## 1. Placing Newton in the history of natural philosophy



Traditionally, Newton would be characterized as a mathematician for
his work on the calculus and as a scientist for his work in physics.
His celebrated talent in mathematics is perhaps equaled not only by
his profound theorizing concerning the physical world, but also his
influential experimental methods. Indeed, Newton is remarkable for the
fact that his work as a theoretician is matched by his work as an
experimentalist--either aspect of his *oeuvre* would be
sufficient to secure his place in the history of modern science. So in
the popular imagination, and in the history books, Newton is seen as
one of the greatest scientists of the modern period, on a par with few
others (perhaps Darwin or Einstein). This view will continue to
dominate our understanding of Newton in the twenty-first century.



If we attempt to understand Newton's work from an historical
point of view, however, a more complex conception emerges. When Newton
published his principal works, he was not contributing to a
well-established field, he was helping to create modern mathematical
physics. This meant that few of his ideas, methods, or approaches,
whether in mathematics or in experimental physics, could be taken for
granted. From his first papers in the early 1670s, on optics, until
his last days working on the third and final edition of his magnum
opus the *Principia* decades later, philosophers,
mathematicians and experimenters challenged Newton's approach.
This frequently upset Newton, who had a famous, lifelong aversion to
intellectual debate and controversy. But in a sense, it helped to
ensure the importance of Newton's ideas for philosophy.
Obviously, Newton never wrote a philosophical text on the order of
Descartes's *Meditations*, Locke's *Essay*,
or Spinoza's *Ethics*. He never produced what the
*lumieres* who studied him would have called a
"system" of philosophy. But the intense controversies
produced by his mathematical, empirical and philosophical methods and
ideas continually prompted him to broach philosophical topics (Janiak
2015). As a result, he was widely considered a leading philosopher
throughout the Enlightenment. In the first modern history of
philosophy, Brucker's *Historia Critica Philosophiae*,
Newton plays a central role in discussions of the modern era (Volume
4.2: 639-55). He is also a central figure in D'Alembert's
discussion of the emergence of modern science and philosophy: Newton
is listed along with Bacon, Descartes, Locke and Leibniz as a key
figure in the *Preliminary Discourse* (80-83).



The eighteenth-century tendency to discuss Newton's
*philosophy*, rather than his *science*, may have an odd
ring to modern ears. In this case, however, the evolution of the
English language tracks a substantive intellectual development. As a
matter of historical fact, the category of the scientist--along
with that word in English--is a nineteenth-century invention.
Specifically, at a meeting of the British Association for the
Advancement of Science in June of 1833, the Cambridge philosopher
William Whewell coined the word "scientist". Whewell said
that just as the practitioners of art are called
"artists", the practitioners of science ought to be called
"scientists", indicating that they should no longer be
called
 philosophers.[1]
 Indeed, before the early nineteenth century, people like Newton were
called "philosophers", or more specifically,
"natural philosophers". During the seventeenth century,
and well into the eighteenth (at least until 1750, if not later),
figures like Newton worked within the century's old tradition of
natural
 philosophy.[2]
 The modern disciplines of physics, chemistry, biology and so on, had
not yet been formed. (The *words* 'physics' in
English, 'physique' in French, and 'physica'
in Latin were often used, but had a very broad meaning, like
"natural philosophy.") Philosophers who studied nature
investigated such things as planetary motions, the nature of matter,
and the possibility of a vacuum, but they also discussed many aspects
of human beings, including the psyche, and how nature reflects its
divine creator (Hatfield 1996). As the title of Newton's magnum
opus, *Philosophiae Naturalis Principia Mathematica*
(*Mathematical Principles of Natural Philosophy*), suggests, he
intended his work to be in dialogue with Descartes's
*Principia Philosophiae* (*Principles of Philosophy*,
1644). Descartes's *Principles* is a complex text that
includes discussions of everything from the laws of nature to the
nature of God's causal influence on the world. Descartes had
famously promised that his physics required nothing more than the
principles of geometry and pure mathematics (*Principles*, Part
Two, SS64). Although Descartes was a great mathematician, the
author of a major work in geometry in 1637, Newton thought nonetheless
that he had not lived up to this promise, so he would assuredly
introduce *mathematical principles* for natural philosophy.
Just as Descartes had sought to replace Aristotelian or
"Scholastic" methods and doctrines in natural philosophy,
Newton sought to replace Descartes's. It is therefore more
historically accurate and more illuminating to interpret Newton within
the historical stream of natural
 philosophy.[3]



As is well known, natural philosophy in the Aristotelian traditions of
the thirteenth through the sixteenth centuries involved an analysis of
Aristotle's ideas about the natural world, especially within the
Christianized context of the medieval period. Philosophers studying
nature were often actually studying texts--such as commentaries
on Aristotle--rather than conducting experiments or engaging in
observations, and they often did not employ mathematical techniques.
Traditionally, natural philosophy in Aristotelian circles was not
conceived of as a mathematical discipline (unlike, say, optics or
astronomy); instead, it focused especially on the natures of objects
and on causation. In the seventeenth century, natural philosophers
like Galileo, Boyle, Descartes, and Newton began to reject not only
the doctrines of the Aristotelians, but their techniques as well,
developing a number of new mathematical, conceptual and experimental
methods. Newton respected Descartes's rejection of Aristotelian
ideas, but argued that Cartesians did not employ enough of the
mathematical techniques of Galileo, or the experimental methods of
Boyle, in trying to understand nature. Of course, these developments
have often been regarded as central to the Scientific Revolution.
Despite the centrality of these changes during the seventeenth
century, however, the *scope* of natural philosophy had not
dramatically changed. Natural philosophers like Newton expended
considerable energy trying to understand, e.g., the nature of space,
time and motion, but they regarded that endeavor as a component of an
overarching enterprise that also included an analysis of the divine
being. Newton was a natural philosopher--unlike Descartes, he was
not a founder of modern philosophy, for he never wrote a treatise of
the order of the *Meditations*. Nonetheless, his
*influence* on philosophy in the eighteenth century was
profound, extending well beyond the bounds of philosophers studying
nature, encompassing numerous figures and traditions in Britain, on
the Continent, and even in the New
 World.[4]
 Newton's influence has at least two salient aspects.



First, Newton's achievement in the *Opticks* and in the
*Principia* was understood to be of such philosophical import
that few philosophers in the eighteenth century ignored it. Most of
the canonical philosophers in this period sought to interpret various
of Newton's epistemic claims within the terms of their own
systems, and many saw the coherence of their own views with those of
Newton as a criterion of philosophical excellence. Early in the
century, Berkeley grappled with Newton's work on the calculus in
*The Analyst* (1734) and with his dynamics in *De Motu*
(1721), and he even mentioned gravity, the paradigmatic Newtonian
force, in his popular work *Three Dialogues between Hylas and
Philonous* (1713). When Berkeley lists what philosophers take to
be the so-called primary qualities of material bodies in the
*Dialogues*, he remarkably adds "gravity" to the
more familiar list of size, shape, motion, and solidity, thereby
suggesting that the received view of material bodies had already
changed before the second edition of the *Principia* had
circulated widely. Remarkably, in that same year Roger Cotes, the
editor of the second edition of Newton's *Principia,* had
argued in his editor's preface that gravity should indeed be
considered a primary quality along with the more familiar mechanist
properties that had been the subject of so much discussion in previous
years. (Newton himself approached the topic more cautiously.) For his
part, Hume interpreted Newtonian natural philosophy in an empiricist
vein and noted some of its broader implications in his *Treatise of
Human Nature* (1739) and *Enquiry Concerning Human
Understanding* (1750). Newton's work also served as the
impetus for the extremely influential correspondence between Leibniz
and the Newtonian Samuel Clarke early in the century, a correspondence
that proved significant even for thinkers writing toward the
century's end. Unlike the *vis viva* controversy and
other disputes between the Cartesians and the Leibnizians, which died
out by the middle of the century, the debate between the Leibnizians
and the Newtonians remained philosophically salient for decades,
serving as an impetus for Emilie Du Chatelet's
influential work during the French Enlightenment, *Foundations of
Physics* (1740), and also as one of the driving forces behind
Kant's development of the "critical" philosophy
during the 1770s, culminating in the *Critique of Pure Reason*
in 1781. In addition, Newton's work spawned an immense
commentarial literature in English, French, and Latin, including John
Keill's *Introduction to Natural Philosophy* (1726),
Francesco Algarotti's *Newtonianism for the Ladies*(1738), Henry Pemberton's *A View of Sir Isaac
Newton's Philosophy* (1728), Voltaire's *Elements
of the Philosophy of Newton* (1738), Willem Gravesande's
*Mathematical Elements of Natural Philosophy* (1747), Colin
MacLaurin's *An Account of Sir Isaac Newton's
Philosophical Discoveries* (1748), and many more besides.
Moreover, two subsequent Continental editions of Newton's text
contained substantial philosophical engagements not only with his own
ideas, but with those of his potential rivals like the great
mathematician Johan Bernoulli and also Leibniz. The famous
"Jesuit" (or "Geneva") edition of
*Principia mathematica* published by Fathers Le Seur and
Jacquier in 1739-1744 in three volumes engaged substantially with
Leibnizian ideas (Guicciardini 2015). And Emilie Du
Chatelet wrote an extensive "analytical
commentary" as part of her complete French translation of the
*Principia*, published posthumously in 1759. Part of the idea
was to translate Newton's old "geometric" approach
to physics into the new language of analysis, a project that was
intertwined with numerous philosophical issues. Newton's ideas
and methods in mathematics, physics and philosophy therefore continued
to be of substantial importance well into the Enlightenment.



A second aspect of Newton's influence involves thinkers who
attempted in one way or another to articulate, follow, or extend, the
Newtonian "method" in natural philosophy when treating
issues and questions that Newton ignored. Euclidean geometry and its
methods were seen as a fundamental epistemic model for much of
seventeenth-century philosophy--as is well known,
Descartes' *Meditations* attempts to achieve a type of
certainty he likens to that found in geometry, and Spinoza wrote his
*Ethics* according to the "geometrical method".
Propositions deduced from axioms in Euclidean geometry were seen as
paradigm cases of knowledge. We might see Newton's work as
providing eighteenth-century philosophy with one of its primary
models, and with a series of epistemic exemplars as well. But part of
philosophy's task was to articulate precisely what the new
Newtonian method involved. David Hume is perhaps clearest about this
aspect of Newton's influence: his *Treatise* of 1739 has
the subtitle, "An Attempt to Introduce the Experimental Method
of Reasoning Into Moral Subjects", and there can be little doubt
that he meant (at least in part) the method of the *Opticks*
and the *Principia* (DePierris 2012). Indeed, as Hume's
text makes abundantly clear, various eighteenth-century philosophers,
including not only Hume in Scotland but Jean-Jacques Rousseau on the
Continent, were taken to be, or attempted to become, "the Newton
of the
 mind".[5]
 For Hume, this meant following what he took to be Newton's
empirical method by providing the proper description of the relevant
phenomena and then finding the most general principles that account
for them. Of course, one aspect of Hume's work is to provide an
analysis of the concept of causation that is far more extensive than
anything found in Newton, which has a substantial impact on what
counts as an "account" of a phenomenon. This method would
allow us to achieve the highest level of knowledge attainable in the
realm of what Hume calls "matters of
 fact".[6]



Despite the influence of Newton's "method" on
eighteenth-century philosophy, it is obvious that the
*Principia*'s greater impact on the eighteenth century is
to have effected a branching within natural philosophy that led to the
development of mathematical physics on the one hand, and philosophy on
the other (Cohen and Smith, 2002, 1-4). And yet to achieve an
understanding of how Newton himself approached natural philosophy, we
must carefully bracket such historical developments--they did not
solidify until sometime after 1750, a generation after Newton's
death. Indeed, if we resist the temptation to understand Newton as
working within a well established discipline called mathematical
physics, if we see him instead as a philosopher studying nature, his
achievement is far more impressive, for instead of contributing to a
well-founded field of physics, he had to begin a process that would
eventually lead aspects of natural philosophy to be transformed into a
new field of study. This transformation took many decades, involving a
series of methodological and foundational debates about the proper
means for obtaining knowledge about nature and its processes. Newton
himself not only engaged in these debates from his very first
publication in optics in 1672, but his work in both optics and in the
*Principia* generated some of the most significant
methodological discussions and controversies in the late seventeenth
and early eighteenth centuries. These debates concerned such topics as
the proper use of hypotheses, the nature of space and time, the best
understanding of the forces of nature, and the appropriate rules for
conducting research in natural philosophy. Newton's achievement
was in part to have vanquished both Cartesian and Leibnizian
approaches to natural philosophy; in the later eighteenth century, and
indeed much of the nineteenth, physics was a Newtonian enterprise more
than anything. But this achievement, from Newton's own
perspective, involved an extensive, life-long series of philosophical
debates. Those debates focused on numerous substantive issues, but
also included extensive discussions of the proper methodology in
natural philosophy.


## 2. Methodology I: the optics debates of the 1670s



Philosophers have long known about the aspects of Newton's work
that are salient for understanding debates in the early modern period.
For instance, no history of debates about the ontology of space and
time would exclude a discussion of Newton's famous conception of
"absolute" space (see below). Similarly, any discussion of
the role of hypotheses in philosophical reasoning would mention Newton
prominently. These aspects of Newton's work continue to be
significant in contemporary scholarship, but the scope of discussions
of Newton has greatly expanded, encompassing the whole of his
intellectual life. This is especially evident in discussions of
Newton's earliest published work, which was in the field of
optics. In at least three relevant respects, Newton's early work
in optics, which was published in the *Philosophical
Transactions* of the Royal Society beginning in 1672, set the
stage for the principal themes of his long career in natural
philosophy (he remained active well into his seventies). Firstly,
Newton's letter to the Society's secretary, Henry
Oldenburg, often called the "New theory about light and
colors", generated an immediate, extensive, and protracted
debate that eventually involved important philosophers such as Robert
Hooke in Britain and Christiaan Huygens, G.W. Leibniz and Ignatius
Pardies on the Continent (the beginning of the very long title of the
paper is: "A letter of Mr. Isaac Newton, Mathematick Professor
in the University of Cambridge, containing his New Theory about Light
and Colors"). Newton consistently regarded these figures not
merely as disagreeing with his views, but as misinterpreting them.
This experience helped to shape Newton's famous and lifelong
aversion to intellectual controversy, a feature of his personality
that he often mentioned in letters, and one that he would never
outgrow. Secondly, because Newton regarded himself as having been
deeply misinterpreted by his critics, he had recourse to meta-level or
methodological discussions of the practice of optics and of the kinds
of knowledge that philosophers can obtain when engaging in experiments
with light. The novelty and power of Newton's work in the
*Principia* years later would eventually generate similar
controversies that led him to analogous kinds of methodological
discussions of his experimental practice within natural philosophy and
of the kinds of knowledge that one can obtain in that field using
either experimental or mathematical techniques. From *our*
point of view, Newton's science was unusually philosophical for
these reasons. Thirdly and finally, in his earliest optical work
Newton began to formulate a distinction that would remain salient
throughout his long intellectual career, contending that a philosopher
must distinguish between a conclusion or claim about some feature of
nature that is derived from experimental or observational evidence,
and a conclusion or claim that is a mere "hypothesis", a
kind of speculation about nature that is not, or not yet anyway, so
derived. Newton's much later proclamation in the second edition
of the *Principia* (1713), "*Hypotheses non
fingo*", or "I feign no hypotheses", would
infuriate his critics just as much as it would prod his followers into
making the pronouncement a central component of a newly emerging
Newtonian method (see below for details).



