Monday, December 19, 2011

Mathematics and Morality

In our series of essays “Theologia Mathematica”,  we have focussed on philosophical and epistemic issues, very far from the sort of thing discussed in the pulpit of a Sunday.   We have striven both to enrich theism and to defend it against its intellectual detractors -- yet in this special vein of argument, do not aspire so high as Christianity, or indeed morality in general.  Nor have I, really, any insights to share upon this head:  in cases where I do make so bold as to venture onto the public square,  such political or ethical statements as I might hazard  make no claims at all upon any results from physics or from mathematics -- although, as with philosophers and theologians in all times, they are of course informed by logic.

Still, as the subject lies inevitably near at hand, it seems meet to at least put up a bulletin-board, on which we can post any quotes we may come across, which illustrate cross-fertility between the moral and the mathematical spheres.


Koestler, Sleepwalkers , I.2.ii, characterizing the philosophy of Pythagorus:

Numbers are eternal, while everything else is perishable … They permit mental operations of the most surprising and delightful knd, without reference to the coarse external world … -- which is how the divine mind must be supposed to operate.  The ecstatic contemplation of geometrical forms and mathematical laws  is therefore the most effective means of purging the soul of earthly passion, and the principal link between man and divinity.

Koestler, Sleepwalkers , I.2.iv [39]: “It is said that Pythagoras, like St Francis, preached to animals.”


John Henry Newman, Apologia pro Vita Sua (1864):

He who made us, has so willed, that in mathematics indeed we arrive at certitude by rigid demonstration, but  in religious inquiry  we arrive at certitude by accumulated probabilities.

I cite this simply as an amiable proof-text, while disagreeing with basically all of it.

Cardinal Newman

In mathematics, you approach certainty, over the centuries, by experiment, insight, and eventually a proof (or “rigid demonstration”) -- or perhaps a succession of improved proofs, as subtle flaws are found in the first one.

Arriving at -- again not really “certitude”, but what used to be known as moral certitude (“beyond a reasonable doubt”), by accumulated probabilities, strikes me as a nice thumbnail description of the process of sciencetheology, not so much.  Theology additionally relies on Revelation -- or “intuition” -- that inward vision -- as it is mystically known in math.


For mathematics as the science of reckoning, Chesterton has little feeling;  but the more modern conception of math is the science of pattern, and Chesterton has strong intuitions about the spiritual content of shape.

G. K. Chesterton, Robert Louis Stevenson (1927):

Whether or no we see faces in the carpet, we ought to see a mind in the carpet; and in fact  there is a mind  in every scheme of ornament.  There is as emphatically a morality expressed in Babylonian architecture or Baroque architecture  as if it were plastered all over with Biblical texts.


The above concern a fancied moral tinge to mathematics itself.  Quite different is the relatively familiar thesis that moral reasoning can or does proceed more mathematico.  Thus Spinoza.  Or cf. David Hume, Enquiry Concerning the Principles of Morals (1751):  Whether something is to be considered a “crime … consists not in a particular fact … but it consists in certain moral relations, discovered by reason, in the same manner as we discover by reason  the truths of geometry or algebra.”

John Henry Newman, Apologia pro Vita Sua (1864) acknowledges that “every article of the Creed is beset with intellectual dificulties”, yet “ten thousand difficulties do not make one doubt; difficulty and doubt are incommensurate.”   And if you think he is here sidestepping the issue, he adds a telling analogy:
A man may be anoyed that he cannot work out a mathematical problem, of which the answer is or is not given to him, without doubting that it admits of an answer.

Steven Pinker, in The Blank Slate (2002), pp. 192-3, speaks respectfully if non-commitally about the Platonist viewpoint concerning numbers, and goes on to hypothesize that moral truths may have the same status -- “out there” to be discovered, and analogous from planet to planet.  “Our moral sense may have evolved to mesh with an intrinsic logic of ethics  rather than concocting it in our heads out of nothing.”

By the by:  Pinker's richly suggestive book, ranging afar across fields and meadows, adds  in passing  a suggestion of what we might term Aesthetic Realism:  "Even if an art form matured in the West, it may be  not an arbitrary practice  spread by a powerful navy  but a successful product that engages a universal human aesthetic."
Here he has left any area in which I have expertise, so no comment;  read his argument pp. 407-9.

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