Taking the big questions to bits

THE PHILOSOPHICAL COMPUTER: Exploratory Essays in Philosophical Computer Modeling. Patrick Grim, Gary Mar, and Paul St. Denis. MIT Press, 400pp. Pounds 33.95. ISBN 0 262 07185 1

The philosopher's toolkit, hitherto filled with bits of logic, looks set to expand by admitting coding and computation. Logical tools work well with static truth, but they do not get a good grip on processes. Computers on the other hand can show us processes, and also help us look inside them. An executing program after all just is a process.

The book explores the computer as a philosophical tool, and not just as a metaphor to which philosophers appeal ("mind as software"). It is an excursion through self-reference, fuzziness, chaos, fractals, the Game of Life, the iterated Prisoner's Dilemma, and the limits to computation - the first systematic such journey I know of to be packaged into a book and presented as a new paradigm of how to do philosophy.

The book starts off by dealing with various liars. There is the Simple Liar who writes, "This sentence is false". The Simple Liar has had enormous influence on philosophy. Coping with her is, surprisingly, the hardest problem in formal semantics. The book takes a non-standard "dynamic" view of truth, and also deals with more subtle liars, like the Half-Sayer who writes, "This sentence is as true as half its estimated truth-value".

In the dynamic conception, truth is fuzzy and can take a value from zero to one inclusive. The Simple Liar oscillates endlessly between an initial estimated truth-value x, and a second value, one minus x. It turns out that the Half-Sayer generates a sequence of fuzzy truth-values which always converges on the value two-thirds. Other Liars turn out to be chaotic:

"This sentence is as true as it is estimated to be false." You can draw nice two-dimensional truth-process diagrams. But what does all this mean? Possibly less for truth than for belief and reliability. In a second chapter, much of the first chapter's self-referential material is reworked and added to in the context of judgements of truth, where statements about the reliability of statements pile up and interact, and making up your mind can be modelled as a kind of computation.

A third chapter deals with fractal representations of the propositional calculus which are very pretty, and do make you look at that simple system differently. But most readers will find the fourth and fifth chapters, on Hobbes's Time of Warre, the Prisoner's Dilemma, cooperation, Life and Fuzzy Life the most interesting of the six. In the early 1980s the political scientist Robert Axelrod ran two tournaments to find the best strategy in the Prisoner's Dilemma (a situation where cooperation pays but only if it is mutual). When the dilemma is iterated and not played just once it turned out, surprisingly, that Tit for Tat (TFT) - co-operate first time, and then behave like your fellow-prisoner in the previous game - was the best reactive strategy. The book takes the iterated Prisoner's Dilemma and combines it with John Conway's famous Game of Life, in which cells in a two-dimensional grid die, survive, or come alive, depending only on the number of their living neighbours. In the spatialised, iterated Prisoner's Dilemma (SIPD), players in a grid adopt the locally best strategy in a sequence of plays. You can represent the changing population of strategies graphically, and prettily, on the screen. Again TFT does well, and tends to settle down to peaceful co-existence with ALWAYS DEFECT, which never co-operates. Quakers and doormats quickly die out. The book then fuzzifies the Game of Life, which leads to chaos. It fuzzifies the SIPD, and shows that a generous TFT, which sometimes co-operates even after being defected against, does even better than regular TFT. SIPD fuzzification also leads elegantly to a connection with the chaotic liars treated in the first chapter. Finally, the book shows that SIPD is undecidable. If philosophers need to explore, then this is philosophy. It is beginning to look as though the computer will be an important addition to the philosopher's armoury. It may even be that computing will be to 21st-century philosophy what logic has been to the philosophy of the 20th century.

The book suffers from some repetition, and shows its origins in a series of research papers. Nevertheless, it is essential reading for anyone wishing to use computers as a philosophical tool. By exploiting the iterative capability of computers and their capacity to help us visualise processes by throwing them on a screen the book makes an impressive start in supporting a new paradigm in philosophy: executable metaphysics. Code for each of the programs in the book takes up no more than a few hundred lines of, say, Java.

The book comes with an animated Director movie on CD-Rom, for both Mac and PC. Strongly recommended.

Peter Gibbins is Executive Director, Digital VCE and visiting professor in computer science, University of Exeter.