THE DEVELOPMENT OF THE CONCEPT OF LAWS OF NATURE

PETER HARRISON

in Fraser Watts (ed.), Creation: Law and Probability (Ashgate, 2008)

One of the remarkable features of the physical universe is the fact that it seems

to conform to mathematical laws. On most accounts, moreover, these laws are not

simply descriptions of regularities – although some important thinkers have held this

view – but rather they dictate how things must be. Laws of nature, in other words,

seem to capture some kind of natural necessity. Science, it is usually thought, has as

one of its aims the discovery of laws of nature, and the refinement of various

expressions of those laws. That there are laws of nature, however, seems to be a

presupposition of science, rather than the outcome of its investigations. In light of this

we can ask three important questions about such laws of nature: Why are there laws

at all? Why are these laws mathematical? Why are they necessary or, to put it

another way, what gives these laws their exceptionless character? In the seventeenth

century, when the modern notion of laws of nature was first articulated, the answer to

each of these questions entailed reference to God. The very idea of a law of nature,

from the moment of its birth, was thus underpinned by theological considerations.

One of the chief aims of this chapter is to investigate the historical processes that gave

rise to the idea of laws of nature and to provide an account of its theological

foundations.

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It must be stated at the outset that the three questions posed above are ones that

ultimately cannot be answered by the historian. Nonetheless, the logic of those who

pioneered the concept is of importance for its ongoing viability. After all, if the

theological assumptions that provided the underpinning of the idea of laws of nature

in its infancy no longer prevail, it may be that the concept itself is no longer

sustainable. In other words, we can profitably ask whether subscription to a particular

conception of natural laws entails some tacit theological commitment. This is partly

why a historical inquiry such as this is worth pursuing. It is also important to

acknowledge that what now constitutes a ‘law of nature’ amounts to quite different

things in different sciences. Thus, what was a more or less unitary notion in early

modern physics has now become somewhat equivocal. The main focus of this paper

will be mathematical laws of nature as they first appear in the realm of physics,

although brief mention will be made of the later development of laws in the biological

sciences.

ORDER IN THE MEDIEVAL UNIVERSE

Historians are generally agreed that the modern concept of physical laws of

nature, understood as mathematical descriptions of exceptionless regularities, first

emerged in the West during the early modern period – the era of Galileo, Kepler,

Descartes and Newton.i It does not follow from this, of course, that those in previous

historical periods entertained no conceptions of the orderliness of the natural world,

nor even that use of the expressions ‘natural laws’ or ‘laws of nature’ was completely

unknown before the modern period. Yet there is something quite distinctive about the

early modern formulation and these distinctive features played an important part in

the development of modern science. In order to understand the novelty of the

seventeenth-century understanding of laws of nature it is necessary to consider briefly

the idea of natural order that prevailed during the Middle Ages.

From about the eleventh century onwards, with the reintroduction of Aristotle’s

writings to the Latin West, ideas about the natural world were dominated by

Aristotelian thought. For the Greek philosopher and his medieval followers the

orderliness of the cosmos derived from the immanent properties of natural objects.

3

Thomas Aquinas (c. 1225-74), who successfully integrated many Aristotelian

conceptions into medieval theology, was to speak of ‘the order that God has

implanted in nature.’ii This order did not manifest itself in absolutely invariant rules,

however, because these implanted natural powers would on occasion miscarry, giving

rise to exceptions to the usual course of events. Aquinas pointed to the example of

individuals born with six fingers.iii

Nature was thus understood as ‘that which is wont

to occur in things for the most part, but it is not everywhere in keeping with what

always occurs’.iv

Genuine science had no interest in attempting to comprehend the

exceptional or ‘accidental’ within its explanatory framework, however. This was

because on the Aristotelian understanding, scientific knowledge was concerned with

unchanging essences.v Ideally, moreover, scientific knowledge was knowledge that

was capable of logical demonstration.vi

Given this view of the nature of science, it might seem as if mathematical

reasoning would play a primary role. Yet the division of labour within the Aristotelian

sciences conspired against the use of mathematics in explanations of natural

phenomena. Aristotle had carefully distinguished between natural philosophy, the

science concerned with causal explanations in the ‘real world’ as it were, and

mathematics, which in his view dealt with human constructions.vii

In this respect

Aristotle differed from Plato who was a mathematical realist. The study of the

motions of the celestial bodies, to take the most pertinent example, could thus be

treated under two distinct rubrics. In the sphere of natural philosophy, the causes of

the motion of the stars and planets were considered. In mathematical astronomy,

however, mathematical descriptions provided the basis for calculations of the

positions of heavenly bodies. Oversimplifying the matter somewhat, in the former

discipline a realist stance was adopted, in the latter an instrumentalist stance.viii

Thus

a mathematical description might be regarded as ‘saving the phenomena’ – that is,

providing an account that yielded good predictions – without being taken as a true

causal explanation of the relevant motions.ix

This was precisely the point that

Osiander attempted to make in his controversial preface to the Copernicus’s De

revolutionibus (1543). The hypothesis of a sun-centred system, Osiander explained,

was to be located within the disciplinary framework of mathematical astronomy, not

natural philosophy. The heliocentric system, he implied, though physically impossible

4

in natural philosophical terms, had merit by virtue of its capacity to deliver slightly

better mathematical predictions of the positions of various heavenly bodies.x

It is also important to bear in mind that Aristotle had proscribed transfer of the

methods of one science to another. This meant that mathematics was not to be used in

the sphere of natural philosophy.xi

However, in what Aristotle had referred to as

‘subalternate sciences’ – astronomy, optics, and mechanics – some mathematical

treatment of particular subjects was permitted. Aquinas was to call these scientiae

mediae (middle sciences). These were also known as ‘subordinate sciences’ and, from

the sixteenth century onwards, were referred to as ‘mixed mathematical sciences’.xii

The exact terminology is less important than the fact that they were regarded as

something less than complete sciences. What is important about these subordinate

disciplines is the development within them of rules (regulae), such as rules of

refraction and reflection. At this time, however, these were thought of more as rules

of calculation than laws of nature in the modern sense.

Another aspect of medieval science that is directly relevant to this discussion is

Aristotle’s distinction between the natural and the artificial. In the Aristotelian scheme

of things study of the operations of machines – artificial man-made objects – was

relegated to ‘arts’ rather than the speculative sciences (which included the more

elevated disciplines of natural philosophy and mathematics).xiii

As we have seen,

insofar as the workings of machines called for mathematical analysis, such analysis

fell within the mixed mathematical sciences. Study of mechanical processes was

considered to be about the manipulation of nature, not nature itself. This was

consistent with the Aristotelian tendency to regard the operations of nature as

analogous to that of an organism rather than a machine, and was also in keeping with

Aristotle’s assumption that the cosmos was eternal – that is to say, not a created

artefact. As we shall see, the early modern conception of nature as a machine and a

divine artefact would make possible a novel union of physics as the study of nature

with mechanics as the study of artificially induced motions.xiv

Finally, it should be conceded that a vocabulary of ‘natural laws’ did exist

during the middle ages. However, its primarily reference was to the sphere of

morality.xv

In Aquinas’s typology of laws, for example, ‘eternal law’ – ‘the

5

government of things in God the Ruler of the universe’ – occupies the highest place.xvi

Next comes ‘natural law’, which for Aquinas referred to the participation of rational

creatures in the eternal law. For the rational creature this entailed ‘a natural inclination

to its proper act and end’.xvii

This teleological notion, according to which the moral

behaviour of rational creatures is to be understood as an inner impulse to a proper end,

thus parallels the Aristotelian view of motion in the universe which has all natural

objects moving by inner compulsion, as it were, to their proper place. For Aquinas,

moreover, the precepts of the natural law are universal and exceptionless, and are

capable of being intuited by any rational agent.

