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[Beyond the Limits of Thought] [By: Priest, Graham] [February, 2003]
This is a philosophical investigation of the nature and 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 theorized by Kant and Hegel. He offers new interpretations of Berkeley's master argument for idealism and Kant on the antinomies. He explores the paradoxes of self-reference and provides a unified account of the structure of such paradoxes. The book goes on to trace the theme of the limits of thought in modern philosophy of language, including discussions of the ideas of Wittgenstein and Derrida.This second and extended edition includes new chapters on Heidegger and Nagarjuna as well as reflections on reactions to the first edition.
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First published January 1, 1995
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Displaying 1 - 12 of 12 reviews
July 3, 2023
Get used to it: paradox and contradiction are inherent in human thought. So one could conclude from reading this fascinating book by Australian philosopher Graham Priest. Priest is the primary champion of dialetheism, a philosophical position that allows some contradictions to be true and is based on extensions of classical logic - systemic extensions in the formal realm that are metaphorically similar to Einstein’s extensions of Newtonian’s physical realm. Priest argues that the classical Law of Non-Contradiction has too long held the western mind hostage and kept it from exploring other types of truth and developing other forms of logic such as paraconsistent logics. It is at the boundaries of human thought that these kinds of dialetheias or true contradictions arise most prominently.
In this volume Priest examines the boundaries of thought in four areas, 1) the limits of expression, 2) the limits of conception, 3) the limits of cognition (what can/can’t be known), and 4) the limits of iteration (what can/can’t be calculated, operated, i.e., the mathematical infinite). The book proceeds mostly historically, examining examples of the limits of thought in pre-Kantian philosophy such as Cratylus, Aristotle, Cusanus, Sextus, Aquinas, Leibniz, Berkeley, then explores the limits of thought in Kant’s noumena, categories, and antimonies, and then Hegel’s conceptions of infinity. Later Priest explores modern forms of mathematics and logic starting with Cantor, Russell, Ramsey, Zermelo, Von Neumann, then on into the limits of language with Frege, Wittgenstein, Quine, Davidson, and Derrida. Most of the chapters are readable by those with little or no experience with logical notation but some of the chapters (8-11) are rather technical. This second edition ends with three new chapters, one on Heidegger, one on Nagarjuna (co-written with Jay Garfield), and one on further reflections on dialetheism.
Priest sees these recurring contradictions at the limits of thought expressing a similar form and has developed what he calls the Inclosure Schema to describe their common structure. Priest concludes that throughout history human attempts to say the unsayable, to bring heaven down to earth (so to speak) have resulted in paradox and contradiction and, despite the many attempts to avoid, ignore, or get around them, they reappear later in new forms. The wise conclusion is to admit that some form of dialetheism is necessary for certain kinds of thought to proceed towards greater types of truth.
I’m not sure why Priest’s work hasn’t been discovered by more nondualist philosophers, those of us who are thoroughly comfortable with a worldview where human thought and reason are understood to be inherently bound by contradiction and paradox. If you are a Mahayana Buddhist, Advaita, Tiantai Buddhist, or Daoist philosopher, you are probably already very familiar with this territory and should be happy that Western philosophers are slowly coming to understand what some philosophies of Asia have known for centuries: that the human mind is coextensive with conventional reality and truth in which all attempts to characterize ultimate-final truth [paramartha-satya], can only come up with paradox, contradiction, dualisms, oppositions, inconsistencies, incompleteness, and the like. Buddhist philosophy consistently employs paradox and contradiction in order to point out the limitations of the mind and its conventional truth-makers, for the purpose of pointing the practitioner’s awareness to the ultimate nondual truth that lies waiting free of all forms of mental grasping. Good places to start on nondual philosophy (for those with a philosophical background) are Huntington’s The Emptiness of Emptiness: An Introduction to Early Indian Madhyamika, Nagao’s The Foundational Standpoint of Madhyamika Philosophy, Ziporyn’s Emptiness and Omnipresence: An Essential Introduction to Tiantai Buddhism, Garfield’s volume of essays Empty Words: Buddhist Philosophy and Cross-Cultural Interpretation, and his magisterial translation of Nagarjuna’s The Fundamental Wisdom of the Middle Way: Nāgārjuna's Mūlamadhyamakakārikā.
