Found Phys (2010) 40: 1611–1624DOI 10.1007/s10701-010-9470-y

The Contingency of Laws of Nature in Scienceand Theology

Lydia Jaeger

Received: 19 December 2009 / Accepted: 24 May 2010 / Published online: 22 June 2010© Springer Science+Business Media, LLC 2010

Abstract The belief that laws of nature are contingent played an important role inthe emergence of the empirical method of modern physics. During the scientific revo-lution, this belief was based on the idea of voluntary creation. Taking up Peter Mittel-staedt’s work on laws of nature, this article explores several alternative answers whichdo not overtly make use of metaphysics: some laws are laws of mathematics; macro-scopic laws can emerge from the interplay of numerous subsystems without any spe-cific microscopic nomic structures (John Wheeler’s “law without law”); laws are thepreconditions of scientific experience (Kant); laws are theoretical abstractions whichonly apply in very limited circumstances (Nancy Cartwright). Whereas Cartwright’sapproach is in tension with modern scientific methodology, the first three strategiescount as illuminating, though partial answers. It is important for the empirical methodof modern physics that these three strategies, even when taken together, do not pro-vide a complete explanation of the order of nature. Thus the question of why laws arevalid is still relevant. In the concluding section, I argue that the traditional answer,based on voluntary creation, provides the right balance of contingency and coherencewhich is in harmony with modern scientific method.

Keywords Laws of nature · Experimental method · Scientific revolution · Creation ·Contingency of laws · Peter Mittelstaedt · John A. Wheeler · Immanuel Kant ·Nancy Cartwright

This article is based on the talk I gave at the symposium in honour of Peter Mittelstaedt on theoccasion of his 80th birthday at the University of Cologne on December 4, 2009.

L. Jaeger (�)Institut Biblique de Nogent-sur-Marne, 39 Grande Rue, 94130 Nogent-sur-Marne, Francee-mail: diretudes@ibnogent.org

1612 Found Phys (2010) 40: 1611–1624

1 The Modern Notion of Law and the Experimental Method

Among other factors, the 17th century scientific revolution was characterised by theabandoning of Aristotelian natures in favour of laws of nature. Newton famouslydeclared at the beginning of his Principia:

The moderns, having rejected substantial forms and occult qualities, have un-dertaken to bring back the phenomena of nature to mathematical laws [1].

The transition from substantial forms to laws was not only a change in vocabu-lary: this new concept is different from any of its scholastic predecessors. There areseveral important aspects of this difference. First, the distinction between natural andviolent movements is rejected. Second, allowance is made for global constraints andfor forces of interaction (instead of explaining everything by intrinsic natures of indi-vidual objects). Third, exact mathematical formulation is considered to be possible.Finally, laws of nature are contingent [2]. This last aspect will be the main focus ofthis paper. It is directly linked to one very important feature of the new methodol-ogy adopted during the scientific revolution: the distinctive place which experimentscame to take in the elaboration and confirmation of scientific theories.

Since the resurgence of Aristotelian thought in the thirteenth century, if not be-fore, scholastic natural philosophers confessed allegiance to empiricism: thought isgrounded in sense perception. Nevertheless, their scientific practice did not includeany planned experimental activity. Observation was claimed to be the basis of scien-tific generalisations, but it was either pre-scientific common sense experience, or itwas taken from written sources without personal verification, or it arose from thoughtexperiments which most certainly were never put to test. Thus Edward Grant speaksparadoxically of an “empiricism without observation [3, p. 181]”:

Solutions to problems about the physical world were almost always resolvedby appeal to rational and logical arguments. Empiricism served this processonly insofar as it provided the ingredients for imaginary thought experiments.But one should never doubt that reason ruled medieval natural philosophy[3, p. 182].

During the scientific revolution, the role of experiments changed significantly:they no longer served to corroborate theories adopted on other grounds, but becamea decisive element in testing existing and developing new theories. The convictionthat natural objects are governed by contingent rules played a predominant role inthis paradigm shift. As the laws of nature could be different from what they actuallyare, pure reasoning is not sufficient to discover them. In order to find them out, wemust go and look at nature’s real behaviour. This link is established very explicitlyin Newton’s empiricism. Roger Cotes, who oversaw the publication of the secondedition of the Principia, voices this point of view when he writes in the preface:

From this fountain [the will of God] it is that those laws, which we call thelaws of Nature, have flowed, in which there appear many traces of the mostwise contrivance, but not the least shadow of necessity. These therefore wemust not seek from uncertain conjectures, but learn them from observationsand experiments [1, p. xxx].

