In the 19th century, when mathematicians tried to consolidate and deeply analyse the scattered mathematical concepts haphazardly developed over the last few centuries, they ran into various paradoxes and inconsistencies. German mathematician David Hilbert developed Hilbert's program in the early 20th century as an approach to resolve this foundational crisis in mathematics. Hilbert proposed a solution by establishing a finite and comprehensive set of axioms to serve as the basis for all existing theories. He aimed to demonstrate the consistency of these axioms through a proof. However, in 1931, mathematician Kurt Gödel published his incompleteness theorems, which revealed that Hilbert's program was unachievable for crucial areas of mathematics. As a result, it became shockingly evident to mathematicians that certain statements can never be proven or disproven, rendering them undecidable! This concept of undecidability is not restricted to mathematics and applies to any logical framework, but of course, in different ways depending on how the particular logical framework has been constructed. And if we look at Indian philosophy from a logical perspective, it is applicable there too! What this means is that there are certain concepts in Indian philosophy that are also undecidable from a logical perspective and trying to answer these undecidable questions leads to a lot of unnecessary confusion. Lets try to analyse and understand some of these undecidable questions in Indian philosophy.
