"Seven Peeks into Infinity," by Ricardo Nirenberg.

1. With some help from dreams, we may think of the world as stratified.  Someone is dreaming that you are reading this; someone is dreaming that someone is dreaming that you are reading this, and so on.  The dreamers may be all the same, or they may be different persons; the dreams may stop at a supreme one which is then called Reality, or they may go indefinitely on; if they go indefinitely on, they may do so linearly or periodically, in circles.  All those multiple possibilities have been entertained, or dreamt of, by individuals or by sects, innumerable times through the centuries.  The unending alternatives used to be terrifying, as they would be still today, if we were paying attention.

 

2. The state and its laws came into being as a way to stop infinite revenge which might have pushed our species into extinction; God the demiurge or prime mover was postulated so as to stop the infinite regress of causes.  All such cuts and postulated stops, all those dogmatic tactics that preclude a potentially infinite sequence of operations belong to theology and perhaps exhaust it.  For that reason, the state and its theory, politics, must ultimately be based on theology.  The same was the case with the axiomatic method in geometry invented by the Greeks, so long as the axioms were taken to be self-evident truths— the paradoxical notion of a self-evident truth being the epitome of theology.

 

3. Pascal is the first case in history of a great mathematician who was also a great theologian; later, Leibniz and Cantor might lay a claim to that eminence; but Pascal is still the most profound, and, perhaps because of it, the most often misunderstood.  Just as the Eastern European, Orthodox nations are said to have missed the Renaissance, Russian thought and the Russian soul are supposed to have skipped Descartes altogether and favored Pascal instead.  That is the central contention in Lesley Chamberlain’s Motherland: A Philosophical History of Russia, New York, 2007, and it seems to have been shared by Isaiah Berlin, her mentor.  The thought about Pascal’s influence in Russia appears already in Lev Shestov (1866-1938), the Ukrainian Jew who proclaimed Dostoevsky’s Man from the Underground “the real Critique of Pure Reason” (rather than Kant’s); Shestov whose philosophy proposes to revive Tertullian’s defiant boast “Credo quia absurdum est”—I believe it because it is absurd.  I have written about Shestov and Pascal elsewhere. 1. 

I’d like to add now that all those people’s take on Pascal is based, as far as I can tell, mostly on two famous pensées, “Le cœur a ses raisons, que la raison ne connaît point” (277 in the Brunschvicg edition) and the following one, “C’est le cœur qui sent Dieu, et non la raison” (278).  Thus the Russian soul —so the story goes— prefers the warmth of the heart over the coldness of reason, affects over syllogisms, the particular over the general, conceptual, or abstract: the Russian soul would be irrational by choice.  As the great poet Fyodor Tyutchev put it: “Who would grasp Russia with the mind? / For her no yardstick was created: / Her soul is of a special kind, / By faith alone appreciated.” 2

But, regardless of the actual inclination of the Russian soul, that is a poor and partial reading of Pascal.  What he means by “cœur” and by “raisons de cœur” he explains in several places:  his reasons of the heart are the basic principles from which all reasoning must start and which cannot be provided nor proved by reason.  « Le cœur sent qu’il y a trois dimensions dans l’espace, et que les nombres sont infinis » (282).  That space has three-dimensions and that numbers are infinite: the two statements are quite different in nature but nevertheless have this in common, that they are not of the type usually called “reasons of the heart.” They are rather of a scientific type, and they are far deeper and more basic than Kant’s examples of synthetic a-priori judgments.  But don’t panic; I am not getting there; let’s instead go back to Pascal’s theology.

Nothing in nature is infinite according to Pascal (pensée 121); only number is infinite, and it is number which lends things their multiplicity.  Putting this together with 278 and 282 above, we conclude that infinite number, which multiplies things, and God, who creates them, both exist not by nature, not by reason, but by virtue of an axiom of the heart.  Rational theology, dear to Aquinas, to Suárez, to the Jesuits, for Pascal can only take us up to this: whether we want to do math or put our faith in God, in both cases we must begin by silencing reason and listening to the heart.

 

4. The first successful anti-theological thrust in modern times, the first time infinity was allowed to go on unperturbed, on its own momentum, must have been well after the Jesuit cardinal Bellarmine sent Bruno to the stake in Rome in 1600 for proposing an infinite number of worlds.  Perhaps that moment, the first modern moment of laissez aller, occurred when the French mathematician Augustin-Louis Cauchy, a dévot, an ultra and a friend of the Jesuits, produced a logically rigorous definition of limit, the one which our Calculus courses call “epsilons and deltas.”  That was in the early nineteenth century, the period of Romanticism, and the word “infinite” was much used and abused to mean that something was beyond reason, understanding, expectations, measure, phenomena, or words.  Human orgasm and its pleasures are often infinite in Baudelaire.

 

5. We find the following connection of Romanticism with infinity in T.E. Hulme 3, the English aesthetician admired by the sculptor Jacob Epstein and by the poets Robert Frost, T.S. Eliot, and Ezra Pound (all of them Americans, incidentally).  Classicism in art, Hulme says, is always based on the recognition and acceptance of the strictly finite nature of man—finite and fallen, perpetually afflicted by the inherited original sin.  The Romantic, on the other hand, believes that man is an infinite reservoir of new possibilities.  Linked to this typology, classicism is politically conservative —reactionary if you will—,  recognizing that only a strong tradition and a strong discipline are able to keep humanity away from horror, while romanticism believes, like Rousseau, in our inborn goodness and, like Condorcet, in infinite progress.  Hulme didn’t make any bones of showing his preference for classicism and conservatism.

