## 1. Du Chatelet's *Magnum Opus* on Natural Philosophy: *The Foundations of Physics*: Introduction to the text




It is likely that Du Chatelet's interest in writing a
text on Newtonian physics began to form around 1736 when Voltaire was
working through his own ideas for a text on Newton, eventually
published in 1738 (*Elements de la philosophie de
Newton*). Du Chatelet's distinct advantage over
Voltaire on this project was her superior mathematical training, given
that she sought out and benefitted from the tutelage of several of
Europe's leading mathematicians. One such engagement was to have
significant impact on both her own text on natural philosophy and on
the fate of her reputation as an original and innovative thinker. This was her
engagement with Samuel Koenig, who arrived at Cirey in 1739 to tutor Du
Chatelet in mathematics shortly after Du Chatelet
benefitted from similar tutelage under Maupertuis (Zinsser 2006,
162).




The significant--and positive--impact upon her text on
natural philosophy followed from the fact that Koenig brought with him
to France, and to Du Chatelet, the Leibnizian-inspired ideas of
Christian Wolff. This may have contributed to a critical change in Du
Chatelet's project, for Newtonian physics alone no longer seemed
to her to be the correct way of explaining various features of the
natural world. Still, it is quite possible that Koenig's influence on
Du Chatelet has been over-estimated, for when Du
Chatelet's earliest version of the *Institutions de
physique* (hereafter *Foundations*) was approved by the
censor Pitot--before Du Chatelet's tutoring sessions with
Koenig--Pitot mentioned that the text already contained ideas
from
 Leibniz.[1]
 Nonetheless, in her later, published version of the
*Foundations*, it is possible that she came to see more
forcefully the need for metaphysical foundations for the phenomena
that Newton so powerfully describes in mathematical terms (e.g. Janik
1982, 93 and 102). And so, in 1738, Du Chatelet withdrew her
*Foundations* from imminent publication in order to massively
redraft it. The final product, published in 1740, would include an
Introduction followed by ten chapters on topics of metaphysics
touching on issues such as the principles of knowledge (chapter 1),
God (2), space and time (5 and 6) and four chapters on matter and
bodies (7 through 10). Only then does the text deal with physics of an
essentially Newtonian character.




The significant--and negative--impact upon her reputation as
an original and innovative thinker followed from Koenig's accusation,
upon the publication of Du Chatelet's *Foundations*, that
she had plagiarized his ideas within the text, though given the point
made above, that Leibnizian ideas were already present in the text she
wrote before Koenig's arrival, his charge seems
misplaced. Nonetheless, this stain upon the originality and power of
Du Chatelet's intellect remained in some form or another until
the mid-twentieth century when William Barber concluded that her
thought was "essentially derivative" of a number of her
male contemporaries, particularly Voltaire (Barber 1967). Others have
argued for the originality of her views, and (Barber aside), this
interpretation has been the dominant one since Ira O. Wade presented
his careful case for her intellectual independence--again,
particularly from Voltaire (Wade 1947). In what follows, more evidence
is provided in favor of the growing belief that Du Chatelet is
not a mere parrot of her more famous male contemporaries' views.




One way of characterizing Du Chatelet's
*Foundations* is to show that it is a reaction against Cartesian
natural philosophy and in favor of Newtonian physics. In the main, this
is correct. Indeed, by the time Du Chatelet turned her attention
to the project of the *Foundations*, the popularity of Cartesian
natural philosophy was on the wane in France, the popularity of
Newtonain physics was on the rise, and Du Chatelet was in the
thick of these movements. Still, two facts should give us pause when
making the general claim just articulated. The first is that Cartesian
*natural philosophy* and Newtonian *physics* have
different scopes, with the former presenting a unified system of
metaphysics grounding and constraining the physics that follows from
the metaphysics. Indeed, Du Chatelet's commitment to
developing a natural philosophy (rather than writing simply about
physics) required that she find an appropriate metaphysics to ground
Newtonain physics, thus presenting a unified system to replace the (in
her and others' view) defunct system of Descartes.




The second fact that ought to give us pause is that Du
Chatelet was remarkably even handed and open minded about her
reaction to various thinkers. She seems to have been swayed neither by
national prejudice nor by the authority of whatever great men were most
favored in France in her time. She prescribed being guided by truth in
one's philosophical decisions about what to adopt and what to
reject from the various metaphysicians and physicists whose work was
animating intellectual circles in her time (IP *Avant-Propos*
VII, X and XI). She herself was remarkably in line with this principled
approach. So while it is true that, in the main, she rejects Cartesian
natural philosophy, she is still appreciative of Descartes'
advances in, for example, geometry, dioptrics and method (IP
*Avant-Propos* V, p.
 118).[2]




One interesting element of what could be characterized as her
admiration of Descartes' method is that the *Foundations*
fairly closely tracks the structure of Descartes' project in his
*Principles of Philosophy*. Both texts start with indubitable
principles of knowledge, which, in the first instance, lead to
conclusions about the metaphysics of God. These conclusions allow one
to gain knowledge of the metaphysical structure of the world, which in
turn grounds physical laws that allow the observer to make scientific
sense of the world (Lascano 2011, 742-3; c.f. Zinsser 2006,
173). This underscores at least that the two thinkers had a shared
interest in developing a unified natural philosophy with a well-worked
out, and fairly robust, metaphysics detailed first. Another highly
plausible reading of Du Chatelet's mimicking of Descartes'
mature work is that she sees herself offering a new natural philosophy
to replace the largely rejected Cartesian system, just as Descartes
before her aimed to replace the old Scholastic natural philosophy with
his *Principles of Philosophy*. This interpretation is born out
by a comparison of the two texts, for there are important divergences
between them, not just on the details in the metaphysics, but also on
the range of topics addressed. For Descartes' forays into what we
would now call "science" included not only astronomy and
physics, but planned sections on living bodies and on the human being,
including its soul, thus promising to touch on topics such as human
health and morals (in keeping with his metaphor of the tree of
philosophy offered in the preface to the *Principles*). In
contrast, Du Chatelet's text deals exclusively with physics,
leaving the broader array of natural philosophical topics and moral
philosophy left untouched. Still, the overall similarity in structure
between the two texts indicates her affinity, at least with respect to
her overall project, with Descartes. Here, we examine a few crucial
moments in her *Foundations*, underscoring how she and
Descartes compare and contrast on these points, with an eye to showing
some central aspects of her own brand of natural philosophy, and some
of the ways in which Du Chatelet fit (and did not fit) into the
French Enlightenment (especially with regard to Newtonianism and
scientific methodology).


