The central concern of Indian logic as founded in nyāya is epistemology, or the theory of knowledge. Thus Indian logic is not concerned merely with making arguments in formal mathematics rigorous and precise, but attends to the much larger issue of providing rigour to the arguments encountered in natural sciences (including mathematics, which in Indian tradition has the attributes of a natural science and not that of a collection of context free formal statements), and in philosophical discourse. Inference in Indian logic is ‘deductive and inductive’, ‘formal as well as material’. In essence, it is the method of scientific enquiry. Indian ‘formal logic’ is thus not ‘formal’, in the sense generally understood: in Indian logic ‘form’ cannot be entirely separated from ‘content’. In fact, great care is exercised to exclude from logical discourse terms, which have no referential content. No statement, which is known to be false, is admitted as a premise in a valid argument. Thus, the ‘method of indirect proof’ (reductio ad absurdum) is not accepted as a valid method−neither in Indian philosophy nor in Indian mathematics−for proving the existence of an entity whose existence is not demonstrable (even in principle) by other (direct) means of proof.
The central concern of Indian logic as founded in nyāya is epistemology or the theory of knowledge. Thus Indian logic is not concerned merely with making arguments in formal mathematics rigorous and precise, but attends to the much larger issue of providing rigour to the arguments encountered in natural sciences (including mathematics, which in Indian tradition has the attributes of a natural science and not that of a collection of context free formal statements), and in philosophical discourse. Inference in Indian logic is ‘deductive and inductive’, ‘formal as well as material’. In essence, it is the method of scientific enquiry. Indian ‘formal logic’ is thus not ‘formal’, in the sense generally understood: in Indian logic ‘form’ cannot be entirely separated from ‘content’. In fact, great care is exercised to exclude from logical discourse terms, which have no referential content. No statement, which is known to be false, is admitted as a premise in a valid argument. Thus, the ‘method of indirect proof’ (reductio ad absurdum) is not accepted as a valid method−neither in Indian philosophy nor in Indian mathematics−for proving the existence of an entity whose existence is not demonstrable (even in principle) by other (direct) means of proof.