## 1. Life and Works



Marin Mersenne was born on 8 September 1588 near Oize in the
French region of Haut-Maine (nowadays the Sarthe). He came from a
family of merchants and small landowners. After studying at the
college du Mans, he was sent in 1604 to the newly created Jesuit
college of La Fleche, where he received the established Jesuit
education, coupling humanist--Ciceronian--and Aristotelian
traditions (Dear 1988). He may have met there the young Rene
Descartes, who entered La Fleche in 1606, although it is
unlikely that their friendship started then, as Descartes was 8 years
his junior. When he left the college, Mersenne completed his training
in theology, Greek and Hebrew in Paris at the College Royal and
at the Sorbonne where he was instructed by the Thomist theologians
Francois Ysambert and Philippe de Gamache (see Coste 1648;
Armogathe 1994). Attracted to the strict rule of the Minims, a
Franciscan order recently introduced into France, he took the habits
in 1611, and after periods of novitiate and teaching in Meaux, Paris
and Never, was recalled to Paris in 1619 at the new house on the Place
Royale (the present Place des Vosges) where he remained permanently,
apart from a few trips to the French provinces, to the Netherlands in
1630, and to Italy from 1644 to 1645.



From the years 1620 onward, Mersenne deployed overflowing intellectual
activity. Through the mediation of Claude Fabbri de Pereisc whom he
had met in 1616, he was introduced to the Parisian intellectual elite,
and later to Pierre Gassendi with whom he remained close friends. In
Paris, he associated with the mathematician Claude Mydorge, and,
perhaps through him, renewed acquaintance with Descartes. Mersenne
called on Descartes's mathematical expertise on questions of
optics. His questions led Descartes to his first formulation of the
law of refraction, which he was to publish later in his 1637
"Dioptrics". Mersenne was among those attending the famous
meeting of 1628, at the residence of the apostolic nuncio, where
Descartes, having revealed his project of founding the sciences on a
new method, had been encouraged to do so by the highest religious
authorities. After Descartes left for Holland, Mersenne remained in
close contact with him through correspondence. He was privy to most of
Descartes's secret addresses, which made him the man one has to
see in order to get access to the French exile, to send him letters or
questions. Only four letters from Mersenne to Descartes are extant,
but 146 letters from Descartes--about a quarter of his known
correspondence--testify to the intensity and continuity of the
exchange. Mersenne endlessly provided Descartes with books, fresh
information, and editorial services, requesting in exchange answers to
queries of all sorts. Acting as mediator in Descartes's
controversies, with Fermat, Roberval, Beaugrand, Morin, or
Voetius, he sometimes caused quarrels himself, through his
indiscretions, such as the one which made Descartes definitively fall
out with his erstwhile mentor Isaac Beeckman. Mersenne also acted as
intermediary for the edition of the *Meditationes de prima
philosophiae*, and was instrumental in the gathering of the six
sets of objections that were added to the text with Descartes's
responses, including those of Hobbes and Gassendi. He contributed
himself to the objectiones, penning the second set ("gathered by
the R. P. Mersenne from the mouth of various theologians and
philosophers", AT IX-1: 96; Buccolini 2019) and perhaps parts of
the sixth.



Mersenne's dealings with Descartes were only a small part of the
network of intellectual communication that he built up throughout his
career. He was largely responsible for introducing Galileo into
France, offering in 1630--without receiving an answer--to
publish his future work on the *Two Chief Systems of the
World*. In 1634, he published *Les Mechaniques de
Galilee*, a free translation of a manuscript on mechanics
by the Florentine scholar, completed with ideas borrowed from
Guidobaldo and Stevin, and with original comments of his own, and, in
1639, the *Nouvelles pensees de Galilee*, a
translation or adaptation of certain parts of the *Discorsi a due
nuove scienze*, published in Italy one year earlier. Mersenne was
also in regular contact with English scholars. He translated into
French the *De Veritate* of Herbert of Cherbury (although the
book had been placed in the Index, i.e., the list of prohibited books
published by the Catholic Church); in good terms with Hobbes (Baldin
2020), he published one of his optical treatises, and
Sorbiere's French translation of the *De Cive*. He
corresponded with Kenelm Digby and Lord Cavendish and others.



In Paris, a small scientific circle of mathematicians and physicists
gradually formed around Mersenne. From 1633 or so, meetings were
organized on Thursdays at the houses of one or another of his friends
or protectors. This "Academia Parisiensis", as it came to
be called, brought together men such as Etienne Pascal,
Mydorge, Hardy, Roberval, Fermat. It was later to welcome the young
Blaise Pascal, and Jacques Le Pailleur who was to become the
group's leader when Mersenne died in 1648. Discussions were
mostly "mathematical" (MC V: 209). Mersenne used to submit
problems of his own invention to his friends, and some were often
remarkably stimulating and the origin of important discoveries such as
the "roulette" problem, solved by Roberval in 1634; and
then more indirectly by Fermat and Descartes. Mersenne himself
undertook to establish a first list of what will eventually be called
the "Mersenne primes", prime numbers that can be written
in the form 2n [?] 1 (for some integer *n*),
whose properties and determination are still topical questions in
contemporary mathematics. Mersenne envisaged his meeting group, and
his own net of correspondents, as the prototype for a larger
institution that would bring scholars together in a pacified Europe,
foreshadowing the foundation of the later Academie des sciences
in 1666, or the Royal Society in England (MC V: 301-302, and
Goldstein 2013)



In 1623 and 1625, Mersenne published three massive philosophical
works. The *Questiones celeberrimae in Genesim* (which covers
almost 1900 folio columns), a commentary on the six first chapters of
the book of Genesis, larded with long scientific and philosophical
digressions, was intended as an apology of Christian religion against
all forms of "atheism". It contains attacks on various
Platonist, cabbalistic and hermetic authors such as Bernardino
Telesio, Pietro Pomponazzi, Giordano Bruno, Jacques Gaffarel, or the
English hermetic author, Robert Fludd. The tone is virulent, sometimes
offensive, and the book attracted several outraged answers. Fludd in
particular reacted in his *Sophia cum moria certamen* (1629)
which itself drew a long reply from Gassendi, writing upon
Mersenne's request (Gassendi 1630). The same inspiration governs
*L'Impiete des Deistes*, published
in French the next year. It is a point-by-point refutation of the 106
*Quatrains du Deiste* or *Anti-Bigot*, a long
anonymous poem denouncing Christian revelation, bigoted superstition
and belief in a personal God. Mersenne's response, written as a
dialogue between a deist and a theologian, leads to the conversion of
the deist, to whom the existence, justice and mercy of the Christian
God are demonstrated. Dedicated to Richelieu, and perhaps written on
command, the book may be seen as taking part in a larger campaign
orchestrated by the French state and the catholic church, at a time
that witnessed Vanini's execution in Toulouse, the trial of
Theophile de Viau, and a strengthening of repressive measures against
anti-Aristotelian philosophical novelties. *La Verite
des sciences* (1625) is a dialogue between an alchemist, a skeptic
and a Christian philosopher, the latter opposing both the
over-confidence of the first and the excessive doubts of the second.
The second, third and fourth parts of the book, dealing with
arithmetic and geometry, is an 800-page compilation of ancient and
recent achievements in the mathematical sciences, intended to show
that there are regions of human knowledge immune from doubt, and which
do not contradict Christian wisdom.