Found Phys (2010) 40: 1611–1624 1613

2 The Contingency of Laws in a Theistic Setting

The conviction that laws of nature are contingent, and not necessary, stemmed, at thebirth of modern science, from the doctrine of creation. For Judaeo-Christian theism,the world, with its order, is grounded in God’s will; it takes its origin from a freeact. Thus it might not exist, or it could be different from what it is. The world, andby consequence natural order, is thus contingent and not necessary. Newton himselfwrote in an unpublished manuscript:

The world might have been otherwise then it is [. . .] Twas therefore not neces-sary but a voluntary & free determination yt it should bee thus [4].

The belief that laws of nature are instituted by God at creation is routinely ex-pressed in the texts of this period. It is found in John Locke’s writings [5]. RobertBoyle frequently speaks of the laws of motion established by the Author of things [6].For him, one can only talk of laws in a loose, metaphorical sense, for he “cannot con-ceive how a body devoid of understanding and sense, truly so called, can moderateand determine its own motions, especially as to make them conformable to laws, thatit has no knowledge or apprehension of.” The expression “laws of nature” is usedfor regularities maintained by God’s “ordinary and general concourse”, “for brevity’ssake, or out of custom [7].” And Descartes is famous for including not only laws ofnature, but also “eternal truths”, that is laws of mathematics and logic, under the freeexercise of divine will.1

Not only do laws of nature proceed from God’s will, the beauty and order of ourworld is such that it cannot be explained otherwise than by invoking the Creator. Laytheologian Boyle laboured ceaselessly in order to demonstrate God’s existence andwisdom from the exquisite arrangement of nature, as revealed by the new sciences.In a similar vein, Roger Cotes, Newton’s spokesman, was convinced that only God’smighty work of creation can explain natural order:

Without all doubt, this world, so diversified with that variety of forms and mo-tions we find in it, could arise from nothing but the perfect free will of Goddirecting and presiding over all [1, p. xxx].

3 The Validity of Laws of Nature Without Metaphysics

If the natural order is contingent, the question of why laws are valid immediatelysurfaces. In the original setting of modern science, the question found its answerin the divine will: the natural order has been instituted and is continuously upheldby the Almighty God. Although this answer still finds its advocates today,2 manyscientists work outside such a theistic setting. Probably, most of them simply avoidthe question, using the best available knowledge of laws of nature in order to solve

1For the creation of natural law see [8]. For the creation of eternal truths see [9].2A survey conducted in the 1990s indicates that 40 percent of American scientists believed in a personalGod who would answer prayer (the same percentage as in 1916) [10].

1614 Found Phys (2010) 40: 1611–1624

concrete problems, without ever asking why these laws hold. Thus it is significant thatPeter Mittelstaedt explicitly raises the question: “Why are laws of nature valid?”3 Theinterest he takes in the grounds for the validity of laws is in line with his more generalapproach to physics: not limiting himself to a pragmatic use of scientific knowledge,he is open to investigate fundamental questions arising in physics research.

Mittelstaedt examines several possible strategies to explain the validity of laws ofnature, without appealing to metaphysical resources. He is fully aware of the fact thatnone provides an all-sufficient answer to the question raised and that generalisingthem, even when one takes them all together, would go far beyond what is warrantedby our current knowledge. Thus they are proposed as only tentative suggestions andshould not be seen as a conclusive answer to the question why laws of nature arevalid. It is nevertheless significant that Mittelstaedt self-consciously explores thesestrategies as an alternative to the theistic explanation of laws of nature:

It [is] not clear whether all laws of nature can be explained in this way. How-ever, what matters here is, that there are strategies for explaining and justifyinglaws of nature and that these strategies [. . .] don’t make use of extra-scientificsources. If it turns out in this way that there are no gaps and all laws of na-ture can be fully understood, then Hawking’s statement [. . .] that “it would beperfectly consistent with all we know to say that there is a Being who was re-sponsible for the laws of nature”, is not correct. [. . .] More precisely, in thiscase there is no need for an additional explanation of the laws of physics by aSupreme Being [12].

In what follows, I will briefly present and assess the explanations offered by Mit-telstaedt. My aim is to evaluate the hope it is reasonable to invest in them as alterna-tives to the grounding of natural order in creation. In an effort to be complete, I willinclude an additional strategy of whom Nancy Cartwright is the main contemporaryadvocate, although it is in sharp contrast with Mittelstaedt’s understanding of scienceand he does not consider it a viable option.

3.1 Option 1: Laws of Mathematics

As Mittelstaedt points out, one may count—at least partially—the laws of arithmetic,of geometry of three-dimensional space and of probability as laws of nature be-cause they apply to physical reality and do so rigorously. Their validity is groundedin mathematical reasoning and thus does not seem to need any further justification[11, p. 310, cf. chap. 4].