In the earlier version of my review, I noted that Priest’s project lacked adequate methods of confirming the inherent paradox of the mind, suggesting that nondual meditation practices could provide such confirmation. No doubt meditation practices can enhance and complement the kind of dialectical reasoning that issues from exploring the boundaries of the human mind, but as Buddhism teaches, neither practice nor study alone can reveal the ultimate – both are critical to revealing the Nondual Absolute.
Nonetheless, the nondual philosophers of Asia have employed dialectical reasoning together with meditation for centuries and have arguably developed a deeper and more complete understanding of the nature of the mind and consciousness due to that combination. In meditation the limits of thought are revealed and confirmed in ways that conventional methods of argumentation, discourse, language, and conceptualization are unable to. I suspect those attracted to Priest’s dialetheic works are also paying attention to various forms of meditative confirmation practices.
Whatever your background, if you are a philosopher and are interested in the larger metaphysical questions of philosophy—God, infinity, the absolute, fundamental ontology, or simply limits and boundaries, Priest’s book will delight you. I can also recommend Priest’s other books Doubt Truth to be a Liar, In Contradiction: A Study of the Transconsistent and An Introduction to Non-Classical Logic.
3-12-22, updated, edited
6-2-23, edited
In this volume Priest examines the boundaries of thought in four areas, 1) the limits of expression, 2) the limits of conception, 3) the limits of cognition (what can/can’t be known), and 4) the limits of iteration (what can/can’t be calculated, operated, i.e., the mathematical infinite). The book proceeds mostly historically, examining examples of the limits of thought in pre-Kantian philosophy such as Cratylus, Aristotle, Cusanus, Sextus, Aquinas, Leibniz, Berkeley, then explores the limits of thought in Kant’s noumena, categories, and antimonies, and then Hegel’s conceptions of infinity. Later Priest explores modern forms of mathematics and logic starting with Cantor, Russell, Ramsey, Zermelo, Von Neumann, then on into the limits of language with Frege, Wittgenstein, Quine, Davidson, and Derrida. Most of the chapters are readable by those with little or no experience with logical notation but some of the chapters (8-11) are rather technical. This second edition ends with three new chapters, one on Heidegger, one on Nagarjuna (co-written with Jay Garfield), and one on further reflections on dialetheism.
Priest sees these recurring contradictions at the limits of thought expressing a similar form and has developed what he calls the Inclosure Schema to describe their common structure. Priest concludes that throughout history human attempts to say the unsayable, to bring heaven down to earth (so to speak) have resulted in paradox and contradiction and, despite the many attempts to avoid, ignore, or get around them, they reappear later in new forms. The wise conclusion is to admit that some form of dialetheism is necessary for certain kinds of thought to proceed towards greater types of truth.
I’m not sure why Priest’s work hasn’t been discovered by more nondualist philosophers, those of us who are thoroughly comfortable with a worldview where human thought and reason are understood to be inherently bound by contradiction and paradox. If you are a Mahayana Buddhist, Advaita, Tiantai Buddhist, or Daoist philosopher, you are probably already very familiar with this territory and should be happy that Western philosophers are slowly coming to understand what some philosophies of Asia have known for centuries: that the human mind is coextensive with conventional reality and truth in which all attempts to characterize ultimate-final truth [paramartha-satya], can only come up with paradox, contradiction, dualisms, oppositions, inconsistencies, incompleteness, and the like. Buddhist philosophy consistently employs paradox and contradiction in order to point out the limitations of the mind and its conventional truth-makers, for the purpose of pointing the practitioner’s awareness to the ultimate nondual truth that lies waiting free of all forms of mental grasping. Good places to start on nondual philosophy (for those with a philosophical background) are Huntington’s The Emptiness of Emptiness: An Introduction to Early Indian Madhyamika, Nagao’s The Foundational Standpoint of Madhyamika Philosophy, Ziporyn’s Emptiness and Omnipresence: An Essential Introduction to Tiantai Buddhism, Garfield’s volume of essays Empty Words: Buddhist Philosophy and Cross-Cultural Interpretation, and his magisterial translation of Nagarjuna’s The Fundamental Wisdom of the Middle Way: Nāgārjuna's Mūlamadhyamakakārikā.
In the earlier version of my review, I noted that Priest’s project lacked adequate methods of confirming the inherent paradox of the mind, suggesting that nondual meditation practices could provide such confirmation. No doubt meditation practices can enhance and complement the kind of dialectical reasoning that issues from exploring the boundaries of the human mind, but as Buddhism teaches, neither practice nor study alone can reveal the ultimate – both are critical to revealing the Nondual Absolute.