## 2. First Principles of Knowledge




Descartes famously writes in the preface to the *Principles*
that "the whole of philosophy is like a tree. The roots are
metaphysics, the trunk is physics, and the branches emerging from the
trunk are all the other special sciences, which may be reduced to three
principal ones, namely medicine, mechanics, and morals" (AT
VIIIa, 14; CSM 1, 186). Metaphysics is his starting point, but
*what* Descartes means by metaphysics, and what falls under the
rubric of metaphysics for him, is crucial to understanding his project,
and for understanding Du Chatelet's conceptual relation to
him. One of the central innovations Descartes makes in the field of
metaphysics is to include metaphysical claims about the mind of the
knowing subject (Hatfield 1990, 11-17). This element of metaphysics
leads Descartes very quickly into a discussion of first principles of
knowledge, such as his belief that the knowing subject is capable of
rationally intuiting further metaphysical principles because God has
implanted innate ideas about them within human souls.




Du Chatelet's starting point--her first chapter
of the *Foundations*--is also a consideration of first
principles, but she starts immediately with first principles of
knowledge, and hers are very different from Descartes'. Indeed,
her first principles are distinctively Leibnizian and Wolffian, and
number exactly two; they are the principle of contradiction (hereafter
PC) and the principle of sufficient reason (hereafter PSR). In what
follows, we present some general ideas that are helpful to bear in
mind when thinking about Du Chatelet's use of the PC and
PSR. We then draw some important conclusions regarding these principles
as they are found in Wolff, noting points on which Wolff departs from
Leibniz with regard to first principles of knowledge. And finally, we
turn to a consideration of how Du Chatelet employs these
principles in her work.




There are a number of different ways of articulating the PC,
including the
 following.[3]


1. *A* is *A*, and cannot be ~*A*.
2. For any proposition *P*, it is not the case that *P* is
both true and false.
3. For any proposition *P*, *P* is either true or
false.
4. For any proposition *P*, if *P* is false, then ~*P*
is true.
5. For any proposition *P*, if *P* implies a contradiction,
then *P* is false.
6. For any proposition *P*, if *P* is or is reducible to an
identical proposition, then *P* is true.




(1) equates the PC with the Principle of Identity. (3) through (5)
bring together the Law of Non-Contradiction (hereafter LNC) and the Law
of the Excluded Middle (hereafter LEM) within the PC. These versions of
the PC rely upon opposition based in *contradictories*. That is,
P and ~P are mutually inconsistent and cannot be both true (LNC), and
they are mutually exhaustive (LEM). (6) relies upon the LNC only, and
not the LEM. This formulation of the PC, that is, relies upon
opposition based in *contraries*. For example, "P is
happy", and "P is sad" are contraries and thus
mutually inconsistent and cannot both be true (LNC). But they are not
mutually exhaustive, because they both can be *false* (and thus,
the LEM does not hold in these cases). The PC can be intended as a
logical, ontological or psychological principle. As a logical
principle, the PC is about opposite *assertions*. As an ontological
principle, the PC is about *properties* in a *subject*.
As a psychological principle, the PC is about what is possible and,
especially, impossible to believe. Finally, the PC can operate in
different realms. For example, it can operate in the realm of
*modality*, perhaps serving to pick out necessary truths.
Alternatively, it can operate in the realm of *standard areas of
human inquiry*, perhaps serving as the foundation of mathematics
(but perhaps not in metaphysics, natural theology, physics, and many
other disciplines).




As with the PC, there are different ways of articulating the PSR,
including the
 following.[4]


7. There is nothing that is without a reason why it is, and is not
otherwise. (Also: For any fact or event that obtains or exists, there
is some reason why it obtains or exists, and is not otherwise.)
8. There is no effect without a cause. (Also: any existing thing
must have something, either within its nature or outside of itself, as
its cause.)
9. For any proposition P that is true, there is an explanation for
its truth.
10. It is impossible to fail to account for something if you have
enough information (even though humans often do *not* have
enough information).
11. There are no brute facts.




The PSR embodies the position that everything is explainable and
thus intelligible. The PSR can also be used to explain a number of
different things, including the coherence of a thing's
*essence*, that essences have a *cause*, and the
*existence* of things. These points can also be captured by the
depiction of the PSR as the principle which accounts both for the
possibility of things (i.e. due to the coherence of their
*essences*), and for the actualization of essences (i.e. there
is a *cause* of their actualization which thus brings them into
*existence*). Sometimes the PSR is taken to have a very wide
domain (e.g. all truths and all events), while sometimes the PSR is
taken to have a narrower domain. For example, the domain of the PSR is
sometimes only events, but not truths, even while some truths (but not
mathematical truths) can be translated into events. Or, as another
example, sometimes the domain of the PSR is taken to be only the domain
of *contingent truths* but not *necessary truths*.
Sometimes the domain of the PSR is taken to be *all truths*,
with the sufficient reason for the truth of necessary truths being that
their negation violates the PC. There are different ways of thinking of
the relation between the PC and the PSR, the two most prominent being,
first, that the PC and the PSR are equally fundamental, and, second,
that only the PC is fundamental, with the PSR either playing a role of
secondary importance or being derived from or proven by the PC.
Finally, as with the PC, the PSR can operate in different realms. For
example, it can operate in the realm of *modality*, perhaps
serving to explain contingent truths. Alternatively, it can operate in
the realm of *standard areas of human inquiry*, perhaps serving
as the foundation of metaphysics, natural theology, physics, and many
other disciplines (but not mathematics).




As should be clear from the above, there is no single and settled
version of either the PC or the PSR, different thinkers employ them
differently, and sometimes a single thinker employs them differently in
different periods of their thought or in different texts and contexts.
In what follows, we sketch one respectable interpretation of
Wolff's use of these principles--together with notes on
where he departs from Leibniz's (admittedly multi-faceted) use of
the principles--at least in part because Wolff's approach
does seem to be fairly close to Du Chatelet's own.




For Wolff,[5] the
PC is fundamental, and it is an innate first
principle. Methodologically, Wolff starts with the psychological
impossibility of believing or judging that something both is and is
not. Wolff thus accepts version number 2 above of the PC, and he
starts with the first person awareness of one's psychological
inability to not accept the PC so presented. This psychological
awareness further reveals the logical impossibility of any proposition
that asserts that something is both true and false at the same time,
and the logical impossibility of a proposition that asserts contraries
further reveals the ontological fact that something cannot have
contrary properties. The PC first and primary job, then, for Wolff is
to divide impossible concepts and things--concepts and things
that embody a contradiction--from possible concepts and
things--concepts and things that do not embody a
contradiction. Possible concepts for Wolff include both necessary
truths and contingent truths. Thus, the fundamental and first job of
the PC for Wolff includes the work of dividing both necessary and
contingent truths from impossible truths. As result, in the realm of
modality, the PC serves to identify not only necessary truths, but
also contingent truths, *pace* Leibniz for whom, in the realm
of modality, the PC serves to identify necessary truths. Once
impossible concepts and things are isolated from the rest, the PSR
enters to further explain aspects of possible things. It does so in
two ways. First, the PSR acts as a "principle of being" in
the sense that there is a sufficient reason to explain the essence of
any possible being; there is a sufficient reason why a being's essence
is as it is. This role for the PSR is relevant in the case of both
necessary beings and contingent beings, and on this point, Wolff once
again divergences from Leibniz in that the latter often (though not
always) restricts the role of the PSR to that of providing an
explanation for why contingent beings, though not necessary beings,
are as they are. For Leibniz (usually), the PC explains why necessary
beings (and truths) are as they are. Still, the divide between Wolff
and Leibniz on this point may be narrower than it seems, because for
Wolff, the sufficient reason why a necessary being is as it is just is
that the PC establishes this. The second way in which the PSR enters
the picture to further explain aspects of possible things for Wolff is
that it acts as a "principle of becoming". In this role,
the PSR gives the causes or grounds for why a possible being becomes
actual as opposed to remaining possible but non-actual.




