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:
- S is P
- S is ~P
- S is (P · ~P)
- 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:
- S is P
- S is notP
- S is P.notP
- S is not P.notP
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's2.
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):
- [One thinks:] “I dwell perceiving the world as finite. Therefore I know that this world is finite and bounded by a circle.”
- [Another thinks:] “I dwell perceiving the world as infinite. Therefore I know that this world is infinite and unbounded.”
- [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.”
- [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:
- Is it the case that one attains the goal by means of knowledge?
- Is it the case that one attains the goal by means of conduct?
- Is it the case that one attains the goal by means of both knowledge and conduct?
- 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
I
|
II
|
III
|
IVa
|
IVb
|
IVc
|
|||||||||||||||||||||||
P
|
notP
|
P
|
·
|
notP
|
~
|
(
|
P
|
·
|
notP
|
)
|
~
|
(
|
P
|
v
|
notP
|
)
|
~
|
P
|
·
|
~
|
notP
|
|||||||
A
|
T
|
T*
|
T
|
F
|
T
|
T
|
T
|
F
|
T
|
T
|
T
|
F
|
T
|
F
|
F
|
T
|
||||||||||||
B
|
T*
|
F
|
F
|
F
|
F
|
T
|
F
|
F
|
F
|
T
|
T
|
F
|
F
|
T
|
F
|
T
|
F
|
|||||||||||
C
|
F
|
T*
|
F
|
F
|
T
|
F
|
F
|
T
|
F
|
F
|
T
|
T
|
T
|
F
|
F
|
F
|
T
|
|||||||||||
D
|
F
|
F
|
F
|
F
|
F
|
T*
|
F
|
F
|
F
|
T*
|
F
|
F
|
F
|
T
|
F
|
T*
|
T
|
F
|
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.
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.
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.
<http://www.earlham.edu/~peters/courses/log/transtip.htm>
Walshe, Maurice, trans. The Long Discourses of the Buddha: A
Translation of the Dīgha Nikāya. 1987. Boston: Wisdom
Publications, 1995.
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