted to algorithms can be accounted for by the availability of an arbitrary random function. Humans, then, might not be rule-bound, but Gödelian arguments also suggest how the relevant sort of nonalgorithmicity may be trivially made available to machines

Feferman, S. (1996). Penrose's Godelian argument. Psyche 2:21-32. (Google | Edit)

Abstract: In his book Shadows of the Mind: A search for the missing science of con- sciousness [SM below], Roger Penrose has turned in another bravura perfor- mance, the kind we have come to expect ever since The Emperor’s New Mind [ENM ] appeared. In the service of advancing his deep convictions and daring conjectures about the nature of human thought and consciousness, Penrose has once more drawn a wide swath through such topics as logic, computa- tion, artiﬁcial intelligence, quantum physics and the neuro-physiology of the brain, and has produced along the way many gems of exposition of diﬃcult mathematical and scientiﬁc ideas, without condescension, yet which should be broadly appealing.¹ While the aims and a number of the topics in SM are the same as in ENM , the focus now is much more on the two axes that Pen- rose grinds in earnest. Namely, in the ﬁrst part of SM he argues anew and at great length against computational models of the mind and more speciﬁ- cally against any account of mathematical thought in computational terms. Then in the second part, he argues that there must be a scientiﬁc account of consciousness but that will require a (still to be found) non-computational extension or modiﬁcation of present-day quantum physics

Gaifman, H. (2000). What Godel's incompleteness result does and does not show. Journal of Philosophy 97 (8):462-471. (Cited by 3 | Google | More links | Edit)

Abstract: In a recent paper S. McCall adds another link to a chain of attempts to enlist Gödel’s incompleteness result as an argument for the thesis that human reasoning cannot be construed as being carried out by a computer.1 McCall’s paper is undermined by a technical oversight. My concern however is not with the technical point. The argument from Gödel’s result to the no-computer thesis can be made without following McCall’s route; it is then straighter and more forceful. Yet the argument fails in an interesting and revealing way. And it leaves a remainder: if some computer does in fact simulate all our mathematical reasoning, then, in principle, we cannot fully grasp how it works. Gödel’s result also points out a certain essential limitation of self-reflection. The resulting picture parallels, not accidentally, Davidson’s view of psychology, as a science that in principle must remain “imprecise”, not fully spelt out. What is intended here by “fully grasp”, and how all this is related to self-reflection, will become clear at the end of this comment

George, A. & Velleman, Daniel J. (2000). Leveling the playing field between mind and machine: A reply to McCall. Journal of Philosophy 97 (8):456-452. (Cited by 3 | Google | More links | Edit)

George, F. H. (1962). Minds, machines and Godel: Another reply to mr. Lucas. Philosophy 37 (January):62-63. (Annotation | Google | Edit)

Gertler, Brie (2004). Simulation theory on conceptual grounds. Protosociology 20:261-284. (Google | Edit)

Abstract: I will present a conceptual argument for a simulationist answer to (2). Given that our conception of mental states is employed in attributing mental states to others, a simulationist answer to (2) supports a simulationist answer to (1). I will not address question (3). Answers to (1) and (2) do not yield an answer to (3), since (1) and (2) concern only our actual practices and concepts. For instance, an error theory about (1) and (2) would say that our practices and concepts manifest a mistaken view about the real nature of the mental. Finally, I will not address question (2a), which is an empirical question and so is not immediately relevant to the conceptual argument that is of concern here

Good, I. J. (1969). Godel's theorem is a red Herring. British Journal for the Philosophy of Science 19 (February):357-8. (Cited by 8 | Annotation | Google | More links | Edit)

Good, I. J. (1967). Human and machine logic. British Journal for the Philosophy of Science 18 (August):145-6. (Cited by 7 | Annotation | Google | More links | Edit)

Gordon, Robert M. (online). Folk Psychology As Mental Simulation. Stanford Encyclopedia of Philosophy. (Cited by 8 | Google | More links | Edit)

Abstract: by, or is otherwise relevant to the seminar "Folk Psychology vs. Mental Simulation: How Minds Understand Minds," a National

Grush, Rick & Churchland, P. (1995). Gaps in Penrose's toiling. In Thomas Metzinger (ed.), Conscious Experience. Ferdinand Schoningh. (Google | Edit)

Hadley, Robert F. (1987). Godel, Lucas, and mechanical models of mind. Computational Intelligence 3:57-63. (Cited by 1 | Annotation | Google | Edit)

Hanson, William H. (1971). Mechanism and Godel's theorem. British Journal for the Philosophy of Science 22 (February):9-16. (Annotation | Google | More links | Edit)

Hofstadter, Douglas R. (1979). Godel, Escher, Bach: An Eternal Golden Braid. Basic Books. (Cited by 65 | Annotation | Google | More links | Edit)