With this general background on our two great principles in place,
together with how these principles operate in Wolff (sometimes in
contrast with how they operate in Leibniz), we now turn to a
consideration of how these principles operate in Du
Chatelet's opening chapter of the *Foundations*.
While we cannot here do full justice to Du Chatelet's
account of the first principles of knowledge, we provide some essential
background to these principles in order to set the stage for an
evaluation of other central aspects of her natural philosophy as
presented in the *Foundations*.




As with Leibniz and Wolff, Du Chatelet's two primary first
principles of knowledge are the PC--'the basic axiom upon
which all truths are founded', which is consequently the
foundation of all certainty (SS4)--and the PSR (SS8).
These two principles operate *not* by opening up a category of
metaphysical truths that are innate to our minds. Rather, they operate
by giving universal (perhaps one would want to call these
innate)[6]
*procedures* for delineating what is possible from what is
impossible, and then for determining what is necessary and what is
actual (as opposed to non-actual) from among the range of
possibilities. Du Chatelet's first use of the PC, then, is
decidedly Wolffian for its task is to separate the impossible from the
possible.




The PC is foundational in all our thinking. At its most basic, this
principle seems to be, for Du Chatelet, the principle that: for
any proposition P, if P implies a contradiction, then P is false (5
above): 'For, if one once granted that something may exist and
not exist at the same time, there would no longer be any
truth...' (IP SS4). According to Du Chatelet once
this principle as stated is acknowledged, one can divide claims into
the impossible and the possible: 'It follows from this
[principle] that the impossible is that which implies contradiction,
and the possible does not imply it at all' (IP SS5). The
possibles include the possibilities from among which God created the
world.




But the PC does more work for Du Chatelet than just separating
out the possible from the impossible, and on this point, she leans more
toward Leibniz's use of this principle than toward Wolff's
use of it, for the PC secondarily divides the category of the possible
into truths that are necessary from those that are contingent. At this
second stage, she seems to be employing a new conception of the PC. To
show this, we examine her way of distinguishing between necessary and
contingent truths. Necessary truths are 'truths which can only be
determined in a single way, for this is what is meant by the term
*necessary*' (IP SS7). Immediately after this
(admittedly odd) definition she contrasts necessary truths with
contingent truths, 'that is to say, when a thing can exist in
various ways' (IP SS7), indicating that necessary truths are
claims about things that can exist in only one way. To use her own
examples to further clarify (IP SS8), geometrical truths are
necessary because, for example, a triangle (generally conceived) can
exist in only one way, i.e., it is a figure whose three angles added
together are equal to the sum of two right angles. We cannot conceive
of it in any other way. Conversely, truths about the posture Du
Chatelet finds herself in are contingent because she can exist in
many ways, i.e., standing, sitting, lying down and so forth. Implicit
here is a version of the PC which states that for any proposition *P* if
*P* is or is reducible to an identical proposition, then *P*
is necessarily true (6 above, with the modality of necessity
added). For 'triangle' and 'a figure whose three
angles added together are equal to the sum of two right angles'
can be reduced to an identity statement (triangles can exist only in
that one way) while 'Du Chatelet' and 'sitting
down' cannot be reduced to an identity statement (Du
Chatelet can exist in many other
ways).[7] A
crucial lesson to be drawn from her approach just outlined is that she
takes the human's everyday experience--including our
psychological inability to imagine, for example, necessary geometrical
truths differently than how they are--as telling us something
metaphysically true about the world itself. That is, like Wolff, she
starts with a psychological rendition of the PC, but draws ontological
conclusions from this starting point.




According to Du Chatelet, the PSR is '[t]he principle on
which all contingent truths depend...' (IP SS8). Given
what follows, the most consistent way to interpret Du Chatelet's
claim here is *not* to assume that the PSR picks out all
contingent truths, for this is clearly the work of the PC (when that
latter principle is used to identify necessary truths, with the
leftovers therefore being contingent). Rather, Du Chatelet seems
quite clearly to mean that the PSR explains why the contingent truths
*that actually obtain in the world* do obtain. Thus, she seems
to accept the second of Wolff's ways in which the PSR further explains
aspects of possible things: the PSR acts as a "principle of
becoming". It also acts as a "principle of being" in
so far as it explains essences, but it explains the essences of
contingent things, while the essences of necessary things are
explained by the PC for her (*pace* Wolff, but in keeping with
Leibniz's usual approach). So, immediately after her definition of the
PSR given above, she writes that:



> 
> 
> When asking someone to account for his actions, we persist with our
> own question until we obtain a reason that satisfies us, and in all
> cases we feel that we cannot force our mind to accept something without
> a sufficient reason, that is to say, without a reason that makes us
> understand *why the thing is what it is*, rather than something
> completely different. (IPSS8, emphasis added)




According to this interpretation of the PSR, it is the principle
that explains why some contingent truths actually obtain while others
do not (there is no sufficient reason for these others to obtain). The
PSR is also the reason that led God to actualize this world from among the
various possibilities (IP SS9); that is, to reiterate the
interpretation offered here, it is the principle that explains why our
contingent universe exists rather than any number of other such
possible, but not necessary, universes. The PSR serves as (a) the principle of
becoming (b) of contingent beings only.




Du Chatelet indicates what the PSR requires of us as
investigators of nature. In the closing sections of her chapter on the
nature of body (SS162-4), she makes clear that since full
knowledge of contingent truths is too complex for humans to grasp
through rational intuition (IP SS9), we need to turn to some other
way of learning them. But because God is bound by the PSR, we cannot
appeal directly to his will as the 'explanation' of these
truths, and so we must turn to proximate causes rather than the
ultimate cause for explanation. We must investigate nature in order to
try to discern causes of effects--that is, in order to discern
the sufficient reason why effects obtain. Empirical observations that
we have of how bodies actually do operate in the actual world will
lead the investigator to beliefs about features of bodies. These
features, however, are not taken to be certainly true as a result of
their being supposedly known by introspection into our innate ideas
(as they are for Descartes). It may be, therefore, that we are unable
to know the sufficient reason for why actuals exist as they do exist,
though we surely know that there *is* a reason, for our
experience tells us that actual beings were chosen to exist rather
than not to exist. But God knows the sufficient reason, and it is the
reason why he actualized the beings that he did: "Without the
principle of sufficient reason, one would no longer be able to say
that this universe, whose parts are so interconnected, could only be
produced by a supreme wisdom, for if there can be effects without
sufficient reason, all might have been produced by accident, that is
to say, by nothing" (IP SS8, p. 129).