By the end of the 1620s, Mersenne's former animosity towards the
anti-aristotelians authors withered, giving way to a more lenient if
not tolerant approach. Galileo whom he had listed among the dangerous
ones in 1623 is now the object of great praise. Mersenne seemed much
less concerned with the proliferation of atheists and heretics, and he
expressed regrets about the offensive tone of his previous works
(Letter to Rivet 12 nov. 1639, MC X: 599). His travel to Holland in
1630 put him in contact with Protestant scholars, such as Andre
Rivet and the Socinian Ruarus, who became regular correspondents.
Mersenne who used to vilify the heretics, was now taken to task for
his sympathies with the enemy, and he was sometimes dubbed the
"Huguenot monk". In any case the staunch defense of
orthodoxy of the first works is nowhere to be found in
Mersenne's next publications, which, from 1634 onward, are
almost entirely devoted to the promotion of the mathematical sciences,
broadly conceived. It has been a question among biographers and
commentators whether these changes reflect a conversion to a new
agenda or a new philosophical outlook. Robert Lenoble (1943: 38)
considers that until 1634, Mersenne was still looking for a better
philosophy of nature and held provisionally to Aristotelianism,
"whereas at that date he discovered what he had sought for many
years, namely Mechanism". Sylvie Taussig (2009b) considers that
Mersenne went through a serious crisis, both moral and intellectual,
at the end of the 1620s, and that under the influence of Peiresc and
Gassendi he came to adopt a more skeptical outlook on philosophical
and religious matters. Without denying Mersenne's change of tone
and accent, Garber (2004) and Dear (1988) tend to underplay the extent
and meaning of Mersenne's "conversion" to the new
philosophy, considering that his agenda of promoting mixed mathematics
was to him still compatible with a traditional philosophical
outlook--"the learning of the schools", that Dear
described as conjoining Christianized Aristotelianism, Renaissance
humanism and a skeptical or probabilistic approach to philosophical
matters. We shall come back to these issues in due course.



The five treatises published in a row in 1634 are representative of
the kind of intellectual productions Mersenne would henceforth offer.
Two of them (*Questions inouyes*, and *Questions
theologiques...*) are eclectic lists of
"curious" questions, intended for entertainment
(*recreation*) as well as for instruction of the
learned: can one walk on water without miracle? How many grain of
sands can be contained in the sphere of the earth ? From where does
the satisfaction come when one believes one has found a new
demonstration or truth? In these questions metaphysical, apologetic
and even theological considerations are (in spite of the title of the
second treatise) barely present. The *Questions harmoniques*
and the *Preludes to the harmonie universelle* prepare
the way for the publication of Mersenne's great achievement on
musical theory, The *Harmonie Universelle* (1636-7),
where he offers what is still considered a major contribution to the
scientific understanding of "consonance" and acoustics.
Finally the *Mechaniques de Galilee* illustrate
Mersenne's constant interest in physico-mathematical questions
of Galilean type, that is Archimedean mechanics stricto sensu, dealing
with basic machines, such as the lever, the wheel, the pulley, but
also the sciences of motion, free fall, ballistics, pneumatics,
hydrostatics, and optics. Mersenne pursued these interests in the
1640s, when he started to make his own campaigns of experiments in
order to verify Galilean numerical data on free fall and on the
velocity of a cannon ball, especially during his journey to Italy
(1644-1645) where he met Torricelli. These researches resulted
in the publication of his *Cogitate physico-mathematica* (1644)
and his *Novarum observum physico-matheaticarum* (1647), which
includes in its first part a treatise by Roberval on the system of the
world. A book on optics was to be published after Mersenne's
death (*L'Optique et la catoptrique*, 1651).


## 2. Scientific Apologetics



Mersenne was indubitably an heir to the Thomistic view of a necessary
synthesis between Christian faith and philosophy. As expressed in the
praefatium of the *Quaestiones in Genesim*, it is "a duty
of the learned to refute atheists", the tacit assumption being
that "true philosophy never contradicts the teachings of the
Church" (ID II: 490-1). This synthesis was vindicated in
the rather troubled political, and religious context of early
seventeenth-century France, which still bore the scars of half a
century of religious wars, and appeared exposed and vulnerable to what
Catholics considered a severe crisis of orthodoxy, raging on all
fronts. A rising tide of libertines, deists, skeptics, cabbalists,
alchemists, and naturalist metaphysicians, all more or less
consciously in league with the Protestants, seemed to Mersenne on the
verge of overwhelming the "true" Christian faith. Mersenne
often pointed out the connection between Protestantism and the various
forms of heterodoxy and atheism: the Calvinist belief in
predestination 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 his
children", or simply to own that there is no God at all (ID II:
589). So, Mersenne's early-interventions may be seen as taking
part in the larger movement of "re-catholization" of the
French state after the pacification allowed by the Edit de Nantes. In
this regard, Mersenne's advocacy of a harmonious conciliation of
faith and reason was not without similarities with a noted feature of
Galileo's "cultural program" in the same years: both
wanted to contribute to the Counter-Reformation, and both defended the
specific idea that Catholics should not leave to Protestant heretics
the monopoly of reason and scientific knowledge. Mersenne was however
wary of any anti-Aristotelian philosophical novelties (including those
of Galileo himself), as he saw them as *ipso facto* dangerously
verging towards contesting religious truth. According to Garber
(2004), the Aristotelian framework, particularly prominent in the
first works, was adopted not so much for its philosophical virtues as
such, but rather as a rampart of orthodoxy, as a tried doctrine, that
has long proved its ability to be harmoniously conjoined with
Christian 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 to
fanaticism. As Mersenne stated in the preface to the
*Quaestiones* (1623):



> 
> 
> These men who desire to found a new philosophy, and to demonstrate it
> from fundamental principles, never regard the glory of God. Rather
> they strive with an ignorant obsessive zeal [*cacozelia*], by
> which they seek to shake up and overturn the Catholic religion, if
> they 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 the
*Quaestiones* were not simply a defense of natural religion but
also, and perhaps primarily, a defense of catholic faith (and its
mysteries) against the caricature conveyed in a growing number of
writings, that represented it as resulting from superstition and
ignorance:



> 
> 
> It is appropriate to Catholics, and especially to theologians to know
> the sciences and to scrutinize God's works, not only because we
> thus receive the meaning of His will as from the pages of a Book, but
> also because we show how unfounded is the atheist's
> representation of Catholics as melancholic, agitated with thousands
> scruples and superstitions. (QG: col 2 - translation here and
> elsewhere from the author, unless otherwise indicated)
> 
> 
> 