It is obvious that this strategy only applies to a very limited subset of laws. Theidea that the whole web of laws of nature is endowed with mathematical necessityhas hardly any credentials to claim for it. Why would there exist only one consistentset of laws? In fact, philosophers and scientists have been busy inventing alternativeworlds to ours. Every falsified scientific theory offers another model of such a world.To imagine that pure mathematics would suffice to select the right theory would be a

3Title of part III [11, pp. 307–345].

Found Phys (2010) 40: 1611–1624 1615

return to the method of Greek and scholastic science, dominated by Reason. Experi-ments could still have some place in this “final” physics, as concrete situations mightbe too complex to trace by logical deductions right down to the level of individualsettings. But experiments would be no more than heuristic means in the context ofdiscovery. The justification of a scientific theory would be Reason’s privilege, as itstruth would be a matter of mathematics alone.

Two additional considerations reinforce the conviction that mathematics cannot bethe answer to the validity of laws, at least not the complete answer. The first argumentis rather speculative and one may legitimately doubt its conclusive force. The secondis less disputed—and disputable—and highlights a principled limit to any logicalexplanation of natural order.

The first argument takes into consideration that logically necessary does not equalnecessary simpliciter. In fact, some (very few) philosophers adopt the risky posi-tion that a kind of contingency may even apply to logic. In the Middle Ages, PierreDamien, followed by some nominalists, defended the idea that divine omnipotencecould not be limited even by laws of logic; thus for example, God could change thepast [13]. In a similar vein, Descartes was convinced that “eternal truths” were notnecessary per se, but had been created by God (although we are not able to apprehendthe possibility that they are not valid). Quine is an example of a recent philosopher,working outside the theistic framework, who does not accept the idea that logic isabsolutely necessary. In fact, he is not convinced by the strict distinction between thea priori and the a posteriori, one of the dogmas of empiricism he rejects [14].

Many resist this first consideration as too extravagant. In fact, it has the distinctivedisadvantage that we can only point to it in a semi-intuitive way, but not think orstate it clearly. Thought and language presuppose, for their proper functioning, thelaws of logic. Thus how could the proposition that the laws of logic may not bevalid have any clear content? The second consideration, however, does not sufferfrom the same drawback. It simply points out that the application of mathematicalstructures to physical reality always introduces an irreducible contingent factor. Theassociation of a mathematical concept with an element of physical reality is basedon experimentation and introduces a synthetic component that needs to be explained[15, 16]. An additional complication is introduced by the fact that scientific theoriesdo not directly apply to realistic situations because of the complexity of the latter.A law is typically formulated for an ideal, simplified setting and neglects numerousprovisos (some of which we may not even be able to state explicitly). As Mittelstaedtpoints out, “the laws and theories of physics are not images of the real world but rathertools for constructing correct models of the world.” Applying these tools to the realworld is “a difficult task, in particular since there are no general rules for consideringor neglecting ceteris paribus conditions of the physical laws which we find in thetextbooks [11, p. 306].” It thus follows that even laws of nature which are laws ofmathematics always contain an element of contingency, since their application to thereal world is not simply a matter of logic. The question remains, therefore, of whythey are valid.

1616 Found Phys (2010) 40: 1611–1624

3.2 Option 2: Law Without Law

A second rather striking strategy to explain the validity of laws was dubbed by the in-novative physicist John Wheeler “law without law”: a macroscopic law may emergefrom the simple fact that a great many sub-systems are involved, where no specificlaw governs the behaviour of the microscopic systems. In his Oersted Medal Re-sponse (1983), he applies this idea to Boltzmann’s law in thermodynamics. This ele-gant exponential law emerges solely from statistical considerations using the law oflarge numbers (and the conservation of the total energy), without supposing any lawgoverning the individual microsystems [17], [11, pp. 315–316].

Mittelstaedt took up Wheeler’s suggestion for quantum mechanics and showedhow it explains here the striking fact that the objectively undetermined outcomes ofindividual measurements nevertheless give rise to a statistical law which is strictlydetermined by the preparation of the system and the measured observable [18]. Hisproof uses recent results which have made it possible to develop a probability-freeversion of quantum mechanics. In fact, probability predictions logically follow fromthe description of individual quantum systems by the state of the system and theassumption that the objective properties of the system can be obtained with certaintyby measurements [19], [20].4

Despite the great interest of these deductions, we nevertheless have to ask, in thecontext of our inquiry, if they really provide a complete and satisfactory explanationof laws of nature, or more specifically of those macroscopic laws concerned by theprogramme “law without law”. Right from the outset, one should notice that the rea-soning used here presupposes that the law of large numbers can be used to describethe emergence of structure from numerous microscopic processes. The element ofcontingency introduced by applying mathematics to material reality is still present:the presence of numerous elementary factors does not gain us anything at this level.