Two important aspects of Du Chatelet's broader philosophy are
captured by this passage just quoted. The first is that she takes the
natural world to be a whole whose parts are systematically
interconnected. This natural systematicity is crucial to her
scientific method, it sets her apart from many of her French
Enlightenment peers, but there are nonetheless important limits to her
willingness to call upon systematicity in her approach to
investigations of the natural world. We address these points in
SS5 and SS6 below. The second important point implicit in the
above-cited passage is that she clearly sides with what we would now
call the intellectualist side of the voluntarist-intellectualist
debate. Crudely, the debate centers around whether God's will or God's
intellect takes precedence in his actions with respect to the created
world, including the act of creation itself. A voluntarist would say
that God's will takes precedence, and God could will anything to be
the case. Whatever he wills just would be true and
good *because* he willed it. Thus, God could have willed 2+2=5
to be true, and it would thereby be true. Conversely, an
intellectualist would say that God's intellect takes precedence in his
actions with respect to creation, including creation itself. He first
understands what is true and good, and then he wills that certain
things should attain
*because* his intellect understands the truth and goodness of
them (and his benevolence guides his choice). Earlier, Du
Chatelet wavered on how to interpret the relation between God's
will and intellect, but by the time she wrote the
*Foundations*, she had clearly settled for the intellectualist
side, and the PSR guides God in his choices no less than it guides
humans. On this point, she is squarely in opposition to Voltaire who
suggests that we should not search for, in his words,
"sufficient causes" in nature for natural phenomena;
rather we should bear in mind that the first cause of nature's
activities is to be referred to God's will and
 power.[8] 
It is enough to appeal
to this as the source of phenomena, and then leave it at that. Du
Chatelet dissents from this approach, and not just because it
mistakes, in her view, God's nature. Rather, it is an appeal we ought
not to make *as scientists* (IP SS162), for it is an
utterly unscientific approach to a natural problem, putting the cause
of the phenomena wholly beyond our ability to investigate 
 it.[9] 
We return to this point in SS5 below.




Two further points are of particular importance in Du Chatelet's
discussion of first principle of knowledge. The first is her noting
that the term "principle" "has been much
abused", especially by "the Scholastics, who could
demonstrate nothing [and who] chose unintelligible words for their
principles" (IP SS1, p. 125). The PSR, she later tells us,
banishes these unintelligible principles such as "plastic
natures, vegetative souls" (IP SS10, p. 131). Without
detailing how the PSR might banish such other principles, we focus on
Du Chatelet's own conception of the sort of intelligible
*metaphysical* principle identified by the PSR, for she favors
the mechanical philosophy over, for example, plastic natures and
vegetative souls. According to Du Chatelet, one must explain how
a mechanism can produce a plant relying, for example, upon an
explanation of how each particle of matter is able to produce the
effect that it does (IP SS10 and SS12, p. 131-2) through
simple motion. Accounting for natural change by appeal to bits of
matter interacting through lawful motion and contact--but not by
appeal to plastic natures and vegetative souls--is consistent
with the PSR.




The second point of particular importance in Du
Chatelet's discussion of first principles of knowledge is
what may be taken as her moderate form of nativism, in contrast with
Descartes' much stronger form. Du Chatelet does not have the
sort of first principles of knowledge, together with a commitment to
voluntarism, that lead to the doctrine of innate ideas, as we see in
Descartes. That is, Descartes has been characterized as a voluntarist
who believes that God created the eternal truths through an act of
will; God did not understand, through an act of the intellect, that the
eternal truths just are true independently of any will, his own
included. Fine details on Descartes' position with respect to the
voluntarist-intellectual debate aside, it is true that he does believe
God endowed all rational creatures with innate ideas of the eternal
truths such that we might all come to know their certain truth despite
the fact that they could have been otherwise. Du Chatelet does
not endorse this kind of nativism. But it is true that, unlike Locke
for
 example,[10]
she does think there are some
universally held principles such as the belief that something cannot be
and not be at the same time (PC), and to this degree, she does seem
committed to some sort of nativism. But because of her requirement that
one *demonstrate* a contradiction (in the case of the PC) or
that one *demonstrate* the reasons one has for one's
actions (in the case of the PSR, e.g. IP SS8, p. 128-9) in
employing these universally-held first principles of knowledge, her
nativism is of a different and weaker form than is Descartes'
nativism. Hers describes innate rules of reasoning that (as we shall
see) can then be used to develop a metaphysics, while Descartes'
nativism directly delivers robust metaphysical information about the
world. Once again, we see shall the impact of this characteristic of Du
Chatelet's starting point upon her methodology as well as
her understanding of the relation between physics and metaphysics.



## 3. God




One of Descartes' first *metaphysical* first principles that he
proves is the existence and nature (as benevolent) of God. His primary
reason for this is to call upon a benevolent God as a guarantor of the
truth of his clear and distinct ideas. Immediately after her
discussion of her first principles of knowledge, Du Chatelet
also turns to metaphysical first principles that can be derived from
the epistemology, and she too turns to a proof for the existence and
nature of God. But her reasons for doing so are different from
Descartes' immediate reasons as just articulated. For Du
Chatelet, as Marcy Lascano has rightly argued, "wanted to
provide a ground for physics that would explain the rational basis of
the workings of the universe. Proving that an eternal, good and
rational being created the universe would provide such a ground"
(Lascano 2011, 743). In Du Chatelet's words, "[t]he study
of nature elevates us to the knowledge of the supreme being; this
great truth is even more necessary, if possible, to good physics than
to morality, and it ought to be the foundation and conclusion of all
the research we make in this science" (IP SS18, p. 138). As
shown above, Du Chatelet believes in the interconnectedness and
systematicity of the natural world as a whole, and she believes that
this is a crucial general reason why God has chosen to actualize this
world. And so, it seems humans *do* have cognitive access to
this sufficient reason for why God chose this world as opposed to any
other world. In fact, Du Chatelet links the interconnectedness
and systematicity of the natural world as a whole with perfection
(SS26), thus indicating that God's sufficient reason for his
choice of this world over any other possible worlds in a further
principle, namely, the Principle of the Best. Du Chatelet's
belief in the interconnectedness and systematicity of the natural
world as a whole is the key to her method and physics, even though
(as shown below) there are limits to the role that can be played in
physics by these metaphysical features of the world. Nonetheless,
establishing the existence of God as one who would choose to actualize
such a world is Du Chatelet's next crucial step.




