Concept
Catuṣkoṭi
Overview
Catuṣkoṭi (Sanskrit; Devanagari: चतुष्कोटि, Tibetan: མུ་བཞི, Wylie: mu bzhi, Sinhalese:චතුස්කෝටිකය) refers to logical argument(s) of a 'suite of four discrete functions' or 'an indivisible quaternity' that has multiple applications and has been important in the Indian logic and the Buddhist logico-epistemological traditions, particularly those of the Madhyamaka school.
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 :
P ; that is being.
not P ; that is not being.
P and not P ; that is being and that is not being.
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:
Animals understand love
Animals do not understand love
Animals both do and do not understand love
Animals neither do nor do not understand love
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
An example of this is, when the simple propositions are connected by the particle _or_; as, Either A is B or C is D; or by the particle _if_; as, A is B if C is D. In the former case, the proposition is called _disjunctive_, in the latter, _conditional_: the name _hypothetical_ was originally common to both. As has been well remarked by Archbishop Whately and others, the disjunctive form is resolvable into the…
John Stuart Mill, A System of Logic
States what Catuṣkoṭi is.
The objects of opinion are many things, and the ternary number denotes a multitude, as "Thrice happy Grecians"; for which reason Pythagoras admits the ternary. This sect of philosophers is called the Italic, by reason Pythagoras started his school in Italy; his hatred of the tyranny of Polycrates enforced him to abandon his native country Samos.
Plutarch, Complete Works of Plutarch — Volume 3
States what Catuṣkoṭi is.
Examples of the latter are: 'The mind is no elephant:' 'A lion is no table;' propositions which are correct but absurd, exactly like the identical propositions: 'A lion is a lion;' 'Mind is mind.' Propositions like these are undoubtedly the truth of the immediate, or, as it is called, Qualitative judgment. But they are not judgments at all, and can only occur in a subjective thought where even an untrue abstraction…
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Catuṣkoṭi is.
Philosophers who discussed Catuṣkoṭi
Related ideas
- Sandhinirmocana Sutra
- Buddhist logico-epistemology
- Sentient beings (Buddhism)
- Pyrrhonism
- Thomas McEvilley
- Propositional logic
- Śūnyatā
- Indian logic
- View (Buddhism)
- Nihilism
- Nagarjuna
- Paradox
- Pāramitā
- Fyodor Shcherbatskoy
- Sanskrit
- Sutra
- Zen
- Ajñana
- Dialectic
- Madhyamaka
- Mūlamadhyamakakārikā
- Early Buddhist schools
- Sādhanā
- Maya (religion)
Place in the tradition
Part of Dialetheism.