The field of optics has its origins in the Ancient Greek period, when
figures like Euclid and Ptolemy wrote works on the subject, but they
often focused primarily on the science of vision, analyzing (e.g.) the
visual rays that were sometimes thought to extrude from the eye,
enabling it to perceive distant physical objects. In the early modern
period, Kepler and Descartes each made fundamental contributions to
the field, including the discovery of the inversion of the retinal
image (in the former case) and an explanation of refraction (in the
latter case). Newton's work helped to shift the focus of optics
from an analysis of vision to an investigation of light. In "New
theory about light and colors", published in the
*Philosophical Transactions* in 1672, Newton presented a number
of experiments in which sunlight was allowed to pass through one or
two prisms in order to probe some of its basic features. The paper
recounts a number of experiments that Newton says he had conducted
several years earlier. But what precisely counts as a *feature*
of light? Numerous philosophers during the seventeenth century,
including Hooke and Huygens, developed doctrines concerning the
fundamental physical nature of light in answer to the question: is
light a stream of particles (or "corpuscles"), or a wave?
Both Hooke and Huygens were wave theorists. This question obviously
continued to have relevance into the twentieth century, when
wave-particle duality was discovered. In his experiments with the
prism, however, Newton apparently sought to investigate something
else, viz. what he calls "the celebrated *Phenomena of
Colours*". Newton's various prism experiments, which
he describes in considerable depth, suggested what he called a
"Doctrine" that he expresses in thirteen consecutive
numbered propositions. Included in these propositions are the
following claims about features of rays of light: first, the rays of
light that emerge when sunlight passes through a prism exhibit various
colors; second, these colors differ in their "degrees of
Refrangibility", which means that they exhibit and retain an
index of refraction, even when they are passed through a second prism;
third, these colors--or colorful rays--are not modifications
of sunlight itself, but are "*Original* and *connate
properties*" of it; and, fourth, these facts mean that
although ordinary sunlight appears white, or perhaps colorless, to our
perception, it actually contains numerous colors within it, which can
be experimentally revealed. This final point suggests, in turn, that
from Newton's point of view, colors are not solely perceived, or
even perceptible, aspects of physical objects; they can also be
conceived of as hidden features of light which cannot be perceived
directly under any ordinary circumstance (the physical influence of
the prism is required for them to become perceptible).



From a contemporary point of view, Newton's 1672 paper exhibits
an intriguing blend of experimental evidence and philosophical
argumentation. The latter hinges on Newton's interpretation of
the concept of a property or a quality, as the following passage,
which follows the "Doctrine" expressed in thirteen
propositions, tellingly reveals:



> 
> 
> These things being so, it can be no longer disputed, whether there be
> colours in the dark, nor whether they be the qualities of the objects
> we see, no nor perhaps, whether Light be a Body. For, since Colours
> are the *qualities* of Light, having its Rays for their entire
> and immediate subject, how can we think those Rays *qualities*
> also, unless one quality may be the subject of and sustain another;
> which in effect is to call it *substance*. We should not know
> Bodies for substances, were it not for their sensible qualities, and
> the Principal of those being now found due to something else, we have
> as good reason to believe that to be a substance also. (Newton
> 1959-, vol. 1: 100)
> 
> 
> 



Newton seems here to be arguing as follows: since rays of light have
colors as basic features, we should regard these colors as qualities
or properties of the rays (despite the fact that these properties are
imperceptible under any ordinary circumstance); but doing so requires
us to think of the rays as bearers of qualities, which is to say, as
substances in their own right. And if rays of light are substances,
this means that we cannot also think of them as qualities or
properties of anything else. This last point follows from a widely
accepted notion of a substance at the time, one easily found in
 Descartes[7],
 viz., that substances are those items that can exist independently of
other items (whether they can exist independently even of God is a
further question that we can ignore here). And if we cannot think of
rays of light as properties or qualities, then they are not waves, for
waves are features of some medium--think of waves on the surface
of a lake. Newton concludes: light is a stream of particles (he does
use the word 'perhaps' to hedge a bit here). Clearly,
philosophical argumentation is a significant aspect of Newton's
reasoning in this paper, as are various philosophical concepts. It is
intriguing to ponder the question, what overall conception of
"sensible qualities" does Newton presuppose in this piece?
If a ray of sunlight passes through my window, the fact that it
appears white to me does not undermine Newton's view (or so he
thinks) that the ray actually contains a series of colors as its
"qualities". Are these qualities "sensible" if
their presence can be detected only through the use of one or more
prisms but never through the inspection of the sunlight through
ordinary means (unaided perception, glasses, a magnifying glass,
etc.)? These are apt to strike us as canonical philosophical
problems.



Newton's line of argument quoted above became one of the
centerpieces of the debate that his paper generated. In some parts of
his paper, when Newton wrote of the "rays" of light, he
had evidently intended to remain neutral on the question of whether
the rays are particles or waves (this is reminiscent of the ancient
Greek practice of avoiding physical discussions of visual rays). But
then towards the paper's end, Newton added his new line of
argument, which employed some philosophical analysis together with
some experimental evidence to support the conclusion that rays of
light cannot be waves after all. Newton's critics pounced. This
led to the first problem he encountered in response to his paper: what
he calls his "theory" of light and colors was not merely
rejected, but rather immediately misunderstood, at least from his own
perspective. Just days after Newton's paper was read at the
Royal Society, Robert Hooke responded with a detailed letter to
Oldenburg. In the first few sentences, Hooke indicates that from his
point of view, Newton's "Hypothesis of saving the
phenomena of colours" essentially involves the contention that
rays of light are particulate, rather than
 wavelike.[8]
 Hooke argues, in contrast, that light "is nothing but a pulse
or motion propagated through an homogeneous, uniform and transparent
medium;" that is, he argues that light is indeed wavelike. He
makes it perfectly clear, moreover, that his hypothesis--the name
did not carry a negative connotation in his work--can save the
phenomena of colors just as well as Newton's, which is to say,
his hypothesis is compatible with the experimental evidence Newton had
gathered. Evidently, the line of argument in the passage quoted above
caught Hooke's eye. Among philosophers, he was not alone. In a
letter to Huygens explaining Newton's theory of light, Leibniz
writes that Newton takes light to be a "body" propelled
from the sun to the earth which, according to Leibniz, Newton takes to
explain both the differential refrangibility of rays of light and the
phenomena of
 colors.[9]
 Since Newton had employed the concepts of substance, quality and
sensible quality when concluding in his paper that light is
(presumably) particulate, we are apt to regard the paper as
contributing to important discussions within philosophy. After the
extensive correspondence, and controversy, generated in response to
Newton's early optical views and experiments, he often
threatened to avoid engaging in mathematical and philosophical
disputes altogether. He insisted to friends and colleagues that he
found intellectual controversy unbearable. But he never followed
through with his threat to disengage from discussions in natural
philosophy, sending many important letters throughout his long
intellectual career.


## 3. Newton's relation to Cartesianism



Like many philosophers who worked in the wake of Galileo and of
Descartes, it seems that Newton never extensively analyzed
Aristotelian ideas about nature. He would have encountered such ideas
in the curriculum at Trinity College, but there is not much evidence
that he took them seriously. Instead, he focused on the
"modern" thinkers that enterprising young students were
told to read outside of the standard
 curriculum.[10]
 And in England in Newton's day, the greatest modern philosopher
of nature was thought to be Descartes (Heilbron 1982: 30). There is
substantial evidence that Newton took Descartes's ideas very
seriously, and expended considerable energy thinking them through and
eventually coming to criticize them. Some of that evidence comes from
a manuscript that was first transcribed and published in 1962 by the
great historians of science, Marie Boas Hall and A. Rupert Hall. The
untitled manuscript, now known as "*De
Gravitatione*" after its first line, has been the subject of
extensive discussions over the past fifty years because it indicates
the depth of Newton's interest in Cartesian ideas in metaphysics
and natural philosophy. Despite its importance to contemporary
understandings of Newton's relation to Cartesianism, and much
else besides, *De Gravitatione* is not without its problems.
First and foremost, the manuscript lacks a date, and there is no
scholarly consensus regarding its precise
 provenance.[11]
 Second, the manuscript was never finished, so it is difficult to
assess its relationship with Newton's mature thinking in
philosophy. Finally, the manuscript was not published during
Newton's lifetime, so there are questions about whether it
represents his considered views. Despite these facts, the text
contains a treasure trove of arguments concerning Cartesian ideas. For
instance, it dispels the easily formed impression that Newton sought,
in the *Principia*, to undermine a Leibnizian conception of
space and time, as his defender, Samuel Clarke, would attempt to do
years later in the correspondence of 1715-16 (discussed below).
Although Leibniz did eventually express what became the canonical
early modern formulation of "relationalism" concerning
space and time--the view, roughly, that space is nothing but the
order of relations among physical objects, and time nothing over and
above the succession of events involving those objects--and
although Newton and Clarke were highly skeptical of such a view, it is
misleading to read the *Principia* through the lens provided by
the later controversy with the Leibnizians. Newton's extensive
attempt in *De Gravitatione* to refute Descartes's
conception of space and time in particular indicates that the Scholium
should be read as providing a replacement for the Cartesian
 conception.[12]
 That is, Newton had a Cartesian, and not a Leibnizian, opponent
primarily in mind when he wrote his famous articulation of
"absolutism" concerning space and time. Unlike questions
about Newton's methods and his apparent deviation from the norms
established by mechanist philosophers like Descartes and Boyle,
Newton's conception of space and time, along with his view of
the divine being, did not immediately engender a philosophical debate.
It was Leibniz more than any other philosopher who eventually
succeeded in fomenting a philosophical debate in which the
"Newtonian" conception of space, time and the divine would
play a central role (see below). But Leibniz's philosophical
views were relatively unknown when Newton first formed his
conception--to the young Newton writing the *Principia*,
Leibniz was another mathematician and not yet a contributor to natural
philosophy. Instead, it was Descartes's view of space, the
world, and God, which he pondered in his youth and eventually came to
reject.



Newton took special interest in the Cartesian view of space and body,
and in related views concerning the causal relations between minds and
bodies and between God and the bodies that constitute the natural
world. Like many of Newton's contemporaries in Cambridge in
those days, he encountered these Cartesian views within the context of
Henry More's then famous discussions of Cartesianism (a term
coined by More himself). Beginning with his correspondence with
Descartes in 1648 (Lewis 1953), and continuing with a series of
publications in later years, many of which Newton owned in his
personal library (Harrison 1978), More argued that Descartes made two
fundamental mistakes: first, he wrongly contended that extension and
matter are identical (and that the world is therefore a plenum); and
second, he mistakenly believed that God and the mind were not extended
substances, which made their causal interactions with such substances
mysterious. Just as Princess Elisabeth of Bohemia had raised
fundamental objections to Cartesian dualism (see Shapiro 2007) in the
early 1640s, More raised similar objections against the Cartesian view
of the divine a few years later (Lewis 1953). Descartes agreed with
More's suggestion that God can act anywhere on nature if he so
chooses, and came very close to accepting More's contention that
such a view entails that God must be present within the world wherever
he in fact chooses to act. For how could God part the Red Sea,
suggested More, unless God were present precisely where the Red Sea is
located? Of course, More agreed that God is not made of parts, cannot
be imagined, and cannot be affected by the causal activity of material
bodies--the causal arrow flows only in one direction. But More
concluded that God is extended in his own way. If one fixes
Descartes's two basic mistakes, one obtains what More regarded
as a proper philosophical view: space is distinct from matter because
it is extended but penetrable, whereas matter is extended but
impenetrable; and, in tandem, all substances are extended, but whereas
some, such as tables and chairs, are impenetrable, others, such as the
mind and God, are penetrable and therefore not
 material.[13]
 Newton was deeply influenced both by More's criticisms of
Descartes and by his positive philosophical conception of space and
the divine.



In a number of texts, including *De Gravitatione*, the famous
discussion of space and time in the Scholium to the
*Principia*, and the discussion of God in the General Scholium,
Newton made his generally Morean attitudes perfectly clear. He
rejected the Cartesian identification of extension and matter, arguing
that space itself exists independently of material objects (and their
relations), and he contended that all entities, including the human
mind and even the divine being, are extended in the sense that they
have spatial location, even if they are extended in ways that
distinguish them from ordinary material
 bodies.[14]
 In Newton's hands, space becomes a fundamental concept of
natural philosophy, an attitude that is foreign to Cartesians. As
Newton puts it in a famous passage from *De Gravitatione*:



> 
> 
> Space is an affection of a being just as a being. No being exists or
> can exist which is not related to space in some way. God is every
> where, created minds are somewhere, and body is in the space that it
> occupies; and whatever is neither everywhere nor anywhere does not
> exist. And hence it follows that space is an emanative effect of the
> first existing being, for if any being whatsoever is posited, space is
> posited. (Newton 2004: 25)
> 
> 
> 



Space is a fundamental concept in part because Newton not only
conceives of it as independent of objects and their relations, but
because he argues that every entity must somehow connect with space in
some way. For Newton, then, if one follows the Cartesians and thinks
of the mind, or of God, as existing without any spatial
location--as existing either "beyond" the natural
world or somehow outside of it--then that is equivalent to
conceiving of them as non-existent. Newton does not shy away from
making this conception of the divine explicit in his public writings,
despite the fact that it was anathema to his Cartesian and Leibnizian
contemporaries. In the General Scholium to the *Principia*,
which was added to the second edition of the text in 1713, for
instance, he famously writes of God:



> 
> 
> He endures always and is present everywhere, and by existing always
> and everywhere he constitutes duration and space. Since each and every
> particle of space is *always*, and each and every indivisible
> moment of duration is *everywhere*, certainly the maker and
> lord of all things will not be *never* or *nowhere*
> ... God is one and the same God always and everywhere. He is
> omnipresent not only *virtually* but also
> *substantially*; for active power cannot subsist without
> substance. (Newton 1999: 941)
> 
> 
> 



For Newton, just as bodies are present in some spatial location, God,
an infinite being, is present throughout all of space throughout all
of time. There could not be a clearer expression of agreement with
More in his debate with the Cartesians concerning the substantial
presence of the divine within space.



