Against Rationality-Part I

I guess four years is a wee bit too late to vent my anger at life, the universe and everything in general and the engineering world in particular, but hell, better late than never. Plus, four years of harrowing experiences in the midst of scientists and engineers does things to you, and I have to say some things before I go a little balmy in the head.

So this post (and a few more to come) is about "rationality", "logic", "reason", "science", "intellect", "intelligence" and so on and so forth. It is about the standard dogma that is indoctrinated into so many Indians, most of whom land in such grotesque places as the IITs. It is about the belief, reiterated till it becomes fact, that yes, life is logical, that reason, cause and effect are things of infallible accuracy and unfailing integrity. More particularly, it is about the high status we accord to science, logic and reason, and the farthings we throw at everything else.

So let me start. Being, unfortunately, a science student myself, I will let this first post follow "logic" through science.

Science itself is logical, and so is mathematics, so what use would it be to look at logic within the framework of science? Actually a lot, and for that precise reason. Science is something we always regard as being logical, in other words, being derived from fixed, though maybe unknown, rules. Rules, of deduction, inference and reasoning. We science people like so much to lay down rules, to lay down formulae, and to exclaim with unabashed pride that, hey, this sequence of symbols on paper explains everything!

Towards the end of the 19th century, this was the general mood prevalant among mathematicians. Mathematical proofs were getting more and more formal, with fixed rules of inference, and mathematical logic had firmly taken ground. Mathematical proofs were becoming more and more "mechanical". Hilbert, as part of his 20 problems, asked the obvious question (Entscheidungsproblem): How mechanical are mathematical proofs? Does there exist a set of axioms and a set of inference rules that will lead, "logically", and hence "mechanically", to every known theorem in the book?
If Hilbert's proposition was true, all that you needed for mathematics was a set of symbols, and a set of axioms and inference rules operating on those symbols. Nothing more. What those symbols meant, or if they had any meaning at all, would be insignificant. Meaning would essentially a matter of book-keeping
Then came Kurt Godel, and his Incompleteness theorem: For any formal logical system that was consistent, there was always a statement that would be true if your axioms were true, but that you could never prove by the rules of logic. In other words, logic, the simple rules of inference, would not suffice to determine or prove this statement, and yet this statement would be true. The way you could prove this statement was to talk about the meaning of the statement, something that logic was incapable of doing.

The point I want to drive home is this: logic is not how theorems are proven. Logic is not how science happens. Science and Mathematics, though they seem driven by logic, are not driven by logic, or at least not logic in the sense of a set of axioms and inference rules. What it is that drives them, and what kind of "logic" is involved, well, I'll harp on that on my next post.