Hutton, A. (1976). This Godel is killing me. Philosophia 3 (March):135-44. (Annotation | Google | Edit)

Irvine, Andrew D. (1983). Lucas, Lewis, and mechanism -- one more time. Analysis 43 (March):94-98. (Annotation | Google | Edit)

Jacquette, Dale (1987). Metamathematical criteria for minds and machines. Erkenntnis 27 (July):1-16. (Cited by 3 | Annotation | Google | More links | Edit)

Ketland, Jeffrey & Raatikainen, Panu (online). Truth and provability again. (Google | Edit)

King, D. (1996). Is the human mind a Turing machine? Synthese 108 (3):379-89. (Google | More links | Edit)

Abstract: In this paper I discuss the topics of mechanism and algorithmicity. I emphasise that a characterisation of algorithmicity such as the Turing machine is iterative; and I argue that if the human mind can solve problems that no Turing machine can, the mind must depend on some non-iterative principle — in fact, Cantor's second principle of generation, a principle of the actual infinite rather than the potential infinite of Turing machines. But as there has been theorisation that all physical systems can be represented by Turing machines, I investigate claims that seem to contradict this: specifically, claims that there are noncomputable phenomena. One conclusion I reach is that if it is believed that the human mind is more than a Turing machine, a belief in a kind of Cartesian dualist gulf between the mental and the physical is concomitant

Kirk, Robert E. (1986). Mental machinery and Godel. Synthese 66 (March):437-452. (Annotation | Google | Edit)

Laforte, Geoffrey; Hayes, Pat & Ford, Kenneth M. (1998). Why Godel's theorem cannot refute computationalism: A reply to Penrose. Artificial Intelligence 104. (Google | Edit)

Leslie, Alan M.; Nichols, Shaun; Stich, Stephen P. & Klein, David B. (1996). Varieties of off-line simulation. In P. Carruthers & P. Smith (eds.), Theories of Theories of Mind. Cambridge University Press. (Google | More links | Edit)

Abstract: In the last few years, off-line simulation has become an increasingly important alternative to standard explanations in cognitive science. The contemporary debate began with Gordon (1986) and Goldman's (1989) off-line simulation account of our capacity to predict behavior. On their view, in predicting people's behavior we take our own decision making system `off line' and supply it with the `pretend' beliefs and desires of the person whose behavior we are trying to predict; we then let the decision maker reach a decision on the basis of these pretend inputs. Figure 1 offers a `boxological' version of the off-line simulation theory of behavior prediction.(1)

Lewis, David (1969). Lucas against mechanism. Philosophy 44 (June):231-3. (Cited by 10 | Annotation | Google | Edit)

Lewis, David (1979). Lucas against mechanism II. Canadian Journal of Philosophy 9 (June):373-6. (Cited by 7 | Annotation | Google | Edit)

Lindstrom, Per (2006). Remarks on Penrose's new argument. Journal of Philosophical Logic 35 (3):231-237. (Google | More links | Edit)

Abstract: It is commonly agreed that the well-known Lucas–Penrose arguments and even Penrose’s ‘new argument’ in [Penrose, R. (1994): Shadows of the Mind, Oxford University Press] are inconclusive. It is, perhaps, less clear exactly why at least the latter is inconclusive. This note continues the discussion in [Lindström, P. (2001): Penrose’s new argument, J. Philos. Logic 30, 241–250; Shapiro, S.(2003): Mechanism, truth, and Penrose’s new argument, J. Philos. Logic 32, 19–42] and elsewhere of this question

Lucas, John R. (1967). Human and machine logic: A rejoinder. British Journal for the Philosophy of Science 19 (August):155-6. (Cited by 3 | Annotation | Google | More links | Edit)

Abstract: We can imagine a human operator playing a game of one-upmanship against a programmed computer. If the program is Fn, the human operator can print the theorem Gn, which the programmed computer, or, if you prefer, the program, would never print, if it is consistent. This is true for each whole number n, but the victory is a hollow one since a second computer, loaded with program C, could put the human operator out of a job.... It is useless for the `mentalist' to argue that any given program can always be improves since the process for improving programs can presumably be programmed also; certainly this can be done if the mentalist describes how the improvement is to be made. If he does give such a description, then he has not made a case

Lucas, John R. (1984). Lucas against mechanism II: A rejoinder. Canadian Journal of Philosophy 14 (June):189-91. (Cited by 2 | Annotation | Google | Edit)

Lucas, John R. (1970). Mechanism: A rejoinder. Philosophy 45 (April):149-51. (Annotation | Google | Edit)

