The Minim friar Marin Mersenne (1588–1648) played a central rolein French intellectual life of the first half of the seventeenthcentury. At a time when scientific periodicals were still sorelylacking, he was rightly referred to as “The Secretary of LearnedEurope” (“le secrétaire de l’Europesavante”, Hauréau 1877, p. 177) thanks to hissprawling correspondence, which extended his network across the wholeof learned Europe, to his role as translator, editor, disseminator ofscientific information, and to his ability to generate research anddiscoveries by creating “fine questions” (de bellesquestions, Pascal 1658, p. 1) addressed to the foremost scholarsof the time. His tireless activity certainly helped to create a newimage of a mathematical, mechanistic and experimental science in themaking, based on the exchange of information and co-operation betweenEuropean scholars. Part of his fame is also due to his lifelongconnection to Descartes. From the time the latter settled in Holland,Mersenne was his main, and at times unique, correspondent, providinghim with rich information on intellectual life, and relentlesslyquestioning him on philosophical and scientific matters.

Although these features of Mersenne’s activities (as an animatorof scientific life and as Descartes’s friend and correspondent)are the most well-known, they should not conceal Mersenne’s ownoriginal contribution to philosophy. While his first works werepolemic in tone, offering “scientific apologetics”(Lenoble 1943) using arguments taken from the sciences to defendChristian catholic religion against all sorts of heterodox trendsthreatening it, his latter publications (from 1634 onward), far lessconcerned with apologetics, illustrated and promoted the newmechanical, mathematical, and experimental sciences. A key threadrunning through his complex intellectual career, music, understood asthe general science of harmonics, received Mersenne’s constantattention and was the subject of several important publications.

• 1. Life and Works
• 2. Scientific Apologetics
• 3. Metaphysical Issues
  • 3.1 Metaphysics as Rational Theology
  • 3.2 Proofs of God’s Existence
  • 3.3 Voluntarism
  • 3.4 Mersenne and Descartes on Eternal Truths
• 4. Epistemological Issues
  • 4.1 Against the Skeptics
  • 4.2 Mitigated Skepticism and Probabilism
  • 4.3 Mechanism and Experimentalism
• 5. Music and Universal Harmony
• Bibliography
  • Mersenne’s works and abbreviations
  • Other Primary sources
  • Secondary sources
• Academic Tools
• Other Internet Resources
• Related Entries

1. Life and Works

Marin Mersenne was born on 8 September 1588 near Oizé in theFrench region of Haut-Maine (nowadays the Sarthe). He came from afamily of merchants and small landowners. After studying at thecollege du Mans, he was sent in 1604 to the newly created Jesuitcollege of La Flèche, where he received the established Jesuiteducation, coupling humanist—Ciceronian—and Aristoteliantraditions (Dear 1988). He may have met there the young RenéDescartes, who entered La Flèche in 1606, although it isunlikely that their friendship started then, as Descartes was 8 yearshis junior. When he left the college, Mersenne completed his trainingin theology, Greek and Hebrew in Paris at the Collège Royal andat the Sorbonne where he was instructed by the Thomist theologiansFrançois Ysambert and Philippe de Gamache (see Coste 1648;Armogathe 1994). Attracted to the strict rule of the Minims, aFranciscan order recently introduced into France, he took the habitsin 1611, and after periods of novitiate and teaching in Meaux, Parisand Never, was recalled to Paris in 1619 at the new house on the PlaceRoyale (the present Place des Vosges) where he remained permanently,apart from a few trips to the French provinces, to the Netherlands in1630, and to Italy from 1644 to 1645.

From the years 1620 onward, Mersenne deployed overflowing intellectualactivity. Through the mediation of Claude Fabbri de Pereisc whom hehad met in 1616, he was introduced to the Parisian intellectual elite,and later to Pierre Gassendi with whom he remained close friends. InParis, he associated with the mathematician Claude Mydorge, and,perhaps through him, renewed acquaintance with Descartes. Mersennecalled on Descartes’s mathematical expertise on questions ofoptics. His questions led Descartes to his first formulation of thelaw of refraction, which he was to publish later in his 1637“Dioptrics”. Mersenne was among those attending the famousmeeting of 1628, at the residence of the apostolic nuncio, whereDescartes, having revealed his project of founding the sciences on anew method, had been encouraged to do so by the highest religiousauthorities. After Descartes left for Holland, Mersenne remained inclose contact with him through correspondence. He was privy to most ofDescartes’s secret addresses, which made him the man one has tosee in order to get access to the French exile, to send him letters orquestions. Only four letters from Mersenne to Descartes are extant,but 146 letters from Descartes—about a quarter of his knowncorrespondence—testify to the intensity and continuity of theexchange. Mersenne endlessly provided Descartes with books, freshinformation, and editorial services, requesting in exchange answers toqueries of all sorts. Acting as mediator in Descartes’scontroversies, with Fermat, Roberval, Beaugrand, Morin, orVoëtius, he sometimes caused quarrels himself, through hisindiscretions, such as the one which made Descartes definitively fallout with his erstwhile mentor Isaac Beeckman. Mersenne also acted asintermediary for the edition of theMeditationes de primaphilosophiae, and was instrumental in the gathering of the sixsets of objections that were added to the text with Descartes’sresponses, including those of Hobbes and Gassendi. He contributedhimself to the objectiones, penning the second set (“gathered bythe R. P. Mersenne from the mouth of various theologians andphilosophers”, AT IX-1: 96; Buccolini 2019) and perhaps parts ofthe sixth.

Mersenne’s dealings with Descartes were only a small part of thenetwork of intellectual communication that he built up throughout hiscareer. He was largely responsible for introducing Galileo intoFrance, offering in 1630—without receiving an answer—topublish his future work on theTwo Chief Systems of theWorld. In 1634, he publishedLes Méchaniques deGalilée, a free translation of a manuscript on mechanicsby the Florentine scholar, completed with ideas borrowed fromGuidobaldo and Stevin, and with original comments of his own, and, in1639, theNouvelles pensées de Galilée, atranslation or adaptation of certain parts of theDiscorsi a duenuove scienze, published in Italy one year earlier. Mersenne wasalso in regular contact with English scholars. He translated intoFrench theDe Veritate of Herbert of Cherbury (although thebook had been placed in the Index, i.e., the list of prohibited bookspublished by the Catholic Church); in good terms with Hobbes (Baldin2020), he published one of his optical treatises, andSorbière’s French translation of theDe Cive. Hecorresponded with Kenelm Digby and Lord Cavendish and others.

In Paris, a small scientific circle of mathematicians and physicistsgradually formed around Mersenne. From 1633 or so, meetings wereorganized on Thursdays at the houses of one or another of his friendsor protectors. This “Academia Parisiensis”, as it came tobe called, brought together men such as Étienne Pascal,Mydorge, Hardy, Roberval, Fermat. It was later to welcome the youngBlaise Pascal, and Jacques Le Pailleur who was to become thegroup’s leader when Mersenne died in 1648. Discussions weremostly “mathematical” (MC V: 209). Mersenne used to submitproblems of his own invention to his friends, and some were oftenremarkably stimulating and the origin of important discoveries such asthe “roulette” problem, solved by Roberval in 1634; andthen more indirectly by Fermat and Descartes. Mersenne himselfundertook to establish a first list of what will eventually be calledthe “Mersenne primes”, prime numbers that can be writtenin the form 2ⁿ − 1 (for some integern),whose properties and determination are still topical questions incontemporary mathematics. Mersenne envisaged his meeting group, andhis own net of correspondents, as the prototype for a largerinstitution that would bring scholars together in a pacified Europe,foreshadowing the foundation of the later Académie des sciencesin 1666, or the Royal Society in England (MC V: 301–302, andGoldstein 2013)

In 1623 and 1625, Mersenne published three massive philosophicalworks. TheQuestiones celeberrimae in Genesim (which coversalmost 1900 folio columns), a commentary on the six first chapters ofthe book of Genesis, larded with long scientific and philosophicaldigressions, was intended as an apology of Christian religion againstall forms of “atheism”. It contains attacks on variousPlatonist, cabbalistic and hermetic authors such as BernardinoTelesio, Pietro Pomponazzi, Giordano Bruno, Jacques Gaffarel, or theEnglish hermetic author, Robert Fludd. The tone is virulent, sometimesoffensive, and the book attracted several outraged answers. Fludd inparticular reacted in hisSophia cum moria certamen (1629)which itself drew a long reply from Gassendi, writing uponMersenne’s request (Gassendi 1630). The same inspiration governsL’Impiété des Déistes, publishedin French the next year. It is a point-by-point refutation of the 106Quatrains du Déiste orAnti-Bigot, a longanonymous poem denouncing Christian revelation, bigoted superstitionand belief in a personal God. Mersenne’s response, written as adialogue between a deist and a theologian, leads to the conversion ofthe deist, to whom the existence, justice and mercy of the ChristianGod are demonstrated. Dedicated to Richelieu, and perhaps written oncommand, the book may be seen as taking part in a larger campaignorchestrated by the French state and the catholic church, at a timethat witnessed Vanini’s execution in Toulouse, the trial ofTheophile de Viau, and a strengthening of repressive measures againstanti-Aristotelian philosophical novelties.La Véritédes sciences (1625) is a dialogue between an alchemist, a skepticand a Christian philosopher, the latter opposing both theover-confidence of the first and the excessive doubts of the second.The second, third and fourth parts of the book, dealing witharithmetic and geometry, is an 800-page compilation of ancient andrecent achievements in the mathematical sciences, intended to showthat there are regions of human knowledge immune from doubt, and whichdo not contradict Christian wisdom.