Newton also took issue with Cartesian ideas about motion. His
rejection of Cartesian views of space, and his embrace of space as a
fundamental concept in philosophy following More's influence,
aligns with his famous discussion of space and time in the Scholium
that follows the opening definitions in the *Principia*. This
text influenced nearly every subsequent philosophical discussion of
space and time for the next three centuries, so its contours are well
known (see DiSalle 2006: ch. 2). In his *Principles of
Philosophy* of 1644, Descartes had distinguished between the
"ordinary" and the "proper" view of motion:
whereas the ordinary view presents motion as a body's change of
place, the philosopher knows that properly speaking, motion is a
body's change of relations to the bodies that surround it
(recall Descartes's plenum). Newton contends in *De
Gravitatione* that this idea of proper motion, according to which
the motion of a body is at least partially a function of its relations
to other bodies, is in tension with Descartes's own laws of
nature, also presented in the *Principles*. For according to
the conception of (what we now call) inertia that Descartes presents
as his first two laws, a body moving rectilinearly will continue to do
so unless caused to deviate from its path--hence a body's
motion is not a function of its spatial relations to other bodies, but
rather of its *causal* relations. That is, according to the
first two laws, changing a body's spatial relations to others
bodies will not alter its rectilinear motion unless a causal
interaction occurs. This tension runs deep in the Cartesian system.
Newton's Scholium reflects his idea that the concept of motion
in the *Principia* ought to cohere with the laws of motion he
endorses. He distinguishes between absolute and relative motion, true
and apparent motion, and mathematical and common motion (the same
distinctions hold for time, space and place). The former item in each
of these three pairings is a concept that coheres with the laws of
motion. Newton's first law reflects Descartes's laws: it
is a new version of the principle of inertia, one incorporating the
concept of an impressed force. Since this law indicates that a
body's motion is not a function of its spatial relations to
other bodies, but rather of whether forces are impressed on
it--which replaces the Cartesian concept of causal interactions
that involve only impact (see below)--Newton cannot rely on a
body's motion relative to other bodies if he is to avoid the
kind of tension he found in the Cartesian view. Hence he indicates
that a body's true motion--rather than its apparent motion,
which depends on our perceptions, or its relative motion, which
depends on its spatial relations--is a body's change of
position within space itself. That is, true motion should be
understood as absolute motion. This means, in turn, that we must
distinguish between the common idea of space, according to which space
is conceived of as involving relations among various objects (like the
space of our air), and the mathematical idea, one presumably obtained
from geometrical reasoning, that space is independent of any objects
or their relations. In order to account for the idea that true motion
is absolute motion, then, the famous "absolute space" is
postulated.



Newton was perfectly well aware that the notion of absolute space is
not
 unproblematic.[15]
 For instance, if a body's true motion just *is* its
absolute motion, its motion with respect to space itself, then the
imperceptibility of space would appear to render any detection of true
motion difficult, if not hopeless. Indeed, how would we detect any
body's true motion on this view? We might be able to detect a
body's changing spatial relations with its neighbors, but not
its changing relationship with space itself! Newton's solution
to this problem is ingenious. Under certain circumstances, we can
detect a body's true motion by detecting its acceleration. We
can do so when the body is rotating or has a circular motion, for such
motions often have detectable effects. This is one way of
understanding what has become one of the most famous, if not infamous,
experimentsof the early modern period, Newton's bucket.
(He grew up in part on a farm in the English countryside, and often
used deceptively simple examples.) If one takes an ordinary bucket and
fills it with water, and then attaches a rope to the top of the
bucket, one can then twist the rope and let it go in order to make the
bucket spin. When the bucket full of water spins around, we can detect
the water's acceleration by its changing surface. As Newton puts
it, using his laws of motion, the water endeavors to recede from the
axis of its motion (hence its changing surface). But even an observer
untutored in physics would grasp the importance of the water's
changing surface--that is, perceiving the effect does not depend on
understanding the laws. In this way, despite the fact that Newton
wishes to conceive of the water's true motion as its absolute
motion within space itself, which cannot be perceived, he shows his
readers how they might detect the water's true motion through
its effects. Newton provides another simple experiment to illustrate a
similar point. If two balls are joined together by a rope and then
spun around, say over one's head, then the changing tension in
the rope will indicate that the balls are accelerated. Since any
acceleration is a true motion--although not all true motions are
accelerations, since a so-called inertial motion is not--this
case indicates that we can detect a body's true motion even
though space itself is imperceptible. In this way, Newton did not
merely develop an alternative to the Cartesian view of motion, along
with its allied conception of space; he presented a view that could be
employed to pick out some of the true motions of objects within
nature. Once one has found a true motion, one can then ask what
*caused* that motion (for Newton, as we will see, it is forces
that are understood to cause motions). As the last line of the
Scholium in the *Principia* indicates, that is one reason that
Newton wrote his *magnum opus* in the first place.



Newton's idea of space, then, fulfilled at least two roles.
First, it enabled him to avoid the tension between the concept of true
motion and the laws of motion of the kind found in Descartes. Second,
it also enabled him to articulate what he took to be God's
relation to the natural world. Many regarded his achievements as an
important advance over the Cartesian system. However, it would be a
mistake to think that Newton vanquished Cartesian ideas within his
lifetime: even in England, and certainly on the Continent,
Cartesianism remained a powerful philosophical force for several
decades after Newton published his primary
 works.[16]
 Typically, however, Descartes's followers emphasized the
importance of his ideas about the mechanisms that pervade nature
rather than his views of space and time. In that arena, Newton's
views were especially prominent, and came in for significant criticism
from Leibniz.


## 4. Methodology II: the *Principia*



Many legends concerning momentous events in history are apocryphal,
but the legend of Halley's visit to Newton in 1684 is not: it
explains what prompted Newton to write his *magnum opus*. In
August of 1684, Edmond Halley--for whom the comet is
named--came to visit Newton in Cambridge in order to discover his
opinion about a subject of much dispute in celestial mechanics. At
this time, many in the Royal Society and elsewhere were at work on a
cluster of problems that might be described as follows: how can one
take Kepler's Laws, which were then considered among the very
best descriptions of the planetary orbits, and understand them in the
context of dynamical or causal principles? What kind of cause would
lead to planetary orbits of the kind described by Kepler? In
particular, Halley asked Newton the following question: what kind of
curve would a planet describe in its orbit around the Sun if it were
acted upon by an attractive force that was inversely proportional to
the square of its distance from the Sun? Newton immediately replied
that the curve would be an ellipse (rather than, say, a
 circle).[17]
 Halley was amazed that Newton had the answer at the ready. But Newton
also said that he had mislaid the paper on which the relevant
calculations had been made, so Halley left empty handed (whether there
was any such paper is a subject of dispute). But he would not be
disappointed for long. In November of that year, Newton sent Halley a
nine-page paper, entitled *De Motu* (on motion), that presented
the sought-after demonstration, along with several other advances in
celestial mechanics. Halley was delighted, and immediately returned to
Cambridge for further discussion. It was these events that
precipitated the many drafts of *De Motu* that eventually
became *Principia mathematica* by 1686. Several aspects of the
*Principia* have been central to philosophical discussions
since its first publication, including Newton's novel
methodology in the book, his conception of space and time, and his
attitude toward the dominant orientation within natural philosophy in
his day, the so-called mechanical philosophy, which had important
methodological consequences.



When Newton wrote the *Principia* between 1684 and 1686, he was
not contributing to a preexisting field of study called mathematical
physics; he was attempting to show how philosophers could employ
various mathematical and experimental methods in order to reach
conclusions about nature, especially about the motions of material
bodies (Janiak 2015, Chapter One). In his lectures presented as the
Lucasian Professor at Cambridge, Newton had been arguing since at
least 1670 that natural philosophers ought to employ geometrical
methods in order to understand various phenomena in
 nature.[18]
 The *Principia* represented his attempt to reorient natural
philosophy, taking it in a direction that neither his Aristotelian
predecessors, nor his Cartesian contemporaries, had envisioned. He did
not immediately convince many of them of the benefits of his approach.
Just as his first publication in optics in 1672 sparked an intense
debate about the proper methods for investigating the nature of
light--and much else besides--his *Principia* sparked
an even longer lasting discussion about the methodology that
philosophers should adopt when studying the natural world. This
discussion began immediately with the publication of the
*Principia*, despite the fact that its first edition contained
few explicit methodological remarks (Smith 2002: 138-39). It
intensified considerably with the publication of its second edition in
1713, which contained many more remarks about methodology, including
many attempts at defending the Newtonian method. Indeed, many of
Newton's alterations in that edition changed the presentation of
his methods. Discussions of methodology would eventually involve
nearly all of the leading philosophers in England and on the Continent
during Newton's lifetime.



In Cartesian natural philosophy, all natural change is due to the
impacts that material bodies make upon one another's surfaces
(this is reflected in Descartes's first two laws of nature). The
concept of a force plays little if any role. Unlike Descartes, Newton
placed the concept of a force at the very center of his thinking about
motion and its causes within nature. In that regard, his reactions to
the shortcomings of Cartesian natural philosophy parallel
Leibniz's, who coined the term "dynamics", and who
obviously regarded force as a fundamental concept in metaphysics as
well (Westfall 1971). But Newton's attitude toward understanding
the forces of nature involved an especially intricate method that
generated intense scrutiny and debate amongst many philosophers and
mathematicians, including Leibniz (Garber 2012). Newton's
canonical notion of a force, which he calls a *vis impressa* or
"impressed force", is the notion of an "action
exerted on a body" that changes its state of motion. This was a
confusing notion at the time. Perhaps it is not difficult to see why
that should be so. To take one of Newton's own examples: suppose
I hit a tennis ball with my racquet--according to Newton, I have
impressed a force on the tennis ball, for I have changed its state of
motion (hopefully!). We have a reasonably good idea of what the tennis
ball is, of what the racquet is, and even of what I am, and a
Cartesian might wish to stop her analysis there. But what exactly is
this "force" that I impressed on the tennis ball? The
ball, the racquet and I are physical things of one sort or another,
but is the force physical? Is it not physical? It does not seem likely
that a force is itself a physical thing in the sense of being a
substance, to use a philosophical notion popular in Newton's day
(as we saw above in his first optics paper). The reason is that in
Definition Four in the *Principia*, which defines an impressed
force for the first time, Newton remarks: "This force consists
solely in the action and does not remain in a body after the action
has ceased". So when I hit the tennis ball over the net, the
force I impressed on it was the action of hitting the ball, or an
action associated with hitting the ball, and not a property of me or
of the ball after the action had ceased. This idea confused many of
Newton's readers. By the mid-eighteenth century, the time of
Hume's analysis of causation in the *Treatise* and the
*Enquiry*, many philosophers started to think that actions and
other kinds of event are important items to have in one's
ontology, and they often contended in particular that causal relations
hold between *events*. But in Newton's day, philosophers
typically regarded objects or substances as the causal relata. Indeed,
one actually finds an equivocation between thinking of events and
thinking of objects as the relevant causal relata even in Hume: in his
*Enquiry*, he first defines a "cause" so that
"objects" are the causal relata, but then gives an example
in which one of the relata is the vibration of a string
(*Enquiry*, SSVII, 51). So actions were difficult to
analyze, left out of analyses, or conflated with objects. As a result,
Newton's conception of force proved confusing, even to his most
sympathetic interpreters. Moreover, it was unclear to many of
Newton's mechanist readers how his forces fit into their rather
austere ontological view that material bodies consist solely of
properties such as size, shape, mobility and solidity.



Newton did try to clarify his method of characterizing forces. If one
brackets the question of how to understand forces as ephemeral actions
that do not persist after causal interactions have ceased, one can
make progress by conceiving of forces as *quantities*. In
particular, since Newton's eight definitions and three laws
indicate that forces are proportional to mass and to acceleration, and
since mass--or the quantity of matter, a concept Newton
transformed from its Cartesian origins, where it was understood as a
measure of a body's volume--and acceleration are both
quantities that can be measured, Newton gives us a means of measuring
forces. This is crucial to his method. If one thinks of forces as
measurable quantities, moreover, then one can attempt to identify two
seemingly disparate forces as in fact the same force through thinking
about measuring them. For instance, in Book III of the
*Principia*, Newton famously argues in proposition five and its
scholium that the centripetal force maintaining the planetary orbits
is in fact the same as the force of gravity, viz., the force that
causes the free fall of objects on earth. This was a revolutionary
idea at the time, one rendered possible in the first place by
Newton's way of thinking about forces as quantities. This idea
then led Newton to the even more revolutionary view in proposition
seven of Book III that all bodies gravitate toward one another in
proportion to their quantity of matter. That is, it led him to the
idea of universal gravity, a view that shocked many of his Continental
readers in its boldness. This helped to unify what were once called
superlunary and sublunary phenomena, a unification that was obviously
crucial for later research in physics. The idea was enabled by
Newton's abstract way of understanding forces--without
conceiving of a force as involving any specific mechanism or type of
physical interaction, Newton thought of forces as quantities that are
proportional to other features of nature.



