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Fourfold Predication in Early Buddhism by John Emmer

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Fourfold Predication in Early Buddhism
John Emmer

Here is the first of my real papers for any of my classes here. Don't expect any profound insights that will move you very far along the path to Awakening - unless of course that path for you travels through an attempt to understand certain logical patterns in Early Buddhist writings...

John Emmer

Buddhist Philosophy
Prof. Sumana Ratnayaka
SIBA, August, 2012

The Fourfold Analysis of Predication in Early Buddhism

A certain fourfold pattern of propositions, or rather perhaps a certain family of fourfold propositions, appears often in the Pali Canon. An example from one of the debates in the Kathāvattu follows:

Theravādin: Does (a person or) soul run on (or transmigrate) from this world to another and from another world to this?
Puggalavādin: Yes.
Th: Is it the identical soul who transmigrates from this world to another and from another world to this?
Pg: Nay, that cannot truly be said . . . (complete as above)
Th: Then is it a different soul that transmigrates. . . .
Pg: Nay, that cannot truly be said. . . . (complete as above)
Th: Then is it both the identical and also a different soul who transmigrates . . . ?
Pg: Nay, that cannot truly be said. . . .
Th: Then is it neither the identical soul, nor yet a different soul who transmigrates . . . ?
Pg: Nay, that cannot truly be said. . . .
Th: Then is it the identical, a different, both identical and also different, neither identical, nor different soul who transmigrates . . . ?
Pg: Nay, that cannot truly be said. . . .
(ellipses and italics in original, Aung 26-27)

This example actually contains five options, as the standard four are combined for the fifth. Kalupahana symbolizes the four alternatives as:

  1. S is P
  2. S is ~P
  3. S is (P · ~P)
  4. S is ~(P · ~P)

Symbolized in this manner, the scheme seems to contain an obvious contradiction (III) and a tautology (IV), making those two statements useless to consider, let alone whatever it might mean to assert all of them together. What sense then can we make of this scheme?

Not everyone has assumed that one could make sense of these propositions. For example, Poussin takes them to be a “four-branched dilemma” that indeed violates the law of contradiction (Jayatilleke 333). This interpretation is extremely unfair to the source material, and does not bear up under even the slightest investigation. However, it is easy to see how one could reach this conclusion if one uses a symbolization like that given above. Jayatilleke therefore offers the following alternative notation and explains how it better represents how the fourfold propositions are used:

  1. S is P
  2. S is notP
  3. S is P.notP
  4. S is not P.notP
(136 136n2)

The point of his 'notP' notation as opposed to '~P' is to represent that P and notP are contrary propositions rather than contradictory ones. He gives the example of pleasure and pain: if 'S is P' (I) is interpreted as 'he experiences pleasure', then 'S is notP' (II) may mean 'he experiences pain', which is not the same as 'he does not experience pleasure', since a person could experience pleasure in one part of the body while experiencing pain in another at the same time, which can be understood as the meaning of 'S is P.notP' (III) (341)[1]. This distinction successfully saves the scheme from outright contradiction. However, Jayatilleke goes on to say that 'S is not P.notP' (IV) then represents “the person whose experiences have a neutral hedonic tone, being neither pleasurable nor painful” (341). This brings us to a problem I have with the both Kalupahana's and Jayatilleke's symbolization of the fourth proposition. I do not understand why they both use conjunction here rather than disjunction.

Kalupahana's symbolization follows an example where he gives a statement of type IV from the Canon as “The world is both neither eternal nor not eternal” (49) and Jayatilleke's Canonical example is “this world is neither finite nor infinite” (340), which corresponds well to the example of a person experiencing neither pleasure nor pain. However, Kalupahana's “S is ~(P · ~P)” surely means “the world is not both eternal and not eternal” and Jayatilleke's “S is not P.notP” surely means “the world is not both finite and infinite” or “he does not experience both pleasure and pain”. A better symbolization of the fourth proposition would therefore be “S is ~(P v ~P)” for Kalupahana's scheme or “S is not (P v notP)” in Jayatilleke's[2]. This symbolization matches statements like “the world is neither finite nor infinite”.

Not only does the symbolization with disjunction match the example English statements of both authors better, but it also provides a stronger alternative to the third proposition. The symbolizations of both Kalupahana and Jayatilleke for IV simply negate III, leaving a statement that could be asserted in conjunction with either I or II without contradiction. For example, it is not contradictory to state both “he does not experience both pleasure and pain” and “he experiences pleasure”, so long as he is not also experiencing pain. But if I say, for IV, “he experiences neither pleasure nor pain”, then I cannot at the same time assert any of the other propositions without contradiction. This would seem to be valuable for Jayatilleke, who claims that, for the early Buddhists, “when one alternative was taken as true, it was assumed that every one of the other alternatives were false” (346). I have presented these alternatives with their truth tables in the appendix to make the truth relationships between the alternative propositions clear.

