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every inference is subject to ‘syād.' As formulated by Mallisena (c. 1290 C.E.) in his Srādvūda Manjari such doubt is intrinsic in any valid inference. While to know certain facts required to develop an (partial) understanding of what it is - āsti, it is a case of never know all the necessary facts to elaborate what it is not - nästi. Obviously the "whole,' alluded to in the answer of Mahāvīra, is the sum total of is and is not, in the sense of a system that is described by Set Theory.
Logical syllogisms are based on intrinsically rigorous mathematical methods that assure internal consistency and completeness. Sensory system with intrinsic limitations and the linearity of conventional language fragments knowledge, as with the conceptualization of a whole elephant by the knowledge of its body parts not only requires the knowledge of its morphology, habitat, social surrounding, and the course of its personal history and genealogy. More over it is always colored by personal experiences and not necessarily by a set of facts, rules and laws to organize the observable. Hence, the piecing together of the available fragmented information is postulated by the doctrine of anekantavada by Mahāvīra.
What is not known falls in the realm of agyān, and it is clearly distinguishable from the wrong, unverified and contradictory knowledge which could be categorized as mithyāgyān. Later Jain saint scholar philosophers such as Samantabhadra, Siddhasena, Mallavādi and Jinabhadragani articulated and elaborated that doubt is worthy of deeper intellectual inquiry with a true value in relation between mithyāgyān and doubt.
Like asti and năsti, syād (doubt) and contradictions have deeper intellectual roots that go back at least 3000 years. The Aristotelian inference syllogisms based on two states - true and false - have been developed in the form of Boolean Algebra, which is the foundation for modern computer science. In an attempt to explore the truth inherent in doubt, Prof. G.N. Ramachandran of the Institute of Science in Bangalore India has developed a second and third order Boolean Matrix Algebra (Mathematical Philosophy Report #79,1990). This approach applied to understand the deeper structure of syādvāda and saptabhangi syllogisms provides insights.
In the Indian tradition, the inference schema is illustrated by examples such as the following one:
There is fire on the hill (based on the fact that) There is smoke on the hill (the rationale is that)
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