Role of Space Time in Jainas Syadavada and Quantum Theory

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

Page 42

Role of Space-Time in Jaina's Syādvāda
In the above table, negation is classical, disjunction is exclusive and conjunction happens to be the negation of the classical counterpart. The implication is expressed as (0 − y) = (lo v ¥) V ( A v) and the equivalence is expressed as (4) V (yo). Again using the above truthtable 13 one may verify the following: (1) ( V ) is a tautology, (2) (A) is a contradiction, (3) Modus Ponens holds, (4) Modus Tollens holds, (5) Disjunctive Syllogism holds, (6) Hypothecatival Syllogism holds, (7) Addition fails, (8) simplification fails, (9) Conjunction fails, (10) Commutation holds, (11) Association holds for 'V' but fails for 'A' (12) De Morgans' Law fails, finally (13) Double Negation holds.
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Appendix II
cl
Adequate system of Connectives: It is shown in the works on logicc that the set of classical connectives, V11 and A, is adequate to express any truth-function. Since the exclusive disjunction 'V' we have introduced in our logical system can be expressed in terms of the above set, in the form
cl
(α V B) = (α V1 B) A da A B), the set, V and 'A' of our deviant logic for compatible observables is adequate.
In the case of incompatible observables as well, the set 1, 'V' and 'A' is also adequate to express any truth-function in this case, as the conjunction 'A' used in our logical system is seen from the truth-tables 12 and 13 to be the negation of the classical conjunction 'A'. Hence a well-formed formula (wffj of the type oV (WAX) for EP's corresponding to incompatible observables can be expressed in terms of T. 'V, 'A' and as
follows:
16V (AX)
三
[16V (^x)] ^ ][ ] ^ 。(¥ ^ x)]
cl
c1
= []φ V. ](ψ Λ χ)] Λ.] Λ.](Ψ Λ .χ)]
cl
c1
cl