Despite his evident success in obtaining what we now call the law of
universal gravitation, Newton admits that he lacks another kind of
knowledge about gravity; this lack of knowledge directly reflects an
aspect of his abstract characterization of forces. In the General
Scholium, he reminds his readers that gravity is proportional to a
body's quantity of matter (its mass) and reaches across vast
distances within our solar system, adding: "I have not as yet
been able to deduce from phenomena the reason for these properties of
gravity, and I do not feign
 hypotheses".[19]
 With this phrase, one of the most famous in all of Newton's
writings, he returned to a key theme of his very first optical paper
from forty years earlier, viz. the proper role of hypotheses and of
hypothetical reasoning within natural
 philosophy.[20]
 Some of Newton's interpreters have regarded this phrase as
signaling a strong commitment to the broad doctrine that all
hypotheses concerning natural phenomena ought to be avoided in
principle. This interpretation is sometimes coupled with the view that
some British philosophers in the late seventeenth century regarded
Cartesianism as overly reliant on hypotheses in reaching conclusions
about phenomena. But this interpretation may be hard to square with
Newton's texts. For instance, in the Scholium to Proposition 96
of Book I of the *Principia*, Newton discusses hypotheses
concerning light rays. Similarly, in query 21 of the *Opticks*,
he proposes that there might be an aether whose differential density
accounts for the gravitational force acting between bodies. In light
of such examples, one can read the General Scholium's
pronouncement in this way: a philosopher concerned with explaining
some feature of nature--such as the fact that gravity is
inversely proportional to the *square* of spatial separation,
rather than, say, the *cube*--may legitimately entertain
and propose hypotheses for consideration, but she may not
"feign" the hypothesis in the sense of taking it as having
been established either through experiment, observation, or some form
of reasoning (including mathematical reasoning). Hence Newton thinks
that he has established the fact that gravity acts on all material
bodies in proportion to their quantity of matter, but he has
*not* established the existence of the aether. What, then, does
Newton's slogan *hypotheses non fingo* actually rule out?
By the time of the General Scholium, Newton was increasingly embroiled
in philosophical disputes with Leibniz. After reading the copy of the
*Principia* that Newton had sent him, Leibniz wrote an essay
("Tentamen") on the causes of planetary motion for the
famous journal *Acta Eruditorum*. In order to account for the
motions of the planetary bodies in his *Tentamen,* published in
1689, Leibniz introduces *ex hypothesi* the premise that some
kind of fluid surrounds, and is contiguous to, the various planetary
bodies, and then argues that this fluid must be in motion to account
for their
 orbits.[21]
 Newton may have argued that Leibniz had "feigned" the
hypothesis of the vortices. That is, he would have objected to
Leibniz's conclusion that there must be vortices in the solar
system (as opposed to the suggestion, for instance, that we try to
detect their presence through observations of things like comets). A
debate between the two philosophers on this score would bring them to
the question of the mechanical philosophy: whereas Newton would object
to Leibniz's reasoning on methodological grounds, Leibniz would
reply that Newton's theory of gravity involves action at a
distance, which his vortex hypothesis avoids (see below for more
details).



Once the *Principia* was published, Newton had a vexed
relationship with the mechanical philosophy, an orientation within
natural philosophy that is associated with nearly every significant
early modern philosopher, including Descartes, Boyle, Huygens,
Leibniz, and
 Locke.[22]
 One of the reasons for this complex relationship can be understood if
we consider Newton's attitude toward forces in an abstract way.
His second law indicates that a body moving rectilinearly will
continue to do so unless a force is impressed on it. This is not
equivalent to claiming that a body moving rectilinearly will continue
to do so unless another body impacts upon it. A *vis
impressa*--an impressed force--in Newton's system
is not the same as a body, nor even a quality of a body, as we have
seen; but what is more, some impressed forces need not involve contact
between bodies at all. For instance, gravity is a kind of centripetal
force, and the latter, in turn, is a species of impressed force. Hence
a body moving in a straight line will continue to do so until it
experiences a gravitational pull, in which case it will deviate from a
straight line motion, even if no body impacts upon it. Indeed, the
gravitational pull might originate with a mass that is millions of
miles away. As we have seen, an impressed force is an action exerted
on a body. Hence the gravity exerted on a moving body is an action
(the Latin term is *actio*), which is obviously a causal
notion. This is not an empirical claim *per se*; it is merely a
reflection of Newton's laws, together with his notion of an
impressed force, and his further idea that gravity is one kind of
impressed force. These elements of the *Principia* make
conceptual room for a causal interaction between two bodies separated
by a vast distance, one enabled by Newton's concept of an
impressed force. Aspects of this idea became known in philosophical
circles as the problem of action at a distance (Hesse 1961). Many of
Newton's most influential contemporaries objected vigorously to
the fact that his philosophy had made room for--if not explicitly
defended--the possibility of distant action between material
bodies. Leibniz and Huygens in particular rejected this aspect of
Newton's work in the strongest terms, and it remained a point of
contention between Newton and Leibniz for the rest of their lives.
Both Leibniz and Huygens were convinced that all natural change occurs
through contact action, and that any deviation from this basic
mechanist principle within natural philosophy would lead to serious
difficulties, including the revival of outmoded Aristotelian ideas. By
the seventh proposition of Book III of the *Principia*, as we
have seen, Newton reached the following conclusion (1999: 810):
"Gravity acts on all bodies universally and is proportional to
the quantity of matter in each". Leibniz eventually accused
Newton of regarding gravity as a kind of "occult quality",
that is, as a quality of bodies that is somehow hidden within them and
beyond the philosopher's understanding. They understood Newton
to be saying that gravity is a kind of hidden power to attract
embedded in material bodies.



Newton was well aware that the *Principia's* methodology
of discovering the forces present in nature was controversial, and not
merely because of questions about action at a distance. So when he
revised the text, under the editorship of Roger Cotes, for publication
in a second edition in 1713, he added other methodological remarks.
These remarks included what Newton called "*regulae
philosophandi*", or rules of philosophy, which became the
focal point of vigorous discussion and debate well into the eighteenth
century. The first two rules concern causal reasoning, but it is the
third rule that generated the most debate, for it involved both an
aspect of Newton's controversial argument for universal gravity
and also a rare public statement by Newton of what he regarded as the
"foundation" of natural philosophy. The third rule
concerns an induction problem: we have perceptions and experiments
that provide us with knowledge of the objects and natural phenomena in
our neck of the universe, but on what basis can we reach a conclusion
concerning objects and phenomena throughout the *rest* of the
universe? Newton himself reached such a conclusion about gravity in
proposition seven of Book III of the *Principia*. Part of
Newton's answer is presented in rule 3:



> 
> 
> Those qualities of bodies that cannot be intended and remitted [i.e.,
> increased and diminished] and that belong to all bodies on which
> experiments can be made should be taken as qualities of all bodies
> universally.
> 
> 
> 



We know, say, that a clump of dirt has certain qualities such as
extension and mobility, but how do we know that the entire earth has
such qualities? It surely lies beyond the reach of our experiments, or
at any rate, it did in Newton's day. Newton says that the sun
and the earth interact according to his law of gravity, but how do we
know that the sun contains a quantity of matter, that it is a material
body with the same basic qualities that characterize the earth or the
moon? It wasn't at all obvious at the time that the sun is a
material body at all. Newton thinks that gravity reaches into the very
center of the sun, but what did anyone in 1713 know about such things?
Newton glosses his third rule in part as follows, connecting it with
his laws of motion:



> 
> 
> That all bodies are movable and persevere in motion or in rest by
> means of certain forces (which we call forces of inertia) we infer
> from finding these properties in the bodies that we have seen. The
> extension, hardness, impenetrability, mobility, and force of
>  inertia[23]
>  of the whole arise from the extension, hardness, impenetrability,
> mobility and force of inertia of each of the parts; and thus we
> conclude that every one of the least parts of all bodies is extended,
> hard, impenetrable, movable, and endowed with a force of inertia. And
> this is the foundation of all natural philosophy. (Newton 1999:
> 795-96)
> 
> 
> 



Many of Newton's readers in 1713 would have granted him the
following inference: although we do not have any perceptions of, say,
the interior of the earth, or even of many ordinary objects within our
grasp, we can reasonably infer that everything with certain basic
properties--something akin to what John Locke, borrowing a term
of Robert Boyle's, called the "primary
qualities"--at the macroscopic level is comprised of
micro-particles that are characterized by those same basic properties.
But at the end of his gloss of Rule 3, Newton applies this same (or
analogous) reasoning to the force of gravity, arguing as follows:
since we experience the fact that all bodies on or near the earth
gravitate toward the earth--in cases such as free fall--and
that the moon gravitates toward the earth, etc., we can infer that all
bodies everywhere gravitate toward all other bodies. This argument
would appear to suggest that gravity--which, as we have seen, is
a kind of impressed force, an action--is somehow akin to
qualities like extension and impenetrability. So is Newton suggesting
that gravity is actually a *quality* of all bodies? He did not
explicitly endorse that claim, but Cotes did in a famous passage in
his editor's preface (Newton 1999, 391-92). Many understood
Cotes to be speaking for Newton, just as they interpreted Clarke a few
years later. Leibniz and his followers pounced: if Newton regards
gravity as a quality, as a power of attraction, then he had indeed
revived the occult qualities of the Scholastics, for here we have a
quality that is not explicable in mechanical terms. Unlike the usual
properties of extension, impenetrability and mobility discussed by
Cotes, gravity seemed like a hidden power. This topic became the
subject of intense debate throughout the first half of the eighteenth
century (see the last section below).


## 5. The aftermath of the *Principia* I: relations with John Locke and Richard Bentley



Although the first editions of Newton's *Principia* and
of Locke's *Essay* were published a mere three years
apart (in 1687 and 1690, respectively) their authors worked
independently and did not influence the first editions of one
another's principal texts. But then in 1688, Locke wrote a
sympathetic (anonymous) review of the *Principia*. And right
around the time of the publication of the first edition of the
*Essay*, Newton and Locke became close friends and apparently
influenced each other's thinking about philosophy, religion, and
theology in various ways (they first met in London in 1689). For his
part, Locke called him the "incomparable Mr. Newton" on
several occasions (e.g., in correspondence: Locke 1823: vol. 4: 55;
and the next long quotation below). Most historians think that each
questioned the standard Anglican interpretation of the Trinity,
contending that Jesus of Nazareth was not a divine figure on the same
level as God the creator. Interpreting the Bible through historical
and philosophical analysis in a fashion that was not constrained by
standard Anglican doctrine in the late seventeenth century was
fantastically important to Newton, occupying his attention for many
years. Given their controversial and politically sensitive nature, his
so-called anti-Trinitarian views were largely kept secret among a
small circle of friends. However, Newton trusted Locke enough to send
him a very long letter--entitled "Two Notable Corruptions
of Scripture"--to present him with the evidence for
Newton's view that the original version of Christianity was
corrupted beginning in the 4th century by the introduction
of the doctrine of the Trinity (Newton 1959-, vol. 3:
83-129). Locke was apparently sympathetic with Newton's
approach. With respect to their public views, Newton and Locke were
often taken to represent two aspects of the same
experimental-philosophical approach toward the close of the
seventeenth century (Stein 1990; Wilson 1999: 196-214; and
Domski 2012). It is perhaps not difficult to understand why, for
Newton was mentioned in one of the most famous passages in all of
Locke's writings. In the Epistle to the reader of Locke's
*Essay Concerning Human Understanding*, we read:



> 
> 
> The Commonwealth of Learning, is not at this time without
> Master-Builders, whose mighty designs, in advancing the sciences, will
> leave lasting monuments to the admiration of posterity; but every one
> must not hope to be a Boyle, or a Sydenham; and in an age that
> produces such masters, as the great Huygenius, and the incomparable
> Mr. Newton, with some other of that strain; 'tis ambition enough
> to be employed as an under-labourer in clearing ground a little, and
> removing some of the rubbish, that lies in the way to knowledge; which
> certainly had been very much more advanced in the world, if the
> endeavors of ingenious and industrious men had not been much cumbred
> with the learned but frivolous use of uncouth, affected, or
> unintelligible terms, introduced into the sciences, and there made an
> art of, to that degree, that philosophy, which is nothing but the true
> knowledge of things, was thought unfit, or uncapable to be brought
> into well-bred company, and polite conversation. (Locke 1975: 10)
> 
> 
> 



Clearly, Locke seeks in this passage, among other things, to align his
work in the *Essay* with the work of figures such as Newton.
Here we find, at the opening of Locke's magnum opus, the
suggestion that he is content to be an "under-labourer", a
thinker who helps to clear the way for the advance of knowledge. But
his list of four "master builders"--Boyle, Sydenham,
Huygens, and Newton--might strike us as an odd pairing: what do
these four have in common exactly? It has recently been argued that
Locke regarded the four as representing the new "experimental
philosophy", and that Locke himself should be interpreted as
strongly supporting that orientation within natural philosophy more
generally (Anstey 2011: 220). This would become a popular conception
of Newton's philosophical approach, one that played a
substantial role in the Enlightenment.



Locke may have regarded Newton as a fellow enthusiast for the
experimental philosophy, but there are reasons to think that his
embrace of the mechanical philosophy presented him with a difficulty
in interpreting the consequences of Newton's theory of universal
gravity in the *Principia*. For Newton's theory seemed to
be in tension with a mechanist constraint on views of causation, at
least from Locke's own point of view. In the first edition of
the *Essay*, Locke articulated a central tenet of mechanist
thinking about causation when he wrote: "bodies operate by
impulse and nothing else" (*Essay*, II.viii.11). Impulse
refers here to contact action. In correspondence with Locke that would
prove to be influential, Bishop Edward Stillingfleet questioned this
view from the *Essay*, contending that Locke must jettison the
idea of human liberty if he insists that bodies can operate solely by
impulse, presumably on the grounds that the human will cannot be
understood to cause bodily action in that manner. In a famous
exchange, Locke responded in part by reformulating his commitment to
the mechanist view that all causation involving material bodies must
be by contact (impulse) alone:



> 
> 
> It is true, I say, that 'bodies operate by impulse and nothing
> else'. And so I thought when I writ it, and can yet conceive no
> other way of their operation. But I am since convinced by the
> judicious Mr. Newton's incomparable book, that it is too bold a
> presumption to limit God's power, in this point, by my narrow
> conceptions. The gravitation of matter toward matter by ways
> inconceivable to me, is not only a demonstration that God can, if he
> pleases, put into bodies, powers and ways of operations, above what
> can be derived from our idea of body, or can be explained by what we
> know of matter, but also an unquestionable and every where visible
> instance, that he has done so. And therefore in the next edition of my
> book, I shall take care to have that passage rectified. (Locke 1823:
> vol. 4: 467-8).
> 
> 
> 



This was not merely his privately held view. For instance, near the
beginning of his *Elements of Natural Philosophy*, Locke
writes:



> 
> 
> Two bodies at a distance will put one another into motion by the force
> of attraction; which is inexplicable by us, though made evident to us
> by experience, and so to be taken as a principle in natural
> philosophy. (Locke 1823: vol. 3: 305)
> 
> 
> 



In this way, Locke held the common view that Newton's theory of
universal gravity was incompatible with the mechanical
philosophy--and perhaps, unintelligible to us for that very
reason--and when forced to choose between these two options, he
evidently sided with Newton, thinking that his theory was supported by
"experience". He did so by endorsing the view that God
must have added "powers" or "ways of
operations" to material bodies that cannot be derived from our
idea of body. Such powers or ways of operations would in this case
result in gravitational interactions, presumably amongst bodies that
are spatially separated from one another by great distances. Yet from
Locke's point of view, the fact that Newton's theory
convinces him that such powers exist does *not* entail that
that theory renders gravity "conceivable": even if the
theory of universal gravity is correct, it does not allow us to
understand how matter--what Locke would call "extended
solid substance"--can interact gravitationally with other
matter when the bits of matter are not in contact with one another
(Downing 1997). So Locke has concluded that bodies can operate on one
another through some means other than impulse, but he retains his
firmly held belief that any such operation is not intelligible to us.
Locke accepted the conclusion that spatially separated bodies causally
interact with one another in accordance with the law of universal
gravitation, but concluded that the law itself did not render that
causal interaction intelligible. This is precisely the kind of
reaction to Newton's theory of universal gravity bemoaned by
Leibniz, who would argue that any operations or powers attributed to
material bodies must meet the basic criterion of intelligibility
established by the mechanist approach; he might also be inclined to
argue that any laws regarded as governing the interactions of bodies
must also meet that criterion by being derivable in some way from our
basic concept of matter (see below). Regardless, this is an excellent
example of a case in which Newton's theory in the
*Principia* had a direct impact on the development of
philosophical views of causation in the late seventeenth century.



