TCS Daily

Searching for Bobby Fischer's Platonic Form

By Kenneth Silber - April 6, 2004 12:00 AM

Chess is not just a mentally challenging game to play. It is also a game that generates examples and analogies relevant to a broad range of intellectual concerns. If you do a search for "chess" here at TCS, you will find, among other things, Arnold Kling's discussion of man-versus-machine chess, Lee Harris's illustration in chess terms of the difference between rational and irrational enemies, Iain Murray's likening of Russian global-warming policy to a knight's move, and a piece by me noting philosopher Daniel Dennett's evocation of chess computers in his argument for the compatibility of free will and determinism.

I am a competent chess player (unlike Kling, that is), albeit no threat to the world's grandmasters. After falling off in participation for a few years, I have recently played frequently -- perhaps a bit too frequently -- aided by the ready availability of opponents at chess websites like this. I find the game to be not only fun but also rife with philosophical implications. It reinforces certain lessons of everyday philosophy, for instance the importance of trying hard (my games vary widely in quality, depending on effort and attention) and maintaining some humility (just when I think I've gotten good, someone comes along and wipes the board with me).

Chess also provides a window into some more arcane philosophical matters. The remainder of this article will focus on two difficult, and interrelated, questions. The first has to do with the nature of reality; the second is about the prospects for human and artificial intelligence in grappling with reality. In both cases, the search for an answer leads through a board game with 32 pieces and 64 squares.

Do Abstract Objects Exist?

No doubt, many college freshmen have rolled their eyes at the uselessness of Philosophy 101 when asked whether there exist perfect circles or other ideal entities. But a great deal rides on the longstanding philosophical debate about abstract objects. If, say, the number 12 has an existence independent of its particular manifestations in egg cartons and the like, then a view that the world consists solely of physical objects is inadequate.

This has potential religious implications; in a recent TCS essay, Edward Feser identified Platonism, or belief in a realm of abstract entities, as a key assumption underlying Western religion. Of course, believing in perfect circles does not necessarily entail believing in God; philosopher Keith Augustine has defended a naturalistic worldview that takes abstract objects into account. So, while debating Platonism will not settle an argument about religion, it does shake up easy assumptions about what does and does not exist.

To my mind, Platonism (whether in religious form or not) is a dispiriting philosophy. Its emphasis on another realm seems conducive to distaste for the messy, familiar world. Furthermore, as physicist Lee Smolin noted in his excellent book The Life of the Cosmos, Platonism calls into question whether there is any such thing as novelty. If the contents of the universe are just a playing-out of possibilities that exist in a timeless realm, then there is nothing truly new about them. Every flower, every mountain, every painting is merely a sample from a preexisting set of possible flowers, mountains or paintings.

What does this have to do with chess? The game actually complicates the question of whether abstract objects exist. Consider the Ruy Lopez, a common chess opening named after Ruy Lopez de Segura, a priest and chess expert in 16th-century Spain. White opens with a pawn, knight and bishop; black parries with pawn and knight, then decides how to respond to the bishop. The subsequent moves carry numerous, ramifying possibilities.

The various lines of attack and defense following the Ruy Lopez opening have different pros and cons. Some strategies are better than others. (The Steinitz Defense, where black pushes the queen's pawn on move three, is regarded as a bit dubious.) But no one has yet figured out any definitive best strategy for black or white. Hence, the Ruy Lopez is still played frequently by grandmasters in tournament competition, with varying outcomes.

Did the Ruy Lopez exist before its 16th-century namesake started playing it? A Platonist might say it did, as part of an abstract set of all possible chess openings. But chess itself has a finite history. The game originated around the seventh century A.D., and its modern rules became standard in the 15th century, not long before Ruy Lopez de Segura was playing. Platonic ideals are normally defined as timeless, yet in this case they seem also to be historically grounded. The world of abstractions seems to depend on our world.

Perhaps in some sense, all chess moves, positions and games are "out there," but they have a rather limited existence if nobody plays them. Interestingly, it appears physically impossible for any computer or other material entity ever to store complete information about the game. By some estimates, the number of possible chess games exceeds the number of particles in the universe.

Will Computers Outthink Humans?

Chess has long served as a touchstone for the progress of artificial intelligence. For years, the best human players retained a clear edge over chess-playing computers. Computers appeared to gain the advantage with the 1997 defeat of the reigning world champion, Gary Kasparov, by IBM's Deep Blue. But since then, the top ranks of chess have settled into an unexpected equilibrium between humans and computers. The computers and grandmasters are both getting better (and the grandmasters are getting better at playing computers).

This is a disappointing state of affairs for enthusiasts of artificial intelligence. Chess, with its demands for calculation and memory, is an activity seemingly well-suited for computers. If computers are making only moderate progress in chess, what prospect is there for them to develop such capabilities as creativity, common sense and consciousness -- let alone the superhuman intelligence that some experts predict?

There is an intriguing connection between this question and the debate over abstract objects. There is a strong streak of Platonism among those skeptical about the prospects for artificial intelligence. Mathematician-scientist Roger Penrose argued in his book The Emperor's New Mind that human intelligence involves not just computation but a grasp of abstract entities such as the Mandelbrot Set. Physicist Stephen Barr gave such ideas a theistic emphasis in his book Modern Physics and Ancient Faith, arguing that the human mind comprehends abstractions because it has an immaterial element.

Maybe. Yet if, as discussed earlier, a Platonic realm would be inimical to novelty, then Platonism seems an unlikely candidate to explain the shortfalls of artificial intelligence. After all, a capacity to produce new ideas and insights is a chief human advantage over computers (in chess and in general). If the Platonist idea is true -- if the Ruy Lopez opening was "out there" awaiting discovery -- then one might expect computers to have bested grandmasters by now, just by diligently searching through sets of possible moves.

In The Life of the Cosmos, Smolin explained how the laws of physics, rather than being timeless, Platonic entities, could have developed in a process of cosmic evolution -- that the universe's most basic rules may exhibit change and novelty. What does that have to do with chess? It could serve as an inspiration for developing new ways to play the game. Already, there are many chess variants, games played with new kinds or numbers of pieces, boards of different sizes or shapes, and so on.

Here, then, is a valuable test for chess-playing computers. How well can they do when confronted with non-standard, and perhaps barely recognizable, versions of the game? Perhaps at some point, computers will be developed that can adapt rapidly to, say, wildebeest chess or something even more exotic. When that day comes, artificial intelligence will have truly arrived.

Ken Silber recently wrote for TCS about dreaming of techno-genie.


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