To realize this aim, Mersenne's strategy was twofold: polemical
and constructive. On the one hand he attacked his polymorph enemy with
the rhetorical instruments of a skilled debater, using the weapons of
the adversaries, or making one refute the other (as in the dialogue
between the alchemist and the skeptic in the first book of *La
Verite des sciences*). Hermetic authors such as
Robert Fludd, or cabbalistic Christians such as Giovanni Pico and
Jacques Gaffarel were vehemently denounced, as they availed themselves
of spurious allegorical interpretations of the Bible. Even when their
reading of the Bible is not wrong, they are dangerous as they make
people believe they can deduce *a priori*, or through divine
inspiration, what can only be known *a posteriori*, through
revelation and experience. Heretic tendencies were pointed out in the
doctrines of the Alchemists, who, in the wake of Paracelsus's
*Mysterium magnum*, tried to give naturalist interpretations of
Christian mysteries, such as the resurrection or the miracle of
Creation. Mages, sorcerers, and adepts of esoteric mysteries such as
the Rosicrucians prosper on men's propensity to superstition.
Naturalist metaphysicians--Bruno, Campanella,
Pomponnazi--who endowed nature with creative powers, verge
dangerously toward pantheism, casting doubt on creation, on the
transcendence and freedom of God. A leading thread in all these
criticisms, is the idea that the Catholic belief in miracles and
mysteries, far from being superstitious, is much more attuned to sound
reason than the doctrines that are opposed to it. A light knowledge of
philosophy may induce some doubts, but the more one knows the
sciences, the more these Catholic beliefs and mysteries are reinforced
and may be vindicated against false religion and atheism. A smattering
of knowledge in optics can for example cast doubt on the truth of
divine epiphanies, but a better knowledge of this same science allows
one to exclude the idea that miracles can be illusions caused by
reflections or refractions and therefore makes more sensible their
divine origin (QG: col. 522, 538). This sort of negative argument
shows that Mersenne's rationalist defense of religion allows for
truths beyond the capacity of men's reason. In this, Mersenne
stand explicitly against the deist. Both allowed for "natural
religion", but whereas the deist denounced the superstition and
anthropomorphism of popular belief, Mersenne reversed the attacks and
denounced the far worse anthropomorphism of one who measures God by
human reason: "it is feebleness of the mind, to believe that our
finite understandings can comprehend the divine attributes or
acts" (ID I: 318-9; see also ID I: 669-70, and
Beaude 1980). This however should not be understood as revealing a
secret inclination towards fideism: religion teaches truths which
surpass reason, "not in destroying it, but rather in perfecting
it" (ID I: 680).



Mersenne's criticisms are based on a careful reading and
exposition of the adverse doctrines, to the point that Mersenne has
been sometimes taken to task for offering the enemies of religion a
much too complacent advertisement. It has been remarked (Carraud 1994:
152) that the discourse of others (*le discours
d'autrui*) holds a distinctive place in Mersenne's
writings: it is neither dismissed as in Descartes, nor deftly
re-appropriated as in Leibniz, but rather faithfully produced and
reported in order to be discussed on its own level and according to
its own merits. This is the case, for example with the cabbalistic
"*sefirot*" and numerological methods which are
patiently, almost sympathetically, expounded in the
*Impiete*. The same holds for Giordano
Bruno's doctrine. However heretical the man was, his arguments in
favor of the infinity and plurality of the worlds (from his *De
Infinito*) are not simply dismissed or brushed aside. The
Christian philosopher reports them quite accurately in the second part
of the *Impiete des deistes*, before
answering and criticizing them.



Apart from its polemical intent, Mersenne's "scientific
apologetics" may be seen as articulating a natural theology
together with a "sacred physics" or "sacred
mathematics". On the one hand a host of rational
arguments--some of them borrowed from the sciences, some from
traditional metaphysics--are brought in to prove God's
existence and demonstrate His attributes. This natural theology is
where Mersenne articulates his main ideas on metaphysics and we shall
come back to it in the next part of this article. On the other hand,
science is used as an instrument of exegesis. The *Quaestiones in
Genesim* contains thus numerous scientific excursuses whose aim is
either to give a scientific (mainly mathematical) exposition of a
biblical content--as when Mersenne "calculates" what
should be the size of Noah's ark, or suggests that our knowledge
of architecture should help us to see the excellence of the temple of
Solomon--or to illustrate a Catholic mystery (such as the triadic
unity of God or the miracle of the Creation) through a mathematical
analogy.



This edifying use of mathematics is perhaps the hallmark of
Mersenne's writings. It is still very much present in later
publications (such as the *Harmonie Universelle*). The minim is
literally fascinated by the almost magical properties of numbers and
geometrical figures, where the most surprising and complicated objects
and properties are generated from the simplest principles. This gives
him a general analogy for religious truths. There are "thousands
of things in the mysteries of faith" that are
"incomprehensible to the pagan and to a peripatetic
philosopher", but that may be made understood by a
"Christian Euclid" (*un Euclide chretien*) :
Mathematics makes the relation of the infinite to the finite sensible,
showing how an infinite motion can be made in a finite space. It can
thus "explain" the union of the two natures in the same
divine person. Although the mathematical point is the humblest object,
"the minim of geometry" (HU III: Livre de
l'Utilite de l'Harmonie, 16), it is in a sense the
closest to God itself. Both are simple, without parts. The point
engenders the line and together with the line, the surfaces, and with
lines and surfaces the bodies. This gives us an insight on how God
engenders the son, the son and God together, the holy spirit, and then
all together the universe. Unity contains all numbers eminently, as
God contains all created acts and all creatures, etc (ibid. 16-17).
Mersenne also likes to suggest mathematical analogies illustrating, or
symbolizing moral virtues. Thus, as the height of a triangle is
measured by a perpendicular line elevated from the basis, the goodness
of 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 of
mathematics. For example:



> 
> 
> mechanics teaches us to live well, either by imitating heavy bodies
> which always seek their center in the center of the Earth, just as the
> spirit of Man must seek his own center in the divine essence which is
> the source of all our spirits, or by maintaining ourselves in that
> perpetual moral and moderate balance which consists of rendering all
> that belongs to Him first of all to God and then to our neighbor. (MC
> IV: 208-09)
> 
> 
> 



The philosophical value of Mersenne's apologetics may be
differently assessed. Mersenne seemed to pay little attention to
contemporary arguments according to which the Bible is not to be taken
literally on questions dealing with nature (see, e.g., Galileo's
1615 Letter to Christina). His exegesis indeed offers a rather rough
example of what will be later called "concordism", the
conception that there cannot be any discrepancy between the teachings
of the sciences and those of the Bible, taken in the most literal
sense. However, the most distinctive aspect of Mersenne's
apologetics, the edifying use of mathematics, although sometimes
naive 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 to
Mersenne's use of mathematics, when he discusses men's
disproportion and God's greatness from the mathematical model of
the infinite divisibility of space, or from a speculation on the two
infinites whose terms are reminiscent of similar passages from the
Impiete.