When the great English natural philosopher Robert Boyle died at the
end of 1691, he endowed a lecture series designed to promote
Christianity against what Boyle took to be the atheism that had
infected English culture after the revolutionary period of the
mid-century. Famous Newtonians such as Samuel Clarke and William
Whiston would eventually give the Boyle lectures. The first
"Boyle lecturer" was the theologian Richard Bentley, who
would eventually become the Master of Newton's *alma
mater*, Trinity College, Cambridge, and who also worked under
Locke's correspondent, Bishop Stillingfleet, himself an admirer
of Newton's (Gascoigne 1985: 65). When preparing his lectures
for publication--they had been presented to a public audience in
London in 1692--Bentley conferred with Newton, hoping to solicit
his help in deciphering enough of the *Principia* to use its
results as a bulwark against atheism (Bentley 1976). Newton obliged,
and a famous correspondence between the two began (eventually
published as Bentley 1756). The exchange is of great philosophical
interest, for Bentley elicited a number of important clarifications
that have no peer within Newton's published *oeuvre*.



Bentley sought Newton's assistance in particular because he
wanted guidance in divining how the theory of the *Principia*
indicates that the solar system must have been designed by an
intelligent agent and could not have arisen through the physical
interactions of material bodies. In the first edition of the
*Principia* in 1687, Newton had made such a claim in a very
brief statement (Newton 1972: vol. 2: 582-3; Cohen 1971:
154-6). In the second edition of the text (published in 1713),
he removed that statement, replacing it with a more extensive
discussion in the new section of the text, added to its end, called
the "General Scholium" (mentioned above). Through their
correspondence, Bentley learned that from Newton's point of
view, the positions of the planets relative to one another--and
especially to the sun--indicate that mere chance, or the ordinary
physical interactions of the planetary bodies, could not have placed
each planet in precisely the right orbit to maintain a solar system
like ours for an extended period of time. With this argument, Newton
seems to be indicating that mere chance would have produced an
unstable planetary system, one in which the planets would eventually
either be too strongly attracted to the sun, falling into it, or too
weakly attracted, flying off into space. In this episode, a theologian
appeals to the new authority of Newtonian natural philosophy when
attempting to undermine atheism. And that was apparently the very kind
of interchange that Boyle had envisioned when endowing the lecture
series.



Newton's correspondence with Bentley is justly famous for
another reason. The criticisms of Newton's theory of gravity by
Leibniz and Huygens, outlined briefly above, would prove essential to
the Continental reception of Newtonian natural philosophy more
generally in the late seventeenth and early eighteenth centuries.
Since Newton held both of these mathematicians in high regard--he
tells Leibniz in a 1693 letter that "Huygens is a master, and
his remarks on my discoveries are brilliant" (Newton 2004:
108)--one might assume that their criticisms would have pressed
Newton into articulating an extensive defense of the possibility of
action at a distance. However, Newton presented no such defense, at
least not explicitly. In fact, there is evidence that Newton himself
may have rejected the possibility of action at a distance, despite the
fact that the *Principia* allows it as a conceptual
possibility, if not an empirical reality. The evidence lies in
Newton's correspondence with Bentley. In February of 1693, after
receiving three letters from Newton, Bentley wrote an extensive reply
that attempted to characterize Newton's theory of gravity, along
with his understanding of the nature of matter, in a way that could be
used to undermine various kinds of atheism. With the three earlier
letters as his guide, Bentley makes the following estimation of
Newton's understanding of the possibility that gravity could
somehow be an essential feature of material bodies:



> 
> 
> (2) And as for Gravitation, tis impossible that That should either be
> coaeternal & essential to Matter, or ever acquired by it. Not
> essential and coaeternal to Matter; for then even our System
> would have been eternal (if gravity could form it) against our
> Atheist's supposition & what we have proved in our Last. For
> let them assign any given time, that Matter convened from a Chaos into
> our System, they must affirm that before the given time matter
> gravitated eternally without convening, which is absurd. {Sir, I make
> account, that your courteous suggestion by your Last, that a Chaos is
> inconsistent with the Hypothesis of innate Gravity, is included in
> this paragraph of Mine.} and again, tis unconceivable, that inanimate
> brute matter should (without a divine impression) operate upon &
> affect other matter without mutual contact: as it must, if gravitation
> be essential and inherent in it. (Newton 1959-vol. 3: 249)
> 
> 
> 



In reply to this letter, Newton refers back to this second
proposition, making one of the most famous of all his pronouncements
concerning the possibility of action at a distance:



> 
> 
> The last clause of the second position I like very well. It is
> inconceivable that inanimate brute matter should, without the
> mediation of something else which is not material, operate upon and
> affect other matter without mutual contact, as it must be, if
> gravitation in the sense of Epicurus, be essential and inherent in it.
> And this is one reason why I desired you would not ascribe innate
> gravity to me. That gravity should be innate, inherent, and essential
> to matter, so that one body may act upon another at a distance through
> a vacuum, without the mediation of anything else, by and through which
> their action and force may be conveyed from one to another, is to me
> so great an absurdity that I believe no man who has in philosophical
> matters a competent faculty of thinking can ever fall into it. Gravity
> must be caused by an agent acting constantly according to certain
> laws; but whether this agent be material or immaterial, I have left
> open to the consideration of my readers. (Newton 2004:
>  102-3)[24]
> 
> 
> 



It certainly seems that Newton was uncomfortable with the very idea of
action at a distance. But of course, things are not always as they
seem in interpretations of difficult philosophical texts: some
historians and philosophers have argued strongly that there are other
readings of the
 letter.[25]
 Rather than rejecting distant action between material bodies *per
se*, they argue, Newton may have been rejecting a particular
version of that idea, one associated with the "Epicurean"
view that gravity is somehow an essential feature of all material
bodies, a stronger view than Newton might wish to endorse. The idea
might be roughly as follows: Newton wanted to leave open the
possibility that God had endowed bodies with a power to act at a
distance on one another, a position that is at least reminiscent of
Locke's view in his correspondence with Stillingfleet (see
above). The reason is that Newton held the standard view at the time
that matter itself is passive, requiring some kind of divine
intervention in order to interact causally with other matter. Again,
one finds a Lockean echo of this idea (which may be no accident):
Locke sometimes suggests that matter itself is passive in the sense
that it cannot move itself; instead, motion must be
"superadded" to it by God. If the world consisted solely
of a bunch of material objects, say rocks floating in interstellar
space, then they would not experience any changes in their states of
motion unless some external force acted upon them. Left to its own
devices, matter is passive and does not move. To argue, as some
"Epicurean" philosophers may have done, that matter itself
essentially contains gravity as a feature, is to deny that matter is
passive; it is to suggest that the rocks in interstellar space would
attract one another and begin to move "on their own",
without any external force influencing them. And this, in turn, might
lead us on a slippery slope to atheism, for on this view, matter would
act on its own, without any divine intervention. Or so Bentley and
Newton might be interpreted.



Clearly, one reasonable motive for uncovering a nuanced interpretation
of Newton's letter to Bentley is the obvious fact that Newton
apparently regarded action at a distance as perfectly possible when
writing the *Principia*. Indeed, it is difficult to reconcile
the *Principia* with the Bentley correspondence. One can argue
that although he left open the possibility of action at a distance in
his main work, Newton himself did not accept that possibility because
of his more general commitments. The debate on such matters continues
unabated. However, regardless of Newton's personal attitude
toward distant action among material bodies, his mechanist
interlocutors and readers continued to object to the physical theory
outlined in Book III of the *Principia* on the grounds that, at
the very least, it left open the conceptual possibility of a kind of
action that cannot in fact exist anywhere in nature. That remained one
of Leibniz's principal objections against Newtonian natural
philosophy throughout the last twenty years of his life, animating his
correspondence with numerous figures, including most prominently the
Newtonian theologian and philosopher Samuel Clarke.


## 6. The aftermath of the *Principia* II: debates with Leibniz



In many ways, Leibniz and Newton grew up in the same philosophical
environment. Each came of age during the heyday of Cartesianism, and
each argued in particular that Cartesian views in natural philosophy
failed to include a sufficiently robust conception of the forces of
bodies in nature. Force would lie at the center of Newton's
mature physics (Westfall 1971), and would become even more central to
Leibniz's thinking, playing an essential role in his metaphysics
as well (Garber 2012). Indeed, in Leibniz's criticisms of
Cartesian physics involving what was later called the *vis viva*controversy (Smith 2006) and in Newton's mature physics,
each argued that Descartes and his followers had failed to understand
the importance of the notion of force. Leibniz and Newton knew one
another as mathematicians already in the 1670s, and as we have seen,
Leibniz discussed Newton's first optical work with Huygens. But
after the publication of the *Principia* in 1687, their
philosophical relationship, which was marked originally by respectful
disagreement, began to develop in earnest. Just two years after the
*Principia* appeared, Leibniz published his *Essay on the
Causes of Celestial Motions* (or *Tentamen*), and then in
1693, the two corresponded with one another on mathematical and
philosophical issues (Newton 2004: 106-9). Leibniz initiated
their discussion in March of 1693: after highlighting Newton's
"astonishing discovery" that the elliptical planetary
orbits found by Kepler can be the result of gravitational attraction
within the solar system, Leibniz contends that these motions must be
caused by "the motion of a fluid medium" (Newton 2004:
106). He had described such a fluid medium, or vortex, in detail in
his own *Essay*. The background to Leibniz's comment is
his unwavering commitment--one shared by Huygens, whose theory of
gravity's cause Leibniz mentions in the same letter--to the
mechanist requirement that all changes in motion must be the result of
material impact. Thus for Leibniz, one can (e.g.) speak of the sun as
attracting the earth as a *facon de parler*, but in fact
the cause of the earth's acceleration, of its true motion around
the sun, is its interaction with a fluid medium. (Descartes was also a
famous proponent of a vortex theory of planetary motion--Aiton
1972: 30-64; Gaukroger 2002: 150-3.) When he replied in
October of 1693, however, Newton did not accept Leibniz's
philosophical olive branch. Leibniz had insisted that the vortex
theory of planetary motion "would not at all detract from the
value and truth of your discovery" that Kepler's ellipses
result simply from the conception of attraction or gravitation (Newton
2004: 107). This olive branch was important because earlier vortex
theorists, especially Descartes, had failed to account for
Kepler's laws, so Leibniz was crediting Newton with advancing
astronomy in this respect (and indeed, he attempted to reflect
Kepler's results in his *Tentamen*). But Newton brushed
aside the olive branch, noting that vortices would disturb the motions
of planets and comets through the solar system. He writes that some
"very fine" matter fills the heavens, adding:



> 
> 
> For since celestial motions are more regular than if they arose from
> vortices and observe other laws, so much so that vortices contribute
> not to the regulation but the disturbance of the motions of planets
> and comets; and since all phenomena of the heavens and of the sea
> follow precisely, so far as I am aware, from nothing but gravity
> acting in accordance with the laws described by me; and since nature
> is very simple, I have myself concluded that all other causes are to
> be rejected and that the heavens are to be stripped as far as may be
> of all matter, lest the motions of planets and comets be hindered or
> rendered irregular. But if, meanwhile, someone explains gravity along
> with all its laws by the action of some subtle matter, and shows that
> the motion of planets and comets will not be disturbed by this matter,
> I shall be far from objecting. (Newton 2004: 108-9)
> 
> 
> 



This is a passage rich with meaning. Leibniz clearly insisted that
vortices, or some physical object or fluid, must be in contact with
the planetary orbits if we are to explain why they deviate from the
tangents along the orbital paths when circling the sun. Newton's
reply is that giant swirling fluids in the heavens would actually
disturb the regular orbital paths and the paths of comets through the
solar system. That reply might be thought of as empirical in
character, for it depends on observational data regarding the actual
paths of the heavenly bodies. But Leibinz's perspective is
obviously not merely empirical in character: he does not postulate
vortices (or anything akin to them) on observational grounds; he
infers their existence because he thinks we know (perhaps we can add,
we know *a priori*) that physical bodies such as comets or
planets can deviate from a rectilinear path--they can
accelerate--only if some other physical item impacts upon them.
Newton has a reply to that kind of view as well: he insists that the
phenomena of the motion of the heavenly bodies "follows"
solely from gravity itself--an impressed force, as we have seen,
and therefore an "action"--in accordance with the
laws of motion and the law of universal gravitation. Since gravity is
an action--clearly, a causal notion--it seems clear that
Newton's answer to Leibniz's idea that vortices cause the
planetary orbits is that gravity itself causes them. It is not much of
a leap to conclude, in turn, that this reply commits Newton to the
idea that bodies involved in gravitational interactions, such as the
sun and the earth, act at a distance on one another through the force
of gravity. It is not hard to divine why Leibniz (and Huygens) would
have concluded that Newton had relinquished any commitment to the
norms of the mechanical philosophy.