More importantly, it is not correct to suggest that macroscopic law springs fromtotal and utter microscopic chaos. Wheeler himself recognizes that “no law springsunguided out of absolute chaos. It demands the guidance of a regulating principle.”5

Classical thermodynamics provides a well-known example: its laws arise from theerratic movements of many particles. Nevertheless, Boltzmann’s law, for example,only applies under the condition of the conservation of the total amount of energy(linked to the time-translation invariance of physical descriptions).

Hence, Boltzmann’s formula is not exactly a “law without law” but a lawthat follows from a weak law-like assumption, the conservation of energy[11, p. 316].

4In this article, Mittelstaedt shows that Einstein’s objection against quantum mechanics—that it uses fun-damental statistical laws—can be met. In fact, quantum mechanical statistical laws can be derived frommathematical statistical considerations combined with the fact that individual systems are not determinedby any law.5See [17], Art. cit., 400. Cf. ibid., 398. In this article, Wheeler studies four cases where order emergesfrom a large number of random events: Boltzmann’s law, phenomena close to a critical point, the randomcoupling of oscillators and the “travelling salesman”. In each case, Wheeler brings to light the regulatingprinciple [17, pp. 399–403].

Found Phys (2010) 40: 1611–1624 1617

In the same way, the state of the system describes the structure of quantum chance,which allows the emergence of a well-defined probability distribution for measure-ments in quantum mechanics, like the detections of a photon counter. One thereforeneeds to qualify Mittelstaedt’s affirmation, when he writes:

A quantum mechanical probability law seems to emerge from objectively un-determined individual events as a ’law without law’ in the sense of Wheeler[18, p. 265].

In fact, the irregular behaviour of a single elementary particle is, according to stan-dard quantum mechanics, objectively undetermined, but nevertheless carries a certainorder described by the state of the system. Hence, the probability distribution of quan-tum phenomena is not strictly speaking a “law without law”. The result obtained isstill of real interest, albeit in a more modest way: it shows that Born’s interpretation isnot required as an additional postulate. Thus the description of quantum phenomenarequires fewer structures than initially expected.

The regulatory principle underlying microscopic behaviour is an element with le-gal structure, which brings us back to the question of its cause. As Deutsch pointsout,

in making a fundamental ’regulating principle’ the new object of his search,Wheeler ipso facto abandons the search for ’law without law’. For a regulatingprinciple is a law [16].

Illuminating as the “law without law” programme may be, it does not live up to itspromise of dispensing with the empirical, contingent character of the natural order.Invoking the law of large numbers can only provide a partial explanation for thisorder, and the question why laws of nature are valid remains.

3.3 Option 3: Laws as Preconditions of Science

In addition to mathematical necessity and randomness (via the law of large numbers),a very promising avenue for explaining the validity of laws of nature goes back toKant: transcendental necessity. As Mittelstaedt puts it:

A law of nature holds necessarily for a certain real entity—an object, a property,or a process—if the validity of the law in question is a necessary preconditionof that entity [11, p. 310, cf. pp. 269–279].

Thus (classical or quantum) objects can only be constituted if certain invarianceprinciples and laws are presupposed.

Transcendental explanations of laws have been a constant feature of Mittelstaedt’steaching and writing [21–23]. He has contributed significantly to the transcendentaldeduction of quantum logic starting from the most general conditions of a formal lan-guage of physics [24], [11, pp. 338–346]. And I still vividly remember the impressionleft on me by his first-year introductory lecture in theoretical physics6 (which somereferred to rather scornfully as the “baby lecture”): instead of being confronted with a

6In the academic year 1984/85 at the University of Cologne.

1618 Found Phys (2010) 40: 1611–1624

collection of more or less arbitrary laws, we learnt to appreciate the coherence of thefundamental laws of classical and relativistic mechanics, derived from the precondi-tions of scientific experiments.

Transcendental deductions of laws are not only a powerful tool; they also providea non-metaphysical explanation for the validity of laws, without committing the errorof scientism, that is the belief that everything can be explained by science alone.Laws are not expected among the results of science; there are instead among thepreconditions for scientific practice. Nevertheless transcendental reasoning does notput an end to the contingency of laws. While showing the coherence of fundamentallaws of classical, relativistic and quantum mechanics, it cannot claim to completelyexplain the natural order.

First, transcendental deductions are only known for some physical laws. Kant him-self was aware of this fact and distinguished between a priori and empirical laws. Hedid not consider that the latter can be deduced by transcendental reasoning. Of course,it is always possible to hope that we will be able to generalize the transcendental de-ductions in the future in order to include all laws. But we have to acknowledge thatour current knowledge is clearly insufficient to justify such hope. For example, wehave at present no clue how to derive such elegant and fundamental laws as the Ein-stein field equations, the basis of General Relativity.7 Second, the fact that (some)laws are transcendental conditions of the scientific method does not imply that theyare necessary: after all, our world could be such that natural science was impossi-ble. Kant himself knew this, because he mentioned the possibility of a chaotic worldwhere sensations could not be organised into a coherent system; in such a world,science would not be possible:

The multiplicity and diversity of empirical laws could be so great that it might[never] be possible for us [. . .] to bring these empirical laws themselves to theunity of kinship under a common principle, if, namely, as is quite possible initself (at least as far as the understanding can make out a priori), the multiplicityand diversity of these laws, along with the natural forms corresponding to them,being infinitely great, were to present to us a raw chaotic aggregate and notthe least trace of a system, even though we must presuppose such a system inaccordance with transcendental laws [26].

