Beyond the Limits of Thought

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This is a philosophical investigation of the nature of the limits of thought. Drawing on recent developments in the field of logic, Graham Priest shows that the description of such limits leads to contradiction, and argues that these contradictions are in fact veridical. Beginning with an analysis of the way in which these limits arise in pre-Kantian philosophy, Priest goes on to illustrate how the nature of these limits was theorised by Kant and Hegel. He offers new interpretations of Berkeley's master argument for idealism and Kant on the antimonies. He explores the paradoxes of self reference, and provides a unified account of the structure of such paradoxes. The book concludes by tracing the theme of the limits of thought in modern philosophy of language, including discussions of the ideas of Wittgenstein and Derrida.
 

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Some Strangeness in the Proportion
A Review of
Beyond the Limits of Thought
by Graham Priest, Oxford University Press, Second Edition, 2002.
(Originally written for the Cognitive Science Society, but this review is accessible to everyone. I own the copyright.)
Eric Dietrich
Dept. of Philosophy
Binghamton University
Binghamton, New York
dietrich@binghamton.edu
I commend to you a marvelous book – a book that shows us just how complex, and, indeed, mysterious, cognition can be. Beyond the Limits of Thought lives up to its name: it will expand your thinking about thinking (though that is not why it has this title).
Strictly speaking, Limits is a philosophy book. I do think every philosopher in the Cognitive Science Society should read it. (I actually think all philosophers should read it.) But I also think all other cognitive scientists – anthropologists, computer scientists, educators, linguists, neuroscientists, and psychologists – should read it, too, for here is a book that tells us something profound about human cognition, about the sort of world we live in, and about being a cognizer of any sort capable of a certain kind of self-reference. Going the other way, Limits is a complacency destroyer. I sometimes think that cognitive scientists, as a whole, are a tad complacent about current progress in the field: "It is slow, to be sure, but we are making steady progress." We are making progress, but we have a very long way to travel, a distance that I think is frequently underestimated. Limits is a good antidote to this.
In this review, I very briefly say what this book is about, and then I raise one objection to it that uniquely derives from research in cognitive science. Specifically, I will suggest that recent work on the illusion of explanatory depth (Rozenblit and Keil, 2002) raises some very interesting trouble for Priest's project.
1. True Contradictions and Dialetheic Limits
Limits is masterfully constructed, sophisticated and witty (in spots), clear and precise. These last two properties are crucial, since the book covers some tricky logical ground. But early on, the reader develops confidence that Priest will be able to explain everything to the reader's satisfaction.
Limits is about one, single cognitive phenomenon: traversing a limit of thought. Priest illustrates this phenomenon over and over again in a very wide variety of philosophical theories concerning thought. Priest shows us this traversing at the limit of what can be expressed, the limit of what can be conceived, the limit of what can be known, and the limit of what can be iterated, to name the main four. What does it mean to traverse a limit of thought? This is the crux of the book, and it is explained initially in the Introduction.
The sort of limits Priest is interested in are the boundaries of specific conceptual processes (expressing, conceiving, knowing, iterating, etc.). They are boundaries beyond which one cannot go, for that is the definition of these limits. But then, strangely, one can go beyond these limits – perhaps only immediately beyond, but still beyond the limit. How is this possible? Via self-reference – the source of many paradoxes. Such non-limiting limits (or gateless gates, as a famous Zen koan as it) have a very peculiar property: they are dialetheic, meaning that they are genuine, existing contradictions (Priest calls them true contradictions). It is a crucial assumption of Limits that certain contradictions obtain, i.e., that they can be validly derived. This, of course, requires rather serious overhaul of some fundamental notions of logic. For example, both the law of noncontradiction, "it is not the case that P and not P," and the law of the excluded middle "for any P, either P or not P" have to go (the law of the excluded middle has always lived under fire, at least in some quarters of philosophical logic.)
An example will make all this clear. Imagine that there are some things that humans simply
 

Contents

The limits of thought in preKantian philosophy
9
The limits of iteration
26
The limits of cognition
43
The limits of conception
61
The limits of thought in Kant and Hegel
79
Kants antinomies
94
Hegels infinities
113
Limits and the paradoxes of selfreference
123
Sets and classes
172
Technical appendix
188
Language and its limits
195
Translation reference and truth
214
Consciousness rules and differance
229
The persistence of inclosure
249
Bibliography
257
Index
266

Vicious circles
141
Parameterisation
155

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