Nonetheless, the nondual philosophers of Asia have employed dialectical reasoning together with meditation for centuries and have arguably developed a deeper and more complete understanding of the nature of the mind and consciousness due to that combination. In meditation the limits of thought are revealed and confirmed in ways that conventional methods of argumentation, discourse, language, and conceptualization are unable to. I suspect those attracted to Priest’s dialetheic works are also paying attention to various forms of meditative confirmation practices.
Whatever your background, if you are a philosopher and are interested in the larger metaphysical questions of philosophy—God, infinity, the absolute, fundamental ontology, or simply limits and boundaries, Priest’s book will delight you. I can also recommend Priest’s other books Doubt Truth to be a Liar, In Contradiction: A Study of the Transconsistent and An Introduction to Non-Classical Logic.
3-12-22, updated, edited
6-2-23, edited
August 12, 2019
This is one of Priest's books on the subject of dialetheism, the position that there are true contradictions: propositions A such that both A and not-A are true. "In Contradiction" addresses the technical aspects of this position, "Doubt Truth to be a Liar" addresses the implications for rationality, and "Beyond the Limits of Thought" is an exegesis of historical discoveries (or purported discoveries) of a particular class of contradiction. Specifically, this book describes the contradictions which arise at the limits of thought: the limits of what is knowable, definable, expressible, describable, iterable, etc. These paradoxes, which appear to be of various kinds (set-theoretic, semantic, etc.), are shown to be instances of a single pattern (the "inclosure schema") and Priest argues convincingly that dialetheism offers the only uniform solution to all inclosure paradoxes.
Priest's writing and argumentation are clear throughout, and his erudition in both the mathematical and philosophical domains of logic is impressive. I find the case he makes here (and elsewhere) for dialetheism convincing, so far. We'll see what I think once I'm done with the more technical "In Contradiction".
Priest's writing and argumentation are clear throughout, and his erudition in both the mathematical and philosophical domains of logic is impressive. I find the case he makes here (and elsewhere) for dialetheism convincing, so far. We'll see what I think once I'm done with the more technical "In Contradiction".
December 12, 2011
This is probably the most comprehensive collection of arguments for dialetheism by the founder and most eloquent proponent of the position in the philosophy of logic that some contradictions are true. It is available in a very expensive hardbound and a pretty expensive paperback. It is well worth the price. The book provides a history of the philosophy of the logic of paradoxes at the limit of expression, infinity, cognition, and conception from Cratylus to Berkeley. The book follows the recent history of the paradoxes of self-reference in semantics and set theory from Russell to Tarski and ends by vsualizing the characteristic nature of these paradoxes in what he calls an inclosure schema, characterized by existence, transcendence, and closure. The second edition includes brilliant discussions of Heidegger and Nagarjuna and a reply to his (many) critics. Perhaps the best philosophy book of the 21st century so far.
Priest maintains that most of the paradoxes that have arisen like bad pennies in the history of philosophy; the Liar, Russell’s paradox, Konig’s paradox, and many more; fall into a common pattern. Russell himself posed the formula for the set-theoretic version of these paradoxes (1905, “On Some Difficulties in the Theory of Transfinite Numbers and Order Types” with notation modified by Priest):
Given a property ϕ and a function δ, such that, if ϕ belongs to all members of u, δ(u) always exists, has the property ϕ, and is not a member of u; then the supposition that there is a class Ω of all terms having property ϕ and that δ(Ω) exists leads to the conclusion that δ(Ω) both has and has not the property ϕ.
Priest is a technical logician and likes to express this in functional notation:
(1) Ω = {x; ϕ(x)} exists and ψ(Ω) (Existence)
(2) For all x ↄ Ω such that ψ(x):
δ(x) ~є x (Transcendence)
δ(x) є Ω (Closure)
My favorite example of this comes from a paper that Priest did with Jay Garfield, the translator of Nagarjuna, entitled “Nagarjuna and the limits of thought”, which is reprinted both in Garfield’s book Empty Words and Priest’s book under consideration here. Nagarjuna says in the MulaMadhyamakakarika (Chapter XVIII; 8):
Everything is real and is not real,
Both real and not real,
Neither real nor not real.
This is the Lord Buddha’s teaching.
Nagarjuna says in the Vigrahavyavartani
By their nature, the things are not a determinate entity. Their nature is a non-nature; it is their no-nature that is their nature. For they have only one nature; no nature . . .
