Saturday, March 12, 2011

What Is At Stake

Realism about mathematics is just a part -- and not the chief part -- of Realism about Reason.   One can actually get along pretty well, from week to week, without having recourse to Algebraic Geometry.  But Reason is at the core of our being and our freedom:  and it is Reason that, in these dark days, finds itself under attack.

The case for Reason has recently been ably and gracefully put by Thomas Nagel, in The Last Word (1997);  I shall not repeat his arguments, but simply urge you to buy his book.

Sheer Reason, however, is difficult to reason about.  Mathematics is thus a useful test case for the larger thesis, since  when the truths of mathematics come to be known, it happens  only by Reason (occasionally supplemented, it may be, by Revelation, which then however feeds smoothly into the usual operations of Reason itself:  exactly like a theorem that has been proved, to your satisfaction, by someone else).   Math has the added advantage of being species-neutral (unlike Ethics, and much else).  It has also proved useful in opposing what Nagel calls “Darwinian imperialism” (p. 133), namely “the ludicrous overuse of evolutionary biology to explain everything about life, including everything about the human mind”.   (I satirized this in an earlier post, “The Urysohn Metrization Theorem:  an Adaptationist Account”.) 

            A psychologist or philosopher, soddened by overlong splashing in the swamps of Raw Feels, will tend to be satisfied, in his Gedankenexperimenten, with the most trivial sort of elementary arithmetical facts, for the organism’s tacit recognition of which  a Darwinian account may seem not too far-fetched, especially to someone who doesn’t really care about mathematical reality anyhow, and thus is easily satisfied.  But hyperDarwinists (not a slur -- that is Dawkins’ self-chosen label) can less readily account for our familiarity with E8. -- Though, to be sure, a deep acquaintance with this object will prove crucial for our species’ survival  when, in the year 30,906, we shall be forced to flee our imploding galaxy for a cosmos in which -- but that is of no account, for Darwinian orthodoxy emphasizes that Natural Selection cannot peek into the future.

And for whoso should say, this is but a shadow-play,  we offer this envoi, from a Thomist, anent the ontological agnosticism of certain linguists:

L’oreille la moins exercée  perçoit aussitôt   sous de tels énoncés  la présence des problèmes qui, sous les noms de réalisme et de nominalisme, ont agité les écoles du moyen âge  pendant au moins trois siècles.  Aujourd’hui, on se contente de tenir ces problèmes philosophiques pour résolus  en vertu d’un simple décret préalable  de ne pas philosopher.  Il ne suffit pourtant pas  qu’une solution ne soit pas philosophique  pour qu’elle devienne scientifique.  Qu’est-ce que cet « object concret »  qui ne serait qu’un « exemplaire »  du concept ?  Platon, Aristote, Abélard et Ockham  demandent aussitôt la parole,  et on ne peut aujourd’hui que se taire  ou reprendre le problème  au point où ils l’ont laissé.
-- Etienne Gilson, Linguistique et philosophie (1969), p. 49

Travaillant au noir,
le détective  se trouve aux prises
avec le Saint-Esprit


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