‘Philosophy Looks At Chess’ and Raymond Smullyan

12 Dec. 2012 | by Peter Wong

As a casual but keen reader on the subject of philosophy, I was curious to come across the title, Philosophy Looks At Chess, edited by Benjamin Hale. It is an anthology of articles that explores various aspects of chess from a philosophical point of view. Many topics in which chess and philosophy intersect are examined by twelve professionals of either field. For instance: Do chess-playing computers really understand chess? Is choosing the right chess strategy analogous to how to deal with ethical problems? This essay collection proves to be a mixed bag in terms of quality and accessibility, so I cannot recommend it wholeheartedly. However, it does have some intriguing pieces, and here I will focus on one of its more readable chapters.

That chapter, ‘To Know the Past One Must First Know the Future: Raymond Smullyan and the Mysteries of Retrograde Analysis’, is by Bernd Graefrath. The author is a well-known figure in chess problem circles – he’s the subeditor of a retro section in The Problemist, for example – but I wasn’t aware that he’s also a professor and PhD in philosophy. (On a personal note, some years ago Bernd took the trouble of sending me a nice letter with the news that he, as the judge of a problem tourney that I participated in, had awarded a First Prize to my work!) His subject is Raymond Smullyan, the famous logician and philosopher who published two popular collections of retro chess problems, The Chess Mysteries of Sherlock Holmes, and The Chess Mysteries of the Arabian Knights.

Graefrath discusses some problems by Smullyan and others to introduce readers to the area of retrograde analysis, in which the solver delves into the past of a chess position. He points out interesting parallels between the ideas displayed in these retros and some philosophical concepts, such as “cognitive optimism” and “antiverificationism”. Thus we see how some of Smullyan’s philosophical viewpoints are evoked by his chess compositions! Take Smullyan’s stance against logical positivism, which holds that any statement is meaningless if it’s incapable of verification or refutation. Such a strict verificationism is incorrect, according to Smullyan, and Graefrath quotes a retro problem that is illustrative of this view.

Raymond Smullyan
The Chess Mysteries of Sherlock Holmes 1979

Indemonstrable mate in 2 moves

Can White mate in two moves in the diagram position? The answer seems to be ‘yes’, but it’s not possible to demonstrate the key move that would solve it. If Black’s last move was …e7-e5, then 1.dxe6 e.p.! (threat: 2.g8=Q) would work, and 1…0-0-0 allows 2.Bb7. However, Black’s last move was not necessarily …e7-e5, and so the en passant capture is only a potential key. Alternatively, Black could have made the last move with the king or the rook, in which case it’s illegal to castle now, and 1.Ke6! would solve, followed by 2.g8=Q. But this white king move cannot be confirmed as the key, because Black could indeed have played …e7-e5 last, implying that 1…0-0-0! is still legal as an escape move. Therefore, regardless of Black’s previous move, a white mate-in-two exists in the diagram – yet this “truth” of the position cannot be verified with a particular key move.

The article touches on Smullyan’s fascination with Eastern mysticism, a subject seemingly at odds with the strict logic of his profession. Graefrath writes, “In the final chapter of The Tao Is Silent, Smullyan presents a dialogue in which a metaphysician and a mystic develop a view that may be most attractive for someone with a high regard for logic, mathematics and the sciences, but still thinks that the area of meaningful discourse is not restricted to this area. They may not even cover the most important questions!” Such an attitude happens to coincide with my own, and I share Smullyan’s enthusiasm for mysticism as a sophisticated form of spirituality. I’d recommend The Tao Is Silent as well as another of his books, Who Knows?: A Study of Religious Consciousness, as excellent introductions to mystical thoughts (or non-thoughts!?). Smullyan is a wonderful writer, and for a taste of his style, check out the allegory ‘Planet Without Laughter’, in which a sense of humour, or “getting a joke”, is brilliantly used as a metaphor for spiritual enlightenment.

‘To Know the Past One Must First Know the Future: Raymond Smullyan and the Mysteries of Retrograde Analysis’ is available online as a preview of Philosophy Looks At Chess on Google Books.