Besides, although Mersenne's "scientific
apologetics" was primarily conceived as a defense of religion
against "atheists", where science is only a tool, it
turned out to be also a defense of mathematical sciences against
whoever might think that they are vain curiosity and must be either
rejected, or at least relativized as inessential knowledge...
This is especially manifest in the later works, where Mersenne gave
free rein to his passion for mathematical sciences. Whereas natural
theology and anti-deistic polemic were no longer dominant themes, he
still vindicated the "usefulness" of mathematics, not only
for men's welfare, but for their edifying virtues. In the next
decades, one could find similar moves in defense of the
"usefulness of natural experimental philosophy" in the
works of Robert Boyle.


## 3. Metaphysical Issues


### 3.1 Metaphysics as Rational Theology



In the *Quaestiones*, Mersenne offered a tripartition of the
theoretical sciences: metaphysics considers "trans-natural
objects, such as God and the angels, that are actually separated from
all matter"; doctrinal sciences--that is
mathematics--deals with objects that are "in truth
material, but considered abstracted from matter, such as the line and
the figure"; natural sciences (physics) considers
"material things as such, for example the heavens or the
elements". (QG: col 92-3). In *La
Verite* (VS I: 50), Mersenne suggested that
metaphysics, although an abstract science, like logic and mathematics,
is nevertheless closer to physics, in so far as their shared aim is to
consider "things as they are in themselves", and not
simply things as they appear to our senses--in this both sciences
"are rightly called sapience". He was later to revise this
coupling, suggesting in his *Questions inouies* (QI: 54)
that metaphysics is closer to mathematics, on account of the fact
that, contrary to physics, metaphysics and mathematics both consider
immutable and eternal objects, and are the only ones among the
sciences capable of being really possessed by men here below.



The definition of metaphysics given in the *Quaestiones* is
strongly reminiscent of Aristotle's Metaphysics E1--where
"prime philosophy" is conceived as strictly concerned with
the separated or immaterial substances, thus with the
"theological" realm. Jean-Luc Marion (1994) pointed out
that although Mersenne, in several places, acknowledges formally
another traditional object for metaphysics, that is the "*ens
quatenus ens*" (the abstracted Being as such, whose science
applies indifferently to all beings, created or uncreated), he seemed
reluctant to give this science (that we now call ontology) any
substance. In a striking passage from the *Quaestiones*,
Mersenne said that "Being" is a name that suits God better
than any of the creatures:



> 
> 
> Among all names "being" is the one that we should ascribe
> to God, rather than all the other ones naming the perfections of
> creatures... God could justly say "I am all Being, as I
> contains all things more perfectly than they can contain
> themselves". This is why all creatures could say "my name
> is non-Being, or non-entity" (*Non Esse, seu non Ens*),
> as, according to Plato, truly all things except God have non-being
> rather than being. (QG: col. 21)
> 
> 
> 



In later works the specificity of ontology was quickly dissolved into
logic on the one hand (an abstract science which shares with ontology
the same principle of non-contradiction, see VS 52-55) and into
rational theology on the other hand, the science of immaterial beings
and first causes. This dissolution may be seen as anticipating
Descartes's own reduction of metaphysics to "prime
philosophy", and, according to Marion, this is a very
significant (albeit a merely negative one) legacy of Mersenne's
work to the history of metaphysics.


### 3.2 Proofs of God's Existence



The bulk of Mersenne's contribution to rational theology is
contained in the 700 or so first columns of his *Quaestiones in
Genesim*, where no less than 35 proofs of God's existence
are reckoned and detailed. The importance of rational demonstration is
directly related to the apologetic project: one cannot simply be
content with the idea that God is immediately known, as this could not
shut the mouths of the atheists. The encyclopedic turn of the
recension is obvious, and Mersenne, ready to use all means available
to contradict the atheists, was not taken aback by the fact that these
proofs belong to various, and sometimes adverse, theological
traditions. After summoning the consensus of all creatures, and the
consensus of all men, Mersenne resorted to cosmological arguments,
arguing, from the contingency of our word, and the contingency of our
own finite existence, that "it is necessary that something
exists by itself". Here Mersenne borrowed from Hugues of Saint
Victor and Jean Damascene.



He also presented at some length the Anselmian argument, arguing that
existence should be attributed to God, on account of the fact that the
very idea of God (that even the insane atheist should have in his
mind) obliges us to consider that nothing greater can exist, and that
existence *in re* is obviously a greater thing than existence
in the mind. Mersenne, who did not mention Aquinas's criticisms,
found the argument "excellent and very pious" (QG: col
37). He also paid much credit to the Augustinian argument from
"eternal truths"--Mathematical truths in particular
would not be possible without the supposition of an eternal mind in
which they reside:



> 
> 
> open your mind's eyes, o atheist, and see how numerous and
> strong are the arguments through which arithmetic asks you to embrace
> the divine unity, without which Arithmetic would not hold, as all
> material unity or numerical is impossible without the supposition of
> divine unity. ... One objects to the atheist's geometry, if
> ever 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 two *a priori* arguments (from
eternal truths and from the idea of a perfect being) are the only two
that are brought in in the Impiete to dispel atheism. In
the *Quaestiones* however more than half of Mersenne's
arguments were *a posteriori* ones: from the creation *ex
nihilo*, from the beauty of creatures, from the given natural law,
from the harmony of the universe... All allowed lengthy
scientific excursuses, demonstrating God's intelligence and
providence through whatever the sciences can show of the order of
things. Among these arguments, Mersenne paid only lip service to the
classical Aristotelian and Thomist "argument from motion",
which states that the world needs an immutable first mover, probably
because he is aware that the argument had been used in Paduan
Aristotelianism in order to defend the coeternity of the world and its
first mover. In the other *a posteriori* proofs, the regressive
move from the creation to the creator was not as likely to subject the
creator to the creation.



Prominent in the *Quaestiones* and
*Impiete*, rational theology tended to recede in
importance in subsequent works. Although in the *Quaestiones*,
Mersenne had hinted at another work ("*perfectum
opus*") to come, it was never written. After 1624 he became
more reluctant to consider proofs of God's existence, hinting in
his correspondence with Ruarus that it might not be possible to give a
truly demonstrative one, however sensible and approved by everyone was
the truth of God's existence. His doubts were now on a par with
the ones he came to entertain regarding demonstrations in physical
matters. In his *Questions theologiques*, he wrote in a
somewhat autobiographical tone, that everyone could see for themselves
that:



> 
> 
> fresh from the Philosophy and Theology courses, they used to imagine
> that they could give a reason for everything, whereas 20 or 30 years
> later they are compelled to confess that they know no reason that
> satisfies them and is so evident and certain that they cannot doubt
> it. (QT: 10)
> 
> 
> 



This may shed some light on Mersenne's role in the writing of
the second objections to Descartes's *Meditations*, where
doubts were cast on the demonstrative character of the Cartesian
proofs of God's existence, and especially on the ontological
proof, whose Anselmian version was so much favoured by Mersenne in his
younger years. It has been argued (Garber 2001), quite convincingly,
that Jean-Baptiste Morin, a member of the Mersenne circle, and the
author of a booklet on God's existence written in a geometrical
fashion (Morin 1635) had an important hand in the composition of the
second objections and that he was probably the one who suggested the
request of presenting the Meditations arguments in a geometrical
manner. Mersenne, however would have concurred with the reservations,
implicit in this demand, concerning Descartes's claim to the
higher certainty of metaphysical demonstrations over mathematical
ones.