Thus it is no longer the contingency of physical order per se which stands in needof an explanation, but the possibility of practising a coherent science. Admittedly,transcendental philosophy has often been considered to provide an explanation forthe possibility of science. But Kantism (both in its original form and in its “neo-Kantian” developments) presupposes rather than explains scientific practice. This is

7Wheeler [25] proposes six such deductions. One should examine them more closely to see to what extentthey shed light on Einstein’s equations. The best-known deduction comes from Hermann Weyl: Einstein’sequations are the simplest second-order quasi-linear differential equations in a Riemann space. But thisdeduction uses logically non-necessary criteria, such as simplicity; does not provide an explanation forthe value of the gravitational constant; postulates, without justification, a second-order equation; does notallow us to eliminate the cosmological term and presupposes the notion of a Riemann space to describespace-time—all of which are contingent elements.

Found Phys (2010) 40: 1611–1624 1619

often forgotten—perhaps because we live in a society where the possibility of sci-ence is considered to be obvious? The fact that scientific practice constitutes a silentpresupposition to our way of life in no way reduces the contingency of its existence.8

The search for an explanation of the natural order is thus still relevant, even afterKant.

3.4 Option 4: Laws as only Partially Valid9

The contemporary philosopher of science Nancy Cartwright has offered a completelydifferent approach to the natural order as described by science. Instead of trying toexplain why physical laws are valid, she considers that we have to take seriously thefragmentary character of our current scientific knowledge and abandon the ideal ofuniversally valid laws:

Science as we know it: [. . .] pockets of great precision; large parcels of qual-itative maxims resisting precise formulation; erratic overlaps: here and there,once in a while, corners that line up, but mostly ragged edges; and always thecover of law just loosely attached to the jumbled world of material things. [. . .]The dappled world is what, for the most part, comes naturally: regimented be-haviour results from good engineering [29, p. 1].

For somebody who adopts such a picture of reality, the question of why laws ofnature are valid loses its interest. It simply is a brute fact about our world that in somevery specific settings (typically in a laboratory) a nomic description is possible. Lawsare valid where and when they are valid; that’s all we can say.

Several passages suggest that the dappled world is motivated by a separation rem-iniscent of the Aristotelian distinction between form and matter, or between actualityand potentiality. As in the Greek picture of science, form only partially “in-forms”matter in Cartwright’s dappled world. Thus, Cartwright seeks to establish “the dis-tinction between the tidy and simple mathematical equations of the abstract theory,and the intricate and messy descriptions, in either words or formula, which expressour knowledge of what happens in real systems made of real materials [30].” She be-lieves that such a distinction enlightens our experimental practice. We cannot movedirectly from theoretical concepts to experimental design:

We need to know about real materials and their properties, what the abstractconcepts amount to there, before we can build anything. But telling us this isno part of theory [29, p. 58].

Theoretical concepts only exist in theory, or—to use scholastic terms—in poten-tiality. To know what really exists—in actuality—one must leave the realm of theoryand look at matter. The world of Ideas, to use Platonic language, has no place for“real systems made of real materials” which physicists are interested in [31].

It is true that Mittelstaedt claims that “physical laws which we find in ourtextbooks and handbooks are not literally applicable to real physical situations

8For a more in-depth discussion of the transcendental strategy to explain the natural order, cf. [27]9This section includes elements taken from [28].

1620 Found Phys (2010) 40: 1611–1624

[11, p. 304];” they “are not images of the real world but rather tools for construct-ing correct models of the world [11, p. 306].” But it would be totally wrong to con-clude that Mittelstaedt is sympathetic to Cartwright’s view of the dappled world. Theprivilege which Cartwright gives to “all things counter, original, spare, strange” [32],results in an attitude which is diametrically opposed to that which is customary inmodern science: According to her scheme one feels no desire to extract increasingamounts of natural order from experimental data which at first glance often seemchaotic. In current scientific practice, the researcher is, of course, aware of the ap-proximate nature of any mathematical description of a given situation: the number offactors involved in every real situation is simply too great to allow a comprehensivedescription. But a research programme, brought to maturity, always includes meansof self-correction. If more precision is required, there is no need to abandon the theo-retical framework; instead a more sophisticated application is developed, to take intoaccount the extra complexity. In fact, the Galilean method of using idealised mod-els is based precisely on the belief that mathematical description does apply to theconcrete things of the material world:

Galileo [. . .] does not compare an “ideal” state to a “deficient” reality; the verydeviation of the real from the ideal can be measured and explained with aneven more complicated model. Rather than comparing reality to the ideal, hecompares the complex to the simple [33].

