Role of Space Time in Jainas Syadavada and Quantum Theory

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

Page 73

Logico-Spatio-Temporal Space
Definition VIII: Two proposition P,,P, are absolutely compa
rable (complete equivalence) ifthey belong to
logic L with the same order and degree. The exact determination of the order and degree at present may appear difficult to evaluate in certain fields due to the construction of a specific-truth-table. However, one can for example in quantum mechanics use analyses o fitters and the idea of a maximum observable set to determine them.
Summarising so far, we see that with respect to a system S one can have Lom (i.e. a logic 'L' of order n degree M)
As we notice by the earlier section, a reference of an event expressed as a proposition does not determine "truth” or "falsehood" (or any truth-values as such) it merely enables to ascertain order and degree of its corresponding logic.
Now we represent an event E with a matrix having spacetime co-ordinates and order, degree forms as follows:
Matrix Formulation of Events (E) of the Dual Manifold (R“, L.)
R^ : Space-time manifold LM: Logico-Manifold where N = 2 (Order)
M = (m,, m.) = (0,1) (degree) Space Time Points X, * {(2, Y;, z)} = (1, t) E R Propositions Y. L'o.1) (Logico-Manifold with Order 2.)
degree (m, m.) = ( 1). A, is a well formed formula corresponding to the propositions Y where degree (A) E LO of Order 2 with truthvalue T. F.
Where probability Supremum (PP.) as P. = 1 correspond degree (A) = { well as (exclusive) ing to truth-value T
Linfirmum ( pp) and the probability
P = 0 to the truth value F.
And