Beyond the Limits of Thought (review)

Imagine that a foundational principle of Western science, logic and reason—perhaps the foundational principle—turns out in certain circumstances to be deeply inadequate, even fatally flawed. This is, in effect, what logician Graham Priest sets out to prove in Beyond the Limits of Thought. The foundational principle at stake is that of "non-contradiction," the axiom of rational belief that asserts that a given state cannot be both true and false at the same time. Since it was proposed and defended by Aristotle in the Metaphysics, the principle of non-contradiction (PNC) has exerted a mighty grip on Western thought, serving to underpin much, if not all, reasoned inquiry. But as Priest makes clear, despite the apparent obviousness of the principle, it has been periodically tested during the course of philosophical history and, when pressed, found seriously wanting.

In this mind-bending (and for the uninitiated, sometimes mind-boggling) book, Graham Priest sets out to show that despite the best efforts of some of the most potent minds in history there are states of "true contradiction." The claim is that when we examine the extreme limits of what it is to say, count,

Reviews Panel: Peter Anders, Fred Allan Andersson, Wilfred Arnold, Roy Ascott, Curtis Bahn, Claire Barliant, René Beekman, Roy R. Behrens, Andreas Broeckmann, Annick Bureaud, Chris Cobb, Robert Coburn, Donna Cox, Sean Cubitt, Nina Czegledy, Shawn Decker, Margaret Dolinsky, Dennis Dollens, Luisa Paraguai Donati, Victoria Duckett, Maia Engeli, Enzo Ferrara, Deborah Frizzell, Bulat M. Galeyev, George Gessert, Elisa Giaccardi, Thom Gillespie, Allan Graubard, Dene Grigar, Diane Gromala, Rob Harle, Craig Harris, Josepha Haveman, Paul Hertz, Amy Ione, Stephen Jones, Richard Kade, Curtis E.A. Karnow, Nisar Keshvani, Julien Knebusch, Daniela Kutschat, Mike Leggett, Roger F. Malina, Jacques Mandelbrojt, Robert A. Mitchell, Rick Mitchell, Mike Mosher, Axel Mulder, Kevin Murray, Frieder Nake, Maureen A. Nappi, Angela Ndalianis, Simone Osthoff, Jack Ox, Robert Pepperell, Kjel yngve Petersen, Cliff Pickover, Patricia Pisters, Michael Punt, Harry Rand, Sonya Rapoport, Edward Shanken, Aparna Sharma, Shirley Shor, George K. Shortess, Joel Slayton, Christa Sommerer, Yvonne Spielmann, David Surman, Pia Tikka, David Topper, Rene van Peer, Stefaan van Ryssen, Ian Verstegen, Stephen Wilson, Arthur Woods, Soh Yeong.

know and think, we unavoidably encounter conditions that are both true and not true at the same time; these conditions are what Priest calls "dialethic" states: "I claim that reality is, in a certain sense, contradictory . . . . What I mean is that there are certain contradictory statements (propositions, sentences—take your pick) about limits that are true" (p. 295).

As Priest would have it, there are four types of limit to thought, and we are introduced to each in part 1 of the book. The general arguments about the limits of expression, iteration, cognition and conception, although not overly complex, are too involved to reiterate here. But, in broad terms, they amount to the same thing in each case: That the unknowable is precisely that which we can know nothing about, and that in knowing we can know nothing about it, we know something about it, which is a contradiction, not to say a paradox. On the face of it, this contradiction may seem no more than a vicious piece of philosophical wordplay, until one learns that the combined efforts of Aristotle, Berkeley, Kant, Frege, Russell, Wittgenstein, Heidegger and Derrida (to name a few) have failed to dispose of this simple, yet unfathomable, conundrum as it appears in its various forms.

The relationship between the limits of thought and contradiction might be described as a vein that runs prominently through the history of Western philosophy—except that it is more like a major artery (p. 6).

By examining some of the key arguments in Western logic concerning the ultimate nature and limits of mind, Priest sequentially disposes of many significant prior attempts to undo the paradoxes that arise. The only conclusion one can draw, according to Priest, is that the nature and limits of mind are actually paradoxical and that rather than deny...