By the end of the 1620s, Mersenne’s former animosity towards theanti-aristotelians authors withered, giving way to a more lenient ifnot tolerant approach. Galileo whom he had listed among the dangerousones in 1623 is now the object of great praise. Mersenne seemed muchless concerned with the proliferation of atheists and heretics, and heexpressed regrets about the offensive tone of his previous works(Letter to Rivet 12 nov. 1639, MC X: 599). His travel to Holland in1630 put him in contact with Protestant scholars, such as AndréRivet and the Socinian Ruarus, who became regular correspondents.Mersenne who used to vilify the heretics, was now taken to task forhis sympathies with the enemy, and he was sometimes dubbed the“Huguenot monk”. In any case the staunch defense oforthodoxy of the first works is nowhere to be found inMersenne’s next publications, which, from 1634 onward, arealmost entirely devoted to the promotion of the mathematical sciences,broadly conceived. It has been a question among biographers andcommentators whether these changes reflect a conversion to a newagenda or a new philosophical outlook. Robert Lenoble (1943: 38)considers that until 1634, Mersenne was still looking for a betterphilosophy of nature and held provisionally to Aristotelianism,“whereas at that date he discovered what he had sought for manyyears, namely Mechanism”. Sylvie Taussig (2009b) considers thatMersenne went through a serious crisis, both moral and intellectual,at the end of the 1620s, and that under the influence of Peiresc andGassendi he came to adopt a more skeptical outlook on philosophicaland religious matters. Without denying Mersenne’s change of toneand accent, Garber (2004) and Dear (1988) tend to underplay the extentand meaning of Mersenne’s “conversion” to the newphilosophy, considering that his agenda of promoting mixed mathematicswas to him still compatible with a traditional philosophicaloutlook—“the learning of the schools”, that Deardescribed as conjoining Christianized Aristotelianism, Renaissancehumanism and a skeptical or probabilistic approach to philosophicalmatters. We shall come back to these issues in due course.

The five treatises published in a row in 1634 are representative ofthe kind of intellectual productions Mersenne would henceforth offer.Two of them (Questions inouyes, andQuestionsthéologiques…) are eclectic lists of“curious” questions, intended for entertainment(récréation) as well as for instruction of thelearned: can one walk on water without miracle? How many grain ofsands can be contained in the sphere of the earth ? From where doesthe satisfaction come when one believes one has found a newdemonstration or truth? In these questions metaphysical, apologeticand even theological considerations are (in spite of the title of thesecond treatise) barely present. TheQuestions harmoniquesand thePréludes to the harmonie universelle preparethe way for the publication of Mersenne’s great achievement onmusical theory, TheHarmonie Universelle (1636–7),where he offers what is still considered a major contribution to thescientific understanding of “consonance” and acoustics.Finally theMechaniques de Galilée illustrateMersenne’s constant interest in physico-mathematical questionsof Galilean type, that is Archimedean mechanics stricto sensu, dealingwith basic machines, such as the lever, the wheel, the pulley, butalso the sciences of motion, free fall, ballistics, pneumatics,hydrostatics, and optics. Mersenne pursued these interests in the1640s, when he started to make his own campaigns of experiments inorder to verify Galilean numerical data on free fall and on thevelocity of a cannon ball, especially during his journey to Italy(1644–1645) where he met Torricelli. These researches resultedin the publication of hisCogitate physico-mathematica (1644)and hisNovarum observum physico-matheaticarum (1647), whichincludes in its first part a treatise by Roberval on the system of theworld. A book on optics was to be published after Mersenne’sdeath (L’Optique et la catoptrique, 1651).

2. Scientific Apologetics

Mersenne was indubitably an heir to the Thomistic view of a necessarysynthesis between Christian faith and philosophy. As expressed in thepraefatium of theQuaestiones in Genesim, it is “a dutyof the learned to refute atheists”, the tacit assumption beingthat “true philosophy never contradicts the teachings of theChurch” (ID II: 490–1). This synthesis was vindicated inthe rather troubled political, and religious context of earlyseventeenth-century France, which still bore the scars of half acentury of religious wars, and appeared exposed and vulnerable to whatCatholics considered a severe crisis of orthodoxy, raging on allfronts. A rising tide of libertines, deists, skeptics, cabbalists,alchemists, and naturalist metaphysicians, all more or lessconsciously in league with the Protestants, seemed to Mersenne on theverge of overwhelming the “true” Christian faith. Mersenneoften pointed out the connection between Protestantism and the variousforms of heterodoxy and atheism: the Calvinist belief inpredestination insensibly drives men toward superstition and atheism,as it appears more difficult to believe that God wants our damnation,than to represent Him as a “cruel Saturn who devours hischildren”, or simply to own that there is no God at all (ID II:589). So, Mersenne’s early-interventions may be seen as takingpart in the larger movement of “re-catholization” of theFrench state after the pacification allowed by the Edit de Nantes. Inthis regard, Mersenne’s advocacy of a harmonious conciliation offaith and reason was not without similarities with a noted feature ofGalileo’s “cultural program” in the same years: bothwanted to contribute to the Counter-Reformation, and both defended thespecific idea that Catholics should not leave to Protestant hereticsthe monopoly of reason and scientific knowledge. Mersenne was howeverwary of any anti-Aristotelian philosophical novelties (including thoseof Galileo himself), as he saw them asipso facto dangerouslyverging towards contesting religious truth. According to Garber(2004), the Aristotelian framework, particularly prominent in thefirst works, was adopted not so much for its philosophical virtues assuch, but rather as a rampart of orthodoxy, as a tried doctrine, thathas long proved its ability to be harmoniously conjoined withChristian faith, and as it were to protect it. By contrast,alternative ways of thinking offered no such guarantee against heresy,as they were often defended with a zeal that was dangerously close tofanaticism. As Mersenne stated in the preface to theQuaestiones (1623):

These men who desire to found a new philosophy, and to demonstrate itfrom fundamental principles, never regard the glory of God. Ratherthey strive with an ignorant obsessive zeal [cacozelia], bywhich they seek to shake up and overturn the Catholic religion, ifthey are able to do it—unless I am mistaken. (QG Praefatio,translated in Garber 2004: 141)

Thus it seems quite clear that the stakes of a book like theQuaestiones were not simply a defense of natural religion butalso, and perhaps primarily, a defense of catholic faith (and itsmysteries) against the caricature conveyed in a growing number ofwritings, that represented it as resulting from superstition andignorance:

It is appropriate to Catholics, and especially to theologians to knowthe sciences and to scrutinize God’s works, not only because wethus receive the meaning of His will as from the pages of a Book, butalso because we show how unfounded is the atheist’srepresentation of Catholics as melancholic, agitated with thousandsscruples and superstitions. (QG: col 2 – translation here andelsewhere from the author, unless otherwise indicated)

To realize this aim, Mersenne’s strategy was twofold: polemicaland constructive. On the one hand he attacked his polymorph enemy withthe rhetorical instruments of a skilled debater, using the weapons ofthe adversaries, or making one refute the other (as in the dialoguebetween the alchemist and the skeptic in the first book ofLaVérité des sciences). Hermetic authors such asRobert Fludd, or cabbalistic Christians such as Giovanni Pico andJacques Gaffarel were vehemently denounced, as they availed themselvesof spurious allegorical interpretations of the Bible. Even when theirreading of the Bible is not wrong, they are dangerous as they makepeople believe they can deducea priori, or through divineinspiration, what can only be knowna posteriori, throughrevelation and experience. Heretic tendencies were pointed out in thedoctrines of the Alchemists, who, in the wake of Paracelsus’sMysterium magnum, tried to give naturalist interpretations ofChristian mysteries, such as the resurrection or the miracle ofCreation. Mages, sorcerers, and adepts of esoteric mysteries such asthe Rosicrucians prosper on men’s propensity to superstition.Naturalist metaphysicians—Bruno, Campanella,Pomponnazi—who endowed nature with creative powers, vergedangerously toward pantheism, casting doubt on creation, on thetranscendence and freedom of God. A leading thread in all thesecriticisms, is the idea that the Catholic belief in miracles andmysteries, far from being superstitious, is much more attuned to soundreason than the doctrines that are opposed to it. A light knowledge ofphilosophy may induce some doubts, but the more one knows thesciences, the more these Catholic beliefs and mysteries are reinforcedand may be vindicated against false religion and atheism. A smatteringof knowledge in optics can for example cast doubt on the truth ofdivine epiphanies, but a better knowledge of this same science allowsone to exclude the idea that miracles can be illusions caused byreflections or refractions and therefore makes more sensible theirdivine origin (QG: col. 522, 538). This sort of negative argumentshows that Mersenne’s rationalist defense of religion allows fortruths beyond the capacity of men’s reason. In this, Mersennestand explicitly against the deist. Both allowed for “naturalreligion”, but whereas the deist denounced the superstition andanthropomorphism of popular belief, Mersenne reversed the attacks anddenounced the far worse anthropomorphism of one who measures God byhuman reason: “it is feebleness of the mind, to believe that ourfinite understandings can comprehend the divine attributes oracts” (ID I: 318–9; see also ID I: 669–70, andBeaude 1980). This however should not be understood as revealing asecret inclination towards fideism: religion teaches truths whichsurpass reason, “not in destroying it, but rather in perfectingit” (ID I: 680).