### 3.3 Voluntarism



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



> 
> 
> all that is produced is finite but God's potentia is without
> measure. 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 he
> did--this however will not prevent us from believing He is all
> powerful, as we distinguish in God the work and the will [*le faire
> et le vouloir*]... it is bad reasoning to conclude an
> infinite effect from an infinite cause when the cause is not acting
> necessarily but freely. (ID II: 304)
> 
> 
> 



For Mersenne the unique perfect egalitarian emanation of God would be
an action *ad intra*, that is the action through which God
contemplates (and loves) Himself in the persons of the trinity. When
one comes to causality *ad extra*, such as creation, one has to
distinguish (ID II: 311-2) between divine power and divine will.
The first contains and addresses infinite possibilities, the second
chooses, from among them, a finite assortment.



Voluntarism concerning the nature and laws of creation may appear as
an important common ground that Mersenne shared with orthodox
(Thomist) scholasticism, and with Descartes. As Lenoble has shown, its
assertion was an essential precondition for the establishment of a
mechanical science, unifying the whole of nature under the contingent
will of God, his initial decisions regarding the distribution and laws
of matter and motion. Mersenne's voluntarism implies that
physics is not about an eternal and immutable object, as God could
have 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 in
the simplest fashion. This is evidenced in the reign of the grace,
where one can clearly see that God did not chose the shortest way to
dispense his grace, as he could have assured our salvation with a
unique act of his will (cf. *Questions Inouies*, p.
344-5] But this hold as well for scientific truths, and explains
for example why Mersenne never considered as decisive Galilean and
Copernican arguments for the motion of the earth taken from the
simplicity of natural order. Mersenne's point was actually quite
close to the argument from divine omnipotence that Pope Urban VIII
suggested to Galileo in 1623, and that Galileo, somewhat ironically,
put in the mouth of Simplicio in the concluding sentences of the 1632
*Dialogo*: Man cannot presume to know how the world really is,
since God could have brought about the same effects in ways unimagined
by humans (see Galileo, 1890-1909, VII, 488).


### 3.4 Mersenne and Descartes on Eternal Truths



Mersenne did not extend his voluntarism to mathematical truths, as
Descartes did in a rather unconventional way. The confrontation of
Mersenne's and Descartes's positions on this theme has
been the object of some discussions in the secondary
literature--see especially Marion 1980; Dear 1988; Carraud 1994;
Fabbri 2008. Descartes first assertions on God's creation of
mathematical truths appeared in a letter to Mersenne of April 15,
1630. Descartes enjoined his correspondent to tell everyone aloud that
the mathematical truths that Mersenne called eternal were not
independent of God, but "have been created by him and depend on
him entirely just as do all the other creatures" (Descartes to
Mersenne, April 15, 1630, AT I: 145). God freely established them, and
impressed them in the minds of men, as a king would in his kingdom.
The statement seems to have surprised Mersenne. The Minim's own
letters are lost, but this can be inferred from the fact that
Descartes in May and June 1630, obviously answers repeated requests
for clarification:



> 
> 
> you ask me *in quo genere causae Deus disposuit aeternas
> veritates* [in what kind of cause God has disposed the eternal
> truths]. I reply to you that it is *in eodem genere causae* [in
> the same kind of cause] that he has created everything, that is *ut
> efficients 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 that
> he was free to make it not true that all the radii of the circle are
> equal--just as free as he was not to create the world. (27 mai
> 1630, AT I: 152)
> 
> 
> 



Mersenne's own considerations on the status of eternal truths in
God's intellect explain why he should have had qualms about
Descartes's puzzling doctrine (which might amount here to no
less than making mathematical truths somehow contingent, depending on
the arbitrary will of God--even though Descartes himself, who
often points out the necessity of mathematical truths, never draws
such consequence). Mersenne position seems closer to cardinal de
Berulle's, and Augustine's *exemplarism*: eternal
truths are exemplar ideas present in God's intellect and
illuminating our own. They proceed from God's nature as His
Verb, but they are not similar to creatures, they are not
"freely" created.



When Mersenne considers God's relation to eternal truth he often
uses metaphors of light and the emanatist vocabulary of
Neo-Platonism--for example in the *Traite de
l'harmonie Universelle*:



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



Or in the *Questions theologiques*:



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



The kind of causality implied here is a causality *ad intra*:
eternal truths belong to God's nature. And in this regard, as
they are "formally" in God and so to speak coeternal with
Him, they should be considered as uncreated and necessitated, as God
himself is not free towards His own nature:



> 
> 
> It is patent that God is entirely free in regard everything that are
> contained only eminently in him, to produce them or not, as He is
> driven necessarily to whatever he embraces formerly as these things
> that are God himself are infinite, eternal, independent. (QG: col
> 436)
> 
> 
> 



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



One important question that has been debated in the literature is
whether Mersenne's position amounts to the idea that
mathematical truths are truly independent of God. The discussion is
not merely about the meaning one is willing to give to the word
"independent" whether it applies or not to something that
is included in God's nature, but it engages deep issues in the
history of metaphysical thought. According to Marion (1980), and
Carraud (1994), the very fact that mathematical truths are considered
as forming the essence of God's intellect means that they do not
depend anymore on God's will. Apparently endorsing a doctrine
that he found mentioned in Suarez (1597, xxxi.12.40), Mersenne
wrote in a much discussed passage of the *Quaestiones*:



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



God would be subjected to mathematical truths just as human intellects
are. He would know them as we know them. This would be the sign that
the doctrine of univocity entered Mersenne's thought, perhaps
under the influence of Kepler, in an irretrievable fashion. This is
also deemed to explain the striking disappearance of rational theology
in Mersenne's writings. Just as metaphysics had been entirely
exhausted by natural theology in the first works, rational theology
ended up being entirely exhausted by mathematics. The latter are not
anymore an analogical resource for theology, but indeed they furnish
the only possible non-analogical discourse on God, "the hidden
object of all mathematical discourse" (Pessel 1987). As a
consequence, Mersenne's apologetics no longer needs to appeal to
rational theology--the mere promotion of mathematical sciences
has become the unique, or best, apology of Christian religion.