However, even with the improved symbolization, we could still assert III with I or II, since III would seem merely to state that both I and II are true (again, see the appendix if this is not clear). Jayatilleke therefore provides an example from the Dīgha Nikāya showing that I and II should be taken as universal propositions incompatible with III or IV (340). The following is Walshe's translation of the passages in question (to disentangle the presentation of the example from Jayatilleke's discussion of it):

  1. [One thinks:] “I dwell perceiving the world as finite. Therefore I know that this world is finite and bounded by a circle.”
  2. [Another thinks:] “I dwell perceiving the world as infinite. Therefore I know that this world is infinite and unbounded.”
  3. [Yet another thinks:] “I dwell perceiving the world as finite up-and-down, and infinite across. Therefore I know that the world is both finite and infinite.”
  4. [A fourth] Hammering it out by reason, he argues: “This world is neither finite nor infinite. Those who say it is finite are wrong, and so are those who say it is infinite, and those who say it is finite and infinite. This world is neither finite nor infinite.”
(numbers and brackets mine, 79 DN I.22-23)

First we note that III here provides a Canonical example of the non-contradictory nature of the alternatives from I and II. Just as a person can experience pain in some part of the body and pleasure in another simultaneously, the third proposition here claims that the world could be finite in some dimensions while being infinite in others. However, what Jayatilleke really wants to call attention to here is the explicit universalization of the first two claims. The first claimant asserts that the world is “bounded by a circle”, or in Jayatilleke's translation, “bounded all around” (340). This rules out the possibility of there being a simultaneous infinitude for any dimension. Likewise, the second claimant's “unbounded” assures us that there is no dimension that is not infinite. If this universal nature of the first two statements and limitation in the third is present in all instances of the fourfold analysis, then combined with our improved understanding of the fourth statement, we do indeed have a mutually-exclusive set of propositions.

There is another important aspect of the previous example that Jayatilleke highlights. Notice that in the first three statements, the claimant's knowledge is said to be based on direct perception of reality. But the fourth claimant is said to have reached his conclusion “hammering it out by reason”. Jayatilleke compares this point of view to Kant's position, after demonstrating in the Antinomies that both the finitude and inifinitude of the world could be proved with pure reasoning, that one must therefore conclude that neither characteristic is appropriately predicated of the world (341). The fourth claimant does not directly perceive the truth of his claim because in his view the terms just do not make sense in experience. Presumably there is no experience corresponding to 'unpredicatability' – one must simply reason it out.

Our understanding of the fourfold analysis so far is that the first two propositions represent contrary but not contradictory universal predications, the third proposition represents limited predications of both contraries, and the fourth represents the position that the predications in question are meaningless or otherwise inapplicable. We have also noted that at most one of the four propositions is to be asserted by anyone claiming consistency. In addition, however, Jayatilleke points out that there are times where all four alternatives can either be rejected or negated.

To reject the alternatives as opposed to negating them is typically represented in the Canon by phrases like “mā h'evaṃ” or “do not say so” as opposed to something like “na h'idaṃ” or “it is not so” (Jayatilleke 346-347). According to Jayatilleke, the former case is found when one confronts a “meaningless question”, such as “is there anything else after complete detachment from and cessation of the six spheres of experience?” (346) When confronted with the four variations of this question, Sāriputta replies with “mā h'evaṃ” to them all (AN.II.161 cited in Jayatilleke 346). This is a well-known tactic used elsewhere in the Canon as well, where the Buddha is known to have refused to answer certain classes of questions. Note also that in the first example provided above, the Puggalavādin responds to each of the alternatives with “that cannot truly be said”.

More problematic is the case where all four alternatives are negated, since according to our truth table analysis, there is no set of truth conditions under which all four alternatives are false (see appendix). Jayatilleke claims that this is equivalent to the problem that Aristotelian logic has with a question like “have you given up smoking?” when asked of a non-smoker (347). The simple answer to this seems to be “no”, unless one adds a premise that anyone who has not given something up is actually still engaged in that practice. Otherwise I am quite happy to say that I have not given up a practice that I have also never started. Even so, I don't see why the Aristotelian could not also reply “one should not say so”, refusing to give the statement a truth value in the same way the early Buddhist might reject a meaningless question.

The example Jayatilleke provides for the fourfold negation provides us with another problem. The example is this:

  1. Is it the case that one attains the goal by means of knowledge?
  2. Is it the case that one attains the goal by means of conduct?
  3. Is it the case that one attains the goal by means of both knowledge and conduct?
  4. Is it the case that one attains the goal without knowledge and conduct?

