In the seventeenth century, European intellectuals developed a new understanding of scientific endeavor, namely to discern natural causes through quantitative measurement. Galileo first challenged the Scholastic supposition that mathematical astronomy was merely ancillary to natural philosophy, and by the middle of the century, both the Cartesian and Newtonian mechanical systems had placed mathematics at center stage, disdaining qualitative physics as irrelevant, unknowable, and misleading. Consistent with their methodology, the mechanists tended to reduce the ontological reality of the natural world to its quantitative aspects, implicitly or explicitly eliminating all categories other than extension, time, space, and motion. In this interpretation, Descartes’ treatment of matter as extension merely formalized an intellectual aesthetic that even his adversaries held in practice. We can easily see this penchant for quantification in Newton’s belief that all physics is mechanical, but we might not expect to find a mania for quantity among those who held a more poetic view of reality. Such an enigma is precisely what we discover in Blaise Pascal, a man who intensely contemplated the ineffable qualitative aspects of human and divine reality, yet remained as thoroughly mechanistic in his treatment of the natural world as Descartes himself. By exploring this dual reality of Pascal’s intellectual life, we can examine how his brand of fideism synthesized the enchanted world of his Catholic faith with a seemingly disenchanted, corpuscular, quantitative science. During his privileged youth, Pascal enjoyed the advantages of a critical scientific education and the company of the greatest French luminaries, including Descartes, Fermat, Roberval, Mersenne, and Gassendi. By the time he published his Essai pour les coniques (1640) at the age of sixteen, Pascal had familiarized himself with the new academy’s mathematical, mechanical and metaphysical theories, and he witnessed their heated squabbles firsthand. Pascal’s formative intellectual environment was uniformly opposed to late Scholasticism and devoted to a mathematical mechanics, yet deeply divided on many physical and philosophical issues. In metaphysical matters, Pascal could never agree with the surly Descartes, though this never translated into the personal contempt that was common among Parisian academics. Descartes, in turn, greatly esteemed Pascal’s judgment; after one of his quarrels with Roberval over the possibility of a vacuum, he huffed, “I will talk to M. Pascal because he discusses things reasonably.”[1] Pascal would spend much of his later life wrestling with the ideas of Descartes, and his final judgment, “I cannot forgive Descartes,”[2] is as much a personal lament as a repudiation of Cartesian doctrine. In disputes about physics, Pascal invariably sided with Gilles Roberval, his principal mathematical and scientific influence. Roberval was arguably the greatest mathematician of his day, yet he received scant credit for his discoveries since he kept many of his methods secret. Much of Pascal’s work developed Roberval’s ideas, and some of his published propositions actually belonged to his mentor.[3] Roberval’s work on the calculus of infinitesimals finally provided the mechanists a geometric model of kinematics, a feat which must have powerfully impressed Pascal, whose writings would exalt geometry as the key to understanding nature. Roberval’s few extant mathematical writings display an aggressive style of proof, pressing forward in developing bold new propositions, while showing little concern for rigorously demonstrating more mundane Euclidean theorems.[4] Descartes also stressed the importance of a theory’s ability to generate new theorems, but Roberval lacked Descartes’ concern for establishing the metaphysical certainty of basic facts. Pascal would later express similar impatience, as he faulted Montaigne for agonizing over “trifles”[5] and came to regard Cartesian metaphysics as “useless, uncertain and painful. And were it true, we do not think all philosophy is worth one hour of pain.”[6] Roberval was also a brilliant experimentalist, and he built the apparatuses Pascal would use to demonstrate the existence of a vacuum and to measure atmospheric pressure. This famous controversy would pit the empiricism of Pascal and Roberval squarely against Descartes’ a priori proof of the impossibility of a void. The dispute over the possibility of a vacuum forced Pascal to articulate his own views on the relationship between physics and metaphysics, as expressed in his confrontation with a Jesuit, Père Etienne Noël, rector of the Collège de Clermont in Paris. In his correspondence with Père Noël (Oct.-Nov. 1647), Pascal maintains that the Aristotelian or Cartesian plenum is not provable, and that a vacuum is at least possible. He criticizes his adversary for basing his arguments on the nature of light and motion, which are unknown, and for failing to consider that the phenomenon of suction may have causes other than “abhorrence” of a void. Pascal appeals to the inadequacy of phenomena for identifying causes, noting that the cosmologies of Ptolemy, Tycho, and Copernicus all account for observed phenomena equally well, so it is ridiculous to “uphold one at the expense of the others”.[7] Pascal’s refutation of Père Noël shows the limits he perceived in both deductive and inductive proofs. A priori proofs suppose knowledge of fundamental natures which science has not yet discerned, and induction from phenomena often underdetermines the theoretical solution. He would later observe, “It is a natural weakness of man to believe he possesses truth directly. For that reason he is always ready to deny anything which is incomprehensible to him.”