Peter Dear criticized Marion's interpretation as implying
something that he did not find in Mersenne, namely that mathematical
truths exist in a kind of platonic separateness, so that God and men
would 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 that
eternal truths causally depend on God, being true emanations of his
nature. Accordingly, Mersenne would not so much insist on independence
but rather on co-implication and coeternity. Whereas Descartes used
to



> 
> 
> see the matter as straight choice between necessary truths holding
> simply because God knew them (having willed them) or God's
> knowing them because they are independently true. (cf. Descartes
> a Mersenne 6 mai 1630, Descartes AT I: 149, and Dear 1988:
> 60)
> 
> 
> 



Mersenne, a rather orthodox scholastic on this point, never recognized
an alternative: both theses should hold together--eternal truths
are true because God knows them, and God knows them because they are
true.


## 4. Epistemological Issues


### 4.1 Against the Skeptics



Mersenne's attitude towards skepticism was complex, changing
over time and somewhat ambivalent. In *L'Usage de la
raison*--a recently rediscovered booklet from 1623, whose
authorship does not seem questionable--one finds arguments
against the vanity of the sciences that are strongly reminiscent of
those expressed around the same time by "Christian
skeptics", such as Montaigne and Charron, or even Cornelius
Agrippa, authors whom Mersenne sternly criticized in his next
publications. Thus, in the "Dedicatory Epistle to Madame de
Vitry", the Minim suggested that our time is badly employed in
studying the sciences, which are plagued with insuperable
uncertainty:



> 
> 
> whenever we raise our eyes to the sky or incline it to the earth, we
> must owe that everything is unknown to us... Who can claim to
> know the number of the skies, their form, their matter, properties and
> accident? One can even find idle-dreamers Copernicans prepared to deny
> the motion of the skies... Who can say if Alchemists are right in
> their promises.
> 
> 
> 



This uncertainty of the "megalocosm" goes together with an
equal puzzlement concerning the littlest creature of the micro-world,
as recent microscopes have shown to the eye that "it is pure
ignorance to say that they are deprived of these several organs that
can be seen in larger creatures". Further, (UR: 37-38) the
author condemned Pythagoras, Archimedes, the alchemists, the
algebraists, etc. for being so much attached to their inventions that
they forget to think of God, and eternal glory...



The change of attitude in the next published works is striking. On the
one hand, in the *Quaestiones* and
*Impiete*, skepticism was presented as a sequel
to Calvinism; and the denunciation of human reason found in Charron
and Montaigne, far from encouraging faith in the mysteries of
Christian religion, was seen as inclining men towards atheism and
libertinism. On the other hand, Mersenne was no longer denouncing the
sciences indistinctly as vain curiosity, his general attitude towards
speculative enquiry was much more positive, especially when one came
to the mathematical sciences, whose apologetic virtues he wanted now
to 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 not
> any one question in Philosophy, that does not raise diverse opinions
> wholly contrary on the same subjects, all of which have their reason
> and nevertheless there is only one that is true. (ID II: 672)
> 
> 
> 



In *La Verite des sciences contre les sceptiques et
les phyrroniens*, the tone changed again. Skepticism was no longer
condemned as a seed of heterodoxy but only in so far as it discourages
men from the practice of mathematical sciences. The skeptical
character is obstinate, but he is no atheist nor heretic in the
disguise (see Descotes, in VS, Introduction), and in the first part of
the book, his arguments against the alchemist's dogmatism are
often endorsed and even reinforced by the Christian philosopher.



Against the epistemological optimism of the alchemist who considers
himself to be in possession of the perfect science, the skeptic
resorts to the traditional arguments of the academic school,
emphasizing that certainty is nowhere to be found, as we have only a
very partial and superficial knowledge of things. We perceive only the
effects and not the profound nature nor the ultimate causes of things.
The true essences evade us. The simplest objects (such as a sheet of
paper) cannot be completely known, because of the infinite number of
relations in which they are involved with other elements of the
universe. It has been shown by G. Paganini that these arguments and
examples are almost verbatim borrowed from the "second
doubt" of Campanella's *Metaphysica*, a manuscript
that was in Mersenne's hands at the time he wrote *La
Verite des sciences*, but that he did not mention as
his source (Paganini 2005 & 2008).



In chapter 11 and 12, the Christian philosopher presents the skeptical
arguments in a new and more radical form. He gives an account of the
ten skeptical tropes of Aenesideme, as Mersenne could have read them
in Sextus Empiricus and Diogene Laertius. These tropes draw on
the varieties of animal constitution in regard pleasures and pains,
the idiosyncrasy of men, the disagreement of the senses, the varieties
of circumstances and dispositions, such as health and disease, sleep
and wakefulness, young age and old age. All show that the information
of our senses is unreliable, just as the reasons we draw from
them.



In answer to these doubts, Mersenne's Christian philosopher
resorts to an eclectic strategy. On the one hand, he adopts the usual
Aristotelian standpoint against skepticism regarding the senses: sense
perception is trustworthy, provided that its exercise takes place in
"normal" and appropriate conditions. Errors occur only
when the senses are affected by disease, or presented with objects
whose distance, illumination, intensity, etc. exceed the normal
range:



> 
> 
> All the deceptions of senses that you object are of no use, for they
> only prove what we concede, namely that each one of our senses, in
> order to judge its object rightly must have all that its nature and
> the perfection of its operation require--this granted, it never
> errs. (VS I: 15)
> 
> 
> 



On the other hand, just as senses are the right judges of their own
proper sensible--the eye of color and light, the ear of sound,
etc.--human intellect also possesses an internal criterion which
allows it to judge its own objects rightly. It has the use of "a
spiritual and universal light that it has of its own nature since the
commencement of its creation" (VS: 193). Here the inspiration is
clearly Augustinian, as it is for Descartes's parent conception
of "lumiere naturelle". The light of the soul does
not give men direct access to divine knowledge, knowledge of essences,
as that would require an eternal glory and a supernatural light. But
it still gives access to a number of *evidentia*, immediate
certainties, whose truth, Mersenne concedes, depends on God's
illumination and God's veracity. Thus, in every realm of
knowledge or human interests, there are truths that are not capable of
doubt, such as "the whole is greater than the part", or
"evil should be avoided".



Another Augustinian aspect of Mersenne's defense is the idea
that doubt itself can be turned into a source of knowledge. For
example, although there are differences in apprehension between
various men, or between men and beasts, we do have the knowledge of
such differences and this is something that cannot be doubted:
"at least one knows that the objects of the senses appear
differently according to the diverse dispositions of the organs"
(VS: 193). Awareness of this sort of facts is what incites men to seek
the laws of appearances--for example, the optical and geometrical
rules that govern variations in perspective. In other terms, it
prompts them to engage into physico-mathematical enquiries.



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



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



In the next decade, reacting to the cogito argument in the
*Discours de la Methode*, Mersenne pointed out to
Descartes how close his use of radical doubt was to that Augustinian
argument (see Gouhier 1978).


### 4.2 Mitigated Skepticism and Probabilism



Richard Popkin has remarked that the great originality of *La
Verite des sciences* resides not so much in its
arguments against the skeptics, as in the fact that this defense of
"the truth of the sciences" concedes so much to the
skeptical outlook. Most of the skeptical claims that are propounded
either by the skeptic or by the Christian philosopher are not really
refuted in the book. They are integrated in a novel view of what one
should expect of scientific enquiry, its true aims and prospects
(Popkin 1956, 2003).



