Tuesday, January 4, 2011


[This is a continuation of a thread begun here.]

The response to these ongoing ponderings has been not as vocal as I might have expected.  True, Bernie Riemann, writing in from the beyond, dropped a nice note; but overall there seems to be a hush, if not actual fidgeting, among the audience.  And yet I know that present company dwells uninterruptedly upon eternal things.  Dwells on them, possibly, tankard in hand (indeed these present notes might not have been so copious, but for the promptings of the cold and blushful); but dwells on them.  Perhaps it is all just too much at once.
So instead I’ll emit, from time to time, a bite-sized Thought for the Day, and maybe keep emitting them if I detect the sound of munching..  They all circle around the same basic idea, and can be consumed individually.

And so… on to our sermonette!

*  *  *
Today’s M&M:  The Ontological Argument

B. Russell, Introduction to Mathematical Philosophy, chapter 18:
If we reject the ontological argument, we seem driven to conclude that the existence of a world is an accident.

This is indeed a problem:  for the ontological argument, whether as originally given or as subsequently tweaked, seems indeed uncompelling (for one thing it could equally lead you to the existence of the Infinite Penguin – who exists indeed, but independently of the argument). And yet I do believe (discovering this belief lying silently within me, like a present with no indication of donor, beneath the tree), that it is not an accident.  Mostly this is on the basis of what I conceive to be common-sense grounds, virtually on the trivial level of what used to be called “ordinary-language philosophy”:  By “accident” we prototypically mean things like:  The milk-jug tipped over; or, Timmy had an unfortunate occurrence in his pants. To light-heartedly apply this same noun to the intricately evolving Riemannian manifold in which we dwell, with its Hilbertian tangent spaces wherein the Maxwell equations and the Ricci tensor are but chorus-like walk-ons in the whole resounding transfinite Gesamtkunstwerk --  no, sorry, c’est un abus de langage.  If you wish to spit upon the magnificence of the Creation (bearing in mind: all things visible and invisible), you are at liberty to do so, but you’ll have to find some better gob to hawk than “accident”.

“The” ontological argument is in any case a general term; there have been several updatings since Anselm.  Most notably, one by the great logician Gödel.  You can find it summarized in Wang’s Reflections on Kurt Gödel, p. 195. 

I can’t make much of it.  But then, many proofs in formal logic have a kind of baffling quality to a non-logician.  If valid, it only goes to show the bare outlines of a God – nothing about… anything that matters to us, really.  If invalid, that’s interesting; for Gödel was perhaps the world’s most logical man, and not notably devout, so one would not imagine he would perpetrate a fallacy out of mere wishful thinking.

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