Developments in the later middle ages and during the eras of the Renaissance

and Reformation saw challenges issued to each of these elements of the medieval

Aristotelian worldview. A renewed emphasis on the omnipotence of God, and on the

divine will in particular, led to a questioning of the autonomy of Aristotelian nature

and of its relative independence from the Deity. The Renaissance witnessed the re-

emergence of a Christian Platonism that stressed the reality of mathematical relations,

opening up the possibility of the application of mathematics to natural philosophical

problems. Other sects of Greek philosophy were also to challenge the monopoly of

Aristotelianism, among them scepticism and the atomism of Democritus and

Epicurus. Atomistic conceptions of matter implied the inertness of nature and hence,

again, challenged the Aristotelian assumption that a purposeful, causal efficacy

resided within natural objects. Later in the sixteenth century, the Protestant

Reformation reinforced these developments by prompting renewed questions about

the appropriateness of the pagan, and putatively unchristianized philosophy of

Aristotle. If God had created the world, it was suggested, and if he ruled it directly,

why should he not issue physical laws analogous to the moral edicts set out in

scripture? If mathematics were a product of the divine mind, rather than just a

construct of human minds, why should geometrical and mathematical relations not be

genuine features of the created order? Finally, if the world were a divine artefact,

would not the distinction between natural and artificial be irrelevant to the study of

nature, and would it not be possible to transfer knowledge gained from the study of

machines to nature itself? The posing of these questions was an important

prerequisite to the emergence of the modern idea of laws of nature.

6

MATHEMATICAL LAWS, DISCIPLINARY DIVISIONS, AND THE SCIENTIFIC

REVOLUTION

In recent times historians have become somewhat wary of speaking about ‘the

scientific revolution’. Some of this reluctance has to do with the protracted nature of

the so-called revolution. Some is also to do with the fact that the study of nature in the

sixteenth and seventeenth centuries was carried out in disciplinary contexts – natural

philosophy, natural history, mathematical astronomy, and so on – that took a quite

different approach to their respective subject matters than do the disciplines of

modern science. No one doubts, however, that within these various disciplines a

number of revolutionary changes took place over the course of the sixteenth and

seventeenth centuries. Some of the most dramatic and closely studied developments

occurred in the sphere of astronomy, and consideration of these changes provides

what is perhaps the clearest illustration of how the notion of laws of nature took on

some of its characteristic features. Most important for our purposes was the

unprecedented union of mathematics and natural philosophy, and the insistence that

an amalgamation of these two disciplines might provide for a realist, rather than an

instrumentalist account of the movements of both celestial and terrestrial bodies.

Many of the canonical figures of the scientific revolution have laws associated

with their names – Galileo’s laws of fall and inertia, Descartes’ laws of motion,

Kepler’s planetary laws, Newton’s laws of motion, Boyle’s Law, Hooke’s Law,

Huygen’s Law, and Pascal’s Principle. Some of the better known of these laws

provide a mathematical account of the motions of heavenly bodies. Kepler’s third law

of planetary motion, for example, states that the square of the orbital period of planet

(the time it takes to orbit the sun) is proportional to the cube of its semi-major axis (its

mean distance from the sun). The articulation of laws such as this was not simply a

consequence of better observational data, but entailed a radical reconception of the

nature of astronomy and natural philosophy. Kepler was conscious of the fact that in

providing a mathematical account of the motions of the heavenly bodies he was

transgressing traditional disciplinary boundaries, and he was aware of the reaction that

this would provoke:

I shall have the physicists [i.e. the natural philosophers] against me in these

chapters, because I have deduced the natural properties of the planets from

immaterial things and mathematical figures…. I wish to respond briefly as

7

follows: that God the Creator, since he is a mind, and does what he wants, is

not prohibited, in attributing powers and appointing circles, from having

regard to things which are either immaterial or based on imagination. And

since he wills nothing except with absolute reason, and nothing exists except

by his will, then let my adversaries say what other reasons God had for

attributing powers, etc. since there was nothing except for qualities.xviii

What is interesting about this passage is the manner in which Kepler invokes

the divine will and his belief in a creator as the justification for, and indeed

the foundation of, his realist mathematical astronomy. The reality of

mathematical relations in the universe is asserted on the basis that God has

instantiated these relations in the created order. In fact Kepler attributed

Aristotle’s inability to conceptualise a world founded on mathematical

principles to the fact that the Greek philosopher had not believed that the

world had been created. A mathematical natural philosophy that was

unacceptable to Aristotle, Kepler wrote, is ‘acceptable to me and to all

Christians, since our faith holds that the World, which had no previous

existence, was created by God in weight, measure, and number, that is in

accordance with ideas coeternal with Him.’xix

All of this makes possible the

conviction that mathematical laws are not just human constructions and

devices for calculation, but rather describe the real relations that obtain

between physical objects in the universe.

Galileo (1564-1642) was also to invoke the notion of God as a creative

mathematician. The world, he wrote in the Dialogue concerning the Two

Chief World Systems (1632), is ‘the creation of the omnipotent Craftsman,

and is accordingly excellently proportioned.’ This mature claim he had

already foreshadowed in The Assayer, in which he famously wrote that the

book of nature had been written by God in mathematical language.xx

Mathematics, in short, was appropriate in discussions of nature because God

had imbued the universe with a mathematical order. Human beings can intuit

this order insofar as they participate in the mathematical truths that inhabit

the mind of God. It is this participation that invests human knowledge of

nature with the requisite certainty.xxi

If the application of mathematical

reasoning to the order of nature involved a deliberate breech of Aristotelian

disciplinary boundaries, Galileo nonetheless adhered to the Aristotelian ideal

of science as yielding certain and demonstrative knowledge. His aim was

8

‘absolute certainty’ and ‘necessary and eternal scientific conclusions’.xxii

Galileo was to argue (as he presented it, on the authority of Augustine) that

particular interpretations of scripture – such as those, for example, that seem

to support a geocentric cosmos – must yield to necessary truths established

in the sphere of science.xxiii

This tactic proved less successful than Galileo

had hoped. But the more important point is that Galileo sought to achieve

the Aristotelian ideal of demonstrative certainty by adopting the distinctly

un-Aristotelian procedure of introducing mathematics into physics.