Thus, the Christian philosopher has no qualm with the skeptical
rebuttal of the alchemist's claim to perfect knowledge in
natural matters. He freely admits that we cannot know everything, and
especially not the causes nor essences of physical things, that
men's capacity is limited by outward appearance and the surface
of corporeal things. In the *Questions inouies*, Mersenne
went as far as to say that we cannot demonstrate the existence of the
external world:



> 
> 
> And we do not have any demonstration by which we are able to persuade
> the opinion of those who might maintain that the earth, the water, the
> stars, and all the bodies which we see are but appearances and
> "species intentionales", supposing God might use these
> species or accidents to make all that we see appear to us. For one is
> not able to say that one knows a single thing as one
> should--according to the laws and the notions which Aristotle and
> other philosophers give of science--if one cannot demonstrate
> that it is impossible that the reason which one supplies, or the thing
> which one proposes, be not true. That is enough to persuade those who
> use reflection that there is nothing certain in physics and that there
> are so few certain things, that it is difficult to propound
> any... (QI XVIII: 53, translated in Mace 1970: 24-25)
> 
> 
> 



Mersenne joins the skeptic in his condemnation of the
Aristotelian's far too optimistic view of science. What is
denounced is not so much Aristotle's physical doctrines or
methods (the Christian philosopher, for example, does not endorse the
skeptical attacks against syllogistic) but rather a mistaken
representation of the epistemic aims of physics, which cannot aspire
to perfect certainty. Bacon's experimental method received no
more favor in his eyes precisely on this account, as it serves a
project 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 never
> arrive at the point of rendering our intellect equal to the nature of
> things. That is why I believe that Verulam design is impossible. (VS
> 212)
> 
> 
> 



Mersenne did not think that our inability to understand the ultimate
cause and intimate nature of things should be an object of lament. The
mere knowledge of effects and appearances might be enough for human
needs. For one thing, it has enough pragmatic virtue, as it can serve
us as a guide in our actions. Besides, as outwards appearances, crust
and superficies may be rigorously described, through measurement and
mathematics, the sort of knowledge that can be gained here is as
perfect and certain as one could wish--although not of the sort
dogmatic physicians and metaphysicians are seeking.



Thus, according to Richard Popkin, Mersenne is not so much refuting
skepticism as he is adopting an attenuated form of it. By openly
discarding research on the causes and essences of phenomena, reducing
the whole of physical science to mathematical knowledge of accidents,
the study of external effects, and the establishment of the laws of
appearances, he invents a "mitigated skepticism", that
Popkin considers as the first lucid expression of the modern
scientific outlook, deemed to become dominant in the following
centuries. This outlook conjugates an entire confidence in the virtues
of physico-mathematical sciences, with a complete positivism (that is,
a deliberate abstention) in regard metaphysical matters.



Recent reappraisals of Mersenne's epistemological views tend to
contest, or at least qualify, Popkin's characterizations.
According to Garber (2004), Mersenne's epistemological frame is
old rather than new. The way he envisions the boundaries between
disciplines remains Aristotelian, and in particular his conception of
the "physico-mathematical" sciences directly comes from
the Aristotelian definition of mixed or subaltern mathematics,
sciences such as astronomy or optics, only dealing with accident and
surface properties of physical things. Far from offering a scientific
substitute to Aristotelian physics, these sciences allow one to
approach nature in a mathematical way "without having to
challenge the full complex of Aristotelianism directly" (2004:
157) in ways that would be perceived as subversive of true religion
and social order.



Dear's study (1988) similarly insists on the deliberately
"un-revolutionary" character of Mersenne's
contribution to the "scientific revolution". Mersenne
never chose to range himself against Aristotelianism, never cast
himself as an innovator. His agenda is formulated in a preexisting
philosophical idiom (the "language of the schools"), and
his ideas display a "borrowed coherence" rather than an
intrinsic one. Mersenne was not a positivist *avant la lettre*;
he admitted that God knows what man cannot verify, that natural kinds
exist in nature, that things do have essential definitions. His
"skeptical" approach to physics is not so much a
watered-down Pyrrhonism intended to show the inconclusiveness of
natural philosophical demonstration, as it is an instrument to
recommend mathematical sciences as an anchor of certainty, where
ordinary natural philosophy stays in doubt and can only be defended in
a probabilistic way. When Mersenne confesses that many questions
cannot he determined, he is not proposing to suspend judgment but
rather to formulate a probable judgment by choosing the most
persuasive opinions. This "probabilism" is, according to
Dear, a legacy of humanist and Ciceronian dialectics, and it remained
constantly present in Mersenne's work, even though, on some
questions the weight of probabilities has changed. This was
particularly the case for the Copernican opinion. Judging it very
unlikely in *L'Usage de la raison* and in the
*Quaestiones*, Mersenne eventually recognized that it was the
opinion best suited to the phenomena observed and therefore the most
probable. However, God's freedom being never constrained,
Mersenne could accept with relative equanimity the final judgment of
the Church. In his *Questions theologiques*, he was to
publish a French translation of the inquisitorial condemnation and of
Galileo's abjuration.



Departing from Garber and Dear's view as well as from
Popkin's, Buccolini (2019) presents Mersenne's
epistemological reflection in *La verite des
sciences* as resolutely anti-sceptical, and strongly connected
with the views expressed by the Jesuit mathematician, Guiseppe
Biancani, in his dissertation on the nature of mathematics (Biancani
1615), arguing for the certainty and scientific status of mathematics.
According to Buccolini, Mersenne's doubts are directed not
against science as such but against the Aristotelian doctrine of
*demonstratio*, his aim being to replace Aristotelian physics
with an entirely intelligible mathematical physics.


### 4.3 Mechanism and Experimentalism



According to Lenoble (1943), Mersenne's mature works, focusing
almost exclusively on "physico-mathematical" sciences,
witnesses the "birth of mechanism". However, as the term
is not an actor's category of the 17th century, one should be
careful in its use. Formulated in its own terms, Mersenne's
standpoint regarding explanations in physics is that we can only
understand what we can do:



> 
> 
> we only know the real reasons for things that we can create with our
> hand and our mind; ... and of all the things made by God, we
> cannot create any, no matter how much subtlety and effort we apply.
> (NO: 8; Lenoble 1943: 384)
> 
> 
> 



This indicates both the foundations and limits of mechanistic
explanations: finding reasons means showing how things can he produced
by mechanical actions--actions of the kind we are capable of when
applying our bodies to external bodies. On the one hand, however, this
mode of genetic explanation can provide only a very superficial
clarification of created things, whose construction and complexity are
either infinite, or go to details and minutiae that our senses are
incapable of perceiving (OC: 89). On the other hand, these
explanations cannot bear the character of necessity since they focus
on objects that are fundamentally contingent and whose inner machinery
could have been constituted differently, had God so wanted:



> 
> 
> one knows all but nothing in physics, if one follows the definition of
> science Aristotle gave; for if it ought to be about eternal and
> immutable 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 pessimism
and metaphysical voluntarism make his version of
"mechanism" very different from the Cartesian, Hobbesian
or Gassendist one. He never conceived mechanical explanations as a new
science of "causes", based on the adoption of new
principles and elements intended to take the place of Aristotelian
substantial forms--such as Descartes's subtle matter or
Gassendi's atoms. Mechanics, as all other mixed-mathematics, was
simply concerned with establishing the laws of phenomena.