Mersenne’s criticisms are based on a careful reading andexposition of the adverse doctrines, to the point that Mersenne hasbeen sometimes taken to task for offering the enemies of religion amuch too complacent advertisement. It has been remarked (Carraud 1994:152) that the discourse of others (le discoursd’autrui) holds a distinctive place in Mersenne’swritings: it is neither dismissed as in Descartes, nor deftlyre-appropriated as in Leibniz, but rather faithfully produced andreported in order to be discussed on its own level and according toits own merits. This is the case, for example with the cabbalistic“sefirot” and numerological methods which arepatiently, almost sympathetically, expounded in theImpiété. The same holds for GiordanoBruno’s doctrine. However heretical the man was, his arguments infavor of the infinity and plurality of the worlds (from hisDeInfinito) are not simply dismissed or brushed aside. TheChristian philosopher reports them quite accurately in the second partof theImpiété des déistes, beforeanswering and criticizing them.

Apart from its polemical intent, Mersenne’s “scientificapologetics” may be seen as articulating a natural theologytogether with a “sacred physics” or “sacredmathematics”. On the one hand a host of rationalarguments—some of them borrowed from the sciences, some fromtraditional metaphysics—are brought in to prove God’sexistence and demonstrate His attributes. This natural theology iswhere Mersenne articulates his main ideas on metaphysics and we shallcome back to it in the next part of this article. On the other hand,science is used as an instrument of exegesis. TheQuaestiones inGenesim contains thus numerous scientific excursuses whose aim iseither to give a scientific (mainly mathematical) exposition of abiblical content—as when Mersenne “calculates” whatshould be the size of Noah’s ark, or suggests that our knowledgeof architecture should help us to see the excellence of the temple ofSolomon—or to illustrate a Catholic mystery (such as the triadicunity of God or the miracle of the Creation) through a mathematicalanalogy.

This edifying use of mathematics is perhaps the hallmark ofMersenne’s writings. It is still very much present in laterpublications (such as theHarmonie Universelle). The minim isliterally fascinated by the almost magical properties of numbers andgeometrical figures, where the most surprising and complicated objectsand properties are generated from the simplest principles. This giveshim a general analogy for religious truths. There are “thousandsof things in the mysteries of faith” that are“incomprehensible to the pagan and to a peripateticphilosopher”, but that may be made understood by a“Christian Euclid” (un Euclide chrétien) :Mathematics makes the relation of the infinite to the finite sensible,showing how an infinite motion can be made in a finite space. It canthus “explain” the union of the two natures in the samedivine person. Although the mathematical point is the humblest object,“the minim of geometry” (HU III: Livre del’Utilité de l’Harmonie, 16), it is in a sense theclosest to God itself. Both are simple, without parts. The pointengenders the line and together with the line, the surfaces, and withlines and surfaces the bodies. This gives us an insight on how Godengenders the son, the son and God together, the holy spirit, and thenall together the universe. Unity contains all numbers eminently, asGod contains all created acts and all creatures, etc (ibid. 16–17).Mersenne also likes to suggest mathematical analogies illustrating, orsymbolizing moral virtues. Thus, as the height of a triangle ismeasured by a perpendicular line elevated from the basis, the goodnessof our actions is measured by the righteousness of our intention(“la droite intention”, VS I: 12). Mixed mathematics,optics, music and mechanics are also mobilized in the moral use ofmathematics. For example:

mechanics teaches us to live well, either by imitating heavy bodieswhich always seek their center in the center of the Earth, just as thespirit of Man must seek his own center in the divine essence which isthe source of all our spirits, or by maintaining ourselves in thatperpetual moral and moderate balance which consists of rendering allthat belongs to Him first of all to God and then to our neighbor. (MCIV: 208–09)

The philosophical value of Mersenne’s apologetics may bedifferently assessed. Mersenne seemed to pay little attention tocontemporary arguments according to which the Bible is not to be takenliterally on questions dealing with nature (see, e.g., Galileo’s1615 Letter to Christina). His exegesis indeed offers a rather roughexample of what will be later called “concordism”, theconception that there cannot be any discrepancy between the teachingsof the sciences and those of the Bible, taken in the most literalsense. However, the most distinctive aspect of Mersenne’sapologetics, the edifying use of mathematics, although sometimesnaïve in its formulations, did have philosophical influence.Pascal, who does not spare his sarcasm on those who think they can“prove God from the course of the moon and the planets”(Pascal 1963: 599, fg. 781), is nevertheless quite faithful toMersenne’s use of mathematics, when he discusses men’sdisproportion and God’s greatness from the mathematical model ofthe infinite divisibility of space, or from a speculation on the twoinfinites whose terms are reminiscent of similar passages from theImpiété.

Besides, although Mersenne’s “scientificapologetics” was primarily conceived as a defense of religionagainst “atheists”, where science is only a tool, itturned out to be also a defense of mathematical sciences againstwhoever might think that they are vain curiosity and must be eitherrejected, or at least relativized as inessential knowledge…This is especially manifest in the later works, where Mersenne gavefree rein to his passion for mathematical sciences. Whereas naturaltheology and anti-deistic polemic were no longer dominant themes, hestill vindicated the “usefulness” of mathematics, not onlyfor men’s welfare, but for their edifying virtues. In the nextdecades, one could find similar moves in defense of the“usefulness of natural experimental philosophy” in theworks of Robert Boyle.

3. Metaphysical Issues

3.1 Metaphysics as Rational Theology

In theQuaestiones, Mersenne offered a tripartition of thetheoretical sciences: metaphysics considers “trans-naturalobjects, such as God and the angels, that are actually separated fromall matter”; doctrinal sciences—that ismathematics—deals with objects that are “in truthmaterial, but considered abstracted from matter, such as the line andthe figure”; natural sciences (physics) considers“material things as such, for example the heavens or theelements”. (QG: col 92–3). InLaVérité (VS I: 50), Mersenne suggested thatmetaphysics, although an abstract science, like logic and mathematics,is nevertheless closer to physics, in so far as their shared aim is toconsider “things as they are in themselves”, and notsimply things as they appear to our senses—in this both sciences“are rightly called sapience”. He was later to revise thiscoupling, suggesting in hisQuestions inouïes (QI: 54)that metaphysics is closer to mathematics, on account of the factthat, contrary to physics, metaphysics and mathematics both considerimmutable and eternal objects, and are the only ones among thesciences capable of being really possessed by men here below.

The definition of metaphysics given in theQuaestiones isstrongly reminiscent of Aristotle’s Metaphysics E1—where“prime philosophy” is conceived as strictly concerned withthe separated or immaterial substances, thus with the“theological” realm. Jean-Luc Marion (1994) pointed outthat although Mersenne, in several places, acknowledges formallyanother traditional object for metaphysics, that is the “ensquatenus ens” (the abstracted Being as such, whose scienceapplies indifferently to all beings, created or uncreated), he seemedreluctant to give this science (that we now call ontology) anysubstance. In a striking passage from theQuaestiones,Mersenne said that “Being” is a name that suits God betterthan any of the creatures:

Among all names “being” is the one that we should ascribeto God, rather than all the other ones naming the perfections ofcreatures… God could justly say “I am all Being, as Icontains all things more perfectly than they can containthemselves”. This is why all creatures could say “my nameis non-Being, or non-entity” (Non Esse, seu non Ens),as, according to Plato, truly all things except God have non-beingrather than being. (QG: col. 21)

In later works the specificity of ontology was quickly dissolved intologic on the one hand (an abstract science which shares with ontologythe same principle of non-contradiction, see VS 52–55) and intorational theology on the other hand, the science of immaterial beingsand first causes. This dissolution may be seen as anticipatingDescartes’s own reduction of metaphysics to “primephilosophy”, and, according to Marion, this is a verysignificant (albeit a merely negative one) legacy of Mersenne’swork to the history of metaphysics.

3.2 Proofs of God’s Existence

The bulk of Mersenne’s contribution to rational theology iscontained in the 700 or so first columns of hisQuaestiones inGenesim, where no less than 35 proofs of God’s existenceare reckoned and detailed. The importance of rational demonstration isdirectly related to the apologetic project: one cannot simply becontent with the idea that God is immediately known, as this could notshut the mouths of the atheists. The encyclopedic turn of therecension is obvious, and Mersenne, ready to use all means availableto contradict the atheists, was not taken aback by the fact that theseproofs belong to various, and sometimes adverse, theologicaltraditions. After summoning the consensus of all creatures, and theconsensus of all men, Mersenne resorted to cosmological arguments,arguing, from the contingency of our word, and the contingency of ourown finite existence, that “it is necessary that somethingexists by itself”. Here Mersenne borrowed from Hugues of SaintVictor and Jean Damascene.

