Buddhist Logic Overview

Audience: readers familiar with classical logic who want to understand a non-Western logical tradition that developed independently and reached different conclusions about truth, inference, and the limits of predication.

Learning goal: understand the structure of Buddhist formal inference, the catuṣkoṭi, and their relationship to Western non-classical logics.

A different starting point

Western logic, from Aristotle through Frege, begins with the structure of propositions and asks: which inferences preserve truth? Indian logic, in the pramāṇa tradition, begins with the structure of knowledge and asks: which cognitive processes produce valid cognition? This difference in starting point produces a logic that is epistemological from the ground up — not a formal system applied to knowledge but a theory of knowledge that generates formal constraints.

Dignāga (c. 480–540 CE) codified Buddhist inference in the Pramāṇasamuccaya. A valid inference requires a reason (hetu) that satisfies three conditions (trairūpya):

1. Presence in the subject (pakṣadharmatā): the reason must actually characterize the thing being reasoned about. (The mountain has smoke.)
2. Presence in similar cases (sapakṣe sattvam): the reason must occur in at least some cases where the target property holds. (Smoke occurs in the kitchen, where there is fire.)
3. Absence from dissimilar cases (vipakṣe asattvam): the reason must be absent from all cases where the target property does not hold. (Smoke does not occur in the lake, where there is no fire.)

This three-aspect schema is not a syllogism in the Aristotelian sense. It does not decompose propositions into subject-predicate form or operate through term-logic. It operates through the co-occurrence and exclusion of properties — a pattern closer to Mill’s methods of induction or to relevance logic’s requirement that premises be genuinely connected to conclusions.

The catuṣkoṭi and non-classical truth

The catuṣkoṭi (tetralemma) predates the pramāṇa tradition — it appears in the earliest Buddhist texts and receives systematic deployment in Nāgārjuna’s Mūlamadhyamakakārikā (c. 2nd century CE). Its four corners — affirmation, denial, both, neither — challenge the foundations of classical logic:

• The “both” corner violates bivalence and the law of non-contradiction. It admits what paraconsistent logic calls dialetheia — true contradictions.
• The “neither” corner violates the law of excluded middle. It admits propositions that are genuinely indeterminate — a position shared with intuitionistic logic.

The catuṣkoṭi thus occupies a logical space that neither classical, intuitionistic, nor paraconsistent logic fully captures on its own. It is broader than any single Western non-classical logic, admitting both gaps (intuitionistic “neither”) and gluts (paraconsistent “both”) simultaneously.

Nāgārjuna uses this exhaustive structure negatively: he shows that no metaphysical thesis survives all four corners. Inherent existence cannot be affirmed, denied, both, or neither. The purpose is not to establish a four-valued logic but to demonstrate that the very framework of predication — assigning truth values to propositions about inherent natures — is inadequate to the way things actually are. Things arise dependently, and dependent arising does not admit the kind of determinate truth that logical frameworks (including the catuṣkoṭi itself) presuppose.

Connection to Western non-classical logics

The Buddhist logical tradition anticipated several developments in Western non-classical logic by more than a millennium:

• Dignāga’s trairūpya requires that the inferential connection be genuine — not just truth-preserving but grounded in the actual co-occurrence of properties. This parallels relevance logic’s demand that premises be relevant to conclusions, and contrasts with classical logic, where any truth-preserving inference is valid regardless of content connection.
• The catuṣkoṭi’s “neither” corner parallels intuitionistic logic’s rejection of excluded middle — the recognition that some propositions are neither proved nor refuted.
• The catuṣkoṭi’s “both” corner parallels dialetheism’s acceptance of true contradictions.
• The pramāṇa framework parallels the proof-theoretic orientation of intuitionistic logic — truth is tied to the cognitive processes that produce it, not to an independent reality that determines it.

These are structural parallels, not identities. The Buddhist tradition developed in a different philosophical context, addressed different problems, and made different assumptions about the relationship between logic and liberation. The parallels show that the pressure to move beyond classical logic is not culturally parochial but arises wherever thinkers take seriously the limits of binary predication and the role of the knower in constituting knowledge.

Check for understanding: How does Dignāga’s three-aspect schema differ from Aristotle’s syllogism in its treatment of the connection between premises and conclusion?