This reflection on nature and the limits of mechanistic science was
accompanied by truly experimental activity. Mersenne was convinced
that mathematical sciences of nature cannot settle for common and
vague observation. It urgently required "well-controlled and
well-performed experiments" (HU I: 167), facts that were
artificially generated and precisely measured. Mersenne was aware
that, even when rigorously performed, an experiment is not always
enough to establish the law of phenomena: two series of experiments
can diverge very little and yet express very different laws.
Measurement can only be approximated, and this has a bearing on the
certainty of mixed mathematics, which is partially compromised to the
extent that it deals with physical objects. Reason must therefore, as
far as possible, always accompany and discipline observation, without
which one is vulnerable to considerable misunderstandings.



Mersenne made a considerable effort to do and redo experiments that
his predecessors (most notably Galileo) had not always had the sense
to present precisely. Thus, on the subject of the increase in speed
during falling motion on an inclined plane, he conducted a precise
campaign of measurements that enabled him to criticize Galileo's
numerical results, and eventually express doubts on the validity of
the law itself (Palmerini 2010). As usual, he expressed his
reservations concerning our capacity to determine with certainty the
causes of gravity: "it is just as difficult to find the real
cause as to demonstrate whether the earth is stable or mobile"
(*Traite des mouvements*) and he placed back-to-back the
reasons put forward by his contemporaries--positive and real
quality, air pressure, magnetic attraction--which could only
partially account for the phenomenon in its precise numerical
dimensions. As Peter Dear has shown, Mersenne's approach to the
science of motion was inductive in nature, not centered, as it was in
Galileo, on the abstract physical process, but rather on "a
generalized description of cases, whose details and precise parameters
held an importance altogether lacking in Galileo" (Dear
1994).


## 5. Music and Universal Harmony



Of all the mixed-mathematical disciplines in which Mersenne took an
interest, music was undeniably the one to which he devoted the most
effort and passion. His 1623 *Quaestiones* already included a
long musicological digression on the therapeutic power attributed to
the music of the Hebrews, and generally to the music of the Ancients,
whose harmonics he dreamed of restoring. The idea was taken up and
developed in the 1627 *Traite de l'harmonie
universelle*, published under the transparent pseudonym of
"Sieur de Sermes". The science of intellectual music and
the understanding of the proportions that govern nature, lost through
negligence, 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 true
function: elevating the senses above material objects, rather than
linking them together. Mersenne's great work on musical theory,
the eight books of *Harmonie Universelle*, was published from
1636 to 1637. It presents a great many editorial variants, as Mersenne
never ceased to work on it, annotating his own copy. The important
"Traite de la nature du son", which constitutes the
first part of the work, focuses on the study, undertaken in a
mechanistic spirit, of acoustic quantities, their physical nature and
their effects on physiology and passions. Mersenne, drawing on Isaac
Beeckman, establishes experimentally the laws connecting the
vibration, the length and tension of the strings, making an important
contribution to acoustic science.



Epistemological, metaphysical and aesthetic aspects are intertwined in
Mersenne's musical agenda. Music was to Mersenne a
mixed-mathematical science, just as astronomy, whose primary aim was
to "save the phenomena" through more or less plausible
hypotheses. The musical phenomena par excellence is
"consonance", that is the fact that certain sounds put
together are agreeable to the ear. Recent musical practices, new
instruments and polyphonic music had disclosed new modes of consonance
that were previously unknown, and Mersenne saw his proper task in an
effort to find the best physico-mathematical hypotheses that would be
able to account for them, and could be used to invent more
"perfect" musical pieces (chants). Seeking such
hypotheses, Mersenne relentlessly asked his correspondents how they
could account for the fact that certain sounds put together are
agreeable and others not. For example, in November 1627, he asked a
correspondent in Rome:



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



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



In spite of those discrepancies, Mersenne was truly fascinated by the
fact that the human mind, in its musical appreciation, is so to speak
attuned to mathematical harmonies. The perception of consonance
although mediated (and perhaps distorted) by our feeling, is not mere
sensual pleasure, as Descartes, for example, seemed to think. Properly
understood, it has a rational dimension, as it discloses to men the
"universal harmony", the underlying mathematical order
that is present at every level of reality, and that connects them
together. Mersenne could have found in Kepler's *Harmonices
mundi* the idea of such an archetypal harmony, ordering each level
of reality, and innate to the human mind. He did not accept however
Kepler's rather dismissive view of music, which had led him to
define harmonics in purely geometrical terms, stripped from whatever
is sensorial and "acoustic" in it.



Contrary to what is sometimes held, the seeming adoption of an
integral mechanism in the last musical works is no renunciation of the
metaphysical consideration in harmonics. According to De Buzon (1994:
127, my translation), the causes and effects of consonance are indeed
treated physically, but the pleasure taken to harmonics, "albeit
an ordinary experience, is a phenomenon that is entirely
theological". Musical pleasure shows both our destination and
our state in this world. It raises us to the contemplation of the
divine unity, which is so to speak embodied in musical unison:



> 
> 
> consonances depend on the unison as lines on the point, number on
> unity, and creatures on God. That is why the more they approach it the
> sweeter they become; because consonances have nothing sweet nor
> agreeable but that which they borrow from union of their sounds, which
> is the greater as it approaches unison. (HU II: Livre Premier des
> consonances, 15, translated in Mace 1970: 13)
> 
> 
> 



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



In considering the general interconnection of sciences, Mersenne
granted music an almost architectonic function. All the sciences
borrow something from each other. As manifested in the encyclopedic
character of the *Harmonie Universelle*, music was for Mersenne
as the connecting principle of the various disciplines, allowing for
their exposition. A thorough investigation of musical properties
requires forays into theology, moral philosophy (the passions of the
soul), optics, arithmetic and geometry, and of course mechanics as
sounds are motions of the air, that have to be accounted for in a
mechanical way. Conversely, and at a deeper level, music may be seen
as a total science, theoretically capable of representing the
proportions that exist between all parts of the mechanical
universe:



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



In particular music may teach men how, through motions, objects
communicate their properties to the senses, which themselves are like
instruments, more or less well attuned to the external motions of the
sensible. Music would then become the general science of the
properties of the sensible, a kind of general aesthesis uniting mixed
mathematics in one universal science, whose acquisition would make our
elevation to the consideration of the first cause easier (QT:
161).