Lucas, John R. (1971). Metamathematics and the philosophy of mind: A rejoinder. Philosophy of Science 38 (2):310-13. (Cited by 4 | Google | More links | Edit)

Lucas, John R. (1961). Minds, machines and Godel. Philosophy 36 (April-July):112-127. (Cited by 72 | Annotation | Google | More links | Edit)

Abstract: Goedel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, then it would not be false, but would be true, since in any consistent system nothing false can be provedin-the-system, but only truths. So the formula "This formula is unprovable-in-the-system" is not provable-in-the-system, but unprovablein-the-system. Further, if the formula "This formula is unprovablein- the-system" is unprovable-in-the-system, then it is true that that formula is unprovable-in-the-system, that is, "This formula is unprovable-in-the-system" is true. Goedel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true---i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines

Lucas, John R. (1996). Mind, machines and Godel: A retrospect. In Peter Millican & A. Clark (eds.), Machines and Thought. Oxford University Press. (Annotation | Google | Edit)

Lucas, John R. (1968). Satan stultified: A rejoinder to Paul Benacerraf. The Monist 52 (1):145-58. (Cited by 10 | Annotation | Google | Edit)

Abstract: The argument is a dialectical one. It is not a direct proof that the mind is something more than a machine, but a schema of disproof for any particular version of mechanism that may be put forward. If the mechanist maintains any specific thesis, I show that [146] a contradiction ensues. But only if. It depends on the mechanist making the first move and putting forward his claim for inspection. I do not think Benacerraf has quite taken the point. He criticizes me both for "failing to notice" that my ability to show that the Gödel sentence of a formal system is true "depends very much on how he is given

Lucas, John R. & Redhead, Michael (2007). Truth and provability. British Journal for the Philosophy of Science 58 (2):331-2. (Google | More links | Edit)

Abstract: The views of Redhead ([2004]) are defended against the argument by Panu Raatikainen ([2005]). The importance of informal rigour is canvassed, and the argument for the a priori nature of induction is explained. The significance of Gödel's theorem is again rehearsed

Lucas, John R. (1970). The Freedom of the Will. Oxford University Press. (Cited by 22 | Google | More links | Edit)

Lucas, John R. (ms). The Godelian argument: Turn over the page. (Cited by 3 | Google | Edit)

Abstract: I have no quarrel with the first two sentences: but the third, though charitable and courteous, is quite untrue. Although there are criticisms which can be levelled against the Gödelian argument, most of the critics have not read either of my, or either of Penrose's, expositions carefully, and seek to refute arguments we never put forward, or else propose as a fatal objection one that had already been considered and countered in our expositions of the argument. Hence my title. The Gödelian Argument uses Gödel's theorem to show that minds cannot be explained in purely mechanist terms. It has been put forward, in different forms, by Gödel himself, by Penrose, and by me

Lucas, John R. (1976). This Godel is killing me: A rejoinder. Philosophia 6 (March):145-8. (Annotation | Google | Edit)

Lucas, John R. (ms). The implications of Godel's theorem. (Google | More links | Edit)

Abstract: In 1931 Kurt Gödel proved two theorems about the completeness and consistency of first-order arithmetic. Their implications for philosophy are profound. Many fashionable tenets are shown to be untenable: many traditional intuitions are vindicated by incontrovertible arguments

Lyngzeidetson, Albert E. & Solomon, Martin K. (1994). Abstract complexity theory and the mind-machine problem. British Journal for the Philosophy of Science 45 (2):549-54. (Google | More links | Edit)

Abstract: In this paper we interpret a characterization of the Gödel speed-up phenomenon as providing support for the Nagel-Newman thesis that human theorem recognizers differ from mechanical theorem recognizers in that the former do not seem to be limited by Gödel's incompleteness theorems whereas the latter do seem to be thus limited. However, we also maintain that (currently non-existent) programs which are open systems in that they continuously interact with, and are thus inseparable from, their environment, are not covered by the above (or probably any other recursion-theoretic) argument

Lyngzeidetson, Albert E. (1990). Massively parallel distributed processing and a computationalist foundation for cognitive science. British Journal for the Philosophy of Science 41 (March):121-127. (Annotation | Google | More links | Edit)

Martin, J. & Engleman, K. (1990). The mind's I has two eyes. Philosophy 65 (264):510-515. (Annotation | Google | Edit)

Maudlin, Tim (1996). Between the motion and the act. Psyche 2:40-51. (Cited by 4 | Google | More links | Edit)

McCall, Storrs (1999). Can a Turing machine know that the Godel sentence is true? Journal of Philosophy 96 (10):525-32. (Cited by 6 | Google | More links | Edit)

6.1a	The Turing Test [87]

6.1b	Godelian arguments [86]

6.1c	The Chinese Room [104]

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