The process of idealisation in modern science does not in any way reintroduce theideal world, as used in Greek science; it only makes sense in a scientific approachunashamedly involved in this “lowly” world.

4 Created Laws Provide both Coherence and Contingency

All four schemes for explaining laws without recourse to metaphysics providethought-provoking answers to the question why laws of nature are valid. WhereasCartwright’s approach shows itself to be in tension with modern scientific method-ology, the first three strategies endorsed by Mittelstaedt offer precious insights tothe coherence of physical theories and can therefore count as solid, though partial an-swers. The understanding they supply should not be understated; nevertheless one hasto be careful not to stretch them too far. The hope that they can be generalised, so thatthey could be applied to all physical laws, would not only go far beyond our currentknowledge, but would also contradict the empirical methodology of modern science.Since the 17th century scientific revolution, physical theorizing has been inspired bythe conviction that laws are contingent and thus cannot be discovered or justified byreason alone. Providing a final explanation solely based on mathematics, randomnessand transcendental deductions would be the end of empirical science, at least as faras fundamental structures are concerned. Experiments could still play a role, but onlyas heuristic means needed because of the complexity of real situations which wouldrender calculations, though in principle available, practically impossible.

Thus Peter Mittelstaedt’s question of why laws of nature are valid is still withus. For those who are not content to put it aside, immersing themselves in doing

Found Phys (2010) 40: 1611–1624 1621

science, without ever asking the big questions, the idea of creation has much to berecommended. Historically, it constituted the metaphysical framework in which mod-ern science originally emerged. Conceptually, it provides the contingency appropriatefor empirical science. Are we then back to a God-of-the-gaps approach, offering asfar as possible rational explanations for laws of nature and resorting to God’s willwhen we do not know how to go further in accounting for the natural order describedby physics? Or put otherwise: Can “Hawking’s statement [. . .] that ’it would be per-fectly consistent with all we know to say that there is a Being who was responsible forthe laws of nature’ [12]” only survive because our scientific understanding of laws isincomplete?

To be sure, the idea of creation implies that our world is contingent. Thus it iscrucial for this understanding that the natural order is not necessary in its entirety.10

But this does not mean that the idea of creation is simply called in to explain the non-necessary aspects of physical laws. First, it should be noted that all three explanationsof laws of nature which are explored by Mittelstaedt, even taken together and pushedto their limits, leave a measure of contingency, as was shown above: the contingencyintroduced by the application of mathematics to physical reality, the contingency ofregulating principles, the contingency of the possibility of doing science. Thus theydo not threaten the theological explanation of the natural order.

More important, it is striking that a created world exhibits the right kind of contin-gency to allow empirical science. In fact, not all kinds of contingency are the same.The contingency in Cartwright’s dappled world, for example, is not well-adapted tothe modern scientific method. This is also the case with regard to the contingency ina world formed by a demiurge (characteristic of Greek science). Contrary to creationex nihilo, the demiurge works with preexisting matter. His work is only contingentinsofar as he is a bad craftsman; to the extent that he excels in his craft, the work pro-duced corresponds to the telos he was aiming for. If there is any deviation from therational essence of things, it amounts to imperfection: it is a result of the demiurge’slimitations—either his fallible skills as a craftsman or the resistance of matter, whichexisted prior to his action. Under no circumstances can the world produced by thedemiurge be the object of an empirical science. Inasmuch as his work is a success, itis entirely transparent to reflection; the essence of things can be rationally deduced be-cause they proceed from the plan of an intelligence that is not transcendent; and thus,experimentation is not necessary to understand nature. Inasmuch as it is imperfect,the demiurge’s world does not allow science—either empirical or rational—becausethe difference from the initial telos does not follow any no rule but arises from anirrational principle [34].

Creation as a voluntary act of the omnipotent Intelligence can, on the other hand,provide a basis for the empirical method that has governed the new scientific approachsince the seventeenth century. The concept of creation combines rational work andfree act, in such a way that the contingency no longer amounts to imperfection, butexpresses the freedom of the all-powerful Creator, as Wolfhart Pannenberg observes:

10Unless one wants to plead (in analogy to the creation of eternal truths in Descartes) that the natural ordercould appear to us to be necessary whilst being in reality, from God’s perspective, contingent.

