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Modern Physics and Syadvada 109
Mixture
P><P +R><R
Avayakta and Nonexistence
6. (4) and (2), at
different times; or two boxes at the same time.
7. (4) and (3), at
different times; or three boxes at the same time.
Mixture
Avayakta and Existence and
Nonexistence 1P></+PR ><RI+L><L||
Syadvada Reasoning
The Syadvada dialectic (Syad means "May be") was formulated by Jaina thinkers probably more than two thousand years ago. Syadvada asserts that the knowledge of reality is possible only by denying the absolutistic attitude. According to the Syadvada scheme every fact of reality leads to seven ways or modes of description. These are combinations of affirmation and negation:
(1) Existence, (2) Nonexistence, (3) Occurrence (successive) of Existence and Nonexistence, (4) Inexpressibility or Indeterminateness, (5) Inexpressibility as qualified by Existence, (6) Inexpressibility as qualified by Nonexistence and (7) Inexpressibility as qualified by both Existence and Non-existence.
The fourth mode of inexpressibility or avayakta is the key element of the Syadvada dialectic. This is especially well brought out by our discussion of waveparticle duality in modern physics. (See. also P.C. Mahalanobis, and J.B.S. Haldane. Sankhya, May 1957, Indian Statistical Institute Calcutta. Their papers deal with the significance of Syadvada for the foundations of modern statistics.)
Take any meaningful statement. Call it 'A'. It may describe a fact of experience. It could be proposition of logic or mathematics. The Syadvada dialectic demands that in the very nature of things the negative statement is also correct. Denote by not-A the negative statement of 'A'. The conditions under which the two statement, A and not-A, are correct cannot, of course, be the same. (In general) the respective conditions are mutually exclusive. Given a statement 'A' it may not be at all easy to discover the conditions or situations under which not-A holds. It may even appear at the time impossible. But faith in
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