Copyright © Interdisciplinary Encyclopedia of Religion and Science.
No part of this article may be reproduced, stored in a retrievial system or transmitted without the prior permission of the Editors.
To refer to the content of this article, quote: INTERS – Interdisciplinary Encyclopedia of Religion and Science, edited by G. Tanzella-Nitti, P. Larrey and A. Strumia, http://www.inters.org

Laws of nature

Giuseppe Tanzella-Nitti

I. The Notion of Natural Law and its Use in the Sciences. 1. The Notion of Law and its Classical Reference to the Presence of a Law-Maker. 2. The Terminology Concerning Laws used in the Natural Sciences. - II. The Principle of Lawfulness as the Basis of Scientific Knowledge. 1. Why Does Science Speak of Laws? 2. Law and Regularity in Several Specific Fields. 3. Natural Laws, Elementary Properties and Physical Constants. - III. The Debate over the Status of Natural Laws, Arena of Comparison between Scientific, Philosophical, and Theological Thought. 1. A few Historical Clarifications . 2. The Vision of the Laws of Nature in the Modern Age . 3.More Recent Views. 4. God, the Universe and Laws: a Unique Topological Cosmology. - IV. Reflections in Contemporary Science on the Meaning of Natural Laws. 1. What is the Nature of the Laws of Nature? 2. The Intelligibility of the Laws of Nature and the Search for their Unification . 3. An Evolutionary View of the Laws of Nature: from Being to Becoming? 4. Special Aspects in the Field of Biology. - V. Towards an Ontological Analysis of the Laws of Nature: Scientific Laws, Natural Laws and the Metaphysical Notion of “Nature” - VI. For a Theology of Natural Laws. 1. The Cosmos, Place of the Covenant between God and Human Beings. 2. Stability of the Laws of Nature and God's Faithfulness. 3. The Inexorability of Natural Laws and the Problem of Physical Evil.

The concept of law is a highly analogic concept. It first appeared in a legal/social context and was later extended to the scientific/rational realm, where it became important, first, in the study of harmony and numerical proportion (Pythagoras) and, later, after the discovery of the experimental method, in the mathematical language used to describe physical phenomena (Galileo, Newton, Leibniz). Because of the ease with which mathematical formalism has been used in the natural sciences, the notion of law in these disciplines has been widely applied. It appears, however, rather frequently in not a few of the social sciences (Economics, Sociology, etc.), though with a different epistemological slant. The study of the meaning of the laws of nature is typically the object of the philosophy of science. We will focus our discussion on pointing out the interdisciplinary import of our subject-matter, or in other words, to emphasize different conceptions of nature as regards the laws at work in nature, the cause of the laws, and the debate over their relationship with a law-maker.

1. The Notion of Natural Law and its Use in the Sciences

1. The Notion of Law and its Classical Reference to the Presence of a Law-Maker. The proper context for the notion of “law” is the social/civil context. It contains the idea of an order, of a “dictate” (lat. lex , from the Greek, léghein , to say), but it is not far from the idea of a tie, or bond (lat. ligare ). Like its synonym “norm” (gr. nómos ), law signifies a positive prescription whose purpose is to “regulate”, that is, to “order with measure”, the behavior of members of a community. This immediately implies a reference to an “authority” who is responsible for the law as well as, and especially, the order and end which this authority intends to reach or introduce with the law. Because the concept of law implies that of an authority, the religions of the world have placed the notion of God at the basis of the idea of law in a very natural and almost instinctive way. This is proven by the fact that up to the modern era, the concept of law, even in its strictly social and civil context, was never understood without reference to its theological connotations.

The religious experience of Israel has played a significant role in human culture. One of the most important events of the history of Israel is the giving of the “Law”, that is the Decalogue (cf. Dt 5,1-22). The Jewish law, which stands out with respect to extra-biblical traditions for its depth and transcendence, shares with the law of other peoples the purpose of regulating the relationships between human beings and God, and among the members of the human society. In keeping with the biblical message, Christian theology, which in a certain sense extends the notion of law from the positive, civil sphere to the cosmic and later to the natural, moral one, would introduce, with the philosophy of Thomas Aquinas, the notions of “divine law” and of “natural law”. The former concerns the plan for the world “conceived from eternity by God”, through which the Creator leads all things towards their end with provident wisdom ( lex eterna est ratio divinae gubernationis ; cf. Summa Theologiae , I-II, q. 93). The latter can be recognized in the law inscribed by the Creator into human nature (cf. Ps 19,8-15; Rom 2,14-16). The human conscience, in recognizing this “natural law”, is able to distinguish good from evil and command the will to perform the corresponding acts (cf. Summa Theologiae , I-II, q.94). The human person participates in the law with human liberty, that is, according to his and her “natural reason”, which is characteristic of the human nature as such. On the other hand, the irrational creatures follow the law according to an “inclination” willed by the Creator and related to their specific essence. But even in this case, in Thomistic thought, one speaks of “natural laws” as a participation in the eternal law, preserving an analogy with the rational and personal world where laws can be recognized and obeyed freely. According to a proper analogy of proportionality ( ANALOGY, II.2), and not a simple metaphor, God the Creator is seen as the “legislator” who “orders and disposes all things with measure”, as the transcendent authority on Whom all laws rest. Without any need to identify the Creator of the world with the law, or with laws, the universal, eternal, and stable character of laws can be easily derived from some of God's philosophical attributes. The laws draw from God's truth and manifest it, especially in their regularity or “lawfulness”, suggesting also their relationship to the notions of constancy and faithfulness. We will deal with the relationship between the biblical image of God and epistemology of natural law later (see below, VI).

