Role of Space Time in Jainas Syadavada and Quantum Theory

Author(s): Filita Bharucha
Publisher: Shri Satguru Publications

Page 40

Role of Space-Time in Jaina's Syadväda
The above discussion shows that when a, is true (or when B, is true), then a, V B. (signifying successive measurements of (A and B) and a, A B (which signifies simultaneous measurements of A and B) are two mutually exclusive EP's. Similarly if Q, and y, are the EP's corresponding to two incompatible observables Pand Q, we assert that the presence of 0 (0 y) entails the presence of (, Vy, v 10, A y.). It is easy to verify that 0,[(0, Vw.)V 10, AW)] is a tautology and that if ¢, is true (or if y, is true), then [(0, VY) V T(0, Ay)] is also true.
Notice the presence of (0, Ay) in the case of incompatible observables instead of (0, 1 y.). Hence when o, is true (or when
, is true), then (0, V4.) (signifying successive measurements of P and Q) are two mutually exclusive EP's and incomplete.
(2) For compatible observables, one easily verifies that a (or B) is entailed by (a, AB.). This means that if(a, AB) is true then a, as well as B, is true and that (a, AB) a (or B) is a tautology. In similar fashion, one finds that 0, (or y.) is entailed by l(0, Ay) where 0, and y, are the EP's for two incompatible observables.
(6) Concluding remarks: We have shown that the basis of logical statements, as is often claimed, is no just a priori, but as to take into account empirical truths. A Logic originated and developed during the classical period cannot but be at variance with empirical truths of quantum mechanics developed to explain the behaviour of the microworld. If logic is claimed to be empirical, is it merely dropping a well-known law of classical logic and nothing else? We answer this question by saying that it is much more. If the logic is empirical, then one must investigate the empirical meanings of the basic connectives like those of disuntion and conjunction in the light of new insights two measurement processes of the microworld. Do the classical meanings of these connectives, which have been