Again as part of my collaboration with (Western) logicians (about which you can read this post and the further ones linked from it), I was confronted with the question of whether Classical (Aristotelian) Logic applies to Mīmāṃsā. For the ones of you who have stopped studying logic long ago, this amounts to ask whether Mīmāṃsā authors would agree that at each given time, either A or “non-A” is true (and, as a consequence, that there is no middle way between these two alternatives, or tertium non datur).
My first reaction to the question was that Mīmāṃsā authors obviously comply to the principle of non contradiction. First of all, because the Mīmāṃsā school is straightforwardly empiricist and refutes the Jain (and Mādhyamika) attempts to make mutually contradictory statements look as both true at the same time.
Furthermore, as Tillemans (2013) has argued, it is very hard to find any school of Indian philosophy which did not accept it, and even in the Buddhist Mādhyamika (which has been at times identified as upholding some form of dialethism, see again Tillemans 1009 on Yasuo Deguchi, Jay Garfield, and Graham Priest) one finds clear statements about the fact that violating the principle of mutual contradiction (parasparavirodha) is a fatal fallacy:
But if the opponent did not desist even when confronted with a
contradiction (virodha) in his own position, then, too, as he would
have no shame, he would not desist at all even because of a logical
reason and example. Now, as it is said, for us there is no debate
with someone who is out of his mind. (Candrakīrti, Prasannapadā 1.2)
Furthermore, Mīmāṃsā authors recognise inference (anumāna) as an instrument of knowledge and although the Mīmāṃsā inference is slightly different from the better-known Nyāya one, it still presupposes that one can infer from an invariable concomitance either the presence or the absence of something, e.g., the presence of fire on a smoky mountain or the absence of it in a pond (thus, no intermediate possibility is accepted).
When directly confronted with an objection concerning the principle of non contradiction Mīmāṃsā authors do not deny its validity and as an aside describe it:
As for what has been said [by the Buddhist opponents], namely that “It is illogical that in a single real entity (vastu) two contradictory aspects (rūpa) simultaneously occur”, this is also wrong.
Also, in the case [of our theory] there is no mutual contradiction, because no [such contradiction] is grasped |
[In fact,] it is not the case that one knows the one once the other is excluded, like it would be the case with mother-of-pearl and silver (where a shiny object can either be an instance of silver or of mother-of-pearl) ||
When there is a contradiction, at the denial of one [alternative], the other is known [to be true]. But in the topic under consideration is it not so, hence, what would be the contradiction?
(yad apy abhihitam “itaretaraviruddharūpasamāveśa ekatra vastuni nopapadyate” iti, tad api na samyak. parasparavirodho ‘pi nāstīha tadavedanāt | ekabādhena nānyatra dhīḥ śuktirajatādivat || yatra virodho bhavati, tatraikatararūpopamardena rūpāntaram upalabhyate. prakṛte tu naivam iti ko virodhārthaḥ (Mīmāṃsā answer within Bhaṭṭa Jayanta’s Nyāyamañjarī 5, section 3.1, Kataoka 2010, p. 193).
This appears to confirm my initial impression about the applicability of Classical Logic to Mīmāṃsā. Please note, however, that Buddhist Pramāṇavādins are much stricter than Mīmāṃsā authors when it comes to applying logic to reality. For Mīmāṃsā authors, reality is the ultimate litmus test for each cognition, so that one cannot decide of the truth of an abstract proposition about the world in a way that contrasts what we directly perceive. In other words, Buddhist Pramāṇavādins are ready to say that “Everything that exists is momentary” and to conclude that our perception of lasting things is illusory. Mīmāṃsā authors, by contrast, contend that the Buddhist syllogism about momentariness must be wrong, since it clashes with our perceptions.