We shall not go into the details of her argument for the existence and
nature of God (see Lascano 2011). We simply note here that hers is a
cosmological argument for the existence of God, specifically one
starting from the existence in the world of contingent beings. Thus,
her distinction between necessity and contingency as developed in her
material on the PC and the PSR, together with further use of the PSR
in her chapter on God, lead to her particular proof for God's
existence. She argues:



>  All that exists has a sufficient reason for its
> existence. The sufficient reason for the existence of a being must be
> within it, or outside it. Now the reason for the existence of a
> contingent being cannot be within it, for if it carried the sufficient
> reason for its own existence, it would be impossible for it not to
> exist, which is contradictory to the definition of a contingent
> being. So the sufficient reason for the existence of a contingent
> being must necessarily be outside it.... This sufficient reason
> cannot be found in another contingent being, nor in a succession of
> such beings, since the same question will always arise at the end of
> this chain, however it may be extended. So it must come from a
> necessary Being that contains the sufficient reason for the existence
> of all contingent beings, and for his own existence, and this being is
> God. (IP SS19.5-6, p. 139, translation altered)




Lascano has noted the influence of both Leibniz and Locke on Du
Chatelet's cosmological proof (Lascano 2011,
*passim*). She also notes that Du Chatelet makes a similar
mistake to one Aquinas makes in his Five Ways, in assuming that an
infinite chain of causes cannot simply extend into the past with no
need of a supermundane cause (Lascano 2011, 756). It is a shame that Du
Chatelet's acquaintance with the ideas of Samuel Clarke
(Hutton 2012) did not extend as far as his cosmological proof from
contingency to necessity for the existence of God, for if it had, then
perhaps she would have sidestepped this error. Nonetheless, again as
Lascano points out, her proof is a notable improvement on
Locke's, and the key point to be drawn from her discussion of
God is that articulated above, namely the importance to Du
Chatelet's scientific endeavors of God and the nature of
the world he creates.


## 4. Metaphysics




In the preface to the *Foundations*, Du Chatelet writes:
"It is certain that there are a number of points in metaphysics
which lend themselves to demonstrations just as rigorous as the
demonstrations of geometry, even if they are different in kind"
(*Avant-propos*, XII). Du Chatelet's first
epistemological principles thus help to establish what she takes to be
the certain truth of some metaphysical claims. At least two of these
claims, she believes, are necessarily true (see below for the kind of
necessity at work here). So, for example, and echoing Leibniz, because
of the infinite divisibility of extension, and because atoms are
extended, atoms cannot be the ultimate beings of nature; simple
substances (or monads) must be such beings, and the PC establishes
this *necessary* (in Du Chatelet's mind) metaphysical
fact (IP SS121). The argument for this runs as follows. Atoms,
defined as *indivisible*, extended particles of matter are
actually *divisible*, and thus their very definition, taken
together with the fact of their divisibility, implies a contradiction.
So atoms cannot be the necessary beings out of which matter is
composed; indeed, they are by definition impossible. How does Du
Chatelet justify the claim to atoms' divisibility? She justifies
this claim based upon the PC: 'there is no contradiction in the
divisibility of extended things,' and atoms are extended thing
(IP SS121). Notice here, she must be relying upon a conceptual
divisibility rather than a physical divisibility (for atoms are
defined as *physically* indivisible), though one could bolster
this argument by claiming that if an atom is conceptually divisible by
us, then it is physically divisible by an omnipotence God, and
therefore is in neither way indivisible. Indeed, the divisibility of
*anything*--atoms or something else--that is extended
indicates that extension is *composed* and not simple; it is
composed out of the parts into which it can be divided (IP
SS120). So nothing extended--neither atoms nor any other
piece of extension--can serve as the simple beings out of which
composed beings are made. Only things that are unextended can serve as
those simple beings (IP SS122). Since this conclusion follows from
the PC, it is a conclusion about the *necessary* constitution
of the simple beings of our universe.




This introduces a further feature of Du Chatelet's PC in
addition to those identified above. The PC, in the case of simple
beings, establishes both the necessary *existence* and
*nature* of simple beings. That is, simple beings are
necessarily unextended (their nature), and they necessarily must exist
so as to explain the fact of existing composed, extended
beings--a fact established by our experience that such composed
beings do indeed exist. But this is what we might call a
*hypothetical* necessity (as opposed to what we might call an
*absolute* necessity). That is, these necessary facts about the
simple beings of our world obtain only on the hypothesis that our
world actually does exist. God could have not created our world, and
had he so chosen to not create any world, then simple beings which
actually exist (with the nature of being unextended) need not have
existed at all.




This discussion of Du Chatelet's understanding of the (hypothetically) 
necessary metaphysical constitution of the world further underscores a
point about her first principles of knowledge mentioned above. While
the fundamental metaphysical truth that only unextended beings can
serve as the simple beings of the created world--simple beings
out of which complex beings are made--may be repugnant to sense
and imagination, reason (as captured by her PC in this case) demands we
believe it (IP SS135). But this indicates that Du 
Chatelet--like Wolff--may start with a psychological conception of
the PC, but (again like Wolff), she takes this psychological conception
of the principle to indicate that there are underlying logical and
ontological truths which are the source of our psychological response
to contradictions. So one of Du Chatelet's first
principles, in this case, gives us knowledge of metaphysical essences.
Importantly, Du Chatelet takes her conclusion that substances
must be simple in the way just characterized to be necessarily
true on the hypothesis that God chooses to actualize our world.




Moreover, she even uses her PSR to establish other claims about
material substance, claims that she also takes to be necessary in the
same sense of necessity that applies to simple beings (i.e. what we
may call "hypothetical necessity" above). In using the PSR, we observe the
phenomenal facts of our actual world, and we can then posit hypotheses
about what must further be true of substance in order to make those
facts 
 possible.[11]
 We see this method at work in several
sections of the *Institutions*; for example, monads are active,
she concludes, because this would explain the brute fact of motion in
the phenomenal world, and she goes so far as to claim that force is
also necessary to the nature of matter (IP SS139). At the same
time, precisely because things do not always move in the natural
world, this force must be of two kinds: active force--the source
of motion--and passive force, or inertia--the source of rest
(IP SS142). From her letter to Maupertuis of 30 April 1738 (#122),
we know that she was familiar with Leibniz's work on dynamics and
metaphysics, having sought out his articles on the
topics--articles such as "The Brief Demonstration of the
Error of Descartes" and "A Specimen of Dynamics". So
again, phenomena of our actual world that Leibniz details in those
papers lead Du Chatelet to the same conclusions regarding the
metaphysics of substance that Leibniz reaches--namely, that the
unextended simple substances are also internally active, as well as
constrained in their activity, through their possession of active and
passive force, as this claim helps explain the phenomena of the
natural
 world.[12]




