Sunday, January 2, 2011

Credo (concluded)

Bishop Berkeley famously quipped, in his (cogent) critical article on Newton’s fluxions (infinitessimals), that “he who can digest a second or third Fluxion,  need not, methinks, be squeamish about any Point in Divinity.”  Conversely,  might not a certain intellectual tolerance for points of Divinity, pre-dispose one towards seeking the reality behind such initially ill-presented abstractions as the infinitessimals, that they might be put upon a sound footing?  Indeed this has, since Berkeley’s time, been done, for the Calculus as inherited from Leibnez and Newton; and since that time, those very infinitessimals, once spirited away in the new Cauchy formulation, have shown up again unexpectedly at our door, no longer in rags, but smartly outfitted by Robinson.  And indeed these originally disreputable and now revived entities (very small ones, to be sure, but still entities) – which originally, I confess, struck me as rather a sterile abstraction, no doubt true enough in their way, but probably no part of the Palace – have latterly been suggested as just the broom for cleaning out the Augean stables of perturbation theory, of all massively practical things..  Is there nothing the mind of math may dream up, which may not prove someday as routinely serviceable as a hammer?
            Consider again the ill-fated squeamishness of Pythagorus, concerning what we now think of merely as the complement in R of Q.   Might his bias of nominalism been somehow connected to the limits of his theological horizons – Olympus and its rabble of godlings, with their petty jealousies and sordid couplings?  You are not likely to get much of an ontological leg-up from a shag-shanked goatgod; whereas God  the creator of all things visible and invisible…nay, Who dies and yet rises… a God who is One, and yet Three…

1 comment:

  1. Pythagoras, whatever his biases, proved the existence of irrationals in a world that had not yet graduated from iron swords. If this is an example of the warping effect of nominalism, we should hardly be surprised that others were drawn to it!