[8] Although Pascal ridiculed claims of metaphysical certitude in scientific matters, his religious fervor compelled him to uphold Catholic doctrine with absolute conviction. This dual stance would require him to discover a path to religious certainty distinct from that of Descartes. Pascal’s spiritual life oriented toward the contemplative asceticism of the early Fathers of the Latin Church, and St. Augustine in particular. Around the time of the vacuum controversy, Pascal began to associate with the morally rigorous Jansenists, and he gradually became entangled in their subtle theological controversies with the Jesuits.[9] Intense meditations on Augustinian theology and Jansenist ethics forged a man of acute moral and religious sensitivity. The culmination of his spiritual development came on 23 November 1654, when, after meditating on the Passion, Pascal pondered the God of the burning bush, the God of the Patriarchs, “non des Philosophes et des savants. Certitude. Certitude. Sentiment, Joie, Paix. Dieu de Jésus-Christ… Il ne se trouve que par les voies enseignées dans l’Évangile….”[10] Pascal found perfect certainty not in metaphysical speculation, but in a living God who revealed himself to man. Consistent with his Augustinian theology, Pascal assumed a passive role with respect to divine action, whereas Descartes sought to discover God by his own effort. Pascal’s mystical tendencies received further validation from the miraculous cure of his niece by a sacred relic. Revelation and miracles would become central to Pascal’s later proofs of Christianity, enabling him to expound an alternative route to certainty. Pascal’s mature views on the epistemology of natural philosophy emerge in his incomplete work De l’Esprit géométrique (1658-9?), which discusses how geometers discover and demonstrate the truth of propositions. In the first fragment of this essay, he admits that the geometrical method is necessarily imperfect, since it cannot define all terms in an infinite regression, but argues that its excellence consists in knowing what to define and what to demonstrate. Indemonstrable geometrical categories include “space, time, motion, number, equality”. Pascal speaks of mathematical and physical categories indiscriminately, since he believes that the universe consists of “motion, number and space”, yielding the interrelated studies of “mechanics, arithmetic, and geometry”.[11] These categories are all extensive or quantitative; time, for example, is treated as a variable quantity, without reference to our qualitative experience of past, present, and future. Pascal is acutely aware of this disparity between mechanism’s “clear and distinct” categories and our intuitions, but he believes we should not try to bridge this gap with pseudo-definitions.[12] As he would later assert, “We must say summarily: ‘This is made by figure and motion,’ for it is true. But to say what these are, and to compose the machine, is ridiculous.”[13] Pascal accepted that physical reality consisted of extension or quantity, to which qualitative phenomena could be reduced,[14] but he refused to speculate about first principles. The second fragment of De l’Esprit géométrique has the title De l’Art de persuader, suggesting a treatise on rhetoric, but in fact it is a broad outline of how geometrical method can be used to convince others of natural truths. Pascal acknowledges that “the art of persuasion is just as much the art of being ingratiating as of being convincing”, yet holds that human caprice is too diverse to admit general rules for constructing pleasing arguments. This practical limitation confines his “art of persuading” to a restatement of the rules of geometrical proof: “the defining of terms which must be used for clear definitions; the advancement of principles or evident axioms for proving the matter in question; and constant mental substitution, in the demonstration, of definitions for things defined.”[15] He then enumerates several rules for definitions, axioms, and demonstrations. Some rules are Cartesian boilerplate (“Regard as axioms only those things which are perfectly self-evident”), while others are directed against Cartesian speculation (“Define no terms that are already perfectly well known”),[16] but none of them transcend the sterile world of the geometer. Only religious matters are excluded from this cold analysis, since these must “enter the mind through the heart”, whereas his art of persuasion changes hearts by first convincing the mind.[17] Christian apologetics, in Pascal’s view, required an alternative to the geometer’s method. This need was hinted at in De l’Art de persuader, and again in the Pensées: “If we submit everything to reason, our religion will have no mysterious and supernatural element.”[18] Pascal satisfied this deficiency in his Traité qu’il y a des demonstrations d’une autre espèce, et aussi certaines que celles de la géométrie. In this discourse, Pascal argues that historical certainty is as compelling as any geometrical proof. “Que la ville de Londres par example ait esté brulée il y a quelques années, il est certain que cela n’est pas plus vray en soy, qu’il est vray que les trois angles de tout triangle font égaux à deux droits.”[19] Since the Christian religion pertains to the historical order of truth, its veracity may be established through this alternative form of demonstration. By considering the elevated style and thought of the Scriptures, which transcend all other conceptions of the nature of man and divinity, and compiling all that has been written by great men on these subjects, one can construct a proof of Christianity “aussi difficile d’en douter que d’une proposition de Geometrie.”