Related to the introduction of mathematics into the sphere of natural philosophy

was the idea that the cosmos was a divinely created machine. Kepler wrote that the

‘celestial machine’ should be thought of ‘not on the model of a divine, animate being,

but on the model of a clock…. In [that machine] almost all the variety of motions

[stems] from one most simple, physical magnetic force…. And I mean to call this

form of reasoning ‘physics’ [done] with numbers and geometry.’xxiv

The mechanistic

model of the universe meant that the kinds of mathematical applications used in

mechanics, previously one of the mixed mathematical sciences, could now be applied

to nature itself. Such a view called for a rejection of the Aristotelian distinction

between the natural and artificial. René Descartes, one of the pioneers of the new

mechanical approach declared: ‘I do not recognise any difference between artefacts

and natural bodies except that the operations of artefacts are for the most part

performed by mechanisms which are large enough to be perceived.’ Nature’s

operations, on Descartes’ account, were analogous to those of machines, but took

place at a microscopic level beyond the sensory threshold. His conclusion, however,

was clear: ‘mechanics is a division or special case of physics’.xxv

Descartes made a

similar claim in the Discourse on Method to the effect that ‘the laws of mechanics …

are identical with the laws of nature.’xxvi

Similar assertions recur in Le Monde in

which Descartes identifies the ‘rules of collision’ with laws of nature, and in the

Principles of Philosophy in which rules from the sphere of mechanics (laws of inertia

and collision) are also equated laws of nature.xxvii

These are not idle assertions of

some trivial equivalence. Rather they amount to the claim that the rules of mechanics

or optics are to be regarded as eternal and immutable features of the natural world.

For Renaissance Aristotelians, by way of contrast, the ‘laws’ of optics and mechanics

were rules (regulae) pertaining to the methods of these mixed mathematical

9

disciplines. Such principles, in other words, were human constructs, rules of

calculation rather than laws indelibly etched into nature itself. The promotion of these

rules from the realm of human convention to that of nature was thus a major

development, justified by the assertion that these regularities were not the products of

human art, but rather represented discoveries of genuine features of the natural world.

These laws originate in the divine will rather than in the human imagination. The

constancy and immutability of these laws, for Descartes, was underwritten by the

immutability of God.xxviii

While the introduction of mathematics into the sphere of natural philosophy,

along with the idea of the world as divinely ordered machine, were important

prerequisites for the emergence of the modern notion of laws of nature, developments

in two further areas also warrant attention. These concern the related questions of

causation and the nature of matter.

MECHANISM, MATTER, AND CAUSATION

A key characteristic of the notion of laws of nature was the idea of an external

imposition of order onto the world. Such a perspective contrasted with the

Aristotelian view that attributed order to the intrinsic properties of natural things. So

not only was this new conception at odds with Aristotle’s idea that mathematics be

kept separate from natural philosophy and his insistence on maintaining a distinction

between artificial and natural motions, it was also inconsistent with the Aristotelian

view of matter and causation. The idea of divinely imposed laws was more consistent

with the recently revived matter theory of the ancient atomists and with its modern

modification, the corpuscular hypothesis.xxix

Unlike the ontologically rich

Aristotelian world, the sparse world of atoms of corpuscles was unpopulated by the

qualities, virtues, active principles, and substantial forms that had once invested

nature with significant causal agency. This was a causally vacant cosmos that would

be receptive to the direct volitions of the Deity. It was also a world that required

constant creative attention. For this reason, corpuscular theory, in spite of its

traditional associations with atheism, gained increasing acceptance during the early

modern period.xxx

10

Part of the attraction of atomism and corpuscularianism was that God’s control

over nature was no longer mediated by the secondary causes which, on the

Thomist/Aristotelian account, he was said to have implanted within nature. These

developments have been traditionally associated with the rise of theological

voluntarism – a view that stresses the pre-eminence of the divine will in God’s

dealings with the world.xxxi

While there are difficulties with a number of aspects of

the ‘voluntarism and science’ thesis, it can certainly be said that during this period

natural laws were typically understood as expressions of the divine will.xxxii

More

important than voluntarism (although sometimes confused with it) was the growing

popularity of an understanding of causation which held God to be the only genuine

cause in the universe. This was the doctrine of occasionalism. While occasionalism is

most closely associated with Cartesianism and with the philosopher Nicholas

Malebranche in particular, many natural philosophers of the period exhibited strong

occasionalist tendencies.xxxiii

This was because if one removed causal efficacy from

natural objects, as opponents of Aristotle tended to do, it followed that one either had

to remain agnostic about causation or to concentrate causal power in God. Certainly

occasionalism was not an idiosyncratic view, and neither was it an ad hoc attempt on

the part of metaphysical dualists to solve the problem of mental causation. Part of the

reason for the rise of occasionalist understandings of causation at this time is that they

meshed neatly with atomic or corpuscular matter theory.

Interestingly, this was not the first time in the West that atomism and

occasionalism had appeared together as part of an account of divine action in nature.

In the ninth century, Islamic theologians had adopted an atomic metaphysics and had

subscribed to occasionalism. The concern of kalam thinkers such as al-Ash’ari (d.

935) who espoused these views had been to affirm the ultimate authority of God,

which it was believed would have been compromised had causal power been

attributed to natural agents. Discussion continued amongst Islamic scholars

throughout the eleventh and twelfth centuries. Ibn Rushd (Averroës, d.1198) mounted

strong Aristotelian arguments against occasionalism but his views were received more

favourably in the Christian West.xxxiv

Ironically, commitment to occasionalism has

sometimes been identified as a factor that inhibited the growth of Islamic science.

This interpretation is possibly the consequence of identifying Aristotelianism as the

more genuinely ‘scientific’ position. In the seventeenth century it could be said that

11

the reverse was the case, with occasionalism offering a way of explaining motion and

change without requiring recourse to the rich causal resources provided by

Aristotelianism.

Descartes and Malebranche represent the clearest examples of how this doctrine

of causation related to the idea of laws of nature. The differences between their

approach and that of the Aristotelians is nicely set out by historian Dennis Des Chene:

The Aristotelian philosophy takes natural change to be the work of active

powers in nature itself, in which God concurs. The Cartesian interprets it as

the work of God alone, subject to natural laws, appeal to which will help

demonstrate the observed regularities which by the Aristotelian are referred

to the intrinsic powers of material things, and to the ends toward which they

act.xxxv

The Cartesians, however, like many of their contemporaries, retained an attachment to

the Aristotelian ideal of science as certain and demonstrable knowledge. Descartes

thus described his goal as that of establishing a ‘certain science’ or as achieving

‘perfect scientific knowledge’.xxxvi

This certain science was to be premised on an

assumption that the motions of objects in the physical world are best understood in

terms of mathematical descriptions rather than causal powers. Natural philosophers,

Descartes urged, should concern themselves ‘only with objects which admit of as

much certainty as the demonstrations of arithmetic and geometry.’xxxvii

Tiny particles

of matter, evacuated of causal efficacy and other properties, were perfect candidates

for such treatment. As to their motions and what made them necessary and law-like,

this was ascribed to the divine will.

