Saturday, March 14, 2015

Climbing Mount Ineffable


[A Lenten meditation]

Darwinians use a nicely heuristic image for evolution as blind climbings of a fitness-landscape.  Richard Dawkins sharpens the metaphor with the title of his (excellent) book, Climbing Mount Improbable : thus recognizing that, though he is a staunch proponent of Natural Selection, evolving something as nearly perfect as a Penguin  is not a slam-dunk.

The pinnacle of Natural Selection  so far


(Indeed, penguins represent a classic case of Irreducible Complexity:  remove one single feather, and the creature is not nearly so cute.)

Our own essays have recurred to a mountaineering metaphor, in support of Platonism (the Realism position in math).  Namely:  Team A sets out to conquer Mount A from its forbidding southern face;  Team B sets out to conquer Mount B  from its frigid north one.  They meet at the summit, to their mutual surprise.   A equaled B, all along!  This attests to the reality of the mountain, prior to and independent of all human endeavor.  (For ‘mountain’ read:  the truths of mathematics, arrived at independently  by various researchers  using quite disparate methods.)

Now, Imre Lakatos  is neither (statically) Realist nor Nominalist -- he is a Dialectician, and juggles both views.   In the course of a quite intricate examination of the evolution of the Euler characteristic  (don’t imagine you really understand the following sentence unless you have worked through that monograph), he remarks in a footnote:

As far as naïve classification is concerned, nominalists are close to the truth when claiming that the only thing that polyhedra have in common  is their name.  But after a few centuries of proofs and refutations, as the theory of polyhedra develops, and theoretical classification replaces naïve classification,  the balance changes in favour of the realist.
-- Imre Lakatos, Proofs and Refutations (1976), p. 92  (**)


Presumably what motivated this formulation, was the experience of beginning with a hopeful conjecture that soon is drowned in a welter of disparate counterexamples; yet with time and hard analysis, we do progressively manage to sort things out -- as though our fumblings were being guided by something real, though unseen.
Similar remarks, I would cautiously submit (under correction), might apply to the multimillennial evolution of theology, in the Historical Church.

Apart from the dogmatic mouthpiece ‘Episilon’ in his classic dialogue/sotie, Lakatos suggests that we have not reaching the summit of any mathematical mountain, and perhaps never will.  With that I concur wholeheartedly;  only admonishing, that the summit is there.  Nor are we likely to get much insight into the internal workings of the Godhead, this side the eschaton;  but those workings are there as well. 

And so we strategically retreat  to the more modest metaphor of the base-camp.  We never quite reach the summit, but with luck and elbow-grease, we might climb high enough that we can detect the smoke from the campfires of the North Face team.
(The theological analogue here is one of the favorite themes of C.S. Lewis, in The Abolition of Man and other works:  the anticipation of Christian insights in other traditions.)

The mathematical upshot of all this, goes back to a repeated theme of these essays:  the distinction between our (human, contingent, fallible) mathematicizing, and the (antecedently existent, transcending) mathematical truth.   (For anyone who might dispute that, answer this:  Did the Universe even exist, prior to Newton?)

The theological upshot -- Well, longstoryshort:  Don’t go cutting off heads, merely because you imagine you perceive some straw in your neighbor’s eye.



(**)  More pointedly: 

… the problem of finding out where God drew the boundary dividing Eulerian from non-Eulerian polyhedra.  But there is no reason to believe that the term ‘Eulernian’ occurred in God’s blueprint of the universe at all.
-- -- Imre Lakatos, Proofs and Refutations (1976), p. 68

Amen.  But He has a blueprint, of which our notion of “polyhedra” is a primitive glimpse.
Similar remarks might apply to the Trinity.



~

Another parallel:

Consider a theological scholar  working on an apparent inconsistency between two Biblical passages.  Theological doctrine assures him that the Bible, properly uderstood, contains no inconsistencies.  His task is to provide a gloss that offers a convincing reconciliation of the two passages.  Such work seems essentially analogous to ‘normal’ scientific research as depicted by Kuhn;  and there are grounds for supposing that he would not repudiate the analogy.
--  John Watkins, “Against ‘Normal Science’”, in I. Lakatos & A. Musgrave, eds., Criticism and the Growth of Knowledge (1970), p. 33

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