He also presented at some length the Anselmian argument, arguing thatexistence should be attributed to God, on account of the fact that thevery idea of God (that even the insane atheist should have in hismind) obliges us to consider that nothing greater can exist, and thatexistencein re is obviously a greater thing than existencein the mind. Mersenne, who did not mention Aquinas’s criticisms,found the argument “excellent and very pious” (QG: col37). He also paid much credit to the Augustinian argument from“eternal truths”—Mathematical truths in particularwould not be possible without the supposition of an eternal mind inwhich they reside:

open your mind’s eyes, ô atheist, and see how numerous andstrong are the arguments through which arithmetic asks you to embracethe divine unity, without which Arithmetic would not hold, as allmaterial unity or numerical is impossible without the supposition ofdivine unity. … One objects to the atheist’s geometry, ifever one listens to Plato who recognizes God from this very science,as he said that God never ceases to practice geometry. (QG Praefatio:a2)

It is to be noted that the twoa priori arguments (frometernal truths and from the idea of a perfect being) are the only twothat are brought in in the Impiété to dispel atheism. IntheQuaestiones however more than half of Mersenne’sarguments werea posteriori ones: from the creationexnihilo, from the beauty of creatures, from the given natural law,from the harmony of the universe… All allowed lengthyscientific excursuses, demonstrating God’s intelligence andprovidence through whatever the sciences can show of the order ofthings. Among these arguments, Mersenne paid only lip service to theclassical Aristotelian and Thomist “argument from motion”,which states that the world needs an immutable first mover, probablybecause he is aware that the argument had been used in PaduanAristotelianism in order to defend the coeternity of the world and itsfirst mover. In the othera posteriori proofs, the regressivemove from the creation to the creator was not as likely to subject thecreator to the creation.

Prominent in theQuaestiones andImpiété, rational theology tended to recede inimportance in subsequent works. Although in theQuaestiones,Mersenne had hinted at another work (“perfectumopus”) to come, it was never written. After 1624 he becamemore reluctant to consider proofs of God’s existence, hinting inhis correspondence with Ruarus that it might not be possible to give atruly demonstrative one, however sensible and approved by everyone wasthe truth of God’s existence. His doubts were now on a par withthe ones he came to entertain regarding demonstrations in physicalmatters. In hisQuestions théologiques, he wrote in asomewhat autobiographical tone, that everyone could see for themselvesthat:

fresh from the Philosophy and Theology courses, they used to imaginethat they could give a reason for everything, whereas 20 or 30 yearslater they are compelled to confess that they know no reason thatsatisfies them and is so evident and certain that they cannot doubtit. (QT: 10)

This may shed some light on Mersenne’s role in the writing ofthe second objections to Descartes’sMeditations, wheredoubts were cast on the demonstrative character of the Cartesianproofs of God’s existence, and especially on the ontologicalproof, whose Anselmian version was so much favoured by Mersenne in hisyounger years. It has been argued (Garber 2001), quite convincingly,that Jean-Baptiste Morin, a member of the Mersenne circle, and theauthor of a booklet on God’s existence written in a geometricalfashion (Morin 1635) had an important hand in the composition of thesecond objections and that he was probably the one who suggested therequest of presenting the Meditations arguments in a geometricalmanner. Mersenne, however would have concurred with the reservations,implicit in this demand, concerning Descartes’s claim to thehigher certainty of metaphysical demonstrations over mathematicalones.

3.3 Voluntarism

Voluntarism was an important feature in Mersenne’s apologetics.Against what appeared to him dangerous necessitarian tendencies inRenaissance naturalist philosophies, he repeatedly advocatedGod’s essential freedom in regard His creation. God chooses toexert his efficient, transitive causality in whatever way he will.This for instance explains why Mersenne always opposed the idea of aninfinite universe. An infinite world, of the kind postulated byGiordano Bruno, would be very close to a necessary emanation of God,but it is neither required of God’s infinite power, nor does itagree with the nature of a created thing :

all that is produced is finite but God’s potentia is withoutmeasure. No created object is adequate to it. (QG: col. 435)

Mersenne maintained that God is not constrained by His infinite power.As a free cause, he can chose to create a finite universe:

why would God make a finite world, if He could make an infinite one?The answer is: God did not want to do anything else than what hedid—this however will not prevent us from believing He is allpowerful, as we distinguish in God the work and the will [le faireet le vouloir]… it is bad reasoning to conclude aninfinite effect from an infinite cause when the cause is not actingnecessarily but freely. (ID II: 304)

For Mersenne the unique perfect egalitarian emanation of God would bean actionad intra, that is the action through which Godcontemplates (and loves) Himself in the persons of the trinity. Whenone comes to causalityad extra, such as creation, one has todistinguish (ID II: 311–2) between divine power and divine will.The first contains and addresses infinite possibilities, the secondchooses, from among them, a finite assortment.

Voluntarism concerning the nature and laws of creation may appear asan important common ground that Mersenne shared with orthodox(Thomist) scholasticism, and with Descartes. As Lenoble has shown, itsassertion was an essential precondition for the establishment of amechanical science, unifying the whole of nature under the contingentwill of God, his initial decisions regarding the distribution and lawsof matter and motion. Mersenne’s voluntarism implies thatphysics is not about an eternal and immutable object, as God couldhave ordered the word in various manners and with various laws. This,as we shall see, has important epistemological consequences:God’s freedom means that he is not compelled to create things inthe simplest fashion. This is evidenced in the reign of the grace,where one can clearly see that God did not chose the shortest way todispense his grace, as he could have assured our salvation with aunique act of his will (cf.Questions Inouïes, p.344–5] But this hold as well for scientific truths, and explainsfor example why Mersenne never considered as decisive Galilean andCopernican arguments for the motion of the earth taken from thesimplicity of natural order. Mersenne’s point was actually quiteclose to the argument from divine omnipotence that Pope Urban VIIIsuggested to Galileo in 1623, and that Galileo, somewhat ironically,put in the mouth of Simplicio in the concluding sentences of the 1632Dialogo: Man cannot presume to know how the world really is,since God could have brought about the same effects in ways unimaginedby humans (see Galileo, 1890–1909, VII, 488).

3.4 Mersenne and Descartes on Eternal Truths

Mersenne did not extend his voluntarism to mathematical truths, asDescartes did in a rather unconventional way. The confrontation ofMersenne’s and Descartes’s positions on this theme hasbeen the object of some discussions in the secondaryliterature—see especially Marion 1980; Dear 1988; Carraud 1994;Fabbri 2008. Descartes first assertions on God’s creation ofmathematical truths appeared in a letter to Mersenne of April 15,1630. Descartes enjoined his correspondent to tell everyone aloud thatthe mathematical truths that Mersenne called eternal were notindependent of God, but “have been created by him and depend onhim entirely just as do all the other creatures” (Descartes toMersenne, April 15, 1630, AT I: 145). God freely established them, andimpressed them in the minds of men, as a king would in his kingdom.The statement seems to have surprised Mersenne. The Minim’s ownletters are lost, but this can be inferred from the fact thatDescartes in May and June 1630, obviously answers repeated requestsfor clarification:

you ask mein quo genere causae Deus disposuit aeternasveritates [in what kind of cause God has disposed the eternaltruths]. I reply to you that it isin eodem genere causae [inthe same kind of cause] that he has created everything, that isutefficients et totalis causa [as efficient and total cause].(Descartes to Mersenne, May 27 1630, AT I: 151–2).

You ask what necessitated God to create these truths; and I reply thathe was free to make it not true that all the radii of the circle areequal—just as free as he was not to create the world. (27 mai1630, AT I: 152)

Mersenne’s own considerations on the status of eternal truths inGod’s intellect explain why he should have had qualms aboutDescartes’s puzzling doctrine (which might amount here to noless than making mathematical truths somehow contingent, depending onthe arbitrary will of God—even though Descartes himself, whooften points out the necessity of mathematical truths, never drawssuch consequence). Mersenne position seems closer to cardinal deBerulle’s, and Augustine’sexemplarism: eternaltruths are exemplar ideas present in God’s intellect andilluminating our own. They proceed from God’s nature as HisVerb, but they are not similar to creatures, they are not“freely” created.

