Role of Space Time in Jainas Syadavada and Quantum Theory

SR No.: 006772
Original Sutra Author: N/A
Author: Filita Bharucha
Publisher: Shri Satguru Publications
Publication Year: 1993
Total Pages: 82
Language: English
Classification: Book_English
File Size: 3 MB

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Role of Quantum Theory in Deviant Logic
form (a V B) and (a V B2) conjoined by the connective A. These expressions are obtained by conjoining two EP's corresponding to observables which may themselves in incompatible with other, so that it is impossible to say whether the EP's that correspond to (a V B) and (a V ẞ2) are compatible or incompatible with each other. There, within the scope of definition of the connective 'A' which has different truth-tables for compatible and incompatible observables, these EP's cannot be conjoined together by 'A'. This means that this form of the distributive law lies outside the ambit of our logical system. In any case, this form has not even been mentioned by Finkelstein and Putnam. Similarly in the expression (α, A α2) V (ẞ, A ẞ2) = (α, V B1) A (α, V ẞ2) A (α, V B2) A (α2 V B1) A (a2 V B2) the right hand side contains expressions (α, V B1), (α2 V B2) conjoined by the connective 'A'. This expression involves more than two EP's conjoined by the connective 'A' to which it is not possible to give an empirical meaning. Besides the EP's (α, V ẞ1), (α, V ẞ2), may correspond to neither compatible nor incompatible observables and thus cannot be meaningfully conjoined together by the connective 'A'. Hence we shall speak no more about this form of the distributive law in this paper.
Secondly, we consider the form (II) which is the form admissible in our formalism of quantum logic. Here we shall distinguish between two cases: Case (1): The two observables A and B are compatible and the corresponding operators commute. Case (2): The two observables P and Q are incompatible and the corresponding operators do not commute.
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We first consider case (1) In this case, we shall show that the distributive law holds when (a) the operator A has the complete spectrum of one eigenvalue and operator B has two (b) A has the spectrum of 2 eigenvalues, and B also has two and (c) A has the spectrum of 3 eigenvalues and B also has