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suppose a statement P has the truth-vaiue I. Now the negation of P is also I. The conjunction of P and ~ P is again I and the disjunction P and P, i. e. P V ~P is also I. Thus the first four statements of Naya Saptabbangi are respectively P, P, PV~P and PA P and each one of them has the truth-value I. The fifth statement is the conjunction of the first and the fourth statements, the sixth statement is the conjunction of the fourth statement and the second statement and lastly the seventh statement is the conjuction of the fourth statement and the third statement. In this way, obviously according to the rule of conjunction the truth-value of all these three compound statements is I. So the table of seven nayas is like this;
1. P where P is I
2.
~P which is I
3.
PV
4. PA
5.
P) which is 1
6. PA (PAP) which is I
7. (PV~P) A (PAP) which is I
This table becomes logically verified if we maintain that the logic of Nayas is a three-valued logic of Lukasiewicz. Surprisingly enough, the Naya Saptabhangi challenges the law of Excluded Middle, because here PVP which is the classical formulation of the law is not a tautology as its truth-value is I and not T. It further challenges the law of contradiction because here PA P which is the classical formulation of the law is not false but I. It assumes that the truth-value of a conjunction it the falsest, and that of a disjunction is the truest, of the truth-values of its components. Now these epoch-making discoveries of Jaina logicians can be understood in their proper perspectives and further they can be logically, though not historically, linked with the modern developments of three-valued logic.
~
~
P which is 1
P which is I
~
STUDIES IN JAINISM
PA (PA~
2
~
Now it may be asked here as to how and why we should suppose that Jaina logicians knew such important truth-functional connectives or operators as negation, disjunction and conjunction of Lukasiewiczian Three-valued logic. To this we may reply that at first it should be noted that logicians like Vidyananda and Anantavirya have clearly described these operators and secondly it is to be conceded that they have also a clear concept of the
