Anekāntavāda And Syādvāda: Logical Analysis Of Saptabhaṅgī-Naya

Malliṣeṇa^[1] distinguishes a pramāṇa from a durnaya and a naya. According to him, a pramāṇa is always true and for which we assign the truth-value T, but a durnaya is always false for which we assign the truth-value F. The truth value of a naya (incomplete judgement) is different from the truth-value T or the truth-value F hence it is intermediate between these two truth-values. This gives rise to a third intermediate truth value I.

According to Vadi Devasuri's Pramāṇa-naya-Tattvālokālaṁkāra, (3 loc cit.) the above seven predications can be interpreted as follows:

The first predication consists of an affirmative statement. This may mean that an object exists in some respects. The expression 'in some respect' is to be taken in the context of various factors like space, time, substance and mode. For instance, the substance of an object X could be related to the material of which it is made. The space relates to the spatial location of X. The time of existence of X is the present time at which it exists. The mode of X describes its configuration.

Let us represent, the first affirmative predication by a proposition P which takes a truth-value T.

The second predication consists of a negative statement that 'in some respect' an object X is non-existent. Here the word 'may be' (syād) or 'in some respects' is crucial in respect of assigning the truth-value to this predication. To elucidate that the object X may not exist with reference to either space, time, substance or mode we note that on account of restraint 'in some respects' we shall consider the connective of negation (˥) as a 'complete' negation and not as a 'diametrical' negation in the sense of Reichenbach.^[2] Let us represent the second predication by the proposition ˥P which takes the truth-value I, as shown by the following truth-table:

(Reichenbach 4 loc. cit.)

Truth-Table No. 1

The third predication consists of affirmative and negative statements conjunctively made one after another. Since the affirmative proposition P and negative proposition ˥P are taken conjunctively one after another we assign the truth-value T to the non-simultaneous conjunction of the affirmative proposition P and the negative proposition ˥P. We denote this non-simultaneous conjunction of P and ˥P by the notation (P° ˥P).

The fourth predication consists of affirmative and negative statements made simultaneously. Since an object X is incapable of being expressed in terms of existence and non-existence at the same time, even allowing Syād, it is termed 'indescribable'. Hence we assign to the fourth predication which is the simultaneous conjunction of the affirmative proposition P and the negative proposition ˥P, the indeterminate truth-value I and denote the statement corresponding to the fourth predication as (P ˄ ˥) P.

The fifth predication consists in an affirmative statement conjoined with an indescribable statement at the same time. We denote this fifth predication by P ˄ (P ˄ ˥P).

Referring to the column for simultaneous conjunction in the truth-table that follows:

Truth-Table No. 2

We see that since P takes the truth-value T by the first predication and (P ˄ ˥P) is assigned the truth-value I by the fourth predication, the proposition P ˄ (P ˄ ˥P) takes the truth-value I.

The sixth predication consists of a negative statement conjoined with an indescribable statement at the same time. We denote this sixth predication by (˥P) ˄ (P ˄ ˥P). Referring to the column for the simultaneous conjunction (˄) in the table given above, we see that since ˥P takes the truth-value I by the predication and (P ˄ ˥P) is assigned the truth-value I by the fourth predication we see that the proposition ˥P ˄ (P ˄ ˥P) takes the truth-value I.

The seventh or the last predication consists of an affirmative and negative statements made non-simultaneously conjoined simulta­neously with affirmative and the negative statement conjoined simultaneously. This statement is denoted by (P° ˥P) ˄ (P ˄ ˥P). Referring to the columns for the connectives for simultaneous conjunction and for non-simultaneous conjunction in the truth-table No. 2 and noting that P takes the truth-value T by the first predication and ˥P takes the truth-value I by the second predication. We see that (P° ˥P) takes the truth-value T (third predication) and (P ˄ ˥P) takes the truth-value I (fourth predication). The seventh predication thus takes the truth-value I according to the same truth-table.

Hence, we see that the pramāṇa saptabhaṅgī of the Jainas is a table of seven statements which are derived from a true statement by the operations of negation, non-simultaneous and simultaneous conjunctions that are denoted by ˥, °, ˄ respectively.

Let us consider P as a true statement then the pramāṇa saptabhaṅgī can be represented as follows:

(1) P (assertion of P)

(2) Not P ('complete' negation of P) denoted by ˥P

(3) P and non-simultaneously not P (non-simultaneous conjunction of P and ˥P) denoted by P° ˥P

(4) P and simultaneously not P (simultaneous conjunction of P and ˥P) denoted by (P ˄ ˥P)

(5) P and simultaneously (P and simultaneously not P) denoted by P ˄ (P ˄ ˥P)

(6) Not P and simultaneously (P and simultaneously not P) denoted by ˥P ˄ (P ˄ ˥P)

(7) (P and non-simultaneously not P) and simultaneously (P and simultaneously not P) denoted by (P° ˥P) ˄ (P ˄ ˥P)

Pictorially we can depict the pramāṇa saptabhaṅgī as follows with the truth-values to the right:

An object X can be viewed from any one of these seven standpoints. However, since the totality of all these seven possibilities comprises the pramāṇa saptabhaṅgī (Complete judgement of the phenomenal world in terms of seven possibilities), the disjunction, denoted by ˅, of these seven predication should lead to a tautology. We can represent this disjunction as follows:

(P ˅ 1 P) ˅ (P° ˥P) ˅ (P ˄ ˥P) ˅
[P ˄ (P ˄ ˥P)] ˅ [(˥P) ˄ (P ˄ ˥P)] ˅
[(P° ˥P) ˄ (P ˄ ˥P)].

As we have noted earlier, the seven predications, conjoined by the disjunction above, take the truth-value T, I, T, I, I, I respectively. Referring to the column for the disjunction in the truth-value No. 2 and noting that the disjunction is associative as can be easily checked using the same truth-table, we see that the disjunction of all these seven predications is indeed a tautology taking the truth-value T.