Tetralemma

The title of this article is ambiguous. Tetralemma is also a method of systemic structure constellation .

The tetralemma (Gr. Tetra : four, lemma : prerequisite, assumption) is a logical figure consisting of four sentences, which 1. ascribe a property to an object, 2. deny, 3. both agree and deny 4. neither agree , still to agree. The Indian logic knows this figure as Catuṣkoṭi ( Sanskrit : चतुष्कोटि ) or caturidhya (quadruple).

Catuṣkoṭi

Originally, the Catuṣkoṭi is used to consider all possibilities of combining two predicates. In the case of non-contradictory predicates such as sweet and mild, there are no contradictions.

On the other hand, variants with only one predicate are more problematic. For in classical European logic, which goes back to Aristotle, every statement is regarded as either true or false ( proposition of the excluded third party , principle of two-valued ) and a property cannot and cannot be assigned to an object at the same time. A traditional view in Buddhism that arose in ancient India is that there are four possibilities: One statement can

• be true (and only true)
• be wrong (and only wrong)
• be both true and false,
• be neither true nor false.

The statements (koti) 3 and 4 appear to be directly contradictory. Classical Indian texts also seem to assert a conjunction of all four possible expressions. A contradiction can be avoided if, for example, the object areas are restricted to discrete subsets of the discourse universe. Even then, however, if the commutativity of the conjunction and the law of the excluded third party apply, the kotis 3 and 4 appear to be interchangeable and therefore redundant.

The Buddhist philosopher Nagarjuna used the Catuṣkoṭi in two different variants: The first, positive variant is in an example:

• Everything is real
• and unreal,
• both real and unreal,
• neither real nor unreal.

In the negative variant of Catuṣkoṭi it is stated that none of the four possibilities is true.

Attempts to explain

According to Butzenberger's analysis, there are basically three possible ways of responding to the problems of contradiction and redundancy of kotis 3 and 4:

1. Specification of a reconstruction using the means of classical logic, from which the problems can no longer be derived
2. Specification of a reconstruction with the means of non-classical logic, from which the problems can no longer be derived
3. Unsolvability. The catuṣkoṭi is interpreted as irrational or mystical.

According to his presentation, all three options are unsatisfactory. "(3) because she confuses the end with the beginning; (2) because she contradicts many of the statements in the Catuṣko Texteis texts; and (1) because the reconstructions that have been found so far are more like constructions than reconstructions call are ". The fact that "the term 'catuṣkoṭi' is ambiguous and refers to different entities" is also ignored.

Formalization through classical logic

Propositional logic

From the standpoint of Western logic, using the connectives of propositional logic, the four elements of Catuṣkoṭi can be summarized in formulas as follows. X denotes any statement:

formula	description
${\displaystyle X\;}$	affirmation
${\displaystyle \neg X}$	negation
${\displaystyle X\land \neg X}$	both
${\displaystyle \neg (X\land \neg X)}$	neither of them

Since the first two statements contradict each other, according to the rules of propositional logic, the conjunction of all four possibilities (i.e. the positive variant) can only result in a contradiction, i.e. it cannot be correct under any circumstances.

The negative variant (disjunction of the four possibilities) is always true because yes , i.e. the disjunction of the first two elements, is a tautology . ${\displaystyle X\lor \neg X}$

Relational logic

This attempted explanation assumes that the Catuskoti is about the four possibilities that arise when one considers the ratio of a (two-digit) relation on a set to a special element : ${\displaystyle R\;}$ ${\displaystyle A}$ ${\displaystyle a\in A\;}$

1. ${\displaystyle R(a,x)\;}$ only applies to ${\displaystyle x=a}$
2. ${\displaystyle R(a,x)\;}$only applies to elements with ${\displaystyle x\in A}$ ${\displaystyle x\neq a}$
3. ${\displaystyle R(a,x)\;}$applies to as well as to elements with ${\displaystyle x=a}$ ${\displaystyle x\in A}$ ${\displaystyle x\neq a}$
4. ${\displaystyle R(a,x)\;}$ applies to none ${\displaystyle x\in A}$

These four cases exhaust all possibilities and are mutually exclusive.

Other attempts

Nevertheless, among the attempts to use non-classical logics for interpretation in recent times , in addition to, for example, three-valued logics and modal logic , relevance logic has also been brought into play.

Individual evidence

1. ↑ Butzenberger, lc, p. 571f uses the medical textbook Carakasamhita.
2. ↑ Jay L. Garfield, Graham Priest: Mountains are Just Mountains ( Memento of the original from July 18, 2009 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 128 kB). 
3. ↑ See. Butzenberger, 569f
4. ↑ Tsong khapa: Muulamadhyamakaarikaa , trans. N. Samten and J. Garfield, New York: Oxford University Press. 2006
5. ↑ Butzenberger, 570.
6. ↑ Jonardo Ganeri: Indian Logic. In: Handbook of the History of Logic, Vol. 1. Dov M. Gabbay, John Woods (Ed.), Elsevier, Amsterdam 2004, p. 331. ISBN 0444504664
7. ↑ See e.g. BRN Ghose: The Modality of Nagarjuna's Dialectics , in: Journal of Indian Philosophy 15 (1987), 285ff
8. ↑ Jay L. Garfield / Graham Priest : Mountains are Just Mountains ( Memento of the original from July 18, 2009 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 128 kB), draft of chap. 6 in: D'Amato, Mario / Jay Garfield / Tom Tillemans (eds.): Pointing at the Moon . Buddhism, Logic, Analytic Philosophy, Oxford University Press 2009, ISBN 0195381564 . 

literature

• Klaus Butzenberger: Some aspects of the catuskoti with special consideration of Nagarjuna , in: Synthesis Philosophica 1990, 567-580.
• Hans P. Sturm: Neither being nor not being , the square of judgment (catuskoti) and his corollaries in eastern and western thinking, ERGON-Verlag, Würzburg 1996, ISBN 3-928034-72-3