Monday, February 14, 2011

“Philosophy is to be studied, not for the sake of any definite answers to its questions since no definite answers can, as a rule, be known to be true, but rather for the sake of the questions themselves; because these questions enlarge our conception of what is possible, enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation; but above all because, through the greatness of the universe which philosophy contemplates, the mind also is rendered great, and becomes capable of that union with the universe which constitutes its highest good.”

Thus, philosophy does not give definitive answers. It was a profound discovery of the 1930’s, that even a highly precise subject like mathematics, can also pose seemingly accurate questions for which there are no mathematical answers. One of the greatest achievements of 20th century mathematics is a fundamental theorem of Godel. This theorem is set against the background of what we would call logical thinking and deductive reasoning. When we speak about the truth of a mathematical proposition, we imply that it can be deduced by applying a set of “rules”, if you will, or to be more accurate, axioms, to a proposition which you have deemed to be known, to derive the new proposition.

Godel’s theorem tells us that reasoning has limitations in the following sense. In any axiom system, one may write down propositions which can neither be proved or disproved. In other words, they cannot be derived by applying the axioms, nor can their negations be so derived. In the light of G¨odel’s theorem, is the question of arriving at all knowledge placed before us by the Upanishads a valid one? Can we even rely on reasoning to achieve this purpose? This question can be addressed in various ways.

Reading through the Upanishads, it becomes clear that detailed knowledge is not what is meant when one asks for all knowledge. Rather, one implies the essence of knowledge, or the underlying principle of knowledge. To this end, inquiry is a powerful and viable tool, not to be abandoned, even though its limitations are acknowledged in the Upanishads. In addition, language and even the mind are acknowledged as limited for this experience. The claim is made that mind must be transcended through mind by a refinement of inquiry.

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