In his Principles of Philosophy (1644), Descartes first set out his three ‘laws of

nature’. He begins by asserting that ‘God imparted various motions to the parts of

matter when he first created them, and he now preserves all this matter in the same

way, and by the same process by which he originally created it.’ It follows from this,

Descartes concludes, that God likewise always preserves the same quantity of motion

in matter. The principle of conservation of motion is thus underwritten by divine

immutability.xxxviii

The first law is essentially that simple objects remain in the same

state and change only as a consequence of external causes; the second, that objects

tend to move in straight lines; the third concerns rules of collision.xxxix

What gives

these laws their necessity is the fact that they are derived from the divine nature.

Indeed for Descartes all necessary relations – including not only the laws of nature,

12

but also the laws of mathematics and logic – are ultimately dependent on the divine

will. As he explained to his friend Mersenne, ‘the mathematical truths, which you call

eternal, were established by God and totally depend on him just like all the other

creatures.’xl

Descartes thus suggested that there were necessary relations in nature that

derived their necessity from the fact that an omnipotent and immutable Deity had

promulgated unchanging laws and was acting constantly and directly to produce

motion and change in the universe.xli

Malebranche’s occasionalism is simply the logical conclusion of the Cartesian

project, for natural causality is, in a sense, the last of the Aristotelian occult qualities

to be banished from the world. It was Malebranche’s great insight, as Nicholas Jolley

has expressed it, to have realized that ‘the traditional idea of causal powers needs to

be replaced by the more modern notion of natural law.’xlii

For Malebranche, and

indeed all early modern occasionalists, God directly imposed his will on brute matter

in systematic ways that could be described, on analogy with divinely instituted moral

imperatives, as ‘laws’. Necessary connections between two states of affairs,

Malebranche pointed, can only be established by God. Physical necessity, in other

words, was grounded in God, and the exceptionless character of laws of nature was

attributed to divine immutability.

NECESSITY, CONTINGENCY AND CREATION

The culmination of the application of mathematics to the problems of natural

philosophy came with Isaac Newton’s magnum opus Philosophiae naturalis principia

mathematica (‘The Mathematical Principles of Natural Philosophy’, 1687). This

work contains Newton’s three laws of motion along with an articulation of the

universal law of gravity.xliii

The title of the work and the method prescribed within

have become so familiar to modern readers that its novelty is often overlooked. To its

contemporaries, however, the startling combination of approaches recommended in

the title bears witness to the bold new direction of early modern physics. Henceforth,

natural philosophy or physics will be a discipline with mathematical principles.xliv

Newton was also conscious of the fact that explanations couched in terms of laws of

nature represented a distinctively new way of pursuing science. In the Preface to the

first edition of the Principia he pointed out that while the ancients had pursued the

investigation of nature by attempting to identify inherent forms and qualities in things,

13

the moderns ‘have undertaken to reduce the phenomena of nature to mathematical

laws’.xlv

In his other masterwork, the Opticks (1704), Newton also stressed the fact

that phenomena such as gravity are not qualities inhering ‘in the specifick forms of

Things’ but rather result from ‘general Laws of Nature’.xlvi

As with Descartes and Kepler, these laws were directly imposed by God. Roger

Cotes, who penned the Preface to the second edition of the Principia, summarized it

this way: ‘all the laws that are called laws of nature’ come from ‘the perfectly free

will of God.’ Yet the most likely cause of motion in the universe was, as it had been

for Descartes, God himself. Newton wrote in a letter to Richard Bentley that ‘gravity

must be caused by an agent acting constantly according to certain laws, but whether

this agent be material or immaterial I have left to the consideration of my readers.’xlvii

Newton most probably believed the latter.xlviii

In another unpublished remark, he

spoke of ‘an infinite and omnipresent spirit in which matter is moved according to

mathematical laws.’xlix

His correspondent, Richard Bentley, was less circumspect,

declaring in his 1691-2 Boyle Lectures that ‘all the powers of mechanism are

dependent on the Deity’, for ‘gravity, the great basis of all mechanism, is not itself

mechanical, but the immediate fiat and finger of God, and the execution of divine

law.’l Others within Newton’s circle adopted the view that all that happens in nature

does so as the direct consequence of God’s willing it. Isaac Barrow, the first Lucasian

Professor of Mathematics at Cambridge and Newton’s immediate predecessor in that

famous chair, stated simply that ‘the efficient Cause of all Things is God’.li God

governs the world directly, for he ‘uses no other means, instruments or applications in

these productions, than his bare word or command’.lii

The Anglican Divine Samuel

Clarke, who was Newton’s spokesman in the controversy with Leibniz and the most

philosophically able theologian of his generation, also contended that laws of nature

were nothing other than God’s volitions: ‘the Course of Nature, cannot possibly be

any thing else, but the Arbitrary Will and pleasure of God exerting itself and acting

upon Matter continually.’liii

There was a significant difference between the position of Newton and the

Cartesians, however. In fact, much of Cotes’s Preface is given over to highlighting

exactly where that difference lay. According to Cotes, Descartes’ laws had a logical

necessity that could be intuited by the rational mind. This method, he wrote, proceeds

14

on the basis of ‘untrustworthy conjectures’, assumes that nature is characterised by

necessity, and that ‘insignificant’ human beings can arrive at a clear understanding of

those necessary connections through the exercise of reason alone. By way of contrast,

the Newtonian approach was presented as relying less on ‘the internal light of reason’

and more on ‘observing and experimenting’.liv

One difficulty with the method of

‘observing and experimenting’ is whether it could yield the kind of certainties that the

Cartesian approach seemed to offer. How, on the basis of numerous observations,

could one arrive at the notion of an exceptionless mathematical law? This is the issue

that modern philosophers recognise as the problem of induction. Newton seemed to

believe that an appropriate combination of experiment, observation and mathematical

reasoning would provide a heightened level of certainty. Where previous

experimentalists had tended to settle for probabilistic and tentative conclusions,

Newton aimed for mathematical demonstrability, proceeding, in his own words, ‘in

imitation of the method by wch

Mathematitians are wont to prove their doctrines.’lv

This, he thought, would promote a natural science that rejected ‘probabilities’ and was

‘supported by the greatest evidence’. lvi

Among Newton’s peers, other solutions were

offered. Isaac Barrow thought that the philosopher ought to accept any proposition

‘confirmed with frequent Experiments as universally true, and not suspect that Nature

is inconstant, and the great Author of the universe unlike himself’.lvii

That is to say

that we can assume a uniformity in nature’s operations because God is consistent in

all his actions. This seems very much like the Cartesian idea that the constancy of

nature is grounded in the qualities of God. The difference, however, lies in the manner

in which the laws discovered. For Descartes they are intuited from the divine nature,

for the Newtonians they must be discovered by experimentation.

