Role of Space Time in Jainas Syadavada and Quantum Theory

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

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Role of Quantum Theory in Deviant Logic
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time-tested in the classical context, remain unscathed when we look beyond the classical world and peep into the microworld of atoms, nuclie and elementary particles or do they undergo any change? Our investigation has shown that we have to adopt the latter alternative. In this process we find that we have to distinguish between compatible and incompatible observables of quantum mechanics and adopt two different deviant logics for these cases.
Appendix I In this appendix we present two truth-tables 12 and 13 for EP' corresponding to compatible and incompatible observables respectively and list the laws in formal logic which hold and which do not hold in our deviant logics.
[Truth Table (12) & Truth Table (13)]
In the above table, the disjunction 'V' is an exclusive disjunction. The negation and conjunction happen to coincide with their classical counterparts, so do the implemation and equivalence. We have expressed the implication in terms of the above connectives of negation, disjunction and conjunction as (a > B) = ( la VB) V (la AB)
We express the equivalence (a = B) as either (a > B) V I(
B a) or (a B) A (B = a) Using the above truth-table 12, one may easily verify the following;
(1) (a V TQ) is a tautology, (1) (an la) is a contradiction, (3) Modus ponens holds, (4) Modus Tollens holds, (5) Disjunctive Syllogism holds, (6) Hypothetical Syllogism holds, (7) Addition fails, (8) Simplification holds, (9) Conjunction holds (10) Communication holds, (11) Association holds, (12) De Mogan's Law fails and finally (13) Double Negation holds.