Precisely because the elements of matter are simple, unextended active
monads, what we see around us as extended must be merely phenomenal,
and she does endorse this 
 Leibnizian-Wolffian[13]
conclusion.
Throughout her seventh chapter "On the Elements of Body",
she follows the Leibnizian tradition in concluding that metaphysical
reality must consist in unextended monads. Consequently, what we see
in nature as extended must be mere phenomena and not real in the
fullest metaphysical sense. She concludes, for example, that
phenomena, known best through sense, result from the confusion of
simple beings (IP SS152-5), and that just as monads are
characterized by active and passive force (now termed primitive
force), so too are phenomenal bodies to be thought of as possessing
force--both derivative active and passive force (IP
SS158-9). Thus, suppositions such as Newton's that the
natural world can be described with reference to inelastic, invisible,
extended atoms must be suppositions not about ground floor metaphysics
but about the derivative physical world *which is merely
phenomenal* in a broadly Leibnizian sense. This has led Linda
Janik to helpfully characterize Du Chatelet's account of the
created world as a three-tier account (Janik 1982, 106): the basic
metaphysical tier of unextended monads, the subvisible physical tier
of (for Du Chatelet) extended matter which is also imbued with
derivative force, and the visible physical tier of bodies in motion
and at rest. Without working through the details of her picture,
including the coherence or difficulties with it, what this three-tier
account permits is significant separation between metaphysics and
physics. We see this when we consider the following. We can know
*that* there is a systematic interconnection among all elements
of the created world--the PSR, together with what we can derive
of God's nature seem to establish this for Du Chatelet--we
cannot always know all the details of that systematicity. Moreover, we
can expect that this systematicity occurs most fundamentally at the
level of ground floor metaphysics--that is, among unextended
monads. But Du Chatelet does not spell out in detail how exactly
the metaphysical tier and physical tiers are related to each other
(Iltis 1977, 36-7). And so, while the systematic
interconnectedness we experience at the level of phenomena--the
realm of physics, that is--surely has *some* grounding in
metaphysics, crucially, we cannot know many details of the connection
among realms. While it is certainly true that there is some connection
between the metaphysics and physics--for example, the force,
which belongs to monads explains the brute phenomena of motion and
rest in the physical world--physics does enjoy significant
autonomy from metaphysics (Janik 1982, 106; Barber 1967, 
 209).[14] 
We see the impact of
this on her physics in SS6 below.


## 5. Scientific Methodology




Du Chatelet herself spent time running extensive experiments to
gain understanding of various natural phenomena. She set up a lab at
her estate Cirey in which she and Voltaire both undertook experiments
(e.g. Walters 1967). Her descriptions of experiments undertaken to
determine the nature and propagation of fire in her *Dissertation
on the Nature and Propagation of Fire* attest to this fact. She
was also well educated on scientific advancements of her day, most
especially in astronomy and physics. Her comments in the
*Foundations* on scientific methodology focus primarily on her
analysis of the method of great astronomers and physicists. Here, we
focus on her explicit theorizing on the role of hypotheses in science,
for her views on this topic place her clearly at the start of the
hypothetico-deductive tradition in scientific methodology.




At the close of her chapter on hypotheses, Du Chatelet's
 writes: [15]



> 
> 
> And so good hypotheses will always be the product of the greatest
> men. Copernicus, Kepler, Huygens, Descartes, Leibniz, and even Newton
> himself, have all devised useful hypotheses to explain complicated and
> difficult phenomena. The example of these great men, and of their
> successes, should make us see that those who wish to ban hypotheses
> from philosophy, intend harm to the interests of science"
> (IP
>  SS71).[16]
> 




In this declaration, Du Chatelet establishes how out of 
step--though not necessarily entirely to her detriment--she was
with her own milieu. Members of the Royal Society in Britain and
Academie Royale in France in the 18th century tended to
eschew the use of hypotheses, preferring what they took to be a
scientific focus on empirical
 facts.[17]
Moreover, Newton was seen by
many of his admiring contemporaries to have captured the value of the
Societies' approach in his scientific practice and in his famous
 motto *hypotheses non
 fingo*.[18]
Among the most vocal
spokespersons in eighteenth century France for this approach was none
other than Du Chatelet's housemate during her years spent
drafting the *Foundations*, Voltaire who, in his *Elements of
Newton's Philosophy*, contrasts Descartes and Newton along
exactly these
 lines.[19]
In siding with the use of
hypotheses, in once again lauding Descartes for this aspect of
his
 method,[20]
and in suggesting that
Newton himself makes use of hypotheses, Du Chatelet establishes
herself as no mere mimic of 'greater' men of her time. The
fact that this highly innovative chapter survives her massive rewrites
after her tutelage under Koenig also throws into question the doubt
cast upon her originality by Koenig's charge of
plagiarism. Indeed, close examination of the manuscript of what
remains of Du Chatelet's earliest version of the
*Foundations* in the Bibliotheque nationale de France
discloses that her chapter on hypothesis is much more well-worked out
than surrounding chapters, many of which have two significantly edited
drafts. This indicates that she may have fairly clear ideas on this
chapter, even while her thoughts on the rest of the first half of the
book are in considerable
 flux.[21]




Du Chatelet distinguishes those who use hypotheses well from
those who use them badly, and she recognizes a third 
group--those who eschew the use of hypotheses altogether largely due to
perceived misuse of them among their predecessors and contemporaries.
Among those who use hypotheses poorly are those working in the
Cartesian tradition and those in "the Schools" who are
especially guilty of spouting unintelligible jargon (IP
*Avant-Propos* VIII, SS55). The key downfalls of those who
make bad use of hypotheses are the mistakes of taking them as truth (IP
SS62-63), and of building theories and systems upon them that
resemble "fables" and "dreams" (IP SS55)
more than they resemble a science of nature firmly rooted in empirical
knowledge of nature. As a consequence of previous abuse of hypotheses,
Du Chatelet notes that many in her own century have entirely
shied away from their use--or at least claim to have done 
so--which they regard as (quoting Newton) the "poison of
reason and the plague of philosophy" (IP SS55). Du
Chatelet stresses that it is a mistake, however, to believe that
hypotheses are useless in physics just because they have been abused in
the past (IP SS63), and she suggests that hypothetical thinking is
not only useful, but indeed necessary; without hypotheses, almost no progress
would have been made in astronomy (IP *Avant-Propos* VIII,
SS57), and they are also valuable in physics (IP SS55). She
even goes so far as to claim "without hypotheses... there
would be no astronomy now" (IP SS57). To bolster her case,
she details a few recent successes in astronomy which relied pivotally
on the use of hypotheses with theories of Copernicus (IP SS57 and
SS67), Kepler (IP SS58) and Huygens (IP SS57 and SS67)
featured as evidence. Those who refuse to include hypothetical thinking
in their scientific method are guilty of retarding the progress of
science no less than are those who include such thinking but do so
badly (IP SS54).




Du Chatelet believes that hypotheses are *necessary*
because not all phenomena can be explained through reliance upon first
principles alone--there is a gap between first principles and
observed phenomena in the world in the sense that the scientist cannot
deduce the cause of those phenomena directly or through chains of
deduction from the first principles. Neither can experiment directly
tease out such a cause. "Hypotheses are... sometimes very
necessary... in all cases when we cannot discover the true reason
for a phenomenon and the attendant circumstances, neither *a
priori*, by means of truths [identified as principles in SS53]
that we already know, nor *a posteriori*, with the help of
experiments" (IP SS60). And: "[P]hilosophers frame
hypotheses to explain the phenomena, the cause of which cannot be
discovered either by experiment or by demonstration" (IP
SS56).