1622 Found Phys (2010) 40: 1611–1624

The altered value of the notion of contingency is that the contingent is no longerfounded on the non-determinacy of matter but on the freedom of the divine will,as the creational basis of the world and all its parts [35].11

Last but not least, the idea of creation does not only lead to the right kind of con-tingency, it also offers a convincing explanation for the level of necessity, or bettercoherence, which the first three strategies have brought to light. On one hand, it isto be expected that mathematical reasoning can be applied to the physical world if ithas been created by an almighty and rational Being. On the other, when the transcen-dental deductions highlight the agreement between the structures of human cognitivefaculties and scientific theories, this can be understood as a sign of the common ori-gin that the human spirit and nature find in God. The conceptual capacities of thebeing created in the image of God “suit” the world which he is called to explore.Thus it would be wrong to consider that the idea of creation is built on the gaps leftopen by the explanations so far offered for the validity of laws of nature. Even theexplanations themselves, as far as they go, are “at home” in a created world.

We therefore see that the idea of creation provides a worldview capable of ex-plaining both the rational and the empirical element of the modern scientific method.On one hand, it can account for the necessity and coherence which mathematicalreasoning brings to light in our grasp of natural order in modern physics. On theother, it leaves appropriate space for the contingency of nature and provides the rightkind of contingency—based on free action of a rational Creator and not on irrationalGreek matter—resulting in the predominant place of experimentation in the scientificmethod since the 17th century. Thus creation is in tune with the balance betweencontingency and necessity we observe in modern science. As creation was obviouslynot invented to explain this balance (the concept pre-dates the scientific revolutionby many centuries), the observed harmony is striking. All these considerations maycount as evidence for the claim that the idea of creation is no relic from the past, butstill has much to offer today in response to the question why laws are valid.

Acknowledgements I would like to thank Paul Busch and Peter Mittelstaedt for the invitation and theirstimulating remarks. Rachel Vaughan assisted me by smoothing out the English text and by checkingseveral references.

References

1. Newton, I.: Mathematical Principles of Natural Philosophy. University of California Press, Berkeley(1934). Preface Motte, A. (trans.), Cajori, F. (rev.)

2. Jaeger, L.: The idea of law in science and religion. Sci. Christ. Belief 20, 138–142 (2008)3. Grant, E.: God and Reason in the Middle Ages. Cambridge University Press, Cambridge (2001)4. Davis, E.B.: Newton’s rejection of the “Newtonian World-View”: the role of divine will in Newton’s

natural philosophy. Sci. Christ. Belief 3(2), 117 (1991)5. Locke, J.: Essays on the Law of Nature (1663), Essay I, pp. 108–110. Oxford University Press, Oxford

(1954). Van Leyden, W. (ed.)

11This new understanding of contingency is, according to Pannenberg, one of the major contributions ofChristian theology to epistemology; see, for example, [36] and [37].

Found Phys (2010) 40: 1611–1624 1623

6. Boyle, R.: The origin of forms and qualities according to the corpuscular philosophy (1666). In: Stew-art, M.A. (ed.) Selected Philosophical Papers of Robert Boyle, p. 19. Hackett, Indianapolis (1991)

7. Boyle, R.: A free inquiry into the vulgarly received notion of nature, section II (1686). In: SelectedPhilosophical Papers of Robert Boyle, p. 181

8. Descartes, R.: Le monde ou traité de lumière (1630?). In: Adam, C., Tannery, P. (eds.) Œuvres deDescartes, vol. XI, p. 34f. Cerf/Vrin, Paris (1909)

9. Descartes, R.: Méditations métaphysiques, Sixièmes réponses (Latin 1641, French 1647), p. 454f.Flammarion, Paris (1979). Beyssade, J.-M., Beyssade, M. (eds.)

10. Larson, E.J., Witham, L.: Scientists are still keeping the faith. Nature 386, 435f (1997)11. Mittelstaedt, P., Weingartner, P.A.: Laws of Nature. Springer, Berlin (2005)12. Mittelstaedt, P.: On possible relations between physics and theology. In: Loeffler, W., Weingartner,

P. (eds.) Proceedings of the 26th International Wittgenstein Symposium “Knowledge and Belief”,p. 337. Hölder, Pichler-Temsky, Vienne (2003); quoting Hawking, S.: The edge of space-time. Am.Sci. 72, 355–359 (1984)

13. Oakley, F.: Omnipotence, Covenant, and Order: An Excursion in the History of Ideas from Abelardto Leibniz, pp. 42–44. Cornell University Press, Ithaca (1984)

14. Quine, W.V.O.: Two dogmas of empiricism. In: From a Logical Point of View, pp. 20–46. HarvardUniversity Press, Cambridge (1980). The critical response from Putnam, H.: There is at least one apriori Truth. Erkenntnis 13, 153–170 (1978) in the end, does not come to a decision, despite the title