[20] This method would serve Pascal in apologetic works like the Discours sur les preuves des livres de Moyse,[21] and it would shape his treatment of miracles in the Pensées. At a time when theologians sought to demonstrate God through nature or from metaphysical demonstration, Pascal’s historical apologetics pointed toward a specifically Christian religion by focusing on the central events of Christian revelation. By treating Christianity as a historical religion, Pascal relied heavily upon miracles as a basis of faith. Without miracles, “the Church is without proofs”, and there would be no sin in denying Christ. His spiritual model, St. Augustine, declared, “I should not be a Christian, but for the miracles.”[22] Pascal establishes miracles on the foundation of historical certainty he described in the Traité qu’il y a des demonstrations d’une autre espèce, a certainty that is grounded in human testimony and human nature. For example, he argues that it is impossible for the apostles to have invented the story of Christ’s resurrection, since not only is human nature too inconstant to maintain such a secret, but surely the fear of death and torture would have caused them to abandon their scheme.[23] In this clever inversion of Montaigne, Pascal uses the frailty and fickleness of human nature as a basis of historical certainty instead of a cause for doubt. Pascal’s exaltation of miracles was further motivated by his niece’s cure by the Holy Thorn at Port-Royal, thus he condemns those Jesuits who, “unable to doubt that the miracles of Port-Royal are of God, do not cease to doubt still the innocence of that house.”[24] Although miracles are sufficient proofs, people may still doubt them from lack of love (charité).[25] Thus Pascal at once reconciles the existence of unbelief with the idea that Christianity is provable, while maintaining the doctrine that belief in Christ is a moral imperative. Pascal’s use of a humanistic approach to apologetics allowed him to avoid the thorny metaphysical conundrums he found useless and vain. While other mechanists in France and England agonized over the boundary between the natural and the supernatural, or between general and special providence, Pascal considered natural science and matters of faith according to two completely distinct epistemological systems. Although Pascal believed that natural truths did not contradict the historical truths of Christian revelation, his method imposes no necessity to explain one in terms of the other. He sees no need to explain miracles in terms of mechanistic physics, since historical proof suffices to establish them. Similarly, there is no need to discern divine purpose in every natural phenomenon, since matter and motion suffice to explain them. Pascal’s conviction in the existence of two independent paths to certainty allows him to construct two overlapping realities without fear of contradiction. This compatibility is made possible by his austere empiricism, which simply uses the categories of extension, motion and time without trying to define precisely what these are. This leaves our intuitions intact, so that they may be validly used to construct an alternate epistemology. Since empirical science cannot constrain us to a rigid definition of basic categories, we are free to discuss matters such as the mind-body problem and the existence of God on other grounds, as is done in the Pensées. The enigma of Pascal consists in his decision to substantially retain the prevailing corpuscular view of nature, while believing in a mystical order of reality that interpenetrated and co-existed with the mechanistic universe. He was certainly not the only thinker to attempt a reconciliation of mechanism with Christianity, but his solution was exceptional in several respects. He did not insert Christianity into the universe by explicitly fitting God into the mechanistic scheme, as did Descartes or Newton, nor did he place the truths of religion utterly beyond rational demonstration (as did other fideists). Much less did he propose any system of natural theology, on either a priori or a posteriori grounds. Instead, he beheld a world that could be described by two independent, equally valid and certain epistemologies that accounted for different aspects of the same reality. The geometer’s method accounted for all phenomena that varied in intensity, reducing everything to principles of extension and motion. The historical method made intuitive leaps about human nature and the transmission of testimony, yet these were every bit as certain as the axioms of geometry, and people routinely assumed their truth in everyday matters of survival. Pascal’s choice of an historical path to certainty enabled him to advance a specifically Christian apologetic. The actual character of Christ, the apostles, and their miracles became essential to proofs of religion, and the acceptance or rejection of this proof was as much a moral matter as an intellectual problem.
Pascal’s example shows that even the dry, colorless cosmology of French mechanism need not have occasioned a shift toward deism in the eighteenth century. On one level, it seems unbelievable that a passionate ascetic who wrote eloquently of love and beauty could hold that heat, color, sound, indeed, all the ineffable qualities that give the natural world texture and feeling, were reducible to matter and motion. Yet Pascal, unlike Descartes and the eighteenth-century materialists, was unwilling to say what matter and motion are, placing such questions outside the bounds of science. Further, though he believed that qualitative accidents exist only in perception, he did not make psychological reality entirely separate from physical reality, but instead invoked human psychology as a means of proving the physical facts of history. Thus he departed from the skepticism of Montaigne and did not tend toward the modern disconnect between interior knowledge and external reality that would culminate in Kant. For Pascal at least, Cartesian mechanism was utterly powerless to abolish a mythopoeic worldview, making his thought as thorough a repudiation of intellectual historical determinism as one could imagine.