CONCLUSION

If we return to the three questions posed at the outset of this chapter – why there

are laws of nature at all, why they are mathematical, and why they are exceptionless –

we are now in a better position to see how, for those who first articulated the idea of

laws of nature, the answer to each question involved some significant theological

commitment. The idea of a world governed by laws of nature was the result of a new

view of the relation of God to the world in which God is more directly involved in the

operations of nature. Its early modern proponents argued this to be a more ‘Christian’

15

view of nature than the Aristotelian worldview that it replaced. These laws are

mathematical because God was conceptualized as the divine mathematician. The

necessary character of these laws was seen to arise out of the fact that God’s will is

immutable, and hence the laws that he wills into effect are unchangeable.

The subsequent history of the notion of laws of nature, it must be said, has

conspired to conceal the theological origins of the idea. Two distinct developments

are worth brief consideration. First, it must be recognised that the notion of laws of

nature, however much it may have rested on theological convictions, inevitably led to

a desacralization of the natural world. Not only were intrinsic powers and qualities

banished from the world, but the rigid necessity of the new laws of nature meant that

with the passage of time lawfulness came to be regarded simply as an unremarkable

feature of the world itself, and one needing no further explanation. Ironically, the very

constancy of divine action served to make God increasingly irrelevant as an

explanatory mechanism. In the nineteenth century, laws of nature came to be regarded

not as laws imposed on nature by God, but literally as laws of nature itself.

Alternative expressions now include ‘laws of science’ or ‘scientific laws’, reflecting

the elevation of the status of science and scientists, and the corresponding decline in

the emphasis on God’s role in the instantiation of natural laws.lviii

A significant phase

in this development came with the nineteenth-century transformation of natural

history into the science of biology. This transition involved, amongst other things, a

growing rejection of the pace of natural theology in the life sciences, and the assertion

that biology, like physics, had its own laws. Thomas Huxley, who did so much to

promote this process, thus announced that ‘a rational order … pervades the universe’,

it being the task of science to uncover it.lix

God was thus supplanted by the notion of

a ‘rational order’, the existence of which was simply assumed. Huxley also drew an

analogy between the laws of Newtonian physics and the ‘laws’ that were presumed to

characterise the new biological science. Robert Chambers, in his notorious Vestiges of

the Natural History of Creation (1844), had already established the beachhead: ‘The

inorganic [world] has one final and comprehensible law – Gravitation. The organic,

the other great department of mundane things, rests in like manner on one law, and

that is – Development’.lx

Subsequently, Charles Darwin, in the final sentence of the

first edition of the Origin, also equated the law of evolution with the law of

gravitation: ‘whilst this planet has gone cycling on according to the fixed law of

16

gravity, from so simple a beginning endless forms most beautiful and most wonderful

have been, and are being, evolved.’lxi

The persuasiveness of this analogy rested upon

a subtle equivocation, for the ‘laws’ of evolutionary biology are historical or

phylogenetic, and the subjects to which the laws apply are unique organisms.lxii

Nonetheless this was part of the process by which the new biological science was

presented rhetorically as a suitable replacement for an obsolete and theologically

oriented natural history. Robert Young has plausibly suggested that there is a

continuity in this transition, in which one belief system based on natural theology and

divine law replaced a comparable system, one now devoid of supernatural elements

and based instead on notions of natural law and natural selection.lxiii

Common to both

systems was the notion of a nature governed by laws; the transition entailed only a

shift in the understanding of the origin of those laws. Now separated from its original

theistic justifications, the idea of laws of nature was given wider application in the

twentieth century, losing both its deterministic and theistic connotations – witness the

appearance of such statistical laws as the Hardy Weinberg Law in population genetics,

and the more mathematically exact, but no less probabilistic laws of quantum

mechanics. Einstein’s oft-quoted epigram in response to the latter, that God ‘does not

play dice’, reflects the largely forgotten origins of the older view.

Developments in the philosophical realm were also significant for the later

history of laws of nature. In the eighteenth century, David Hume was to agree with

Malebranche and others that causation was not located in nature itself. But neither, for

Hume, was it to be found in the divine will. Rather, causation existed only in the

human mind, in our habit of attributing necessary connections to events that we

observe to be constantly conjoined. Kant formalized this view, asserting that causes

were not a feature of the world in itself, but a feature of the manner in which we

necessarily perceive events in the world. For this reason Kant denied the efficacy of

traditional arguments for the existence of God and, in particular, the cosmological

argument that assumes the reality of causal relations in order to establish the existence

of a first cause.

Contemporary philosophers are divided on even the most fundamental questions

relating to laws of nature. Some still wish to assert that laws of nature capture some

necessary state of affairs. Others support something like a Humean view, according to

17

which laws of nature are significantly mind-dependent. A minority find the problems

associated with each of these views insurmountable, and consequently assert that

there are simply no such things as laws of nature.lxiv

This contemporary confusion

results in part from the fact that the idea of laws of nature has been torn loose from its

original theological moorings. Failure to grasp this point also leads to a degree of

conceptual untidiness in some contemporary discussions of the cosmological

argument in relation to laws of nature. One encounters the idea that science discovers

mathematical laws, and that this provides the premise of a cosmological argument on

the basis of which we can infer the existence of first source of causal intelligibility.

However, if we take into consideration the relevant history, it seems that certain

theistic assumptions are already disguised in the premises of these arguments. A small

consolation, perhaps, is the possibility of an alternative argument – that science,

insofar as it assumes the reality of mathematical laws, operates with a tacitly theistic

assumption about the nature of the universe. Tracing the history of the notion of laws

of nature helps us to see that such lawfulness is not a self-evident feature of the

universe but, as it was originally conceived at least, an implication of certain

theological convictions.

18

NOTES

i The best recent account of the historical origin of laws of nature is John Henry,

‘Metaphysics and the Origins of Modern Science: Descartes and the Importance of

Laws of Nature’, Early Science and Medicine, 9 (2004): 73-114. See also Edgar

Zilsel, ‘The Genesis of the Concept of Scientific Law’, The Philosophical Review, 51

(1942): 245-67; Joseph Needham, ‘Human Laws and the Laws of Nature in China and

the West’, Journal of the History of Ideas, 12 (1951): 3-32, 194-231; Jane Ruby, ‘The

Origins of Scientific Law’, Journal of the History of Ideas, 47 (1986): 341-59; J.R.

Milton, ‘Laws of Nature’, in Daniel Garber and Michael Ayers (eds.), The Cambridge

History of Seventeenth-Century Philosophy (2 vols., Cambridge, 1998), vol. 1, pp.

680-701; Friedrich Steinle, ‘The Amalgamation of a Concept – Laws of Nature in the

New Sciences’, in Friedel Weinert (ed.), Laws of Nature: Essays on the

Philosophical, Scientific and Historical Dimensions (Berlin, 1995), pp. 316-368.

