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
denote it by a'. Thus (EP 1) is of the form M (SA1x>= ai) and (EP II) is of the form M (SA (x.) = lai>. In the present paper, we shall concern ourselves with EP 1's only and drop the suffixes I and II.
Experimental Meaning of Logical
Connectives:
19
In this section we shall consider the problem of introducing this compound statements involving two or more EP's of the type described in the previous section and giving experimental meaning to the logical connectives conjoining them. We first consider the case of an observable represented by the Hermitian operator A with the eigen-value spectrum, a, a....... a, la, la.... 1> are the eigenvectors of A belonging to these eigenvalues. We assume to make measurement on identical copies of the system S prepared to be in the same state 1x> to measure the observable A. We denote, as in section 2, the EP's M (SA1x)=a, as a,. The aforementioned measurements will furnish the results a, or a or a or....., not necessarily in that order, with probability measure associated with each of them. This means that a, or a or are the possible (exclusive) results of the measurement process. If we put n = 2, then we may say that result of this measurement is either a or a, but never both at the same time, when measurements are repeated on the identical samples in the same state. This measurement statement (for n = 2) can be translated into the logical language as a V α, where the connective 'V' is used in the exclusive sense. Let B be another observable with the corresponding Hermitian operator B with the complete set of eigenvectors 1b>. This observable may or may not be compatible with the observable A. The measurements on identical copies of S in the state 1 x> to measure A and B not simultaneously, but successively, should give the results as as
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