Assertions I, II, and III seem to fit the proposed interpretation of the fourfold scheme, but what are we to make of the phrase “without knowledge and conduct” in assertion IV? Do we have here a case of Jayatilleke's “S is not P.notP” as opposed to our preferred “S is not (P v notP)”? It is hard to say without a better understanding of the original Pali, an understanding which I do not yet possess. Jayatilleke does however provide us with a useful explanation of how all these alternatives could be denied: knowledge and conduct are necessary but not sufficient conditions for the goal (347). But this does not help us resolve the problem with the truth-functional representation of the statements (i.e. that there is no set of truth conditions under which they can all be false).

This is probably as far as I can go without a better knowledge of Pali which would enable me to more carefully examine the occurrences of the fourfold schema in the Canon. Also, many more examples would need to be analyzed to determine the applicability of the given interpretation (summarized in the heavily italicized paragraph on page 5). For the time being, however, I am willing to assert that this interpretation, as developed primarily by Jayatilleke but with slight modifications by me, is a good “rule of thumb” for approaching instances of the fourfold schema in the Canon. It is certainly better than declaring the texts to be contradictory and tautological. It provides patterns and angles that one can look for in the texts that help in understanding the arguments being made. Perhaps in the future, with a greater understanding of Pali, I can return to these texts and improve upon the analysis.

Appendix: Truth-Table Analysis


The table above is provided to illustrate the superiority of my proposed rendering of the fourth proposition as IVb (or its logical equivalent of IVc) as well as to simply make more clear the relation of the truth values of the four propositions. If we are to maintain the criterion that the truth of any one of the four propositions implies the falsity of the other three, then each row (A, B, C, and D) should only have a 'T' in the column representative of the propositional truth value (indicated by the placement of the column headers) for exactly one of the four propositions (I, II, III, or IV). These mutually exclusive alternatives are represented with asterisks.

Row A violates the criterion if we do not consider the special qualification for P and notP when used in I and II such that they are universal here but not in III or IV. To represent this, I have presented the 'T' values in I.A and II.A with strike-through, leaving the only proposition which asserts them both as true III.A.

The superiority of IVb and IVc over IVa is shown by the presence of strike-through in cells IVa.B and IVa.C which would violate the exclusivity criterion without some further reasoning for why they should be treated in some special manner to prevent one from saying, for example, that the universe is finite in all respects (I.B) and also that it is finite in some respects but not infinite in any respects (IVa.B). The latter proposition could be interpreted as either equivalent to the former in that 'some' could be equivalent to 'all', or could be taken to mean that the universe is finite in some respects and infinity cannot be predicated of the universe. This could of course be clarified through the use of a predicate logic with quantifiers (which is perhaps the preferable solution since this would also forgo the need for the special strike-through annotation in I.A and II.A) but as long as we are keeping to simple propositional logic it is easier to just use IVb or IVc rather than IVa.

Works Cited

  • Aung, Shwe Zang and Mrs. Rhys Davids. Points of Controversy, or, Subjects of Discourse: Being a translation of the Kathāvattu from the Abhidhammapiṭaka. 1915. Oxford: Pali Text Society, 1993.
  • Jayatilleke, J. N. Early Buddhist Theory of Knowledge. 1963. Delhi: Motilal Banarsidass, 1963.
  • Kalupahana, David J. A History of Buddhist Philosophy: Continuities and Discontinuities. 1992. Delhi: Motilal Banarsidass, 1994.
  • Matilal, Bimal Krishna. The Character of Logic in India. Eds. Jonardon Ganeri and Heeraman Tiwari. Albany: State University of New York Press, 1998.
  • Suber, Peter. Translation Tips. Department of Philosophy. Earlham College. n.d. Web. 22 Aug. 2012. <>
  • Walshe, Maurice, trans. The Long Discourses of the Buddha: A Translation of the Dīgha Nikāya. 1987. Boston: Wisdom Publications, 1995.


  1. Jayatilleke is talking about sukhī, which he translates as “experiencing pleasure, [or] happy” and then switches between using pleasure/pain and happiness/unhappiness in his examples in a way that suggests questions that need not be relevant in this context (e.g. is happiness the same as pleasure and unhappiness the same as pain?), so I have altered his examples to stick to one translation.
  2. Suber also gives the standard translation of the English “Neither p nor q” as “~p · ~q” or “~(p v q)” (tip 6). Replacing his “Neither p nor q” with “Neither P nor notP” and carrying through the replacements to the symbolic representations, we get “~P · ~notP” or “~(P v notP)”, matching my suggested symbolization.