Thursday, October 6, 2011

Paradigm of Babel

As Nietzsche's prophet said, to paraphrase, human history has been unhinged from its orbit, and to wit, voila, the rise of the Axiom of Choice, Zermelo-style, from the pit of the nightmare of scientific reason. Sounds innocuous, sounds like nothing, but there was enough of that stuff going around for D. Hilbert to map out a programme for mathematicians, to find the "foundations" of just what it was that they were so enamored with. It was a singular paradigm at that time, after all; there were diverse areas of mathematics, but they were all building with the same blocks of absolute reality. 

Or so they thought. This set-theoretic stuff was "non-constructive" and somewhat arbitrary, it was a great obstacle-maker that broached its way into pristine Elysium, the pythagorean-platonic summum omnia of effulgent perfection, and stirred shit up. And G. Cantor himself, that original culprit, checked his ass into a mental ward and converted to Catholicism.

Imagine such a world that it was. If those folks were transplanted to the here and now, they'd all freak the freakout of hitherto unforeseen freakage. But c'est la vie, the unhinging has happened. There were non-Euclidean geometries, non-constructive axiomatic systems, the special and general theories of relativity, Gödel's Incompleteness Theorem, quantum theories, fractals, nonlinear Chaos ... and so on. And that's just a corner of the scientific-paradigmatic arena, all of the above splintered and shattered into a mosaic of isolated specializations. The Tower of Babel it is, where one specialist of one field can't understand doodly-squat of what the other specialist in the same field is saying or doing. 

But back to the non-constructive Axiom of Choice. It is the foundation of the in-validation of all paradigms hitherto. There is no objective rhyme or reason why any one paradigm holds water and another doesn't. There is no absolute authority, no absolute frame of reference. Or is there? There is, but paradigms, most of the ones that hold sway, have gone apocalyptically Steampunk, and have barred the way. "None shall pass" the confines, box, and procrustean zones; not without paying the high price of getting labeled a kook, a crackpot, a fraud, a pseudo-this-and-that, a heretic, and so on. And sometimes they get blackballed from the hall of ivory-tower egomaniacs scrambling in their hamster-cages.  They only burn 'em on a virtual stake, nowadays. 

There can be no theory of everything, because that theory will ultimately have to account for itself, and nothing can bootstrap itself into horn-tootin' self-legitimacy.  Would't a theory per se of everything have to include itself in its universe of discourse, or will it have some built-in paradox-busting failsafe that passes the buck from one metalanguage to the next, and so on till the cows come home?  There will always be a hole, and the hole is itself, i.e., if and only if it does not take Mind into account, the living being, the conscious entity, who is doing the thinking, tinkering, piddling, measuring, and observing. That's been the story hitherto. Hugh Everett tried quantum-theorizing sans observer, and universes inflated ad infinitum, into uncountably power-set of the cardinality-of-real-numbers transfinitely many universes. And counting, even as that never-collapsing probability wave has no choice (so to speak) but to keep hopping from one universe to another. 

Unhinged. But Mind does the choosing, not an external authority. The choices get made by epistemological filters, and those filters are chosen for personal reasons. That's the bottom line. When we can appreciate the shambles that paradigms (scientific, religious, and ideological) are, we come to understand that it's all a matter of choices. Choices that cannot be accounted for in terms of the choices that have been made.