I would have liked to ask him what, then, did he make of Baudelaire.  The French poet, usually taken as a founder of modernism, was as complete a reactionary as Joseph de Maistre, as averse to material progress as obsessed with the original sin, while at the same time filling his verse with longing for infinity, which is, according to Hulme, the romantic marker.  Was Baudelaire  a Classicist or a Romantic?

What Hulme thought of 15th-century Humanism is clear because he said so: Pico della Mirandola, Marsilio Ficino and others similarly minded were Romantics, avant la lettre perhaps, yet fully fledged.  For they preached man’s infinite possibilities and the absence of anything that could be boundedly defined as human nature.  Naturally, to extend Romanticism backwards to the 15th century is Hulme’s uncontested right, but, as will usually happen, there is no end to the regress, unless it be by ukase.  We can exercise our right and ask Hulme: what of Heraclitus?  Was he a Romantic too?  For here is a fragment of his (Diels-Kranz 45) which is a founding stone of philosophy: “Were you to go after the limits of the soul, you would never find them, even if you tried each and every road: so deep is the soul’s logos.” 4  In other words, the human heart is an abyss.

And perhaps Hulme would have replied that, Sure, why not, Heraclitus too was a Romantic and a Revolutionary, and not only that, but Parmenides was a Classicist and a Conservative.  Didn’t the one maintain that all is change, and the other that all change is but illusion?

 

6.  Eduard Spranger (1882-1963) was a German professor, a disciple of Wilhelm Dilthey and classifier of types or characters of people in the tradition of La Bruyère.  I don’t know the occasion for his frequent contributions to philosophic journals in Spanish; I did find an interesting one in Imago Mundi, Revista de Historia de la Cultura, Buenos Aires, Marzo-Junio de 1956.  It is an issue wholly dedicated to “The Contemporary Crisis,” a subject of great relevance at that time and readily at the tip of cultivated Western pens, ever since the Great War of 1914-18 and the subsequent publication of Oswald Spengler’s The Decline of the West.  I spend quite some time, and I would spend still more, reading those old, forgotten journals of ideas; for one thing, a number of their editors and contributors were my professors at high school and university; also, one finds gems here and there, like the philosopher Francisco Romero's proposal, in that same issue of Imago Mundi, to found an Institute of the Crisis.  This Romero was a retired Major in the Argentine Army, and Borges used to quip that he was “our major philosopher.”

Spranger’s view of the crisis was that our present culture is constituted by the system of unlimited disposition of means—means of production, of transportation, of communication, of computation, of entertainment, etc.  He does not use the word “infinite,” but we may paraphrase him by saying that our culture is constituted by the expectation of infinite means.  At the same time, in Spranger’s view, our culture is characterized by the absence of ultimate aims or ends.  Paraphrasing again, in Latin end is finis; absence of ends is, thus, in-finity: an infinity of absence and void, but not less of an infinity for that.  We find ourselves caught in the middle of a double infinity therefore—not, as in Pascal, the infinitely large and the infinitely small, but the infinity of means and the infinity of absence of ultimate ends.  Out there, a whole universe of things to buy and of money to be made, and in our heart a crushing emptiness.

 

7.  Around 1750, at the time of the French and Indian Wars, Anne Grant, a young Scottish lady, came to live in Albany, NY, the town where I have lived most of my life.  Thomas De Quincey met her and admired her in London when she was old and had already written her memoirs of the New World.  The picture she paints of Albany is one of pastoral simplicity and delight: contrary to the impulse prevalent in Europe—always wanting to move to more expensive, lavish places—people in Albany cherished their dwellings and had no thought of changing them for better ones. 

Almost fifty years later a French aristocrat, la Marquise de La Tour du Pin, came to Albany as a refugee from the Terror, and left her impressions in writing; one of the things that struck her most forcefully was that here anyone was ready to sell their property if the offer was only slightly above the going price.  She thought this was very different from the European attitude, which was one of holding on to one’s ancestral place.  That those two women could have such opposite views cannot be because the situation in Albany had drastically changed in those five decades; rather, both were articulating a fear which had gripped the European educated classes in the age of Kant, of Don Giovanni and of Celestial Mechanics, the fear that the infinity up in the sky would be replicated by an insatiable, infinite void inside the human heart.  Perhaps those two women perceived (at a time when women were still allowed to be more perceptive than men) the abyss of freedom and meaninglessness which was about to engulf us all.

 

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A last word.  I don’t want to be misunderstood: by temperament and upbringing I am in favor of freedom and meaninglessness.  I cherish the freedom to build my meaning (or not to build it) in the face of the general meaninglessness.  But I fear that this precarious, improbable freedom and this difficult meaninglessness cannot last for long.

 

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1. For instance, in “2 + 2 = 5,” in The Tragic Discourse, Shestov’s and Fondane’s Existential Thought, Ramona Fotiade, ed., Peter Lang, 2006, pages 47-53.

2.Translation by John Dewey in John Dewey, Mirror of the Soul: A Life of the poet Fyodor Tyutchev, Brimstone Press, 2010, reviewed by Donald Rayfield in TLS, June 24 2011, p. 27.

3. “Romanticism and Classicism,” in T. E. Hulme, Speculations, New York and London, 1924, pp. 113-140.

4.My translation.  The Greek text: psychês peírata iòn ouk àn exeúroio, pâsan epiporeuómenos hodón: oúto bathùn lógon échei.