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Graham Priest

05 Nov 2026 - 05 Nov 2026
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    • philosopher of dialetheism, which is the view that some contradictions are true. Mentioned on WS discord
      • John may be interested in checking out Graham Priest’s work on dialethism, in particular his book Beyond the Limits of Thought.
    • wow also has a whole book on Buddhism/Capitalism/Marxism
      • After this, we will turn to Marx’ account of what it is to be a person... this is very similar to the Buddhist view; and where the two accounts differ, the differences do not conflict with each other; rather, they are complementary.
    • Ask Claude
      • Now I have a good picture. Let me give you a comprehensive summary.

      • Graham Priest's Work on Logic Graham Priest is one of the most influential figures in non-classical logic, best known for developing and defending two interconnected positions: Dialetheism — the philosophical thesis that some contradictions are actually true. Not merely that we might believe contradictory things or that contradictions appear in our theories, but that reality itself contains true contradictions. The term was coined by Priest and Richard Routley (later Sylvan) in 1981. Paraconsistent Logic — formal logical systems in which contradictions do not "explode" into triviality. In classical logic, from any contradiction (A ∧ ¬A), you can derive absolutely anything (the principle of ex contradictione quodlibet or ECQ). Paraconsistent logics block this, allowing localized inconsistencies without the whole system becoming trivial. Priest's signature logic is **LP (Logic of Paradox)*, a three-valued logic where propositions can be true, false, or both true and false*. The "both" value is designated (counts as true for inference purposes), which lets contradictions be asserted without explosion. His major works include In Contradiction (1987/2006) which lays out the dialetheist program, and An Introduction to Non-Classical Logic (2008) which has become a standard textbook. He's also done extensive work on Buddhist logic, noting that the ancient Indian catuṣkoṭi (four-cornered negation) anticipated some of these ideas. The primary motivation comes from the semantic paradoxes—the Liar paradox ("this sentence is false"), Russell's paradox in set theory, and similar self-referential tangles. Priest argues these represent genuine true contradictions rather than mere puzzles to be dissolved through hierarchy or restriction.

      • Connections to AI (Particularly GOFAI) The AI connection is substantial, though not always directly credited to Priest himself. The lineage runs through several strands: Belnap-Dunn Four-Valued Logic — Nuel Belnap argued that a sophisticated question-answering machine should employ a four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions. His four values are: true, false, both, and neither. This became foundational for handling inconsistent databases and knowledge bases. AI is actually the most promising field of applications for many-valued logic, offering different areas including expert systems, databases, and knowledge-based systems where one likes to store vague information. Relevance Logic and Knowledge Representation — Most works in belief revision suppose a classical logic setting where the beliefs of the agent are consistent, but in real applications it may easily happen that beliefs are not consistent. In this case it seems reasonable to use paraconsistent logics to derive sensible conclusions from these inconsistent beliefs. This has generated work specifically on using Priest's LP logic for belief revision in AI systems. The Cyc Project — Interestingly, Thomas Macaulay Ferguson, who received his PhD from CUNY and co-authored the Oxford University Press Dictionary of Logic with Graham Priest, is currently an ontologist for the Cyc artificial intelligence project. This represents a direct intellectual lineage from Priest's work into one of the most ambitious GOFAI projects. Cyc has "microtheories" which allow it to reconcile seemingly contradictory facts from different domains, for example classical physics and quantum mechanics. The need to handle inconsistent information gracefully is a constant challenge in large-scale knowledge engineering. Database and Ontology Reasoning — In an open, constantly changing and collaborative environment like the Semantic Web, practical reasoning techniques for ontologies will have to be tolerant to noise and inaccuracies, including the ability to handle inconsistencies in a meaningful way. For this purpose, paraconsistent reasoning based on four-valued logic is employed. Practical Applications — Paraconsistent logic has received increasing interest from researchers in areas as disparate as artificial intelligence, robotics, medical diagnostics, statistical process control, and logistics, with applications including robot navigation, decision support systems, and signal processing. The philosophical motivation is quite practical from an AI standpoint: real-world knowledge bases inevitably contain inconsistencies, whether from conflicting data sources, evolving information, or simple errors. Classical logic makes this catastrophic since any inconsistency lets you prove anything. Paraconsistent approaches let systems continue reasoning sensibly even when their knowledge base isn't perfectly consistent—exactly what you'd want for robust AI systems operating with uncertain, evolving, real-world data.

      • Priest and Buddhist Logic: The Catuṣkoṭi In early Buddhist logic, it was standard to assume that for any state of affairs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time making sense of this, but it makes perfectly good sense in the semantics of various paraconsistent logics, such as First Degree Entailment. Priest's key insight is that what looks baffling under classical logic—where "both" and "neither" would be trivially equivalent or explosive—becomes perfectly coherent in FDE (First Degree Entailment). The four values of the catuṣkoṭi map directly onto Belnap's four truth values: true, false, both, neither. The tradition of using "Four Logical Alternatives," known as catuṣkoṭi, goes back to the 6th century Indian logic. These four alternatives precisely correspond to the aforementioned four values. However, undoubtedly, Belnap was the first to identify the two orders and to emphasise the usefulness of the four values for computer reasoning. But Nāgārjuna goes further—he sometimes rejects all four koṭis, which requires additional logical machinery. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest that none of these options, or more than one, may hold. Priest addresses this by adding a fifth value representing ineffability, hence his book title The Fifth Corner of Four.

