Role of Space Time in Jainas Syadavada and Quantum Theory

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

Page 38

Role of Space-Time in Jaina's Syädväda
It can be seen from the above analysis that the distributive law in the form
(9, V, V....) A (H, VH, V Hz....)
= (, AM) V ( Athy) V (Og A Hy).... V (7, A4) V.... holds for the EP's corresponding to both compatible and incompatible observables. We have seen that this form, but not the other, is meaningful in our empirical logic within the scope of meaning we have assigned to the connectives of disjunction 'V'and of the conjunction 'A'. Another connective we have not mentioned so far and which has a basic function in further development of our logical system is negation'. If we denote the EP: M (Sis) = , as 2, then we shall denote the EP: M (SW) = 2, as a we see that the meaning given to the connective of negation is quasi-classical.
Now that we have given empirical meanings to the connectives 'V', 'A' and 's we set to define some additional connective like those of implication and equivalence for both compatible and incompatible observables. Our definition of implication happens to provide the same truth-table for it, in these cases as in the classical case: a conditional with a true antecedent and a false consequent is false. This requires that in the case of compatible observables we put a B) = (la VB) V (la A B) where a and B are the EP's corresponding to the compatible observables A and B. We illustrate this by the following truth-table 10, which can easily be constructed using the above expression on the right
Truth-Table 10 In the case of incompatible observables, we have (0 V) = (lo vy) v 10 Ay)
where 0 and y are the EP's corresponding to the incompatible observables P and Q. This also leads to the same truth-table 10 given above. In the above two expressions