They call this Nagarjuna’s ontological contradiction. The Inclosure arises as follows:
ϕ(x) is ‘x is empty’
ψ(x) is ‘x is a set of things with some common nature’
δ(x) is ‘the nature of things in x’
If a thing belongs both to the set of things that have some common nature and to the set of things that are empty, it follows that the nature of things is to have no nature. All things both do and do not have a nature. Note that Nagarjuna implies that all things fall into this category. Priest doesn’t go that far. For it is only the special class of things that inhabit the margins of experience that fall into dialetheism, showing that Parmenides’s Law of Non-Contradiction is false for at least one category of situations. This, of course, is the position that Priest has helped to make famous and which has brought down upon him such a host of criticism, from so many, including his old teacher, Susan Haack.
Priest maintains that most of the paradoxes that have arisen like bad pennies in the history of philosophy; the Liar, Russell’s paradox, Konig’s paradox, and many more; fall into a common pattern. Russell himself posed the formula for the set-theoretic version of these paradoxes (1905, “On Some Difficulties in the Theory of Transfinite Numbers and Order Types” with notation modified by Priest):
Given a property ϕ and a function δ, such that, if ϕ belongs to all members of u, δ(u) always exists, has the property ϕ, and is not a member of u; then the supposition that there is a class Ω of all terms having property ϕ and that δ(Ω) exists leads to the conclusion that δ(Ω) both has and has not the property ϕ.
Priest is a technical logician and likes to express this in functional notation:
(1) Ω = {x; ϕ(x)} exists and ψ(Ω) (Existence)
(2) For all x ↄ Ω such that ψ(x):
δ(x) ~є x (Transcendence)
δ(x) є Ω (Closure)
My favorite example of this comes from a paper that Priest did with Jay Garfield, the translator of Nagarjuna, entitled “Nagarjuna and the limits of thought”, which is reprinted both in Garfield’s book Empty Words and Priest’s book under consideration here. Nagarjuna says in the MulaMadhyamakakarika (Chapter XVIII; 8):
Everything is real and is not real,
Both real and not real,
Neither real nor not real.
This is the Lord Buddha’s teaching.
Nagarjuna says in the Vigrahavyavartani
By their nature, the things are not a determinate entity. Their nature is a non-nature; it is their no-nature that is their nature. For they have only one nature; no nature . . .
They call this Nagarjuna’s ontological contradiction. The Inclosure arises as follows:
ϕ(x) is ‘x is empty’
ψ(x) is ‘x is a set of things with some common nature’
δ(x) is ‘the nature of things in x’
If a thing belongs both to the set of things that have some common nature and to the set of things that are empty, it follows that the nature of things is to have no nature. All things both do and do not have a nature. Note that Nagarjuna implies that all things fall into this category. Priest doesn’t go that far. For it is only the special class of things that inhabit the margins of experience that fall into dialetheism, showing that Parmenides’s Law of Non-Contradiction is false for at least one category of situations. This, of course, is the position that Priest has helped to make famous and which has brought down upon him such a host of criticism, from so many, including his old teacher, Susan Haack.
July 16, 2021
The main thesis of the book is to argue that "The only satisfactory uniform approach to all these paradoxes is the dialetheic one, which takes the paradoxical contradictions to be exactly what they appear to be . The limits of thought which are the inclosures are truly contradictory objects". And all these paradoxes are of the same kind: A totality (Closure) with a self reference that denies itself (Transcendence), like Russell's or the Liar's and so on. And while all the solutions discussed ultimately take the Aristotelian way out. The limit (the totality of all collections countenanced by the theory) is said not to exist was more than sufficient, only Cantor's paradox where denying the paradox using this solution results in another paradox because the Domain Principle will be violated.
January 23, 2019
A provocative book, though I felt flawed by the over-reach of its central thesis. Priest is perhaps most well known for his work on paraconsistent logics, some of which allow for dialetheisms or true contradictions. This amounts to heresy to most logicians, though Priest is one of a growing number who have come to accept that the Western belief in the law of non-contradiction brings with it a set of paradoxical consequences.
Though this is a book of logic, the central thesis of this book is that nearly every philosopher in the Western tradition (including a good portion of logical and mathematical progress since the late 19th century) has fallen victim to a hidden contradiction within their own systems of thought. Priest aims to show this with a sprawling historical narrative, ranging from the pre-Socratic writers to the cutting edges of set theory, Wittgenstein, and Heidgger. Of the whole tradition, it is only Hegel who stands out as even aware of the problem; his dialectical pattern, says Priest, uniquely equips him to comprehend the fundamental problem. Eastern thinkers, of whom Nagarjuna is the representative in this book, exemplify a similar way of thinking, challenging the ideals of stability and equilibrium that underwrite so much of our thinking about thinking.