Despite Leibniz's (and Huygens's) criticisms of his theory
of gravity in particular, and his methods in natural philosophy in
general, Newton stuck to his guns. Nearly twenty years after their
illuminating exchange in 1693, Leibniz and Newton narrowly missed a
second opportunity to discuss their philosophical differences
directly. In May of 1712, Leibniz published a letter to Nicholas
Hartsoeker that was highly critical of the Newtonians; it was
published in English translation in the *Memoirs of
Literature*, a journal to which Roger Cotes, the editor of the
*Principia's* second edition, held a subscription (Newton
2004: 109). After Cotes brought Leibniz's criticisms to
Newton's attention--especially the claim that the
*Principia* renders gravitation a "perpetual
miracle" because it does not specify the physical mechanism
underlying it--Newton wrote an intriguing, but only posthumously
published, rebuttal. Here is part of Newton's paraphrase of
Leibniz's original letter:



> 
> 
> But he [i.e., Leibniz] goes on and tells us that God could not create
> planets that should move round of themselves without any cause that
> should prevent their removing through the tangent. For a miracle at
> least must keep the planet in. (Newton 2004: 117)
> 
> 
> 



Newton's response to this Leibnizian charge is illuminating:



> 
> 
> But certainly God could create planets that should move round of
> themselves without any other cause than gravity that should prevent
> their removing through the tangent. For gravity without a miracle may
> keep the planets in. (*ibid*.)
> 
> 
> 



Thus Newton repeats the view he mentions to Leibniz in 1693, viz.,
that the force of gravity itself causes the planets to follow their
orbital paths rather than their inertial trajectories along the
tangents to those orbits, independently of any fluid medium in the
heavens. But in this posthumously published letter, Newton did not
merely repeat his basic understanding of gravity from his 1693
exchange with Leibniz; he also included a wider discussion of
mechanist norms within philosophy more generally. Again, Newton begins
by quoting Leibniz:



> 
> 
> But Mr. Leibniz goes on. "The ancients and the moderns, who own
> that gravity is an occult quality, are in the right, if they mean by
> it that there is a certain mechanism unknown to them whereby all
> bodies tend towards the center of the earth. But if they mean that the
> thing is performed without any mechanism by a simple primitive quality
> or by a law of God who produces that effect without using any
> intelligible means, it is an unreasonable and occult quality, and so
> very occult that it is impossible that it should ever be done though
> an angel or God himself should undertake to explain it". (Newton
> 2004: 116)
> 
> 
> 



In this passage, Leibniz returns to the kind of criticism that he
would present against the "superaddition" view that Locke
presented to Stillingfleet, arguing that philosophers must reject the
idea that gravity could simply be a feature of bodies that God adds to
them, despite the fact that we cannot possibly understand
gravitational interactions based on our idea of body (our idea of
extended solid substances, or another similar idea). Indeed, Leibniz
raises the stakes by contending that God himself could not explicate
how such interactions are possible based on the idea of matter.
Leibniz would argue, perhaps on metaphysical grounds, that any laws
said to govern the interaction of bodies, and any qualities attributed
to bodies, must be intelligible in the terms available to philosophers
through the mechanist orientation. In particular, laws and qualities
must be intelligible in terms of the shape, size, motion and
impenetrability (or solidity) of bodies. In this way, one might
conclude that Locke and Leibniz actually do not necessarily disagree
on whether gravity can be made intelligible in mechanist terms; they
simply disagree on the propriety of the contention that God could
"superadd" a feature to bodies that cannot be made
intelligible in that way.



Newton's reply to Leibniz's argument is illuminating.
Instead of presenting a narrow defense of his view, perhaps by denying
that he has postulated any non-mechanical causation with his theory of
gravity, he challenges the mechanical philosophy itself by contending
that it should not be understood as holding for all natural
phenomena:



> 
> 
> The same ought to be said of hardness. So then gravity and hardness
> must go for unreasonable occult qualities unless they can be explained
> mechanically. And why may not the same be said of the *vis
> inertiae* [force of inertia] and the extension, the duration and
> mobility of bodies, and yet no man ever attempted to explain these
> qualities mechanically, or took them for miracles or supernatural
> things or fictions or occult qualities. They are the natural, real,
> reasonable, manifest qualities of all bodies seated in them by the
> will of God from the beginning of the creation and perfectly incapable
> of being explained mechanically, and so may be the hardness of
> primitive particles of bodies. And therefore if any man should say
> that bodies attract one another by a power whose cause is unknown to
> us, or by a power seated in the frame of nature by the will of God, or
> by a power seated in a substance in which bodies move and float
> without resistance and which has therefore no *vis inertiae*
> but acts by other laws than those that are mechanical: I know not why
> he should be said to introduce miracles and occult qualities and
> fictions into the world. For Mr. Leibniz himself will scarce say that
> thinking is mechanical as it must be if to explain it otherwise be to
> make a miracle, an occult quality, and a fiction. (Newton 2004:
> 116)
> 
> 
> 



The first aspect of Newton's argument is to indicate that
mechanical explanations are predicated on referencing certain kinds of
qualities when investigating natural phenomena, and that these
qualities themselves are therefore not subject to mechanical
explanation. For instance, since mechanist explanations--say, of
the way in which magnets attract iron filings across a
table--must refer to qualities such as the extension of the
bodies subject to the explanations, then we cannot give a mechanist
explanation of extension itself. Of course, Leibniz might reply that
we need not provide any explanation of the basic qualities of bodies
that figure in mechanical explanations, for those properties have been
chosen by the "moderns" precisely because they are
perfectly intelligible on their own, perhaps unlike various qualities
attributed to "Scholastic" accounts of natural phenomena.
The second aspect of Newton's argument is more
intriguing--it also harkens back to Locke's discussion with
Stillingfleet, for Locke had contended that God may have superadded
not only gravity to material bodies, but also the power of thought,
linking them because he believed that neither could be rendered
intelligible using any philosophical means at his disposal. That is,
from Locke's point of view, we know that human
beings--which are, or at least contain, material bodies with
size, shape, motion and solidity, along with parts characterized by
those qualities--are capable of thought, but since we cannot
discern how any material thing could possibly have that capacity, we
conclude that God may have superadded that feature to us, or to our
bodies. Thought and gravity are dis-analogous in the sense that we did
not require anything like Newton's theory to convince us that
human beings can think, but they are otherwise analogous. Newton then
attempts to make the following argument: since Leibniz would have to
agree that thinking is not a mechanical process, and not mechanically
explicable, he must agree that there is at least one aspect of the
world that has the following two features, (1) it is not mechanical;
and, (2) it is clearly not to be rejected on that ground alone. He
attempts to liken *gravity* (as he understands it) to
*thinking* (as he believes Leibniz is required to understand
it), arguing that despite the fact that it is not mechanical--it
cannot be explained mechanically--it should not be rejected on
that ground. This argument may be predicated on the view that human
beings, material things, or at least partially material things, do the
thinking, rather than immaterial things, such as minds or souls, for
if one attributes all thought to an immaterial mind or soul, then
there is no pressure to say that anything in nature, or perhaps even
any aspect of anything in nature, has a feature that cannot be
mechanically explicated. If one accepts Locke's view (apparently
also endorsed by Newton) that we should attribute thinking to material
things, or to aspects of material things, then perhaps Newton has
successfully followed Locke in likening gravity to thought, thereby
making room for aspects of nature that are not mechanical after all.
This vexing issue would continue to generate debates amongst
Newton's and Leibniz's various followers in England, and
on the Continent, respectively.



Leibniz's most extensive debate with the Newtonians would not
occur until the very end of his life. His celebrated correspondence
with Samuel Clarke, Newton's friend and supporter in London in
the early part of the eighteenth century, is his most famous
interaction with the Newtonians, occurring right before his death in
1716 (Clarke and Leibniz 1717). Leibniz fomented the correspondence in
November of 1715 by sending a brief, provocative letter to Princess
Caroline of Wales, one designed to provoke a response from
Newton's circle in London. Leibniz knew well that Princess
Caroline was a leading intellectual and political figure in England at
the time, one who would surely be concerned by Leibniz's
shocking claims about the religious consequences of Newtonian
thinking. He opens his initial letter by mentioning both Locke and
Newton, along with the issues about materiality and thinking that
arose in his near exchange with Newton in 1712:



> 
> 
> Natural religion itself seems to decay [in England] very much. Many
> will have human souls to be material; others make God himself a
> corporeal being. Mr. Locke and his followers are uncertain at least
> whether the soul is not material and naturally perishable. Sir Isaac
> Newton says that space is an organ which God makes use of to perceive
> things by. But if God stands in need of any organ to perceive things
> by, it will follow that they do not depend altogether on him, nor were
> produced by him. (Clarke and Leibniz 1717: L 1: 1-3)
> 
> 
> 



Thus Leibniz charges both Lockeans and Newtonians with presenting
philosophical views of the human and of the divine that lead to
theologically unsavory consequences, such as the idea that the human
soul might be material and the view that God must employ something
akin to an organ in order to perceive happenings in the world. These
were fighting words. Although Locke had died in 1704, he had various
followers in England at the time (Gascoigne 1985: 172-3), and
Newton himself was at the height of his influence: he had by then been
knighted, as Leibniz acknowledges by calling him "Sir" in
his letter, and was at that time President of the Royal Society.
Moreover, Samuel Clarke had given the Boyle lectures in 1704 and again
in 1705, so he was a public figure associated with the state of
Christianity in England. Once Clarke took the bait, replying that same
month to Leibniz's charges, Locke's views quickly dropped
from view and the two focused specifically on Leibniz's numerous
objections to Newtonian ideas and methods. But why did Clarke respond
on Newton's behalf, and what was Newton's actual role in
the correspondence? These questions continue to puzzle scholars (see
Cohen and Koyre 1962; Bertoloni Meli 1999 and 2002; Vailati
1997). There is no documentary evidence, such as letters, between
Clarke and Newton indicating the contours of his role; then again, at
this time, both men lived in London and Clarke was Newton's
parish priest, so the lack of letters or other papers is perhaps
unsurprising. That fact alone is intriguing, for the theological
differences between the two are salient: since Newton was a committed
anti-Trinitarian--a fact known to figures like Locke and to
others such as William Whiston--he may have decided that
Leibniz's contentions about "natural religion" in
England would best be answered by what we might now call a more
mainstream theological figure like Clarke. In any event, there is no
doubt that Clarke was taken by Leibniz and his followers to be
speaking for Newton and his circle. Nonetheless, there are certainly
aspects of Clarke's views that may deviate from Newton's
own opinions, so it would be unwise to (as it were) remove Clarke from
our conception of the correspondence by regarding it effectively as
Newton's work.



Leibniz's side of the correspondence with Clarke is
methodologically characteristic: he leaves much of his own systematic
and complex metaphysical theorizing--including the
monadology--in the background, bringing to the fore only those
elements that are both necessary for his criticisms of the Newtonians
and also likely to garner support from Clarke. Thus the key to many of
Leibniz's criticisms is the principle of sufficient reason
(PSR), which he knows Clarke will endorse (although with a distinct
conception of its scope: Leibniz asserts, while Clarke denies, that
the principle demands that each act of divine willing requires a
reason; for Clarke, divine willing itself is reason enough for some
physical state of affairs to obtain, or event to occur). Leibniz
argues in particular that several key aspects of the Newtonian
worldview are simply incompatible with the PSR, including the idea of
absolute space. If space were in fact completely independent of all
physical objects and all relations among them, as the Newtonians seem
to assert, then a problem arises:



> 
> 
> I have many demonstrations to confute the fancy of those who take
> space to be a substance or at least an absolute being. But I shall
> only use, at present, one demonstration, which the author here gives
> me occasion to insist upon. I say, then, that if space were an
> absolute being, something would happen for which it would be
> impossible that there should be a sufficient reason--which is
> against my axiom. And I prove it thus: space is something absolutely
> uniform, and without the things placed in it, one point of space
> absolutely does not differ in any respect whatsoever from another
> point of space. Now from this it follows (supposing space to be
> something in itself, besides the order of bodies among themselves)
> that it is impossible there should be a reason why God, preserving the
> same situations of bodies among themselves, should have placed them in
> space after one certain particular manner and not otherwise--why
> everything was not placed the quite contrary way, for instance, by
> changing east into west. But if space is nothing else but this order
> or relation, and is nothing at all without bodies but the possibility
> of placing them, then those two states, the one such as it is now, the
> other supposed to be the quite contrary way, would not at all differ
> from one another. Their difference therefore is only to be found in
> our chimerical supposition of the reality of space. (Clarke and
> Leibniz 1717: L 3: 5)
> 
> 
> 



Leibniz's argument is clever at the outset: he bypasses the
thorny problem of determining whether Newton's idea of absolute
space commits him to thinking of space as a substance--a view,
incidentally, which Newton explicitly considers and rejects in *De
Gravitatione* (Newton 2004: 21-2)--by presupposing only
that Newton thinks of space as existing independently of objects and
their relations. If space is indeed independent in this way, then it
would seem that God faces a choice: when creating the world, or
matter, why place (e.g.) the earth in one particular part of space
rather than any other? The parts of space, independently of all
objects and all relations, obviously do not differ from one another in
any respect at all, so it would seem that one could not even
theoretically devise a reason for placing the earth anywhere in
particular, as opposed to anywhere else . (This argument,
incidentally, does not depend on our having the capacity to refer to
places within empty space.) But since space exists, with all its
places, independently of the earth and everything else, then God must
indeed have some reason to place the earth in one place rather than
another--for Leibniz, even the divine will is inert independent
of any reason for (as it were) moving in one direction rather than
another. Finally, Leibniz argues that he himself avoids this problem
by asserting that space is nothing above and beyond the objects in the
world and all possible relations amongst them (hence he holds a kind
of modal relationalist view, in more modern terminology). God faces no
problematic choice on this view, since space does not exist prior to
the creation of the world, or of material objects: to create objects
with spatial relations is *ipso facto* to create space itself,
for it is nothing over and above objects and their relations. If you
like, space for Leibniz just is a way of conceptually grasping all
objects and all possible relations amongst them, all at once. Time,
similarly, is a way of grasping the whole series of events that have
characterized history. Clarke's reply is somewhat disappointing:
he blocks Leibniz's inference by simply denying that the divine
will must have a reason to place (say) the earth in one place rather
than another (Clarke and Leibniz 1717: C 3: 5). The PSR is not
violated in this case, according to Clarke's interpretation of
it, because it requires only this: if the earth appears in one place
rather than another, there must be a reason that it appears there, and
the reason in this case is simply the divine will; there is no further
question about why the divine being made a particular choice rather
than another. In the quotation above, Leibniz speaks of the Newtonians
as endorsing "the reality of space", which Leibniz regards
as "chimerical". This remark highlights another important
aspect of Leibniz's conception of space and time, one that is
often ignored in contemporary discussions, which tend to emphasize
Leibnizian "relationalism" in opposition to Newtonian
"absolutism". Leibniz's view of space and time
connects intimately with broader aspects of his metaphysical
positions: unlike ordinary physical objects, which are constituted by
their parts (they are discrete), and which exhibit features that
involve internal distinctions amongst those parts, he thinks of space
and time as continuous and homogeneous. Leaving aside the monadology,
as he does in his correspondence with Clarke, this means that for
Leibniz, it is physical objects that are real things; space and time
are merely "ideal" or abstract entities whose continuity
and homogeneity signal this special status. It is not merely that
space and time are nothing over and above the events and relations of
objects that exist in our world; it is also the case that they are
ideal: they depend in some way on the human mind for their existence.
Or so Leibniz seems to suggest. This aspect of his view would become
of central importance to later (e.g. Kant's) conceptions of the
Leibniz-Newton debate on the nature of space.



