Scholars of Buddhism since Stcherbatsky's seminal work have recognized formalized Buddhist reasoning as a distinct form of logic. This panel continue in this tradition, exploring both the logical systems articulated in the Buddhist tradition, as well as using the tools of disciplinary logic to interpret Buddhist ideas. In this way, we aim to put logical systems into conversation in a non-reductive manner, showing how Buddhist and Anglospheric formal logic can be mutually illuminating. Presenters will explore the Tarkasastra, a lost Sanskrit text only extant in Chinese, and its treatment of fallacies; connections between intuitionistic logic and Nāgārjuna, especially in his Vigrahavyāvartanī; and the "puzzle" of Dharmakīrti's trairūpya doctrine, which appears to present both implication and its contrapositive as individually necessary for a valid argument, even though these are logically equivalent. In this way, these presentations both think about and with logic in Buddhism, as well as Buddhism through logic.
The key development in the history of logic in India is the formulation and application of the trirupahetu, or the three forms of a (logical) reason. The Tarkasastra (Ru Shi Lun T1633) adopts the trirupahetu to distinguish good arguments from bad arguments (T1633 31b11 ff.).
The Tarkasastra (Ru Shi Lun), as we have it, comprises three chapters. The first chapter is an extended debate pertaining to the claim that there are truths. The second chapter enumerates and critically discusses 16 fallacies (jati). The third lists and explains 22 situations in which a participant in a debate is deemed to have lost (nigrahasthana). The paper critically assesses the text's treatment of five fallacies: the first, the second and the fourth, where the text applies the trirupahetu; and the fifth and sixth, where the text discusses two arguments typically associated with Nagarjuna (3rd century ce).
The famed Buddhist philosopher Nāgārjuna appears to talk in contradictions, denying both that some P is the case and that it is not the case. Both ancient and contemporary interpretations fall in two camps: (1) let the contradiction stand dialethically or (2) qualify Nāgārjuna's negata to escape a contradiction. I offer a third interpretation, drawing on parallels to Brouwer's (1881-1966) intuitionism. To put it succinctly: no qualification is needed, but because Nāgārjuna is in the business of denying without assertion, he also escapes contradiction.
To build my case of interpreting Nāgārjuna in this vain, I focus on his Vigrahavyāvartanī, namely verses 28-29 and their commentary. I give a philosophical defense of my interpretation following Arend Heyting's (1898-1980) intuitionistic logic, which allows for the weak denial of both P and ~P without contradiction. I argue that both Nāgārjuna and the intuitionist advance cases where neither P nor ~P is provable.
Buddhist logicians from Dignāga onward require that a valid logical reason satisfy three modes (trairūpya): (1) the reason holds of the subject; (2) it is present wherever the probandum is present (anvaya); (3) it is absent wherever the probandum is absent (vyatireka). In first-order logic, modes (2) and (3) — ∀x(Hx → Sx) and ∀x(¬Sx → ¬Hx) — are contrapositives, i.e., logically equivalent. Yet Buddhist logicians unanimously insist both are necessary. I call this the “Trairūpya Puzzle.” After examining Oetke’s epistemic solution and Dharmakīrti’s treatment of the equivalence, I argue that the puzzle exposes a genuine limit of extensional formalization. Drawing on Dharmottara’s niyamavat doctrine and Durvekamiśra’s concept of svagata dharma — intrinsic capacities of the reason itself — I conclude that the second and third modes encode intensional content that the material conditional of first-order logic cannot capture. The trairūpya is a presentation of phenomenological relation.