Specifically on theological influences see Francis Oakley, ‘Christian theology and the

Newtonian science: the rise of the concept of laws of nature’, Church History, 30

(1961): 433-57; M.B. Foster, ‘The Christian doctrine of creation and the rise of

modern natural science’, Mind, 18 (1934): 446-68; Peter Harrison, ‘Newtonian

Science, Miracles, and the Laws of Nature’, Journal of the History of Ideas, 56

(1995): 531-53; Alan Padgett, ‘The Roots of the Western Concept of the “Laws of

Nature”: From the Greeks to Newton’, Perspectives on Science and Christian Faith,

55 (2003): 212-21.

ii Aquinas, Summa contra gentiles 3b, 100, tr. English Dominican Fathers (5 vols.,

London, 1934), vol. 4, p. 58; Quaestiones disputatae de potentia dei, Bk. 1, q. 3, a. 8,

rp. 2, English translation, On the Power of God, tr. English Dominican Fathers

(London, 1932), p. 143.

iii Aquinas, Summa contra Gentiles 3b, 99 (vol. 4, p. 57). Such events were known as

‘praeternatural’. See Lorraine Daston, ‘Miraculous Facts and Miraculous Evidence in

Early Modern Europe’, Critical Inquiry, 18 (1991): 93-124

iv Aquinas, Summa contra gentiles 3b, 99 (vol. 4, p. 57).

v Aristotle, Metaphysics 1026b- 1027a, 1064b-1065a. For Medieval and Renaissance

versions of this view see Aquinas, Commentary on the Metaphysics of Aristotle

11.8.2276, tr. John P. Rowan (2 vols., Chicago, 1961), Vol. 2, p. 814; Matteo

19

Palmieri, Civil Life II, in Renaissance Philosophical Texts, ed. Jill Kraye, (2 vols.,

Cambridge, 1997) vol. 2, pp. 149-72 (esp. p. 153).

vi Aristotle, Posterior Analytics 71b-72b. For the reception of this doctrine during the

Renaissance see Peter Dear, ‘Method and the Study of Nature’, in Garber and Ayers

(eds.), Cambridge History of Seventeenth-Century Philosophy, vol. 1, pp. 147-177;

Heikki Mikkeli, An Aristotelian Response to Renaissance Humanism: Jacopo

Zabarella on the Nature of Arts and Sciences (Helsinki, 1992).

vii Aristotle, Posterior Analytics, 75b.

viii This kind of instrumentalism is not quite the same as that espoused within some

contemporary philosophy of science circles, however. See P. Barker and B.R.

Goldstein, ‘Realism and Instrumentalism in Sixteenth Century Astronomy: A

Reappraisal’, Perspectives on Science, 6 (1998): 232-258.

ix Thus Aquinas, e.g.: ‘Yet it is not necessary that the various [mathematical]

suppositions which they [Eudoxus and later astronomers] hit upon be true—for

although these suppositions save the appearances, we are nevertheless not obliged to

say that these suppositions are true, because perhaps there is some other way men

have not yet grasped by which the things which appear as to the stars are saved.

Exposition of Aristotle's Treatise on the Heavens II.17.451, tr. R. Larcher and P.

Conway, (2 vols., Columbus, 1963-4), vol. 2, p. 74.

x ‘For it is not necessary that these hypotheses should be true, or even probable; but it

is enough if they provide a calculus which fits the observations’. Nicolaus

Copernicus, On the Revolutions of the Heavenly Spheres, tr. Charles Glenn Wallis

(Amherst, 1995), p. 3.

xi Aristotle, Metaphysics 989b-990a, 1025b-1026a; On the Heavens 299a-299b. See

also Amos Funkenstein, Theology and the Scientific Imagination (Princeton, 1986),

pp. 35-7, 303-7.

xii See Mikkeli, An Aristotelian Response to Renaissance Humanism, pp. 40-44; J.A.

Weisheipl, ‘Classification of the Sciences in Medieval Thought’, Mediaeval Studies,

27 (1965): 54-90; R.D. McKirahan, Jr., ‘Aristotle’s Subordinate Sciences’, British

Journal for the History of Science, 11 (1978): 197-220; J.G. Lennox, ‘Aristotle,

Galileo, and “Mixed Science”’, in W.A. Wallace (ed.), Reinterpreting Galileo

(Washington, D.C., 1986), pp. 29-51; Peter Harrison, ‘Physico-Theology and the

Mixed Sciences: The Role of Theology in Early Modern Natural Philosophy’, in Peter

20

Anstey and John Schuster (eds.), The Science of Nature in the Seventeenth Century

(Dordrecht, 2005), pp. 165-183.

xiii Pseudo-Aristotle, Mechanics, 847. For a discussion of Aristotle’s distinction

between arts and sciences and its reception during the Renaissance see Mikkeli,

Zabarella on the Nature of Arts and Sciences, pp. 21-34; P.L. Rose and S. Drake,

‘The Pseudo-Aristotelian Questions of Mechanics in Renaissance Culture’, Studies in

the Renaissance, 18 (1971): 65-105.

xiv Alan Gabbey, ‘Between ars and philosophia naturalis: Reflections on the

historiography of Early Modern Mechanics’, in J. Field and F. James (eds.),

Renaissance and Revolution (Cambridge, 1993), pp. 649-679; Peter Anstey, The

Philosophy of Robert Boyle (London: Routledge, 2000), pp. 1-4. Admittedly,

medieval comparisons of the cosmos to a vast machine may be found in Hugh of St

Victor, De arca Noe morali IV.7; Henry of Langenstein Lecturae super Genesim,

I.35va.

xv Jane Ruby and A.C. Crombie have pointed out that Roger Bacon (c. 1210—

c.1292) spoke of ‘laws [lex, leges] of reflection and refraction, and of these

collectively as ‘laws of nature.’ See A.C. Crombie, ‘The Significance of Medieval

Discussions of Scientific Method for the Scientific Revolution’, Critical Problems in

the History of Science (Madison, 1959), p. 89; Medieval and Modern Science

(Garden City, 1959), 24; Joseph Needham, The Grand Titration: Science and Society

in East and West (Toronto, 1969), 310; Ruby, ‘The Origins of Scientific Law’, pp.

343f. Crombie points to the possible influence of the Platonising philosopher Robert

Grosseteste (1175-1253). This is suggestive of an alternative Platonic source of the

modern notion of natural law. However, it is consistent with neither the Aristotelian

understanding of the mathematical sciences, nor the voluntarist tendencies of most of

those who were subsequently to speak of laws of nature in this sense in the early

modern period.

xvi Aquinas, Summa theologiae 1a2ae. 91, 1.

xvii Aquinas, Summa theologiae 1a2ae. 91, 2.

xviii Johannes Kepler, Mysterium Cosmographicum tr. A.M. Duncan (Norwalk, CT,

Abarus, 1999), p. 123.

xix Kepler, The Harmony of the World, tr. and intro. by E.J. Aiton, A.M. Duncan, J.V.

Field (Philadelphia, 1997), pp. 115, 146. The reference to ‘weight, measure, and

21

number’ comes from the Book of Wisdom 11:12, a favourite passage of Augustine.

See The Trinity, XI.iv; The Literal Meaning of Genesis IV, 3, 7-12; Confessions

V.iv.7; Answer to an Enemy of the Law and the Prophets I, 6, 8; Free Will, III, 12, 35.