Obviously, Leibniz's arguments against the Newtonians
highlighted a fundamental difference between his interpretation of the
PSR and Clarke's: where Leibniz held what we might call the
"rationalist" view that all willing, all choice, must
occur for a reason--a requirement from which even the divine
being is not exempt--Clarke held what we might call the
"voluntarist" view that willing, or choice, itself need
not occur for any reason, for it is itself a sufficient reason for
some states of affairs to obtain or event to occur. From
Leibniz's point of view, this renders the will, including the
divine will, opaque or unintelligible: if an agent can act or make a
choice without having any reason for it, then surely the agent is not
rational, and if the PSR demands anything of the world, it is that the
world be rationally intelligible to us. This requirement must hold of
agents and their wills as well. But from Clarke's point of view,
this requirement is too stringent, especially in the divine case: if
we hold that even God must have a reason for choosing to create one
state of affairs rather than another--for choosing, say, to part
the Red Sea rather than the Mississippi River--then we are
*ipso facto* restricting God's freedom. Surely God has
the freedom to choose to do anything at all, or at least, anything
that does not contain or instantiate a contradiction, and for his
part, Leibniz agrees that the principle of contradiction does not
entail the PSR--the latter is a separate and independent
principle which is necessary for metaphysics and natural philosophy to
extend beyond mathematics, which requires only the principle of
contradiction (Clarke and Leibniz 1717: L 2: 1). But he thinks that
Clarke's view leaves us with a God, and indeed with ordinary
agents, who can act arbitrarily, with no reason at all. That is not
the kind of freedom that philosophy seeks; it wishes to see agents as
engaged in rational action. In their differing interpretations of the
PSR, and their correspondingly distinct conceptions of freedom and
reason, the debate between Leibniz and Clarke hits rock bottom.



Leibniz's criticisms of the Newtonians were not restricted to
questions about the nature of space and time; he also revived his old
complaint--one shared by Huygens, as we have seen
above--that Newton's physical theory commits him to the
possibility, if not to the reality, of action at a distance among the
planetary bodies. In one passage in his fourth letter, for instance,
Leibniz writes (Clarke and Leibniz 1717: L 4: 45):



> 
> 
> It is also a supernatural thing that bodies should attract one another
> at a distance without any intermediate means and that a body should
> move around without receding in the tangent, though nothing hinders it
> from so receding. For these effects cannot be explained by the nature
> of things.
> 
> 
> 



As a defender of the mechanical philosophy, Leibniz insists here, as
he had before, that a material body like the Earth would recede along
the tangent to its orbit if it were not impacted upon by some physical
body or bodies, such as a vortex or another kind of fluid filling the
solar system. Clarke's reply to this charge is especially
illuminating (Clarke and Leibniz 1717: C 4: 45):



> 
> 
> That one body should attract another without any intermediate means,
> is indeed not a miracle, but a contradiction: for 'tis supposing
> something to act where it is not. But the means by which two bodies
> attract each other may be invisible and intangible, and of a different
> nature from mechanism, and yet, acting regularly and constantly, may
> well be called natural, being much less wonderful than animal motion,
> which yet is never called a miracle'.
> 
> 
> 



This passage is bound to confuse readers. On the one hand, Clarke is
clearly arguing that the Newtonians refuse to restrict their
understanding of causal interactions in nature to mechanical cases; on
the other, however, he does not accept what many at that time would
have regarded as the obvious implication of this denial of mechanism,
namely that action at a distance is perfectly possible (a move
embraced by some later in the eighteenth century, such as Kant).
Instead, Clarke not only rejects action at a distance, as Newton
possibly had before him; he contends that it isn't even
logically possible! In his various pronouncements to Bentley and
others, Newton never contended that action at a distance was simply a
contradiction and therefore impossible, presumably even for the divine
being, who is typically said to be capable of creating any situation
that does not instantiate a contradiction (although Descartes's
views on the eternal truths are obviously more complicated).
Clarke's view raises a serious problem for Newtonians: if action
at a distance is simply a contradiction, and therefore not a possible
physical situation, even with divine intervention, then how should one
interpret the theory of universal gravity, which certainly
*appears* to indicate that distant action is perfectly
possible, and perhaps even actual? If we interpret the theory as
postulating actual distant action, say between the moon and the earth,
then it clearly must be mistaken; but even if we interpret it less
strongly, as merely postulating that distant action between the moon
and the earth is possible, that would presumably disqualify the theory
as well. Perhaps one can save Clarke's view by contending that
since distant action is logically impossible, Newton's theory
must therefore be interpreted as neutral on that issue. This is one
issue where Clarke's views may differ substantially from
Newton's own. Regardless of whether Clarke represented
Newton's own views faithfully, there is no doubt that his
correspondence with Leibniz helped to shape the agenda of philosophy
in the eighteenth century.


## 7. Newton's impact on philosophy



The history of eighteenth-century philosophy cannot be written without
extensive discussion of Newton's own views and of his influence
on the views of other figures both in England and on the Continent. As
we have seen, when Newton was a young student at Trinity College,
Cambridge, Cartesian views in natural philosophy and much else besides
had replaced the ideas and methods of Aristotle and his followers as
the most important subject for discussion amongst philosophers. In
many ways, Newton eventually succeeded in convincing philosophers that
his own ideas and methods were superior to those of the
Cartesians--especially when it came to thinking about motion and
its causes--but this historical fact did not mean that
Newtonianism, even broadly construed, became the dominant trend in
natural philosophy during Newton's lifetime. On the contrary,
Newton's views continued to be the subject of intense scrutiny
and debate. As we have seen, this was true amongst Leibniz and his
followers (such as Christiaan Wolff) and among fellow mechanists (such
as Huygens). Indeed, a late-seventeenth-century debate between
Cartesian and Newtonian ideas was supplanted by an early eighteenth
century debate between Leibnizian and Newtonian views; the latter
debate would continue in one form or another for the rest of the
century. But even amongst leading Continental mathematicians, some of
Newton's most basic ideas, for instance concerning the forces of
nature, remained the subject of dispute until well into the eighteenth
century. To give just one prominent example that influenced the
development of philosophy, D'Alembert and Euler, two of the
greatest mathematicians of the Enlightenment, had opposite reactions
to Newton's idea that the mass of an object could also be
referred to by the "very significant name" of the *vis
inertiae*, or force of inertia (Newton 1999, 404--see below
for details). These discussions, along with numerous other debates
about space, time, motion were a driving force during the French
Enlightenment. They remained a powerful stimulant to philosophical
theorizing in the 1770s and 1780s, when Kant forged his magisterial
"critical" system of philosophy, an approach that almost
single-handedly set the philosophical agenda of the early nineteenth
century. Hence Newton's influence on the eighteenth century did
not take the form of a single philosophical program or movement;
instead, it was the controversial nature of his ideas and methodology
that drove much of the philosophical discussion.



Newton's ideas and methods were certainly most influential in
Britain, where there grew to be a strong "Newtonian"
movement--also called the "experimental philosophy"
program--by roughly 1700. By the *fin de siecle*, it is
probably safe to say that natural philosophy had become heavily
Newtonian in England, at least in the sense that it had eclipsed both
Cartesianism (Henry 2013: 124 and introduction to Voltaire 1738 [1992,
7]), and other local movements, such as Cambridge Platonism, which had
exhibited a strong influence during the previous generation. One might
put the point somewhat differently: to the extent that there was a
dominant strand in England by 1700, it was the "experimental
philosophy", a view that was associated strongly with figures
such as Boyle, Newton and Locke. Figures such as Hobbes had opposed
this approach to solving philosophical problems, but had failed to
gain nearly as much influence. Perhaps more importantly,
Newton's view of motion, his understanding of space and time,
and his approach to achieving knowledge of natural phenomena, helped
to shape the agenda of British philosophy for the next fifty years. In
addition to Newton's influence on Locke's thinking about
matter and causation, explored above, both Berkeley and Hume expended
considerable energy grappling with the wider consequences and
implications of the Newtonian version of the experimental philosophy.
For his part, Berkeley famously derided many Newtonians methods and
ideas--sometimes exempting Newton himself from his conception of
the worst philosophical excesses of his followers--including the
rise of the calculus among mathematicians (in *The Analyst*)
and the use of the idea of a force as the basic causal concept in
natural philosophy (in *De Motu*--both reprinted in
Berkeley 1992). Berkeley's theory of ideas, which arose in part
from his reflections of what we would now call Locke's
"empiricist" notion of representation, suggested to him
that no idea can be abstract: each idea must represent a
*particular* rather than a universal. Hence we can have an idea
of a particular car, say a yellow two-door sports car, but not of a
car in general, one with no specific characteristics. Similarly, we
can have an idea of a particular shade of yellow, perhaps because
we've just seen a lovely yellow rose at the florist, but not of
yellow in general; and so on. Berkeley then argued that modern
mathematics, especially the calculus, and modern natural philosophy,
especially Newtonian versions of it, were often reliant on abstract
ideas, and therefore philosophically suspect. For instance, he
contended that the very idea of absolute motion was suspect because we
can represent to ourselves only various motions with particular
features related to particular bodies in motion, but
"absolute" motion cannot be rendered *particular*
in anything like this way; it remains abstract (Downing 2005: 235).
Thus although Newtonian views were considered to be essential to the
rise of experimental philosophy in Britain, Berkeley derided them as
insufficiently experimental, or empirical, as overly reliant on
representations of universals and of universal quantities, rather than
on the representation of particulars. In a reflection of
Malebranche's influence, Berkeley also argued that some
Newtonians wrongly attributed genuine causal powers to ordinary
material objects through their use of the concept of impressed force;
wrongly, because Berkeley firmly rejected the notion that any body
could exert any causal power. All causation in Berkeley's system
is due either to the intervention of the divine in the course of
history, or to spirits or minds, which are genuinely causally active.
Finally, in an argument that would prefigure Mach's reactions to
Newtonian conceptions of space, time and motion in the late nineteenth
century--which were expressive of a broad commitment to
"empiricism"--Berkeley contended that absolute space
is a metaphysical aberration: philosophers should not posit any entity
or thing that is beyond all possible perception. In sum, Berkeley was
highly critical of many aspects of the Newtonian program, but for that
very reason, it was Newton's ideas that helped to shape many of
his philosophical projects.



For his part, Hume had a more nuanced reaction to the emergence of the
Newtonian program (cf. Schliesser 2007 and DePierris 2012). He
certainly signaled his endorsement of the experimental
philosophy--itself strongly associated with the Newtonians, along
with figures like Boyle and Hooke, as we have seen--when he gave
his *Treatise* the following subtitle: "being an attempt
to introduce the experimental method of reasoning into moral
subjects". And one might argue that Hume made a kind of Lockean
move when he chose to endorse the Newtonian program specifically in
preference to the mechanical philosophy, which he regarded with
suspicion. A famous comment from his *History of England*
bolsters this interpretation:



> 
> 
> While Newton seemed to draw off the veil from some of the mysteries of
> nature, he showed at the same time the imperfections of the mechanical
> philosophy; and thereby restored her ultimate secrets to that
> obscurity, in which they ever did and ever will remain. (Hume 1854
> [1754-61]: vol. 5: 374)
> 
> 
> 



The difference between Locke and Hume might be that the former, unlike
the latter, nonetheless insisted that mechanism continued to provide
philosophers with a canon for the intelligibility of causation within
nature (Hume's critique of earlier conceptions of causation,
including Locke's, is certainly well known). Hume also expended
considerable effort in interpreting some of the philosophical aspects
or consequences of Newton's theory of gravity and his
corresponding understanding of the nature of matter. In particular, he
wished to provide what we would now call an empiricist interpretation
of Newton's three laws of motion, his concept of mass (quantity
of matter), and his understanding of gravity; in the process, he does
not shy away from interpreting Newton's sometimes confusing
notion of the *vis inertiae* or force of inertia. When students
learn the canonical idea of a Newtonian force, they learn about what
Newton called a *vis impressa*, an impressed force. They also
learn that the mass of a body is not a force at all. But in all three
editions of the *Principia*, Newton himself said that although
the mass of a body is not an impressed force, it could be called by
the "very significant name of force of inertia" because
bodies with mass with resist acceleration (Newton 1999, 404). And to
resist acceleration seemed to Newton like an action that a body
performs, say when some other body collides with it. Now for Hume,
this issue was particularly difficult because he had already contended
that strictly speaking, we have no idea (no representation) of force
or power--these are merely words employed by natural philosophers
without any ideas corresponding to them. Thus he must find an
interpretation of Newton that is not predicated on our ability to form
an idea of forces or powers. In a famous footnote in his *Enquiry
Concerning Human Understanding*, he writes (Hume 1777 [1993:
SSvii.i note 2, 48-49]):



> 
> 
> I need not examine at length the *vis inertiae* which is so
> much talked of in the new philosophy, and which is ascribed to matter.
> We find by experience, that a body at rest or in motion continues for
> ever in its present state, till put from it by some new cause; and
> that a body impelled takes as much motion from the impelling body as
> it acquires itself. These are facts. When we call this a *vis
> inertiae*, we only mark these facts, without pretending to have
> any idea of the inert power; in the same manner as, when we talk of
> gravity, we mean certain effects, without comprehending that active
> power. It was never the meaning of Sir ISAAC NEWTON to rob second
> causes of all force or energy; though some of his followers have
> endeavoured to establish that theory upon his authority. On the
> contrary, that great philosopher had recourse to an ethereal active
> fluid to explain his universal attraction; though he was so cautious
> and modest as to allow, that it was a mere hypothesis, not to be
> insisted on, without more experiments.
> 
> 
> 



In mentioning Newton's speculation that an aether might explain
universal gravity in some sense (for instance, in query 21 to the
*Opticks*), Hume does not appear to be concerned about action
at a distance; instead, he is concerned to argue that this speculation
indicates that Newton himself did not regard his theory as requiring
that we attribute a "power" of gravity to material bodies.
This is important for Hume to establish, not least because he believes
that we can form no representation at all of any such power.
Similarly, when Newton indicates in the *Principia* that we can
conceive of a body's quantity of matter as its *vis
inertiae*, its power of resisting any change to its state of
motion (Newton 1999: 404-5), he is not attributing any power to
that body, but rather employing a means of characterizing its
behavior. Or so Hume contends. In this specific regard, we find an
echo of Berkeley's earlier work: in *De Motu*, Berkeley
argues in particular that although some philosophers misunderstand the
Newtonian theory of gravity as attributing a special force or nature
to material objects, there is an interpretation of Newton that is
consistent with the new theory of ideas. He writes (Berkeley 1992:
*De Motu*, SS6):



> 
> 
> Again, *force*, *gravity*, and terms of that sort are
> more often used in the concrete (and rightly so) so as to connote the
> body in motion, the effort of resisting, etc. But when they are used
> by philosophers to signify certain natures carved out and abstracted
> from all these things, natures which are not objects of sense, nor can
> be grasped by any force of intellect, nor pictured by the imagination,
> then indeed they breed errors and confusion.
> 
> 
> 



There is little doubt, then, that the new British philosophy
represented by Locke, Berkeley, and Hume in the early-to-mid
eighteenth century was concerned to present interpretations of
Newton's work that were consistent with their overarching
philosophical commitments, principles and methods, or to alter those
commitments, principles and methods as necessary.