When Mersenne considers God’s relation to eternal truth he oftenuses metaphors of light and the emanatist vocabulary ofNeo-Platonism—for example in theTraité del’harmonie Universelle:

I consider, therefore the divine essence as an eternal and infinitesun, which darts an infinity of rays on which depend all ourperfections: the goodness of God is one of these rays, whence comeour good inclinations, our virtues and our good works, the other iseternal truth, whence proceed all our truths and our sciences. (THU:59–60, English translation in Dear 1988: 58)

Or in theQuestions théologiques:

the sciences are like the rays of divinity, and it is just asblameable to try to know them without God, than try to know the natureof colours, without knowing the nature of light, which gives thembeing and subsistence. (QT: 202)

The kind of causality implied here is a causalityad intra:eternal truths belong to God’s nature. And in this regard, asthey are “formally” in God and so to speak coeternal withHim, they should be considered as uncreated and necessitated, as Godhimself is not free towards His own nature:

It is patent that God is entirely free in regard everything that arecontained only eminently in him, to produce them or not, as He isdriven necessarily to whatever he embraces formerly as these thingsthat are God himself are infinite, eternal, independent. (QG: col436)

The idea that eternal truths exist necessarily in God, and do notdepend on God’s causality was not new, and Mersenne herebelonged to a rather well established scholastic tradition. Anoriginal feature of Mersenne’s position however is that heconsidered mathematical truths as the very paradigm of eternal truths.As pointed by Dear, this was not a received doctrine. Mathematics usedto be considered not really worthy of the dignity of true sciences, onaccount of the inessential nature of their object and the non-causalcharacter of their demonstrations. Mersenne, in the wake of Biancani(1615) defended the contrary view: mathematics are not only truesciences, but the highest among them, because of their certainty.Besides, their demonstrations are truly causal ones, as Mersenneshowed with the example of numbers where unity appears to be the“material cause” and the intellect, conjoining andcomposing unities, the “efficient” one (cf. VS II: 284).Thus mathematics is able to describe the objects that God’sintellect considered when He created the world, that is the possibilia(Lenoble 1943)—or, better said, mathematics are the sciences ofthe metaphysically necessary attributes of all things.

One important question that has been debated in the literature iswhether Mersenne’s position amounts to the idea thatmathematical truths are truly independent of God. The discussion isnot merely about the meaning one is willing to give to the word“independent” whether it applies or not to something thatis included in God’s nature, but it engages deep issues in thehistory of metaphysical thought. According to Marion (1980), andCarraud (1994), the very fact that mathematical truths are consideredas forming the essence of God’s intellect means that they do notdepend anymore on God’s will. Apparently endorsing a doctrinethat he found mentioned in Suárez (1597, xxxi.12.40), Mersennewrote in a much discussed passage of theQuaestiones:

as other authors say, things are possible per se, independently of anycause, in virtue of the necessary connection and non-contradiction ofterms. (col. 436)

God would be subjected to mathematical truths just as human intellectsare. He would know them as we know them. This would be the sign thatthe doctrine of univocity entered Mersenne’s thought, perhapsunder the influence of Kepler, in an irretrievable fashion. This isalso deemed to explain the striking disappearance of rational theologyin Mersenne’s writings. Just as metaphysics had been entirelyexhausted by natural theology in the first works, rational theologyended up being entirely exhausted by mathematics. The latter are notanymore an analogical resource for theology, but indeed they furnishthe only possible non-analogical discourse on God, “the hiddenobject of all mathematical discourse” (Pessel 1987). As aconsequence, Mersenne’s apologetics no longer needs to appeal torational theology—the mere promotion of mathematical scienceshas become the unique, or best, apology of Christian religion.

Peter Dear criticized Marion’s interpretation as implyingsomething that he did not find in Mersenne, namely that mathematicaltruths exist in a kind of platonic separateness, so that God and menwould be in the same relation to them, would see them the same way.This would imply that God is no more the author of them than men,whereas in Dear’s view, Mersenne, always firmly maintained thateternal truths causally depend on God, being true emanations of hisnature. Accordingly, Mersenne would not so much insist on independencebut rather on co-implication and coeternity. Whereas Descartes usedto

see the matter as straight choice between necessary truths holdingsimply because God knew them (having willed them) or God’sknowing them because they are independently true. (cf. Descartesà Mersenne 6 mai 1630, Descartes AT I: 149, and Dear 1988:60)

Mersenne, a rather orthodox scholastic on this point, never recognizedan alternative: both theses should hold together—eternal truthsare true because God knows them, and God knows them because they aretrue.

4. Epistemological Issues

4.1 Against the Skeptics

Mersenne’s attitude towards skepticism was complex, changingover time and somewhat ambivalent. InL’Usage de laraison—a recently rediscovered booklet from 1623, whoseauthorship does not seem questionable—one finds argumentsagainst the vanity of the sciences that are strongly reminiscent ofthose expressed around the same time by “Christianskeptics”, such as Montaigne and Charron, or even CorneliusAgrippa, authors whom Mersenne sternly criticized in his nextpublications. Thus, in the “Dedicatory Epistle to Madame deVitry”, the Minim suggested that our time is badly employed instudying the sciences, which are plagued with insuperableuncertainty:

whenever we raise our eyes to the sky or incline it to the earth, wemust owe that everything is unknown to us… Who can claim toknow the number of the skies, their form, their matter, properties andaccident? One can even find idle-dreamers Copernicans prepared to denythe motion of the skies… Who can say if Alchemists are right intheir promises.

This uncertainty of the “megalocosm” goes together with anequal puzzlement concerning the littlest creature of the micro-world,as recent microscopes have shown to the eye that “it is pureignorance to say that they are deprived of these several organs thatcan be seen in larger creatures”. Further, (UR: 37–38) theauthor condemned Pythagoras, Archimedes, the alchemists, thealgebraists, etc. for being so much attached to their inventions thatthey forget to think of God, and eternal glory…

The change of attitude in the next published works is striking. On theone hand, in theQuaestiones andImpiété, skepticism was presented as a sequelto Calvinism; and the denunciation of human reason found in Charronand Montaigne, far from encouraging faith in the mysteries ofChristian religion, was seen as inclining men towards atheism andlibertinism. On the other hand, Mersenne was no longer denouncing thesciences indistinctly as vain curiosity, his general attitude towardsspeculative enquiry was much more positive, especially when one cameto the mathematical sciences, whose apologetic virtues he wanted nowto reveal. He maintained however that our reason is weak,contradictory, particularly in regard philosophical (i.e., physical)issues:

if our reasons were not deceitful, how would it come that there is notany one question in Philosophy, that does not raise diverse opinionswholly contrary on the same subjects, all of which have their reasonand nevertheless there is only one that is true. (ID II: 672)

InLa Vérité des sciences contre les sceptiques etles phyrroniens, the tone changed again. Skepticism was no longercondemned as a seed of heterodoxy but only in so far as it discouragesmen from the practice of mathematical sciences. The skepticalcharacter is obstinate, but he is no atheist nor heretic in thedisguise (see Descotes, in VS, Introduction), and in the first part ofthe book, his arguments against the alchemist’s dogmatism areoften endorsed and even reinforced by the Christian philosopher.

Against the epistemological optimism of the alchemist who considershimself to be in possession of the perfect science, the skepticresorts to the traditional arguments of the academic school,emphasizing that certainty is nowhere to be found, as we have only avery partial and superficial knowledge of things. We perceive only theeffects and not the profound nature nor the ultimate causes of things.The true essences evade us. The simplest objects (such as a sheet ofpaper) cannot be completely known, because of the infinite number ofrelations in which they are involved with other elements of theuniverse. It has been shown by G. Paganini that these arguments andexamples are almost verbatim borrowed from the “seconddoubt” of Campanella’sMetaphysica, a manuscriptthat was in Mersenne’s hands at the time he wroteLaVérité des sciences, but that he did not mention ashis source (Paganini 2005 & 2008).

In chapter 11 and 12, the Christian philosopher presents the skepticalarguments in a new and more radical form. He gives an account of theten skeptical tropes of Aenesideme, as Mersenne could have read themin Sextus Empiricus and Diogène Laertius. These tropes draw onthe varieties of animal constitution in regard pleasures and pains,the idiosyncrasy of men, the disagreement of the senses, the varietiesof circumstances and dispositions, such as health and disease, sleepand wakefulness, young age and old age. All show that the informationof our senses is unreliable, just as the reasons we draw fromthem.

In answer to these doubts, Mersenne’s Christian philosopherresorts to an eclectic strategy. On the one hand, he adopts the usualAristotelian standpoint against skepticism regarding the senses: senseperception is trustworthy, provided that its exercise takes place in“normal” and appropriate conditions. Errors occur onlywhen the senses are affected by disease, or presented with objectswhose distance, illumination, intensity, etc. exceed the normalrange:

All the deceptions of senses that you object are of no use, for theyonly prove what we concede, namely that each one of our senses, inorder to judge its object rightly must have all that its nature andthe perfection of its operation require—this granted, it nevererrs. (VS I: 15)

On the other hand, just as senses are the right judges of their ownproper sensible—the eye of color and light, the ear of sound,etc.—human intellect also possesses an internal criterion whichallows it to judge its own objects rightly. It has the use of “aspiritual and universal light that it has of its own nature since thecommencement of its creation” (VS: 193). Here the inspiration isclearly Augustinian, as it is for Descartes’s parent conceptionof “lumière naturelle”. The light of the soul doesnot give men direct access to divine knowledge, knowledge of essences,as that would require an eternal glory and a supernatural light. Butit still gives access to a number ofevidentia, immediatecertainties, whose truth, Mersenne concedes, depends on God’sillumination and God’s veracity. Thus, in every realm ofknowledge or human interests, there are truths that are not capable ofdoubt, such as “the whole is greater than the part”, or“evil should be avoided”.