See also W. Bierwaltes, ‘Augustins Interpretation von Sapientia 11,21,’ Revue des

études augustiniennes, 15 (1969): 51-61. On the reasons for Kepler’s realist stance see

Kenneth J. Howell, God’s Two Books: Copernican Cosmology and Biblical

Interpretation in Early Modern Science (Notre Dame, 2002), pp. 126f.

xx Galileo, Dialogue concerning the Two Chief World Systems, tr. Stillman Drake

(New York, 2001), p. 3; The Assayer, in Discoveries and Opinions of Galileo, tr.

Stillman Drake (New York, 1957), pp. 237f. On the novelty of this understanding of

the book of nature see Peter Harrison, The Bible, Protestantism, and the Rise of

Natural Science (Cambridge, 1998), pp. 1-5.

xxi Galileo, Dialogue concerning the Two Chief World Systems, pp. 11, 118f. For

Galileo’s ‘Platonism’ see James Hankins, ‘Galileo, Ficino, and Renaissance

Platonism’, in Jill Kraye and M.W.F. Stone (eds.), Humanism and Early Modern

Philosophy (London, 2000), pp. 209-237.

xxii Ibid., pp. 119, 471. On Galileo’s understanding of science see Ernan McMullin,

‘The Conception of Science in Galileo’s Work’, in Robert Butts and Joseph Pitt

(eds.), New Perspectives on Galileo (Dordrecht, 1978), pp. 209-57; Arkady Plotinsky

and David Reed, ‘Discourse, Mathematics, Demonstration, and Science in Galileo's

Discourses Concerning Two New Sciences’, Configurations, 9 (2001): 37-64.

xxiii Galileo, Letter to the Grand Duchess Christina in Discoveries and Opinions, pp.

186f., 194. Cf. Augustine, On the Literal Interpretation of Genesis 1.21.

xxiv Kepler to Herward von Hohenberg, 10 February 1605, qu. in Michael Mahony,

‘The Mathematical Realm of Nature’, in Garber and Ayers (eds.), Cambridge History

of Seventeenth Century Philosophy, vol. 1, pp. 702-55 (p. 706).

xxv René Descartes, The Principles of Philosophy, in The Philosophical writings of

Descartes [CSM] tr. John Cottingham, Robert Stoothoff, Dugald Murdoch, and

Anthony Kenny (3 vols., Cambridge, 1984-91) vol. 1, p. 288. Bacon also denied the

significance of the distinction between the artificial and the natural. See Paolo Rossi,

Philosophy, Technology and the Arts in the Early Modern Era (New York, 1970), pp.

138f.

xxvi Descartes, Discourse, CSM vol. 1, p. 137.

22

xxvii

Descartes, The World, CSM vol. I, p. 97; Principles, CSM vol. 1, p. 240.

xxviii Descartes, Principles of Philosophy, CSM vol. 1, p. 286.

xxix Atomism posits indivisible particles and the existence of a void for them to move

in. The corpuscular hypothesis holds that matter is made of invisible, but not

necessarily indivisible, particles. Corpuscularians might also deny the existence of the

void (as Descartes did).

xxx Mersenne thus specifically developed a mechanistic account of nature in response

to the perceived dangers of too close an association of God and nature. See Stephen

Gaukroger, Descartes: An Intellectual Biography (Cambridge, 1997), pp. 146-52. The

relative merits of Epicurean atomism and Aristotelianism in terms of their

compatibility with Christian notions of creation also featured in cosmological debates.

See Harrison, ‘The Influence of Cartesian Cosmology in England’, in S. Gaukroger, J.

Schuster, and J. Sutton (eds.), Descartes’ Natural Philosophy (London, 2000), pp.

168-92. See also Margaret Osler (ed.), Atoms, Pneuma, and Tranquillity: Epicurean

and Stoic Themes in European Thought (Cambridge, 1991).

xxxi From the large body of literature on this topic see, e.g., Foster, ‘The Christian

doctrine of creation and the rise of modern natural science’; Oakley, ‘Christian

theology and the Newtonian science: the rise of the concept of laws of nature’;

Eugene Klaaren, Religious origins of modern science (Grand Rapids, 1977); Peter

Heimann, ‘Voluntarism and immanence: conceptions of nature in eighteenth-century

thought’, Journal of the history of ideas, 39 (1978): 271-83; Margaret Osler, Divine

will and the mechanical philosophy: Gassendi and Descartes on contingency and

necessity in the created world (Cambridge, 1994).

xxxii For a critique of some aspects of this thesis see Peter Harrison, ‘Voluntarism and

Early Modern Science’, History of Science, 40 (2002): 63-89; Harrison, ‘Was Newton

a Voluntarist?’, in J.E. Force and S. Hutton (eds.), Newton and Newtonianism: New

Studies (Dordrecht, 2004), pp. 39-63.

xxxiii Seventeenth-century occasionalists include Arnold Geulincx, Louis de La Forge,

Gérauld de Cordemoy, and probably Antoine Arnauld, Johann Clauberg and

Descartes himself. See Desmond Clarke, ‘Casual Powers and Occasionalism from

Descartes to Malebranche’, in Gaukroger, Schuster, and Sutton (eds.) Descartes’

Natural Philosophy, pp. 131-48; Daniel Garber, ‘Descartes and occasionalism’, in

Steven Nadler (ed.), Causation in Early Modern Philosophy, (University Park, 1993),

23

pp. 9-26; Steven Nadler, ‘Occasionalism and the Question of Arnauld’s

Cartesianism’, in Roger Ariew and Marjorie Grene (eds.), Descartes and his

contemporaries (Chicago, 1996), pp. 129-44; ‘Doctrines of explanation in late

scholasticism and in the mechanical philosophy’, in Garber and Ayers (eds.),

Cambridge history of seventeenth-century philosophy, vol. 1, pp. 513-52; Daniel

Garber, ‘How God causes motion: Descartes, divine substance, and occasionalism’,

Journal of philosophy, 84 (1987): 567-80.

xxxiv D. Gimaret, La doctrine d'al-Ash'ari, (Paris, 1990); M. Fakhry, Islamic

Occasionalism and its Critique by Averroës and Aquinas (London, 1958); Barry S.

Kogan, Averroës and the Metaphysics of Causation (Albany, 1985); H. Brown,

‘Avicenna and the Christian Philosophers in Baghdad’, in S. Stern, A. Hourani, and

Vivian Brown (eds.), Islamic Philosophy and the Classical Tradition (Columbia, SC,

1972), pp. 35-48; L. Goodman, ‘Did al-Ghazali deny Causality?’ Studia Islamica, 47

(1978): 83-120.

xxxv Dennis Des Chene, ‘On Laws and Ends: A Response to Hattab and Menn’,

Perspectives on Science, 8 (2000): 144-63.

xxxvi ‘All knowledge [scientia] is certain and evident cognition.’ Rules for the

Direction of the Mind, CSM vol. 1, p. 10. See also CSM vol. 2, p. 408; CSM vol. 1,

pp. 197, 179, 201; CSM vol. 3, p. 38.

xxxvii Descartes, Rule for the Direction of the Mind, CSM vol. 1, p. 12.

xxxviii Descartes, Principles of Philosophy, § 61, CSM vol. 1, p. 240.

xxxix Descartes, Principles of Philosophy, §§ 61, 63, 65, CSM vol. 1, pp. 240-2.

xl Descartes to Mersenne, 15 April 1630, CSM vol. 3, p. 23.

xli Descartes, The World, CSM vol. 1, pp. 93, 96; Principles of Philosophy, CSM vol.