BIBLIOGRAPHY Pascal, Blaise. Great Shorter Works of Pascal, trans. Emile Cailliet and John C. Blankenagel. Philadelphia: Westminster Press, 1948.
Pascal, Blaise. Œuvres Complètes de Pascal, ed. Jacques Chevalier. Bruges, Belgium: Gallimard, 1954.
Pascal, Blaise. Pensées de M. Pascal sur la religion, et sur quelques autres sujets. Amsterdam: Abraham Wolfgang, 1688. http://gallica.bnf.fr/
Pascal, Blaise. The Provincial Letters, Pensées, Scientific Treatises, trans. Thomas M’Crie, W.F. Trotter and Richard Scofield. Great Books of the Western World, ed. Robert M. Hutchins. Chicago: Encyclopedia Britannica, 1952.
Steinmann, Jean. Pascal, trans. Martin Turnell. New York: Harcourt, Brace & World, 1962.
Walker, Evelyn. A Study of the Traités des Indivisibles of Gilles Persone de Roberval (New York: Columbia University, 1932.

[1] Jean Steinmann, Pascal, translated from the French by Martin Turnell (New York: Harcourt, Brace & World, 1962), 43.
[2] Blaise Pascal, Pensées, translated from the French by W.F. Trotter, in Great Books of the Western World, ed. Robert M. Hutchins, V.33 (Chicago: Encyclopædia Britannica, 1952), [77] 186.
[3] Evelyn Walker, A Study of the Traités des Indivisibles of Gilles Persone de Roberval (New York: Columbia University, 1932), 20-29. Holding the chair of Ramus in the Collège Royal, Roberval dared not publish his own discoveries, since this position was defended in an annual mathematical competition, which Roberval won repeatedly by keeping a step ahead of his competitors.
[4] Ibid., 47-48.
[5] Pascal, Pensées, op. cit., [65] 180.
[6] Ibid., [79] 186.
[7] Blaise Pascal, Reply by Blaise Pascal to the Very Reverend Father Noël, Rector, of the Society of Paris in Paris [Oct.-Nov., 1647] in Great Shorter Works of Pascal, trans. Emile Cailliet and John C. Blankenagel (Philadelphia: Westminster Press, 1948), 47.
[8] Blaise Pascal, The Mind of the Geometrician [1658 or 1659?], in Great Shorter Works of Pascal, op. cit., 197. Pascal recalls several of Père Noël’s fallacious arguments in this fragment.
[9] Blaise Pascal, The Provincial Letters, [1656-58] trans. Thomas M’Crie, in Great Books of the Western World, op. cit. Pascal defends the Jansenist/Augustinian theory of grace, which holds that men are saved by an irresistible efficient grace, given only to some men, without which they would freely choose damnation (whereas the Calvinists believe that God also causes damnation). “Sufficient grace”, given to all men, does not in fact suffice for salvation because of the perversity of human will after the Fall. Pascal argues that the Thomist understanding of “sufficient grace” agrees with Jansenism and contradicts the Jesuit belief that it really does suffice.
[10] Blaise Pascal, Mémorial, in Œuvres Complètes de Pascal, ed. Jacques Chevalier (Bruges, Belgium: Gallimard, 1954), 554.
[11] Pascal, The Mind of the Geometrician, op. cit., 195. “These three things, which, according to the words Deus fecit omnia in pondere, in numero, et mensura, include the whole universe, and have a reciprocal and necessary connection.”
[12] Ibid., 193. Pascal’s example of a pseudo-definition is “time is the motion of a created thing”, which is really a proposition equating time in the intuitive sense with the motion of an object.
[13] Pascal, Pensées, op. cit., [79] 186.
[14] Ibid., [368] 236. Pascal reduces heat to motion: “…it is material like the blow of a stone.”
[15] Blaise Pascal, The Art of Persusasion [1658 or 1659?] in Great Shorter Works of Pascal, op. cit., 204-205.
[16] Ibid., 206-207.
[17] Ibid., 203.
[18] Pascal, Pensées, op. cit., [273] 222.
[19] Blaise Pascal, Pensées de M. Pascal sur la religion et sur quelques autres sujets (Amsterdam: Abraham Wolfgang, 1688), 111.
[20] Ibid., 117-118.
[21] Steinmann, op. cit., p.178.
[22] Pascal, Pensées, op. cit., [811-813] 330.
[23] Ibid., [801] 328.
[24] Ibid., [854] 341.
[25] Ibid., [826] 332; and in Œuvres Complètes, op. cit., [760] 1322.