15. Grene, M.: Note of the editor. In: Grene, M. (ed.) Knowing and Being, p. 120. Routledge & KeganPaul, Londres (1969)

16. Deutsch, D.: On Wheeler’s notion of “Law without Law” in physics. In: Zurek, W.H., Van Der Merwe,A., Miller, W.A. (eds.) Studies and Essays in Honor of John Archibald Wheeler, p. 587. PrincetonUniversity Press, Princeton (1988)

17. Wheeler, J.A.: On recognizing “Law without Law”. Am. J. Phys. LI, 399f (1983)18. Mittelstaedt, P.: The emergence of statistical laws in quantum mechanics. In: Ferrero, M., van der

Merwe, A. (eds.) New Developments on Fundamental Problems in Quantum Physics, pp. 265–274.Dordrecht, Kluwer (1997)

19. Mittelstaedt, P.: The Interpretation of Quantum Mechanics and the Measurement Process. CambridgeUniversity Press, Cambridge (1998), pp. 47–57, pp. 62–64

20. Mittelstaedt, P.: Einstein’s objections against Quantum Mechanics. Phys. Philos. 5–9 (2006). https://eldorado.uni-dortmund.de/handle/2003/22995

21. Mittelstaedt, P.: Klassische Mechanik, pp. 18–50. Bibliographisches Institut, Mannheim (1970)22. Mittelstaedt, P.: Philosophische Probleme der modernen Physik. Bibliographisches Institut,

Mannheim (1989). English transl.: Philosophical Problems of Modern Physics. Riemer, W. (transl.),Cohen, R.S. (rev.), Dordrecht, Reidel (1976)

23. Mittelstaedt, P.: Der Zeitbegriff in der Physik: physikalische und philosophische Untersuchungen zumZeitbegriff in der klassischen und relativistischen Physik. Bibliographisches Institut, Zürich (1989),pp. 41–77, pp. 127–131

24. Mittelstaedt, P.: Interpreting quantum mechanics—in the light of quantum logic. In: Castell, L., Is-chebeck, O. (eds.) Time, Quantum and Information, pp. 281–290. Springer, Heidelberg (2003)

25. Wheeler, J.A.: From relativity to mutability. In: Mehra, J. (ed.) The Physicist’s Conception of Nature,pp. 202–247. Reidel, Dordrecht (1973)

26. Kant, I.: Critique of the Power of Judgement, First Introduction, sec. IV (1790), p. 13. CambridgeUniversity Press, Cambridge (2000). Guyer, P., Matthews, E. (trans.)

27. Jaeger, L.: Ce Que les Cieux Racontent: la Science à la Lumière de la Création, pp. 201–210. Éditionsde l’Institut Biblique/Excelsis, Nogent-sur-Marne/Charols (2008)

28. Jaeger, L.: Nancy Cartwright’s rejection of laws of nature and the divine lawgiver. Sci. Christ. BeliefXXII, 81–86 (2010)

29. Cartwright, N.: The Dappled World: A Study of the Boundaries of Science. Cambridge UniversityPress, Cambridge (1999)

30. Cartwright, N.: How the Laws of Physics Lie, p. 128. Clarendon, Oxford (1983)31. Mueller, I.: Mathematical method and philosophical truth. In: Kraut, R. (ed.): The Cambridge Com-

panion to Plato, pp. 192–194. Cambridge University Press, Cambridge (1992), emphasises, based onThe Republic 530b6-c1, that with Plato, even astronomy is not concerned with the visible heavens,but with the realm of forms

32. Cartwright, N.: Reply. In: Symposium on The Dappled World. Philosophical Books, vol. XLIII, p. 271(2002). quoting Gerard M. Hopkins. “Pied Beauty” (1990)

1624 Found Phys (2010) 40: 1611–1624

33. Funkenstein, A.: Theology and the Scientific Imagination: From the Middle Ages to the SeventeenthCentury, p. 177f. Princeton University Press, Princeton (1986), referring to Blumenberg, H.: DieGenesis der kopernikanischen Welt. Suhrkamp, Frankfurt am Main, 470–488 (esp. 482ff) (1975)

34. Foster, M.: Christian theology and modern science of nature (II). Mind XLV, 4–7 (1936)35. Pannenberg, W.: Die Kontingenz der geschöpflichen Wirklichkeit. Theol. Lit.ztg. CXIX, 1052 (1994)36. Pannenberg, W.: The doctrine of creation and modern science (1989). In: Peters, T. (ed.) Toward a

Theology of Nature: Essays on Science and Faith, p. 36f. Westminster/John Knox Press, Louisville(1993)

37. Pannenberg, W.: Contingency and natural law (1970). In: Peters, T. (ed.) Toward a Theology of Na-ture: Essays on Science and Faith, p. 115f. Westminster/John Knox Press, Louisville (1993)