1, p. 240. Whether Descartes believed in the existence of secondary causes remains a

contested issue. See Helen Hattab, ‘Descartes on Secondary Causes: A Response to

Des Chene’, Perspectives on Science, 8 (2000): 93-116; Garber, ‘How God causes

motion’, and ‘Descartes and occasionalism’.

xlii Nicholas Malebranche, Dialogues on Metaphysics and Religion, ed. Nicholas

Jolley and David Scott (Cambridge, 1997), intro. by Nicholas Jolley, p. xxii. cf. p.

xxvii.

xliii Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, tr.

I. Bernad Cohen and Anne Whitman (Berkeley, 1999), pp. 416f.

24

xliv

See esp. Andrew Cunningham, ‘How the Principia got its Name: Or, Taking

Natural Philosophy Seriously’, History of Science, 28 (1991): 377-92.

xlv Newton, Principia, p. 381.

xlvi Newton, Opticks (New York, 1979), p. 401.

xlvii Newton to Bentley, 25 February 1692, in The Correspondence of Sir Isaac

Newton, ed. H.W. Turnbull (7 vols., Cambridge, 1959-77) vol. 4, p. 438.

xlviii See, e.g. Alexander Koyré, ‘Gravity an Essential Property of Matter’, Newtonian

Studies (Chicago, 1968), pp. 149-63; I.B. Cohen, ‘Newton’s Third Law and Universal

Gravitation’, Journal of the History of Ideas, 48 (1987): 571-93. For a summary of

these interpretations see John Henry, ‘“Pray do not Ascribe that Notion to Me”: God

and Newton’s Gravity’, in James Force and Richard Popkin (eds.), The Books of

Nature and Scripture (Dordrecht, 1994), pp. 123-147. Ernan McMullin frankly

concludes that Newton seemed to have no clear and consistent position on this issue.

Newton on Matter and Activity (Notre Dame, 1978), p. 104.

xlix Draft corollary to Proposition 6 of the Principia, qu. in John Brooke, ‘The God of

Isaac Newton’, in John Fauvel, et al. (eds.), Let Newton Be, ed. (Oxford: Oxford

University Press, 1990), p. 172.

l Richard Bentley, Boyle Lectures, Sermon IV, in The Works of Richard Bentley,

D.D., 6th

edn., ed. Alexander Dyce (3 vols., London, 1836), vol. 3, pp. 74-5.

li Barrow, The Usefulness of mathematical learning explained and demonstrated, tr.

John Kirby (London, 1734), Lecture VII, p. 109.

lii Barrow, ‘Maker of heaven and earth’, (Sermon XII), in Theological works, (3 vols.

London, 1885), vol. 2, p. 303. Cf. Isaac Newton, Unpublished scientific papers of

Isaac Newton, ed. and tr. A. Rupert Hall and Marie Boas Hall (Cambridge, 1962), p.

139; William Whiston, A New Theory of the Earth (London, 1696), pp. 6, 211.

liii Samuel Clarke, ‘The Evidences of natural and revealed religion’, The Works of

Samuel Clarke, D.D., (2 vols., London, 1738), vol. 2, p. 698.

liv Newton, Principia, pp. 397f.

lv Newton to Oldenburg, 21 September 1672, Correspondence, vol. 1, p. 237.

lvi Newton, The Optical Papers of Isaac Newton, Vol. 1. The optical lectures 1670–

1672, ed. Alan Shapiro (Cambridge, 1984), vol. 1, p. 89. Newton’s methodology

remains problematic, however, even to modern interpreters. See Rob Iliffe, ‘Abstract

considerations: disciplines and the incoherence of Newton’s natural philosophy’,

25

Studies in History and Philosophy of Science, 35A (2004): 427-54; Peter Dear,

‘Method and the Study of Nature’.

lvii Barrow, Usefulness, pp. 73-74. For Newton’s response to this problem see G.A.J.

Rogers, ‘Newton and the Guaranteeing God’ in James Force and Richard Popkin

(eds.), Newton and religion: context, nature, and influence (Dordrecht, 1999), pp.

221-36.

lviii Some philosophers maintain a formal distinction between laws of nature and laws

of science. The latter are said to admit exceptions. See Michael Scriven, ‘The Key

Property of a Physical Law—Inaccuracy’, in H. Feigl and H. Maxwell (eds.), Current

Issues in the Philosophy of Science, (New York, 1961), pp. 91-104; Nancy

Cartwright, How the Laws of Physics Lie, (Oxford, 1983); M. Lange, ‘Natural Laws

and the Problem of Provisos’, Erkenntnis 38 (1993): 233-248.

lix T.H. Huxley, ‘The Progress of Science’, [1887], in Methods and Results (New

York, 1894), pp. 60-1.

lx Robert Chambers, Vestiges of the Natural History of Creation (London, 1844), p.

36. Chambers nonetheless suggests that both ‘laws’ are subsets of ‘one still more

comprehensive law’ that originates from God.

lxi Charles Darwin, The Origin of Species (Chicago, 1952), p. 243.

lxii On this equivocation regarding natural laws see George Levine, ‘Scientific

Discourse as an Alternative to Faith’ in Richard J. Helmstadter and Bernard Lightman

(eds.), Victorian Faith in Crisis (Basingstoke, 1990), pp. 225-61 (esp. pp. 236f.);

David L. Hull, Darwin and his Critics: The Reception of Darwin’s Theory by the

Scientific Community (Cambridge, Mass., 1973), pp. 64-74; Ernst Mayr, The Growth

of Biological Thought (Cambridge, Mass., 1982), pp. 36-67.

lxiii Robert M. Young, Darwin’s Metaphor: Nature’s Place in Victorian Culture

(Cambridge: Cambridge University Press, 1985).

lxiv Representatives of the first view include David Armstrong, What Is a Law of

Nature? (Cambridge, 1983); Fred Dretske, ‘Laws of Nature’, Philosophy of Science,

44 (1977): 248-268; Michael Tooley, Causation (Oxford, 1987). Armstrong holds that

laws of nature describe a relation between two universals. David Lewis was the

foremost proponent of a neo-Humean view. See his Counterfactuals (Cambridge,

Mass., 1973), and ‘Humean Supervenience Debugged’, Mind 103 (1994): 473-390.

See also John Earman, ‘The Universality of Laws’, Philosophy of Science, 45 (1978):

26

173-181; Barry Loewer, ‘Humean Supervenience’, Philosophical Topics, 24 (1996):

101-126. Doubting the existence of laws of nature are Bas von Fraassen, Laws and

Symmetry, (Oxford, 1989), and Ronald Giere, Science Without Laws, (Chicago,

1999).