Another Augustinian aspect of Mersenne’s defense is the ideathat doubt itself can be turned into a source of knowledge. Forexample, although there are differences in apprehension betweenvarious men, or between men and beasts, we do have the knowledge ofsuch differences and this is something that cannot be doubted:“at least one knows that the objects of the senses appeardifferently according to the diverse dispositions of the organs”(VS: 193). Awareness of this sort of facts is what incites men to seekthe laws of appearances—for example, the optical and geometricalrules that govern variations in perspective. In other terms, itprompts them to engage into physico-mathematical enquiries.

On a similar line of argument, one could say, following Augustine inDe Civitate Dei (1998, chapter XI, 26) that one cannot doubtthat one doubts, unless admitting an infinite regress:

I do not believe you doubt that [that we can learn science, with greatcontentment] because you experience this every day in yourself, and ifyou doubt it I ask whether you know that you are doubting; if you knowit, you must know something, and consequently you do not doubteverything; an if you doubt that you doubted, I shall force you toadmit infinite regress, which you say you reject, so that wherever yougo, you must confess that there is some truth, and consequently youmust say farewell to your Pyrrhonism. (VS I: 204)

In the next decade, reacting to the cogito argument in theDiscours de la Méthode, Mersenne pointed out toDescartes how close his use of radical doubt was to that Augustinianargument (see Gouhier 1978).

4.2 Mitigated Skepticism and Probabilism

Richard Popkin has remarked that the great originality ofLaVérité des sciences resides not so much in itsarguments against the skeptics, as in the fact that this defense of“the truth of the sciences” concedes so much to theskeptical outlook. Most of the skeptical claims that are propoundedeither by the skeptic or by the Christian philosopher are not reallyrefuted in the book. They are integrated in a novel view of what oneshould expect of scientific enquiry, its true aims and prospects(Popkin 1956, 2003).

Thus, the Christian philosopher has no qualm with the skepticalrebuttal of the alchemist’s claim to perfect knowledge innatural matters. He freely admits that we cannot know everything, andespecially not the causes nor essences of physical things, thatmen’s capacity is limited by outward appearance and the surfaceof corporeal things. In theQuestions inouïes, Mersennewent as far as to say that we cannot demonstrate the existence of theexternal world:

And we do not have any demonstration by which we are able to persuadethe opinion of those who might maintain that the earth, the water, thestars, and all the bodies which we see are but appearances and“species intentionales”, supposing God might use thesespecies or accidents to make all that we see appear to us. For one isnot able to say that one knows a single thing as oneshould—according to the laws and the notions which Aristotle andother philosophers give of science—if one cannot demonstratethat it is impossible that the reason which one supplies, or the thingwhich one proposes, be not true. That is enough to persuade those whouse reflection that there is nothing certain in physics and that thereare so few certain things, that it is difficult to propoundany… (QI XVIII: 53, translated in Mace 1970: 24–25)

Mersenne joins the skeptic in his condemnation of theAristotelian’s far too optimistic view of science. What isdenounced is not so much Aristotle’s physical doctrines ormethods (the Christian philosopher, for example, does not endorse theskeptical attacks against syllogistic) but rather a mistakenrepresentation of the epistemic aims of physics, which cannot aspireto perfect certainty. Bacon’s experimental method received nomore favor in his eyes precisely on this account, as it serves aproject that is no less dogmatic (see Buccolini 2013):

although one may anatomize, and dissolve bodies as much as one wishes,whether by fire, by water, or by the force of the mind, one will neverarrive at the point of rendering our intellect equal to the nature ofthings. That is why I believe that Verulam design is impossible. (VS212)

Mersenne did not think that our inability to understand the ultimatecause and intimate nature of things should be an object of lament. Themere knowledge of effects and appearances might be enough for humanneeds. For one thing, it has enough pragmatic virtue, as it can serveus as a guide in our actions. Besides, as outwards appearances, crustand superficies may be rigorously described, through measurement andmathematics, the sort of knowledge that can be gained here is asperfect and certain as one could wish—although not of the sortdogmatic physicians and metaphysicians are seeking.

Thus, according to Richard Popkin, Mersenne is not so much refutingskepticism as he is adopting an attenuated form of it. By openlydiscarding research on the causes and essences of phenomena, reducingthe whole of physical science to mathematical knowledge of accidents,the study of external effects, and the establishment of the laws ofappearances, he invents a “mitigated skepticism”, thatPopkin considers as the first lucid expression of the modernscientific outlook, deemed to become dominant in the followingcenturies. This outlook conjugates an entire confidence in the virtuesof physico-mathematical sciences, with a complete positivism (that is,a deliberate abstention) in regard metaphysical matters.

Recent reappraisals of Mersenne’s epistemological views tend tocontest, or at least qualify, Popkin’s characterizations.According to Garber (2004), Mersenne’s epistemological frame isold rather than new. The way he envisions the boundaries betweendisciplines remains Aristotelian, and in particular his conception ofthe “physico-mathematical” sciences directly comes fromthe Aristotelian definition of mixed or subaltern mathematics,sciences such as astronomy or optics, only dealing with accident andsurface properties of physical things. Far from offering a scientificsubstitute to Aristotelian physics, these sciences allow one toapproach nature in a mathematical way “without having tochallenge the full complex of Aristotelianism directly” (2004:157) in ways that would be perceived as subversive of true religionand social order.

Dear’s study (1988) similarly insists on the deliberately“un-revolutionary” character of Mersenne’scontribution to the “scientific revolution”. Mersennenever chose to range himself against Aristotelianism, never casthimself as an innovator. His agenda is formulated in a preexistingphilosophical idiom (the “language of the schools”), andhis ideas display a “borrowed coherence” rather than anintrinsic one. Mersenne was not a positivistavant la lettre;he admitted that God knows what man cannot verify, that natural kindsexist in nature, that things do have essential definitions. His“skeptical” approach to physics is not so much awatered-down Pyrrhonism intended to show the inconclusiveness ofnatural philosophical demonstration, as it is an instrument torecommend mathematical sciences as an anchor of certainty, whereordinary natural philosophy stays in doubt and can only be defended ina probabilistic way. When Mersenne confesses that many questionscannot he determined, he is not proposing to suspend judgment butrather to formulate a probable judgment by choosing the mostpersuasive opinions. This “probabilism” is, according toDear, a legacy of humanist and Ciceronian dialectics, and it remainedconstantly present in Mersenne’s work, even though, on somequestions the weight of probabilities has changed. This wasparticularly the case for the Copernican opinion. Judging it veryunlikely inL’Usage de la raison and in theQuaestiones, Mersenne eventually recognized that it was theopinion best suited to the phenomena observed and therefore the mostprobable. However, God’s freedom being never constrained,Mersenne could accept with relative equanimity the final judgment ofthe Church. In hisQuestions théologiques, he was topublish a French translation of the inquisitorial condemnation and ofGalileo’s abjuration.

Departing from Garber and Dear’s view as well as fromPopkin’s, Buccolini (2019) presents Mersenne’sepistemological reflection inLa vérité dessciences as resolutely anti-sceptical, and strongly connectedwith the views expressed by the Jesuit mathematician, GuiseppeBiancani, in his dissertation on the nature of mathematics (Biancani1615), arguing for the certainty and scientific status of mathematics.According to Buccolini, Mersenne’s doubts are directed notagainst science as such but against the Aristotelian doctrine ofdemonstratio, his aim being to replace Aristotelian physicswith an entirely intelligible mathematical physics.

4.3 Mechanism and Experimentalism

According to Lenoble (1943), Mersenne’s mature works, focusingalmost exclusively on “physico-mathematical” sciences,witnesses the “birth of mechanism”. However, as the termis not an actor’s category of the 17th century, one should becareful in its use. Formulated in its own terms, Mersenne’sstandpoint regarding explanations in physics is that we can onlyunderstand what we can do:

we only know the real reasons for things that we can create with ourhand and our mind; … and of all the things made by God, wecannot create any, no matter how much subtlety and effort we apply.(NO: 8; Lenoble 1943: 384)

This indicates both the foundations and limits of mechanisticexplanations: finding reasons means showing how things can he producedby mechanical actions—actions of the kind we are capable of whenapplying our bodies to external bodies. On the one hand, however, thismode of genetic explanation can provide only a very superficialclarification of created things, whose construction and complexity areeither infinite, or go to details and minutiae that our senses areincapable of perceiving (OC: 89). On the other hand, theseexplanations cannot bear the character of necessity since they focuson objects that are fundamentally contingent and whose inner machinerycould have been constituted differently, had God so wanted:

one knows all but nothing in physics, if one follows the definition ofscience Aristotle gave; for if it ought to be about eternal andimmutable objects, and God can change everything that is in physics,one cannot make a science of it. (QT: 9)

The conjoined effects of Mersenne’s epistemological pessimismand metaphysical voluntarism make his version of“mechanism” very different from the Cartesian, Hobbesianor Gassendist one. He never conceived mechanical explanations as a newscience of “causes”, based on the adoption of newprinciples and elements intended to take the place of Aristoteliansubstantial forms—such as Descartes’s subtle matter orGassendi’s atoms. Mechanics, as all other mixed-mathematics, wassimply concerned with establishing the laws of phenomena.