I always reserve the right to skepticism about sweeping historical narratives, and I felt that the project fell flat in places -- either due to a faulty exegesis, or simply trying to hard to locate the pattern of contradiction within such a diverse cast of thinkers. Nevertheless, there is much of interest here. This is a fine example of a philosopher who you read knowing and expecting to disagree and still come away better for the effort.
Though this is a book of logic, the central thesis of this book is that nearly every philosopher in the Western tradition (including a good portion of logical and mathematical progress since the late 19th century) has fallen victim to a hidden contradiction within their own systems of thought. Priest aims to show this with a sprawling historical narrative, ranging from the pre-Socratic writers to the cutting edges of set theory, Wittgenstein, and Heidgger. Of the whole tradition, it is only Hegel who stands out as even aware of the problem; his dialectical pattern, says Priest, uniquely equips him to comprehend the fundamental problem. Eastern thinkers, of whom Nagarjuna is the representative in this book, exemplify a similar way of thinking, challenging the ideals of stability and equilibrium that underwrite so much of our thinking about thinking.
I always reserve the right to skepticism about sweeping historical narratives, and I felt that the project fell flat in places -- either due to a faulty exegesis, or simply trying to hard to locate the pattern of contradiction within such a diverse cast of thinkers. Nevertheless, there is much of interest here. This is a fine example of a philosopher who you read knowing and expecting to disagree and still come away better for the effort.
June 22, 2023
Absolutely excellent work. Priest is somewhat obscure in the public eye because of the semi-esoteric and highly technical nature of his work, which is a tragedy, because he is a first rate thinker. The central thesis of this book is that there are dialethia, or true contradictions, we are embroiled in at the limits of thought, such as the Liar’s Paradox everyone is familiar with, and that all across the history of philosophy, thinkers have run up against this limit, often with fascinating results. This book is surprisingly accessible to those without much experience in formal logic (all you really need is a basic familiarity with some of the quantifying symbols), and is not at all dry considering the subject matter. Chapters 8-11 are a little hairy, as these are by far the most formal, and there are a few sections in here which will simply go over the head of those without a proficiency in formal logic, but they’re not integral to understanding the overall work.
June 26, 2023
A very detailed technical/philosophical look at the contradictions and paradoxes to be found at the limits of thought. I found the section on Nargarjuna especially interesting - I did not understand at all what the Buddhists meant by 'emptiness'!
I read it primarily to see what the author had to say about the paradoxes of early set theory and the 'hamfisted' ways these were avoided. The paradoxes of the infinite and paradoxes of self-reference come up often but these are not the only ones.
The book often becomes overly technical and only suited to a very specialized set of readers which doesn't include me. And I don't have the time for it. Skip over those bits.
The author claims/suggests that our logic itself is deeply flawed and that 'reality' itself is deeply contradictory. If this is so it is amazing that we get by as well as we do. Or do we? What are the practical consequences of such an extraordinary claim?
I read it primarily to see what the author had to say about the paradoxes of early set theory and the 'hamfisted' ways these were avoided. The paradoxes of the infinite and paradoxes of self-reference come up often but these are not the only ones.
The book often becomes overly technical and only suited to a very specialized set of readers which doesn't include me. And I don't have the time for it. Skip over those bits.
The author claims/suggests that our logic itself is deeply flawed and that 'reality' itself is deeply contradictory. If this is so it is amazing that we get by as well as we do. Or do we? What are the practical consequences of such an extraordinary claim?
August 8, 2021
Such a delightful book! I'll probably have to read parts of it again to understand it better but I feel I've already gotten a lot out of it. Yes, there are some parts that feel too technical ( unless you're a logician) but the unified treatment of paradoxes/contradictions from different areas like theology, set theory and language is more than exciting to make you work through it.
November 4, 2021
Fantastic examination of the contradictory ends of philosophical theories, ranging from the Ancient period up until Frege. Scanty on the citations for philosophers like Kant and Hegel, which would make scholars working on those philosophers blush.
August 8, 2017
By far the best philosophical text I happened to read during my brief stint living in a cave as a neo-Benedictian monk.
December 9, 2024
An analytic case for the validity of dialetheism.
Displaying 1 - 12 of 12 reviews