Recall that for Du Chatelet, these first principles include
epistemological principles--the principles of contradiction and
sufficient reason (IP SS4 and SS8). Du Chatelet writes
that "a hypothesis... [must] not be in contradiction with
the principle of sufficient reason, nor with any principles that are
the foundation of our knowledge" (IP SS61). But, presumably,
the principles constraining the sorts of hypotheses the scientist can
posit also include metaphysical principles which can be derived
directly from foundational principles of knowledge. For Du
Chatelet, as shown above, these include the three-tier
metaphysical account she develops, the nature of matter, and so
forth.




In her opening comments on hypotheses, Du Chatelet writes:
"The *true causes* of natural effects and of the phenomena
we observe are often so far from the principles on which we can rely
and the experiments we can make that one is obliged to be content with
probable reasons [hypotheses] to explain them" (IP SS53
emphasis added; c.f. SS56). She anticipates that these probable
reasons aim at truth about the causal structure of the world and not
just at an accurate description and prediction of phenomena. This is
interesting because this situates Du Chatelet squarely within one
particular tradition with respect to hypotheses. Historically, there
have been two key directions in which thinking about hypotheses
developed, indeed from Ancient times, and certainly throughout the
seventeenth and eighteenth centuries as well. According to one 
approach--typified by Ptolemy in pre-modern thought and sometimes
associated with "save the phenomena" type 
explanations--hypotheses are posited merely because they are useful
instruments, mere mathematical calculating devices especially useful
for prediction and scientific practice. The aim with hypotheses,
according to this approach, is not to propose a *true* account
of the nature of things since reaching true conclusions about the world
is not necessarily relevant when formulating hypotheses according to
this tradition which focuses more pointedly on prediction. According to
the second approach--typified by Aristotle in pre-modern thought
and sometimes associated with causal explanations--hypotheses
are posited in order to provide an explanation of how experienced
effects might have come about. The aim is to give a *true*
account of the nature of things, especially the causal nature
of
 things.[22]
In starting off her chapter
on hypotheses with a mention of "the true causes of natural
effects", Du Chatelet indicates her commitment to the
Aristotelian tradition *vis a viz* hypotheses, a point
which becomes abundantly clear as her chapter on hypotheses
proceeds.




Du Chatelet thinks hypotheses are useful (in addition to their
providing a necessary step in scientific method) because "when a
hypothesis is once posed, experiments are often done to ascertain if it
is a good one, experiments which would never have been thought of
without it" (IP SS58). They are useful, that is, for
suggesting innovative experiments. Such experiments can add
plausibility to a hypothesis if the results of them indicate that the
hypothesis captures the truth, but a single experiment which falsifies
a hypothesis is enough to require the scientist to reject it, or at
least, to reject whatever part of the hypothesis is deemed faulty, for
a hypothesis "can be true in one of its parts and false in
another" (IP SS65). As an example to explain how this might
be the case, she cites Descartes' hypothesis of a vortex of fluid
matter being the cause of the gravitational pull of bodies to the
earth. As an example of her remarkable open-mindedness, she rejects the
specifics of Descartes' hypothesis in light of Huygen's
demonstrations that it does not square with observed facts, while also
allowing that "it cannot be legitimately concluded that a vortex,
or several vortices, conceived of in a different way, cannot be the
cause of these movements" (IP SS65). In this case, then,
falsifying data requires that we invalidate only part of
Descartes' hypothesis.




So Du Chatelet takes an extremely friendly view of the role of
hypothesis in scientific reasoning. Still, wary of those who make bad
use of hypotheses, Du Chatelet puts strict limits on their use. A
hypothesis must "not only [explain] the phenomenon that one had
proposed to explain with it, but also that all the consequences drawn
from it agree with the observations" (IP SS58). Herein, we
have the idea that a good hypothesis will explain a plethora of effects
including many not originally under investigation. Du Chatelet
believes that the more such effects that can be explained (as well as the more
experiments performed which turn out as predicted by the hypothesis),
the more probable the hypothesis is. Indeed, Du Chatelet makes
the very strong claim that "hypotheses finally become truths when
their probability increases to such a point that one can morally
present them as certain" (IP SS67), though the
*psychological* context of the passage ("as a very great
degree of probability gains our assent, and has on us almost the same
effect as certainty") indicates that a highly probable hypothesis
is merely highly probable and not strictly true, and 
that Du Chatelet's considered position
is "that hypotheses become the poison of philosophy when they are
made to pass for the truth" (IP, *Avant-Propos*
 VIII)[23].
According to Du Chatelet, part of the scientist's job is to
"have certain knowledge of the facts that are within our reach,
and to know all the circumstances attendant upon the phenomena we want
to explain... for he who would hazard a hypothesis without this
precaution would run the risk of seeing his explanation overthrown by
new facts that he had neglected to find out about" (IP SS61).
So the scientist must become acquainted with many empirical facts so as
to ensure that she is not ignorant of potentially falsifying data (IP
SS64).




Du Chatelet's belief that hypotheses gain strength the
more phenomena they explain indicates a commitment to the idea of
simplicity and systematicity of causes, and the orderly
interconnectedness of cause and effects in the created world. These
features, to recall the discussion above of her PSR, are explicitly
associated with the PSR, and that principle's
*metaphysical*
 dimension.[24]
For not only is the PSR a
principle which guides our own search for knowledge, it is a principle
which guided God in his choices when creating the world (IP SS23)
which, as the best possible world, is "the one where the greatest
variety exists with the greatest order, and where the largest number of
effects is produced by the simplest laws" (IP SS28). So the
ability of hypotheses to explain a plethora of phenomena is a direct
result for Du Chatelet of the real systematicity of the
world's causal structure
 itself.[25]
This point drives home the
suggestion made above that Du Chatelet is squarely in the
Aristotelian tradition with respect to hypotheses; hypotheses are meant
to capture the true causal structure of our systematically
interconnected world, and are not only calculating or predictive
devices by which the scientist merely gives an accurate description of
the phenomena. At the same time, and we shall see this in the next section,
the fairly significant degree of separation between metaphysics and 
physics mentioned at the close of the previous section will put 
strict limits on how much the scientist can appeal to systematic
interconnectedness in 
 physics.[26]




To conclude, let me turn to Du Chatelet's definition of
a useful hypothesis:



> 
> 
> So hypotheses are only probable propositions, which have a greater
> or lesser degree of probability according to whether they satisfy a
> larger or fewer number of the circumstances that accompany the
> phenomena that we want to explain by means of the hypotheses. And since
> a very high degree of probability encourages our agreement so as to
> have nearly the effect upon us as certainty, hypotheses eventually
> become truths for us if their probability increases to such a point
> that this probability can morally pass for certainty.... In
> contrast, an hypothesis becomes improbable in proportion to the number
> of circumstances found for which the hypothesis does not give a reason.
> And finally, it becomes false when it is found to contradict a
> well-established observation. (IP SS67)