This reflection on nature and the limits of mechanistic science wasaccompanied by truly experimental activity. Mersenne was convincedthat mathematical sciences of nature cannot settle for common andvague observation. It urgently required “well-controlled andwell-performed experiments” (HU I: 167), facts that wereartificially generated and precisely measured. Mersenne was awarethat, even when rigorously performed, an experiment is not alwaysenough to establish the law of phenomena: two series of experimentscan diverge very little and yet express very different laws.Measurement can only be approximated, and this has a bearing on thecertainty of mixed mathematics, which is partially compromised to theextent that it deals with physical objects. Reason must therefore, asfar as possible, always accompany and discipline observation, withoutwhich one is vulnerable to considerable misunderstandings.

Mersenne made a considerable effort to do and redo experiments thathis predecessors (most notably Galileo) had not always had the senseto present precisely. Thus, on the subject of the increase in speedduring falling motion on an inclined plane, he conducted a precisecampaign of measurements that enabled him to criticize Galileo’snumerical results, and eventually express doubts on the validity ofthe law itself (Palmerini 2010). As usual, he expressed hisreservations concerning our capacity to determine with certainty thecauses of gravity: “it is just as difficult to find the realcause as to demonstrate whether the earth is stable or mobile”(Traité des mouvements) and he placed back-to-back thereasons put forward by his contemporaries—positive and realquality, air pressure, magnetic attraction—which could onlypartially account for the phenomenon in its precise numericaldimensions. As Peter Dear has shown, Mersenne’s approach to thescience of motion was inductive in nature, not centered, as it was inGalileo, on the abstract physical process, but rather on “ageneralized description of cases, whose details and precise parametersheld an importance altogether lacking in Galileo” (Dear1994).

5. Music and Universal Harmony

Of all the mixed-mathematical disciplines in which Mersenne took aninterest, music was undeniably the one to which he devoted the mosteffort and passion. His 1623Quaestiones already included along musicological digression on the therapeutic power attributed tothe music of the Hebrews, and generally to the music of the Ancients,whose harmonics he dreamed of restoring. The idea was taken up anddeveloped in the 1627Traité de l’harmonieuniverselle, published under the transparent pseudonym of“Sieur de Sermes”. The science of intellectual music andthe understanding of the proportions that govern nature, lost throughnegligence, must be restored and linked to the science of“sensual music”, which addresses our hearing but which,separated from the former, is no longer able to fulfill its truefunction: elevating the senses above material objects, rather thanlinking them together. Mersenne’s great work on musical theory,the eight books ofHarmonie Universelle, was published from1636 to 1637. It presents a great many editorial variants, as Mersennenever ceased to work on it, annotating his own copy. The important“Traité de la nature du son”, which constitutes thefirst part of the work, focuses on the study, undertaken in amechanistic spirit, of acoustic quantities, their physical nature andtheir effects on physiology and passions. Mersenne, drawing on IsaacBeeckman, establishes experimentally the laws connecting thevibration, the length and tension of the strings, making an importantcontribution to acoustic science.

Epistemological, metaphysical and aesthetic aspects are intertwined inMersenne’s musical agenda. Music was to Mersenne amixed-mathematical science, just as astronomy, whose primary aim wasto “save the phenomena” through more or less plausiblehypotheses. The musical phenomena par excellence is“consonance”, that is the fact that certain sounds puttogether are agreeable to the ear. Recent musical practices, newinstruments and polyphonic music had disclosed new modes of consonancethat were previously unknown, and Mersenne saw his proper task in aneffort to find the best physico-mathematical hypotheses that would beable to account for them, and could be used to invent more“perfect” musical pieces (chants). Seeking suchhypotheses, Mersenne relentlessly asked his correspondents how theycould account for the fact that certain sounds put together areagreeable and others not. For example, in November 1627, he asked acorrespondent in Rome:

If the said Galileus be at Rome or if you should know some otherexcellent mathematician-musician, I pray you to find out from him why,of all the sounds put together, only those which form the octave, thefifth, the third, and the sixth and their replicas are agreeable tothe ear, and which of all the dissonances is the most disagreeable oneand why. I have been told that the said Galilei knows this reason. (MCI: 603, translated in Mace 1970: 8)

Mersenne’s own general hypothesis was that consonance was due tothe coincidence of the vibrations of the air, which itself depended oncertain exact ratios in the mechanical properties of the instrument,e.g., the length, tension and breadth of the strings. However, asconsonance was judged by the ear rather than directly by reason,discrepancies were found. For example, experiments showed that the earhears an octave when the tensions of the strings are in a ratio of 1to 4.25, whereas the physico-mathematical, Pythagorean, hypothesisprescribed 1 to 4. So here one would have to find ways to correct, or“discipline” experience through reason, in a move that isquite typical of Mersenne’s epistemology (see Dear 1988).

In spite of those discrepancies, Mersenne was truly fascinated by thefact that the human mind, in its musical appreciation, is so to speakattuned to mathematical harmonies. The perception of consonancealthough mediated (and perhaps distorted) by our feeling, is not meresensual pleasure, as Descartes, for example, seemed to think. Properlyunderstood, it has a rational dimension, as it discloses to men the“universal harmony”, the underlying mathematical orderthat is present at every level of reality, and that connects themtogether. Mersenne could have found in Kepler’sHarmonicesmundi the idea of such an archetypal harmony, ordering each levelof reality, and innate to the human mind. He did not accept howeverKepler’s rather dismissive view of music, which had led him todefine harmonics in purely geometrical terms, stripped from whateveris sensorial and “acoustic” in it.

Contrary to what is sometimes held, the seeming adoption of anintegral mechanism in the last musical works is no renunciation of themetaphysical consideration in harmonics. According to De Buzon (1994:127, my translation), the causes and effects of consonance are indeedtreated physically, but the pleasure taken to harmonics, “albeitan ordinary experience, is a phenomenon that is entirelytheological”. Musical pleasure shows both our destination andour state in this world. It raises us to the contemplation of thedivine unity, which is so to speak embodied in musical unison:

consonances depend on the unison as lines on the point, number onunity, and creatures on God. That is why the more they approach it thesweeter they become; because consonances have nothing sweet noragreeable but that which they borrow from union of their sounds, whichis the greater as it approaches unison. (HU II: Livre Premier desconsonances, 15, translated in Mace 1970: 13)

But musical pleasure also reveals our imperfect and sensuous nature.Thus, for instance, although “unison” is the simplest andmost divine harmony, we tend to prefer in this world other, lessperfect consonances and even dissonance.

In considering the general interconnection of sciences, Mersennegranted music an almost architectonic function. All the sciencesborrow something from each other. As manifested in the encyclopediccharacter of theHarmonie Universelle, music was for Mersenneas the connecting principle of the various disciplines, allowing fortheir exposition. A thorough investigation of musical propertiesrequires forays into theology, moral philosophy (the passions of thesoul), optics, arithmetic and geometry, and of course mechanics assounds are motions of the air, that have to be accounted for in amechanical way. Conversely, and at a deeper level, music may be seenas a total science, theoretically capable of representing theproportions that exist between all parts of the mechanicaluniverse:

it is also easy to conclude that one can represent everything in theworld and, consequently all the sciences, by means of Sound; for,since everything consists in weight, number and measure, and soundsrepresent these three properties, they can signify anything onewishes, excluding metaphysics. (HU 1: 43)

In particular music may teach men how, through motions, objectscommunicate their properties to the senses, which themselves are likeinstruments, more or less well attuned to the external motions of thesensible. Music would then become the general science of theproperties of the sensible, a kind of general aesthesis uniting mixedmathematics in one universal science, whose acquisition would make ourelevation to the consideration of the first cause easier (QT:161).