These attempts by canonical philosophers like Berkeley and Hume to
find what they regarded as a defensible interpretation of Newtonian
forces are mirrored by similar attempts in the writings of leading
mathematicians. For instance, the very same issue discussed by Hume
had already been debated by two of the leading figures in Continental
science, D'Alembert and Euler. For his part, in his famous work,
the *Traite de dynamique* (1743), D'Alembert
expressed a view that is very similar to Hume's (in certain
respects). He proclaimed right at the outset that he wished to develop
a physics that would dispense with the concept of a force altogether
on the grounds that it was an "obscure" idea. He would
"reduce all the principles of mechanics to three, the force of
inertia, compound motion, and equilibrium" (D'Alembert
1743, 3). He immediately explained the first item: the reason that he
could accept Newton's force of inertia is that it's
characterized as a property of bodies, one in virtue of which they
follow the laws of motion, rather than a force or power. So it was not
an obscure notion. Ironically, the great Swiss mathematician Euler had
precisely the opposite reaction: from his point of view, the
"force of inertia" was simply a misnomer, for it was not a
force at all and should therefore be expunged from physics altogether.
Instead, physics should employ only the idea of an impressed force, a
cause of acceleration, which he regarded as a perfectly clear idea. Of
course, history was on Euler's side, indeed so much so that
future generations would not even imagine that so many leading
philosophers and mathematicians during the Enlightenment debated this
topic.



In other respects, in France the intellectual situation was rather
different than in England. Cartesian ideas held sway for many decades
after Newton first emerged on the scene in the 1670s with his optics
papers and in the late 1680s with the *Principia*; they were
especially popular at the Academie Royale des Sciences, unlike
the situation in the Royal Society (Henry 2013: 120). Voltaire became
famous for challenging the Cartesian French orthodoxy, traveling to
England for a celebrated visit and bringing home
"enlightened" ideas about philosophy, politics, and much
else besides in an attempt to foment the emergence and development of
a French Newtonian program. His most important publication in this
regard is probably the *Elements of the philosophy of Newton*
(Voltaire 1738/1992), which attempts to signal the
"errors" of Descartes and to highlight the advantages of
the Newtonian program in "Physique". Of course, Cartesian
ideas and methods retained numerous adherents and defenders in France,
and so the debate between Cartesian and Newtonian ideas flourished in
that environment (cf. Aiton 1972: ch. 8). But even in France,
Cartesianism eventually gave way to a newer version of metaphysics
associated with Leibniz and his German follower and expositor, Wolff.
In 1740, Emilie du Chatelet, published a key text,
*Institutions de physique*, or *Foundations of physics*(see especially the analysis in Brading 2019). In her
text--which was republished in a second edition in 1742 and
swiftly translated into German and Italian--she makes precisely
the kind of argument that presses Hume a few years later to articulate
a conception of the *vis inertiae* that is consistent with the
experimental philosophy. She argues that the Cartesian view that
extension is the essence of body is mistaken; we must conceive of
material objects as exhibiting a "*force
d'inertie*" if we are to understand their physical
interactions properly (Du Chatelet 1742: ch. 1, SS2).
Perhaps not surprisingly, D'Alembert cites her text approvingly
in his *Treatise on Dynamics*. From Du Chatelet's
point of view, this Newtonian conception of body is not inherently
problematic. Problems arise, however, when some Newtonians interpret
the theory of universal gravity as proving that bodies have a property
of attraction or attractive power endowed by God (Du Chatelet
1742: ch. 16, SS385). She accepts the idea that gravity is
proportional to the masses of bodies and inversely proportional to the
square of their spatial separation, arguing that this Newtonian idea
of attraction "marvelously" explains the fall of bodies on
earth, the tides, and various astronomical phenomena, something that
the vortex theory of the Cartesians fails to do. But she denies that
this acceptance entails that she must also accept the conclusion that
bodies have an "essential property" called gravity or
attractive force, contending that such a conclusion transcends the
knowledge available to philosophers (Du Chatelet 1742: ch. 16,
SS388). The reason is that no one had yet demonstrated that there
is no medium for gravity, such as a vortex or an aether: since gravity
may depend on some medium, it may not be essential to matter *per
se*. In this specific way, Chatelet's work is
predicated on the familiar notion that although Cartesianism had been
overthrown by Newtonian ideas and methods, philosophers must
nonetheless develop a proper interpretation of the Newtonian theory of
gravity and of its implications. Yet unlike Voltaire, who not only
rejected Cartesianism, but became famous for his ridicule of
Leibnizian philosophy in *Candide*, Chatelet argued that
philosophers should continue to work on developing the proper
methodology in part by taking seriously the ideas and methods of
Leibniz and Wolff. In particular, Chatelet argued that the
principle of sufficient reason should be a guiding force in
metaphysical theorizing, and as Leibniz had argued, it shows the
fundamental error in Newton's concept of absolute space; she
added that Clarke's method of replying to Leibniz's
argument, viz., that one can develop a non-Leibnizian or voluntarist
conception of the PSR to evade the problem with absolute space, is
underwhelming (Du Chatelet 1742: ch. 5, SS74). She also
argued that if we use the PSR to guide our thinking about science, we
will be skeptical of Locke's solution to the problem of
understanding the philosophical implications of Newton's theory
of universal gravity. The idea that Newton's theory supports the
conclusion that God must have "superadded" gravity to
matter avoids potential problems with asserting that gravity is
"essential" to matter, something she also regards
skeptically, but simply encounters other problems. First, since no one
yet understood whether there was any medium underlying gravitational
interactions, such as an aether, it was premature to conclude that
gravity is a property of matter, even one "superadded" to
it by divine fiat. After all, if there is an aether, then matter may
gravitate because of its interactions with the aether, and not because
of any superadded property. Second, the PSR demands that we seek
rational explanations of natural phenomena in our science, but the
superaddition thesis is predicated on the idea that we simply cannot
understand how matter gravitates toward other matter. Newton's
science is simply taken to indicate that it does so. She was unwilling
to leave the most important conclusion of the Scientific Revolution a
mere mystery.



Euler's rejection of the *vis inertiae* was not his only
major reaction to Newton's science. The question of whether to
accept, and of how to interpret, absolute space, time and motion, and
the related question of how to conceive of the relation between
Newton's work in natural philosophy and the flourishing
Leibnizian-Wolffian metaphysics on the Continent, continued to drive
conversations in the middle of the eighteenth century. Just a few
years after Chatelet published her *Institutions*, Euler
presented a novel approach to these two questions in a short paper
entitled "Reflexions sur l'Espace et le Temps",
first published in 1748 in the *Memoires de
l'Academie des Sciences de Berlin*. The Berlin
Academy had been witnessing a vociferous debate between Wolffians and
Newtonians since 1740 (a debate that would continue until roughly
1759), one in which Euler played a role. Whereas one might regard the
British philosophers, especially Berkeley and Hume, as arguing that
philosophical principles and commitments take a kind of precedence in
driving one's interpretations of the concepts of force, motion,
space and time, Euler argued that natural
philosophy--specifically, mechanics--ought to take
precedence. The famous first sentence of his essay indicates why: he
contends that the principles of mechanics--for instance, the
principle of inertia--are so well established that it would be
foolish to doubt them (Euler 1748: 324). In particular, if one's
metaphysical commitments stand in tension with the concepts of space
and motion found in geometry and mechanics, then one must adjust those
commitments accordingly. Euler then presented a clever argument: the
law of inertia picks out rectilinear motion as a special kind of
motion, so to apply it to bodies in nature, there must be a clear
meaning to the idea of a straight line. But if space is merely the
order of relations amongst material bodies, then any set of reference
bodies we use to determine which motion is straight could itself be in
motion. So to employ the idea of rectilinear motion, we require the
notion of absolute space (see DiSalle 2006, 36-37).



The most important figure in German-speaking Europe to react in depth
to Newton's ideas was surely Immanuel Kant. As a young man, Kant
was influenced by Euler's argument (Friedman 1992: 16-17)
in the 1748
 piece.[26]
 Kant began grappling with Newtonian ideas at the very beginning of
his career--he discussed the inverse-square law in his first
publication (Kant 1747: SS 10)--and they would remain central
both to his magnum opus, the *Critique of Pure Reason* (Kant
1787 [1992]) and to his *Metaphysical Foundations of Natural
Science* (1786 [2002]). In the so-called pre-critical period, Kant
diverged sharply from the approach toward natural philosophy defended
by many Leibnizians in German-speaking Europe by deciding to accept
the Newtonian theory of universal gravity, along with corresponding
aspects of the Newtonian conception of matter, as a starting point for
philosophical theorizing (Friedman 2012: 485-6). He makes this
explicit already in 1763, in *The Only Possible Argument*:



> 
> 
> I will attempt to provide an explanation of the origin of the world
> system according to the general laws of mechanics, not an explanation
> of the entire natural order, but only of the great masses of matter
> and their orbits, which constitute the most crudest foundation of
> nature ... I will presuppose the universal gravitation of matter
> according to *Newton* or his followers in this project. If
> there are any who believe that through a definition of metaphysics
> formulated according to their own taste they can annihilate the
> conclusions established by men of perspicacity on the basis of
> observation and by means of mathematical inference--if there are
> such persons, they can skip the following propositions as something
> which has only a remote bearing on the main aim of this essay. (Kant
> 1763: AK 2: 139)
> 
> 
> 



A rare case of Kantian irony, it seems. Already in this early text,
Kant has clearly broken with his predecessors both in England and on
the Continent, who insisted on disputing Newton's theory of
universal gravity, either on metaphysical or theological grounds.
Instead, Kant's work will be predicated on that theory. But Kant
never became an orthodox Newtonian, any more than an orthodox
Leibnizian (or Wolffian). This is evident from the radically different
fates of two classic Newtonian concepts within the Kantian system: the
idea that the theory of universal gravity shows that gravity is a
feature of material bodies, along with the related concept of action
at a distance, on the one hand; and absolute space, on the other. The
quotation from 1763 above indicates that Kant was willing to endorse
Newton's theory of universal gravity, despite the many
objections raised against it by his Leibnizian predecessors. Indeed,
he was also willing to accept the most radical interpretation of that
theory, one according to which every material body in the world should
be understood as bearing a feature called gravity, one that involves
that body in actions at a distance on all other such bodies. As Kant
puts it dramatically in Proposition 7 of the second chapter of
*Metaphysical Foundations of Natural Science*: "The
attraction essential to all matter is an immediate action of matter on
other matter through empty space" (Kant 1786 [2002: 223]; AK 4:
512). This view is radical in two senses: first, it involves the
highly controversial claim that gravity is essential to matter, which
indicates that a body lacking gravitational interactions would
potentially fail to count as a material entity at all (much as an
earlier generation of philosophers would conceive of extension as
essential to matter); and second, it also involves the debated idea
that material bodies act at a distance on one another. One can
conceivably endorse the latter without endorsing the former,
contending, e.g., that although material bodies in the actual world
act at a distance on one another, perhaps because of a divine plan, it
is perfectly *possible* for material bodies to fail to do so
under distinct worldly conditions (i.e., there may be possible worlds
in which material bodies lack gravity altogether). That is, the
endorsement of action at a distance does not entail the endorsement of
the essentiality claim. Both ideas are controversial, and Kant
strongly endorses them both. This placed him in a rather select group
of radical Newtonians (Friedman 1992: 1 note 2). Kant himself
understood that Newton may not have endorsed these controversial
views, arguing that he was inconsistent on this score (see Remark 2 to
Proposition 7 of chapter 2, AK 4: 514-16; Friedman 2012:
203-21). And yet Kant strongly resisted the other most
controversial Newtonian idea, absolute space, along with the related
idea of absolute motion (Friedman 2012: 35-42). In the
*Critique of Pure Reason*, for instance, Kant expressed a
basically Leibnizian sympathy by arguing that there are fundamental
metaphysical (and perhaps epistemic) difficulties with thinking of
space and time as existing independently of all objects and all
possible relations among them as "actual entities
"(*wirkliche Wesen*--A23/B37) in their own right. He
does so in a passage that (perhaps confusingly) characterizes the
Leibnizians as also defending a kind of realism about space, but we
can focus solely on his criticism of the Newtonians:



> 
> 
> Those, however, who assert the absolute reality of space and time,
> whether they assume it to be subsisting or only inhering, must
> themselves come into conflict with the principles of experience. For
> if they decide in favor of the first (which is generally the position
> of the mathematical investigators of nature), then they must assume
> two eternal and infinite self-subsisting non-entities (space and
> time), which exist (yet without there being anything real) only in
> order to comprehend everything real within themselves. (A39/B56)
> 
> 
> 



If one regards space (like time) as existing independently of all
objects and all possible relations, and yet one admits that space is
causally inert and imperceptible, as one presumably must in the late
eighteenth century, then one is committed to the idea that there is a
kind of infinite and eternal non-entity in the world. Space is a kind
of non-entity, Kant suggests, because on the one hand it is said to
exist independently of everything else, and yet on the other hand, it
is said to be causally inert and imperceptible, which would
distinguish it from every other sort of thing that exists. Kant simply
cannot stomach this metaphysically preposterous notion. It is
therefore incumbent upon him to develop a theory of space (and of
motion) that meets at least two distinct criteria: (1) it coheres with
his understanding of the theory of universal gravity, and of what he
regards as its implication, viz. that gravity is an essential feature
of material bodies; and, (2) it avoids the metaphysically problematic
aspects of Newtonian absolute space. Kant tackles precisely these
tasks in the *Metaphysical Foundations*, which was published in
between the appearance of the first and second edition of the
*Critique*, arguing that we can regard absolute space as a kind
of idea of reason, an ideal that we approach asymptotically in our
theorizing about motion. Absolute space is therefore nothing more than
a kind of ideal within our philosophy, and no longer a harmful aspect
of our ontology.



Newton's influence on the development of philosophy did not end
with the close of the eighteenth century. Most obviously, the concepts
of absolute space and absolute motion continued to play fundamental
roles in philosophical theorizing about space and motion more
generally for the next two centuries, and they remain fundamental to
discussions today (DiSalle 2006). Newton has also had a deep and
lasting influence on numerous other topics in what we now call the
philosophy of science, including the status of our knowledge of
natural phenomena, the best ideas about scientific methodology, the
status of the laws of nature, and much else besides (McMullin 2001 and
Smith 2001). It is no exaggeration to say that Newton has a permanent
place in the history of modern philosophy.