At the start of this section, we mentioned that Du Chatelet is at
the forefront of the emergence of the embrace of the
hypothetico-deductive in scientific explorations. Some have attributed
such a method to Descartes (e.g. Lauden 1981) while others have
disputed this, due to his refusal to devise testing experiments and to
take falsifying data seriously (McMullin 1990, 44; McMullin 2008, 98;
and Sakellariadis 1982, *passim*). On both points, Du
Chatelet departs notably from Descartes due to her very
friendliness to this sort of engagement with the empirical.
Nonetheless, as also mentioned above, she is somewhat out of step with
her own time precisely because of her unabashed endorsement of the
need for hypotheses. Moreover, her endorsement of the Aristotelian
idea of hypotheses, and her belief in the systematic unity of the
natural world, shows that she also embraces there being a relation
between metaphysics and physics, even while she also believes that
there are limits to what we can know about that relation. This is no
surprise given our characterization of her above as a natural
philosopher, a pre-modern stance despite her standing on the cusp of
modern conceptions of hypotheses and scientific methodology. She is
truly standing between two worlds, the old world of natural philosophy
and the soon to emerge new world of modern science as we now know
it.


## 6. Newtonian Attraction




The first ten chapters of the *Foundations* provide the
epistemology, metaphysics and theorizing on scientific methodology
that is meant to provide the foundations for the remaining chapters on
Newtonian physics. An evaluation of the success of that seemingly
paradoxical project must await a much more sustained treatment than
can be given here. Rather, in this final section of this survey of
Du Chatelet's natural philosophy, we focus on one chapter of that
later material both to show ways in which the earlier chapters affect
those that follow, and to show the limits to the characterization of
Du Chatelet as a metaphysical
 systematizer.[27]
 This chapter is chapter 16: On Newtonian Attraction.




In this chapter, she argues against some of Newton's followers
who aimed to universalize Newton's attraction. While Du
Chatelet argues that Newton's theory of attraction is
better than Descartes' vortices at explaining the effects of
gravity, and that Newton's theory of attraction can
satisfactorily explain a wide range of other phenomena such as tidal
movements, the rotation of the earth, and irregularities in the
movement of the moon, she criticizes Newton's disciplines for
extending Newton's theory of attraction too far. In one
especially interesting section, she focuses on the Newtonian theories
(IP SS389-92) of John Freind (1675/76-1728) and John Keill
(1671-1721).




In SS391, titled "The usage that Mss. Freind and Keill have
made of the principle of attraction" (notably, she discusses only
Keill therein), she writes:



> 
> 
> 
> At the end of his *Introductio ad veram Astronomiam*
> (*Introduction to the True Astronomy*), Mr. Keill set several
> propositions, through which he maintains we can deduce geometrically
> the majority of phenomena by means of this attraction, if it is
> powerful in contact.
> 
> 
> 
> 
> According to these propositions, not only are cohesion and chemical
> effects the result of attraction, but so too are the spring of bodies
> and the phenomena of electricity....
> 
> 
> 
> 
> We find the source of all these applications of attraction in the
> questions that Mr. Newton posed at the end of his
>  *Optics*.[28]
> The disciples of this great
> man believed that his doubts might serve even as a basis for their
> hypotheses: but it must be admitted that *some of these hypotheses
> are a bit forced* and that there is a great difference in accuracy
> between the applications of attraction to celestial phenomena and the
> use one makes of it in the other effects just mentioned. Also this
> use of attraction is not as universally received by the same
> Newtonians, as the use of it when one is in fact explaining
> astronomical phenomena. (IP SS391; emphasis
>  added)[29]
> 
> 
> 
> 




In essence, what Du Chatelet disputes in Keill's
universalization of Newton's theory of attraction is his use of
it to explain, among other phenomena, the cohesion of bodies and their
spring, or elasticity. To make *these* claims, which focus
specifically on features intrinsic to bodies rather than on relational
features that bodies bear, Du Chatelet believes these thinkers
must claim that attraction is a property of matter itself
(IP
 SS389-92).[30]
Her mention in this passage
of his "forced" hypotheses alerts us to the fact that she
believes Keill is using hypotheses in forwarding this claim about
matter. As the previous section showed, she can have no quibble
with the fact that he uses hypotheses, yet she clearly dissents from his
hypotheses with respect to the nature of matter and the phenomena he
wishes to explain through this matter theory.




According to Du Chatelet, the PSR positively rules out extending
attraction to account for the nature of matter. How so? The argument
seems to be that if attraction (as some sort of *active*
principle or force) were to be inherent in bodies, then bodies would
always move, and yet bodies always moving is contrary to our
experience of the physical world. There is no sufficient
reason--an inherent *passive* principle within bodies, for
example, to counteract the active force--to account for the brute
fact that bodies are also sometimes at rest. So attraction cannot be
an inherent property of matter (c.f. IP *Avant-propos*
VII). Yet for attraction to explain the cohesion of bodies, it would
need to be an inherent property. So attraction cannot be employed as
the cause of the cohesion of bodies.




Three crucial points for a consideration of Du Chatelet's
scientific method and her position between pre-modern and modern
conceptions of natural philosophy and then science emerge from this
discussion of Newtonian attraction. First, the role played by
experience of the world is crucial for her. If our experience (in this
case, the brute fact that bodies are sometimes at rest) falsifies an
hypothesis (namely, that attraction belongs to matter), then the
hypothesis must be rejected. Second, while Du Chatelet accepts
the systematic interconnection of the created world as a feature of
it, and as a sort of heuristic in our scientific practice, she puts
strict limits on the scientist's appeal to a systematic account of
phenomena, especially in light of falsifying experience. So, while the
universalizing of Newton's theory of attraction to account for a
plethora of phenomena would represent a more interconnected physical
system, this systematicity must be rejected in light of our
experiences of nature. Finally, while it is true that Du
Chatelet thinks a full scientific account must try to give the
causes of phenomena we experience--whether those be causes in the
basic metaphysical tier or causes in the derivative, subvisible
physical tier--when scientists are unable to give a causal
account without violating the empirical facts of nature, then they
ought *not* to give such an account. So while it is true that
Du Chatelet invokes hypotheses in her approach to natural
philosophy, and while it is true that in doing so, she departs
radically from those who believe that the aim of science is to merely
describe (ideally in mathematical terms) the phenomena without appeal
to metaphysical systems underlying those phenomena, the
particular--indeed, very modern--flavor of her theory of
hypotheses puts strict limits on that metaphysics. This underscores
the point made at the close of SS4 above: there is a connection
between metaphysics and physics in Du Chatelet's view, but we
are not always able to ascertain that connection, and so, the
scientist cannot claim systematic unity in physics when doing so runs
roughshod over empirical data or either of her two foundational
principles. While still a natural philosopher, she has taken a
decisive step toward modern science in her masterwork, *Foundations
of Physics*.