Bibliography

Mersenne’s works and abbreviations

• 1623 [UR],L’Usage de la raison, Paris. Edited byClaudio Buccolini, Paris: Fayar, 1 volume, 2002.
• 1623,L’Analyse de la vie spirituelle, Paris,[lost].
• 1623 [QG],Quaestiones celeberrimae in Genesim, followedwithObservationes et emendationes ad Francisci Georgii Venetiproblemata, Paris. [available online]
• 1623 [OF],Observationes et emendationes ad Francisci GeorgiiVeneti Problemata : in hoc opere cabala evertitur, editiovulgata… Paris. [available online]
• 1624 [ID],L’Impiété des déistes,athées et libertins de ce temps combattue et renverséede point en point par des raisons tirées de laphilosophie, Paris.
  • [New edition of the first part under the title]Questionsrares et curieuses […], Paris, 1630.
  • Critical edition by Dominique Descotes, Paris: Champion, 1 volume,2005
• 1625 [VS],La Vérité des sciences contre lesseptiques [sic] ou Pyrrhoniens, Paris. [available online]
  • Critical edition by Dominique Descotes, Paris: HonoréChampion, 1 volume, 2003.
• 1626,Synopsis mathematica, Paris.
• 1627 [THU],Traité de l’harmonie universelle parle sieur de Serme, Paris.
• 1630,Traité des mouvemens et de la chute des corpspesans […], Paris. Reprinted inCorpus: revue dephilosophie, 1986, 2: 25–58.
• 1634Questions Inouyes, edited by André Pessel,Paris, 1985, includes
  • [QI]Questions Inouyes ou recreation dessçavans.
  • [QH]Questions harmoniques.
  • [QT]Les Questions théologiques, physiques, morales etmathématiques.
  • [PHU]Les Préludes de l’harmonieuniverselle.
• 1634,Les Méchaniques de Galilée, Paris.Edited by Bernard Rochot, Paris: Vrin, 1966.
• 1636–1637,Harmonie universelle, Paris (2 volumes).
  • [HU] Facsimile of Mersenne’s own annotated copy from theBibliothèque des Arts et métiers, introduction byFrançois Lesure. Paris, 1963 (3 volumes).
• 1638 [NO],Nouvelles Observations physiques etmathématiques, inHarmonie universelle, volume 2,addition de 1638—copy of Bibliothèque nationale deFrance, Rés V 588.
• 1638,Harmonicorum libri XII […] Harmonicoruminstrumentorum libri IV, Paris.
• 1639,Les Nouvelles Pensées de Galilée,Paris. Edited by Pierre Costabel and Michel-Pierre Lerner, Paris: J.Vrin, 1973.
• 1644,Universae geometriae synopsis andCogitataphysico mathematica, Paris. [available online]
• 1647Novarum observationum physico-mathematicarum, Paris. [available online]
• 1651 [OC],L’Optique et la catoptrique nouvellement miseen lumière après la mort de l’autheur, inLa Perspective curieuse du R. P. Nicéron, Paris. [available online]
• [MC]Correspondance du P. Marin Mersenne, edited byCornelius De Waard, René Pintard, and Bernard Rochot, Paris: G.Beauchesne, 1932–1988, 17 volumes.

Other Primary sources

• [anonymous],L’Anti-bigot ou le Faux Devotieux [=Quatrains du déiste]. (In FrédéricLachèvre,Le Procès du poète Théophilede Viau : 11 juillet 1623–1er septembre 1625, Paris,1909–1928, t. 2, p. 91–126. Reprinted Genève,1968).
• Augustine, 1998,The City of God against the Pagans,translation R. W. Dyson (trans.), New York: Cambridge UniversityPress.
• Biancani, Guiseppe, 1615,De mathematicarum naturadissertatio, Bononiae.
• Bruno, Giordanno, 1584,De Infinito, l’Universo eMondi, London.
• Coste, Hilarion de, 1649,La Vie du R. P. Mersenne[…]. Paris.
• [AT] Descartes, Rene, 1897–1910,Oeuvres deDescartes, 11 volumes, Charles Adam and Paul Tannery (eds),Paris: Vrin. New edition in 1964–1976.
• Fludd, Robert, 1629,Sophia cum moria certamen[…], Frankfurt.
• Galilei, Galileo, 1890–1909,Le Opere di GalileoGalilei. Edizione nazionale, 20 volumes, Antonio Favaro (ed.),Florence: G. Barbera.
• Gassendi, Pierre, 1630,Petri Gassendi theologi epistolicaexercitatio in qua principia philosophiae Roberti Fluddi medicireteguntur, Paris.
• Herbert of Cherbury, Edward, 1639,De la véritéen tant qu’elle est distincte de la révélation, duvray-semblable, du possible et du faux, Paris [Mersenne’sFrench translation ofDe Veritate, Paris 1624]
• Kepler, Johannes, 1619,Harmonices Mundi, Linz.
• Morin, Jean Baptiste, 1635,Quod Deus sit, Paris
• Pascal, Blaise, 1658, Histoire de la roulette, Paris
• Pascal, Blaise,Oeuvres Complètes, L. Lafuma(ed.), Paris: Seuill, 1963.
• Roberval, Gilles Personne de, 1636,Traité deméchanique, Paris.
• Suárez, Francisco, 1597,Disputationesmetaphysicae, Salamanca.

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• –––, 1975, “Marin Mersenne and theseventeenth-century problem of scientific acceptability”,Physis: Rivista Internazionale di Storia della Scienza (FirstSeries), 17: 186–204.
• –––, 1994a,Style of Scientific Thinking inthe European Tradition: The History of Argument and ExplanationEspecially in the Mathematical and Biomedical Sciences and Arts,3 volumes, London: Duckworth.
• –––, 1994b, “Marin Mersenne et lesorigines du langage”, In Claude Blanckaert, Jean-Louis Fischer,and Roselyne Rey (eds),Nature, histoire, société :essais en hommage à Jacques Roger, Paris: Klincksieck, pp.35–46.
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• De Waard, Cornelius, 1936,L’Expériencebarométrique: ses antécédents et sesexplications, Thouars: Impr. nouvelle.
• Dear, Peter, 1984, “Marin Mersenne and the probabilisticroots of ‘mitigated skepticism’”,Journal of theHistory of Philosophy, 22(2): 173–205.doi:10.1353/hph.1984.0025
• –––, 1985, “Mersenne and the language ofphilosophy”, in Klaus D. Dutz and Ludger Kaczmarek (eds),Rekonstruktion und Interpretation: Problemgeschichtliche Studienzur Sprachtheorie von Ockham bis Humboldt Tübinger Beiträgezur Linguistik, Tübingen: Narr, pp. 197–241.
• –––, 1988,Mersenne and the Learning of theSchools, Ithaca, NY: Cornell University Press.
• Del Prete, Antonella, 1995, “L’univers infini: lesinterventions de Marin Mersenne et de Charles Sorel”,RevuePhilosophique de la France et de l’Étranger, 185(2):145–164.
• Duncan, David Allen, 1981,The Tyranny of Opinion Undermined:science, pseudo-science and skepticism in the musical thought of MarinMersenne, PhD thesis, Vanderbilt University.
• Fabbri, Natacha, 2003,Cosmologia e armonia in Keppler eMersenne: Contrappunto a due voci sul tema dell’Harmonicemundi, Florence: Leo S. Olschki.
• –––, 2008,De l’utilité del’harmonie: filosofia, scienza e musica in Mersenne, Descartes eGalileo, Pisa: Edizioni della Normale.
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• Garber, Daniel, 2001,Descartes Embodied, Reading CartesianPhilosophy Through Cartesian Science, Cambridge: CambridgeUniversity Press. doi:10.1017/CBO9780511605994
• –––, 2004, “On the Frontlines of theScientific Revolution: How Mersenne Learned to Love Galileo”,Perspectives on Science, 12(2): 135–163.doi:10.1162/106361404323119853
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• Hamou, Philippe, 2008, “Mersenne”,Dictionary ofSeventeenth Century French Philosophers, London: Thoemmes.
• Hauréau, Barthélémy, 1877,HistoireLittéraire du Maine, vol. VIII, Le Mans: A Lannier.
• Hine, William L., 1973, “Mersenne and Copernicanism”,Isis, 64(1): 18–32. doi:10.1086/351041
• Koyré, Alexandre, 1973, “Une expérience demesure”,Études d’histoire de la penséescientifique, Paris: Gallimard.
• Lenoble, Robert, 1943,Mersenne ou la naissance dumécanisme, Paris: Vrin.
• Mace, Dean T., 1970, “Marin Mersenne on Language andMusic”,Journal of Music Theory, 14(1): 2–34.doi:10.2307/843035
• Marion, Jean-Luc, 1980,Sur la théologie blanche deDescartes, Paris: Presses universitaires de France.
• –––, 1994, “Le concept demétaphysique selon Mersenne”,Les Étudesphilosophiques, 1994(1/2): 129–143.
• Maronne, Sebastien, 2021, “D’une Académiel’autre. Mersenne, Roberval et quelques autres”,Dix-septième siècle (2021/3): 11–30.
• Maury, Jean-Pierre, 2003,À l’origine de larecherche scientifique, Mersenne, Paris: Vuibert.
• Leonardo Messinese, “L’apologia scientifica di P.MarinMersenne”, en Leonardo Messinese (ed.),Agli inizidell’età moderna. Marin Mersenne e Emmanuel Maignan,Siena: Cantagalli, 53–102.
• Paganini, Gianni, 2005, “Mersenne plagiaire? Les doutes deCampanella dans la ‘Verité des sciences’”, enXVII^e siècle, 229(4): 747–767.doi:10.3917/dss.054.0747
• –––, 2008,Skepsis, le débat desmodernes sur le scepticisme, Paris: Vrin.
• Palmerino Carla Rita, 2010, “Experiments, Mathematics,Physical Causes: How Mersenne Came to Doubt the Validity ofGalileo’s Law of Free Fall”,Perspectives onScience 18(1): 50–76. doi:10.1162/posc.2010.18.1.50
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Descartes, René |Descartes, René: epistemology |Descartes, René: modal metaphysics |Galileo Galilei |Gassendi, Pierre |natural philosophy: in the Renaissance |skepticism

Acknowledgments

Some passages in the biographical parts of this entry are borrowedfrom Hamou 2008.