Online research in philosophy

It has been argued, by Penrose and others, that Gödel's proof of his first incompleteness theorem shows that human mathematics cannot be captured by a formal system F: the Gödel sentence G(F) of F can be proved by a (human) mathematician but is not provable in F. To this argment it has been objected that the mathematician can prove G(F) only if (s)he can prove that F is consistent, which is unlikely if F is complicated. Penrose has invented a new argument intended to avoid this objection. In the paper I try to show that Penrose's new argument is inconclusive.

_The Chinese room argument_ - John Searle's (1980a) thought experiment and associated (1984) derivation - is one of the best known and widely credited counters to claims of artificial intelligence (AI), i.e., to claims that computers _do_ or at least _can_ (someday might) think. According to Searle's original presentation, the argument is based on two truths: _brains cause minds_ , and _syntax doesn't_ _suffice for semantics_ . Its target, Searle dubs "strong AI": "according to strong AI," according to Searle, "the computer is not merely a tool in the study of the mind, rather the appropriately programmed computer really _is_ a mind in the sense that computers given the right programs can be literally said to _understand_ and have other cognitive states" (1980a, p. 417). Searle contrasts "strong AI" to "weak AI". According to weak AI, according to Searle, computers just.

Roger Penrose is justly famous for his work in physics and mathematics but he is _notorious_ for his endorsement of the Gödel argument (see his 1989, 1994, 1997). This argument, first advanced by J. R. Lucas (in 1961), attempts to show that Gödel’s (first) incompleteness theorem can be seen to reveal that the human mind transcends all algorithmic models of it¹. Penrose's version of the argument has been seen to fall victim to the original objections raised against Lucas (see Boolos (1990) and for a particularly intemperate review, Putnam (1994)). Yet I believe that more can and should be said about the argument. Only a brief review is necessary here although I wish to present the argument in a somewhat peculiar form.

Sir Roger Penrose, retired professor of mathematics at the University of Oxford and collaborator with Stephen Hawking on black hole theory, has written 'a complete guide to the laws of the universe' called The Road to Reality. His publisher calls it the most important and ambitious work of science for a generation. Penrose caused a furore in the world of consciousness studies with his 1989 book The Emperor's New Mind, which conjectured a new mechanism for consciousness and kept a faithful band of researchers busy for a decade with models based on microtubules and the like. Sadly, the idea fizzled out. The title of the 2002 Tucson 'Toward a Science of Consciousness' conference poetry slam winner was: Microtubules - my ass!

Having, as it is generally agreed, failed to destroy the computational conception of mind with the G\"{o}delian attack he articulated in his {\em The Emperor's New Mind}, Penrose has returned, armed with a more elaborate and more fastidious G\"{o}delian case, expressed in and 3 of his {\em Shadows of the Mind}. The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is an instance of either the fallacy of denying the antecedent, the fallacy of {\em petitio principii}, or the fallacy of equivocation. More recently, writing in response to his critics in the electronic journal {\em Psyche}, Penrose has offered a G\"{o}delian case designed to improve on the version presented in {\em SOTM}. But this version is yet again another failure. In falling prey to the errors we uncover, Penrose's new G\"{o}delian case is unmasked as the same confused refrain J.R. Lucas initiated 35 years ago.

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.

Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever ...

Roger Penrose, in _The Emperor's New Mind_ (1989), writes about the way Mozart perceived music. Mozart did not play a piece in his mind in real time, or even speeded up, but could hold it before him all at once. We all do this, although usually for much shorter riffs than entire symphonies. I have argued that the all-at-onceness of our thoughts and perceptions is at least as inexplicable as what it is like to see red; I think the aural/temporal all-at-onceness makes the point at least as vividly as the visual/spatial all-at-onceness of the curl of smoke in an art nouveau poster.