Abstract
The catuṣkoṭi (Greek: tetralemma; English: four corners) is a venerable principle of Indian logic, which has been central to important aspects of reasoning in the Buddhist tradition. What, exactly, it is, and how it is applied, are, however, moot—though one thing that does seem clear is that it has been applied in different ways at different times and by different people. Of course, Indian logicians did not incorporate the various interpretations of the principle in anything like a theory of validity in the modern Western sense; but the tools of modern non-classical logic show exactly how to do this. The tools are those of the paraconsistent logic of First Degree Entailment and some of its modifications.
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Notes
- 1.
For FDE, see Priest [10], Chap. 8.
- 2.
I note right at the start there are some Buddhist logicians in whose thinking the catuṣkoṭi played no role. This is true, in particular, of the school of Dignāga and Dharmakīrti. Like the Nyāyā, this school of logic endorsed both the Principles of Non-Contradiction and Excluded Middle. See Scherbatsky [18], pt. 4, Chap. 2.
- 3.
Radhakrishnan and Moore [14], p. 289 f. The word ‘saint’ is a rather poor translation. It refers to someone who has attained enlightenment, a Buddha (Tathāgata).
- 4.
See Ruegg [17], p. 1.
- 5.
Tillemans [20], p. 189.
- 6.
- 7.
See Priest [10], Chap. 8.
- 8.
As observed in Garfield and Priest [4].
- 9.
See Priest [7], 4.6.
- 10.
See Ruegg [17], pp. 1, 2.
- 11.
Thanissaro [19].
- 12.
Radhakrishnan and Moore [14], p. 290.
- 13.
All translations from the MMK are from Garfield [2].
- 14.
Instead of \(\varphi (A)\) (etc.), one could have any sentence that contained all the propositional parameters in A.
- 15.
For the proof, see the technical appendix of Priest [12].
- 16.
The Buddhists tadition was not alone in appearing to reject all four of the koṭis sometimes. See Raju [15].
- 17.
The translation is taken from Kassor [5].
- 18.
It is not just Gorampa who finds himself in this position. Any theory according to which there is something ineffable and which explains why it is ineffable is going to be in the same situation. There are many such theories, East and West. See Priest [9].
- 19.
See Priest [8], 5.5.
- 20.
See Garfield and Priest [3], and Deguchi et al. [1]. The contradiction we are dealing with here is closely related to Nāgārjuna’s paradox that the ultimate truth is that there is no ultimate truth. (See Garfield and Priest [3], Sect. 5.) One can say nothing true about ultimate reality—either because there is no such thing, or because it is ineffable. But either way, that is itself an ultimate truth.
- 21.
See [10], 8.2.
- 22.
For a fuller discussion of the construction described in this section, see Priest [13].
- 23.
For details of what follows, see Priest [11].
- 24.
See Priest [11], Sect. 5.
- 25.
In [11], this is formulated not as a relational semantics but equivalently as a functional semantics, where the functional values are sets of truth values. The possibility of applying this construction to the Buddhist four (or five) values, as we hae done here, is noted there in footnote 15.
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Priest, G. (2015). None of the Above: The Catuṣkoṭi in Indian Buddhist Logic. In: Beziau, JY., Chakraborty, M., Dutta, S. (eds) New Directions in Paraconsistent Logic. Springer Proceedings in Mathematics & Statistics, vol 152. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2719-9_24
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