From First Principles - with Logic

Let us Start

Recently a friend remarked "We can start from first principles in science, and prove all the laws that have been derived, logically." The immediate reaction was "Isn't it true that we start from an 'assumption' or an 'axiom' as a first principle? There is no first principle, isn't it?" The next thought is that "To be able to prove everything logically, 'logic' itself must be above everything. On one hand rejecting other lines of thought of a supreme power or consciousness, while on the other, 'logic' being placed above all other axioms, derivations, etc., is absurd, isn't it? So, is science assuming that 'logic' is God?"

These kindle deep thinking on the basis for Science and whether it can provide all answers to us. If logic is not supreme (is there a 'logical' reason why it should have supreme status) and science starts with assumptions / axioms or other premises, then what method, tool or process can we employ to explore, understand and live in this world? We will have to still use 'logic' to help us, but with a different approach. We may have to restrict the 'logic' we use to not use arbitrary starting points.

How do we proceed? When we turn to the Vedas and Upanishads, we find an interesting 'logic' applied to describe the eternal consciousness. The Mandukya Upanishad describes it, using the 'neti, neti' method ('na iti' - not this), to eliminate hypotheses which are not true. At the end of such analysis and application of logic over variety of hypotheses, whatever is left has to be the truth. This, however, needs to be a very thorough application - not a superficial analysis of a few possible explanations, equations, descriptions, etc.

For day-to-day activities, survival, etc., 'formal logic' may be sufficient. We will have a starting point with assumptions and we want to come to a conclusion using 'logical' steps. This helps us deal with the everyday scenarios.  However, for deeper thinking, all-encompassing exploration, etc., this 'logic' is insufficient to help us.

Which came first?

Just like Godel's incompleteness theorem talks of any set of logical statements being insufficient to describe a complete system, 'logic' is also incapable of covering everything we want to know about the universe. It does not seem to lend itself to answer a simple question of "which came first" - the chicken or the egg.

Even Arthur Conan Doyle seems to have hinted at 'neti, neti' method in deduction of the truth by elimination of possibilities. "When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth." says he, in "The Case-book of Sherlock Holmes".

Hence, 'neti, neti' is the logic that can be applied for learning and understanding the universe in which we have manifested, with inputs from the faculties we have. We should not hesitate to use the results from scientific observations of the modern era in analysis and understanding. However it must be tempered with the knowledge that all 'impossible' possibilities must still be eliminated before arriving at conclusions.