      • Tiantai's Threefold Truth Tiantai represents a distinctively Chinese development that's structurally interesting alongside Priest's framework. From a philosophical standpoint, Zhiyi's greatest contribution to East Asian Buddhism has been his doctrine of the Threefold Truth, which is succinctly presented as the addition of a third Truth – the Middle – to Nagarjuna's Two Truths doctrine – Absolute Truth and Conventional Truth – where this third truth is conceived as an overlap between Nagarjuna's two truths. The three truths are:

      • Emptiness (空, kōng): all dharmas are empty of inherent existence
      • Provisional existence (假, jiǎ): yet they arise conventionally through conditions
      • The Middle (中, zhōng): both are true simultaneously In order to avoid thinking of principle versus phenomenon, the Tiantai School established the threefold truth: emptiness, temporariness, and mean. The truth of the zhongdi is really the Buddha-nature. What's crucial here—and what connects to paraconsistent thinking—is that Chi-i defines as superior "the contemplation in which all three truths are discerned simultaneously; this is the perfect and immediate calming and contemplation." This is not a sequential progression where you first see emptiness, then conventional existence, then synthesize them. It's an immediate apprehension of all three as aspects of a single integrated reality. They are viewed as alternate expositions of the same idea as it is recontextualized, to varying degrees of thoroughness as appropriate, even though—as we shall see—they appear prima facie to be in direct contradiction to one another.

      • Connections and Tensions Several interesting threads connect Priest's work to Tiantai: 1. The tolerance of apparent contradiction. This schema provides us with a strong general model of the Tiantai conception of the self-overcoming of suffering, impermanence and non-self, wherein they are overcome by remaining exactly as they were, indeed even more so, and thereby are revealed to also be their own opposites. This notion that something "includes just what it had initially appeared to exclude" resonates with dialetheism's acceptance of true contradictions. 2. Self-recontextualization. Tiantai's radical contextualism—where the identity of anything depends entirely on its context, including the "contextualizer"—has structural similarities to how Priest's plurivalent logics allow the same proposition to take multiple truth values. 3. Huayan's interpenetration. Priest devotes a chapter of The Fifth Corner of Four to Fazang and Huayan. This chapter turns to Huayan Buddhism, and the thought of Fazang. Huayan has a distinctive view of the nature of the interpenetration between conventional and ultimate reality. He uses graph theory to model mutual containment—how each dharma "contains" all others. Chapter 8 gives an interesting way of making sense of the Huayan theory that every part of reality contains every other part. Priest's graph-theoretic model is able to make precise sense of a statement. However, there's significant scholarly pushback on whether Priest correctly interprets these traditions. Priest has set out to show how a multi-valued logic of first-degree entailment may be used to shed light on what philosophers like Nāgārjuna, Candrakīrti, Fazang and Dōgen were up to. The exercise may lose some of its significance if it turns out that Nāgārjuna et al. did not say many of the things Priest takes them to have said. The concern is whether these traditions actually endorse true contradictions (dialetheism proper), or whether they're doing something more subtle—using apparent contradictions pedagogically, or operating at a level where the categories of "true" and "false" don't straightforwardly apply. This research thus acts as both a complement and a critique of formal and logical approaches to catuṣkoṭi... interpreting it within the framework of nonclassical logics such as paraconsistent logic and First-Degree Entailment to accommodate paradoxes and contradictions in Buddhist arguments.

      • The Tiantai Difference One thing that makes Tiantai particularly interesting here is its emphasis on mutual inclusion rather than mere conjunction. Huayan and Tiantai are sometimes contrasted: The Tientai view is radically decentralized - Ziporyn calls it "Omnicentric". Proposing a single source "mind" is idealistic and biased. This "omnidentity" or "omnicentrism"—where every point is equally the center—differs from Huayan's more hierarchical "mind-only" tendency. In Tiantai, the three truths aren't three levels but three aspects of the same reality, each equally ultimate, each containing the others. Form is emptiness and emptiness is form simultaneously, not as a progression. This might actually call for even more exotic logical structures than Priest explores—something closer to what contemporary category theorists do with self-referential structures, or perhaps the kind of "gluing" operations you'd find in topos theory where local truths get assembled into global coherence while preserving inconsistency at the boundaries.

      • Sketch of Further Connections For your interests, I'd suggest exploring:

      • Brook Ziporyn's work on Tiantai—he's the main English-language philosopher working on the formal/philosophical structure of Tiantai thought, and he engages with these logical questions more directly than most Buddhist scholars.
      • **The relationship between Priest's "ineffability" (his fifth value) and Tiantai's "inconceivable" (不思議)**—both point to something beyond the four alternatives, but Tiantai's version seems more dynamic, less like a static fifth value and more like the activity of the three truths interpenetrating.
      • **Whether Madhyamaka-style negation (prasajya-pratiṣedha) requires paraconsistent logic at all**, or whether it operates at a different level—negating the framework of assertion rather than making assertions within it. This is the question of whether the Buddha's silence on the "unanswered questions" is best modeled as a fifth truth value or as a refusal to play the game.
      • The connection to your interest in procedural epistemology—Tiantai's zhiguan (止觀, śamatha-vipaśyanā) meditation is meant to enact the threefold truth, not just represent it. There might be something here about how logical structures emerge from practices rather than being imposed a priori.