Catuṣkoṭi

catuṣkoṭi (T. mu bzhi མུ་བཞི་; C. siju fenbie 四句分別) is translated as "four alternatives," "four possibilities," "four extremes," etc. The four aternatives are a form of argumentation used to categorize sets of propositions.

A common example of is the "four extreme views" of the Madhyamaka school: existence, non-existence, both existences and non-existence, and niether existence nor non-existence.

This type of four-sided argument is also referred to as a tetralemma.

Structure of the argument

In particular, the catuṣkoṭi is a "four-cornered" system of argumentation that involves the systematic examination of each of the 4 possibilities of a proposition, P:

1. P; that is being.
2. not P; that is not being.
3. P and not P; that is being and that is not being.
4. not (P or not P); that is neither not being nor is that being.

These four statements hold the following properties: (1) each alternative is mutually exclusive (that is, one of, but no more than one of, the four statements is true) and (2) that all the alternatives are together exhaustive (that is, at least one of them must necessarily be true). This system of logic not only provides a novel method of classifying propositions into logical alternatives, but also because it does so in such a manner that the alternatives are not dependent on the number of truth-values assumed in the system of logic.

An example of a Catuṣkoṭi using the arbitrary proposition, "Animals understand love" as P would be:

1. Animals understand love
2. Animals do not understand love
3. Animals both do and do not understand love
4. Animals neither do nor do not understand love

Sources

• Buswell, Robert E.; Lopez, Donald S. (2014), The Princeton Dictionary of Buddhism, Princeton University 
• Jayatilleke, K.N. (1967), "The Logic of Four Alternatives", Philosophy East and West, Hawaii, USA: University of Hawaii Press, 17 (1–4): 69–83, JSTOR 1397046 

Further reading

• mu bzhi, Christian-Steinert Dictionary
• mu_bzhi, Rangjung Yeshe Wiki