2. The Terminology Concerning Laws used in the Natural Sciences. As heir to the philosophical terminology which has characterized —and in part, still characterizes— scientific language, the scientific vision of the world makes wide use of the concept of “law”. The most general definition of law is that of a constant and verifiable connection, which can typically be described by logical-mathematical language, between the observable quantities at play in a determined phenomenon. If physical observables are involved, the mathematical formalism is generally expressed with an equation that makes it possible to calculate and predict the behavior of certain quantities as a function of space and time. The “mathematization” of a certain phenomenon is, therefore, the typical condition under which to seek, discover, and describe a certain law of nature. At the same time, reducing the phenomenon to mathematics always implies a certain simplification, if not a real loss, of the complexity or richness of the phenomenon in question: then we deal with a “scientific” representation (that is, a representation which can be scientifically studied) of nature. The “linear” form of a good number of equations associated with the main laws of nature allows for an efficacious treatment and prediction of the phenomenon under study. It is the case, for example, of the 2nd law of mechanics F = ma, or F = m dv/dt, which have the property that the sum of two solutions is also a solution. These include the complete time-reversibility (the form of the equations do not depend on the sign of t, that is, on the direction of the arrow of time). However, non-linear equations are equally common, as, for example, many of the laws of hydrodynamics in which the sum of two solutions is not a solution. In the non-linear case, the possibility of a mathematical treatment is much more limited and, in certain situations, strongly conditioned by the accuracy with which one can set the “initial conditions”. In other words, the set of numerical values of the equations chosen to represent “scientifically” a “natural” phenomenon cannot be solved to determine the “state” of the system in question ( DETERMINISM/INDETERMINISM, II.4). The fact that in the 2nd law of thermodynamics the arrow of time admits only increasing values (of time), implies that many laws which incorporate on some level this law (and not only in a strictly thermodynamic context, but also in the more interesting context of chemical and biological reactions) are irreversible with respect to time. This gives credence to a vision of the world which is no longer only a vision of an ordered and balanced universe, but also one which has a history, which develops and evolves.

In the formulation of a law, two aspects are almost always at play: an inductive, a posteriori , aspect related to observation, and a deductive, a priori one, related to a theory or a set of principles in which one attempts to interpret what is occurring. An example of this is the formulation of the “law of gravity” within a specific “theory of gravitation”, or of “laws of light propagation” in an “electromagnetic theory”, for instance that described by Maxwell's equations. At times it is difficult to distinguish between these two aspects: for example, one speaks of three laws, but also of three “principles” of dynamics, of thermodynamics, etc. Even as early as the period of the development of the scientific method, F. Bacon (1561-1626) and later R. Descartes (1596-1650), used the term “law” to signify both principles and functional relations. Nevertheless, the term “principle”, just like the mathematical term “theorem”, is more often used to describe a system of hypothetical/conceptual character (think, for example, of d'Alembert's or Hamilton's principle in mechanics, or of the conservation theorems), whereas the term “law” always implies an attempt to order or describe an experimental observation.

Classical physics uses a great number of laws which have by now become a part of the standard terminology. They range from Kepler's three laws of planetary orbits to the laws of Coulomb, Ohm, and Faraday for electrical phenomena, from statistical laws, as that of ideal gases or of entropy, to laws of mathematical physics, as Gauss' and Poisson's law. In optics, one speaks of the laws of Fresnel and Huygens, in fluid dynamics of the law of Navier-Stokes and Bernoulli. In cosmology, there is the Hubble's law governing the expansion of the universe and the Period-luminosity law for Cepheids stars (stars whose pulsating period strictly depends on their intrinsic luminosity); with the help of the latter, discovered by Miss H. Leavitt, astronomers succeeded for the first time in establishing a distance scale which extends beyond the confines of our galaxy. In quantum mechanics, one has not abandoned the use of the word “law”: one uses Planck's law, which governs the radiation from a black body, or statistical laws, such as the laws of Fermi and Dirac and of Bose and Einstein, which describe the energy distribution of a gas of different classes of particles, that is, fermions (of which electrons are best known) and bosons (such as photons).

But the concept of law finds application in disciplines other than physics and astronomy. In chemistry, one speaks of the laws of oxidation and reduction and laws of electrolysis; in biology, of the laws of Mendel concerning the passing on of hereditary traits; there are even laws in disciplines such as economics, of which the law of supply and demand is the most famous. As to the social sciences, sociologists have studied the existence of specific laws in the attempt of describing and predicting behavior, trends, and societal reactions to certain environmental, economic, etc. circumstances. These laws must be necessarily “statistical”, since they attempt to describe “sociological” phenomena on a large scale and as a whole —they cannot describe the free behavior of the individual since the behavior of the individual cannot be predicted scientifically. It is precisely the existence of human free will which limits the applicability of laws in the field of human behavior, and makes sociological and economical laws substantially different from the laws of the natural sciences. Any theory or discipline which claims to describe, through the use of laws, all human phenomena exhaustively and deterministically, endorses a view in which psychological and social reactions are seen as necessary consequences of conditioning to which the individual is supposedly subject, and betrays an implicit reductionist vision, if not a wholesale denial of free will.

II. The Principle of Lawfulness as the Basis of Scientific Knowledge

1. Why Does Science Speak of Laws? The extensive recourse to the notion of law in the sciences seems to suggest that there must be an epistemological motivation at root. The reason is that the “regularity” and “stability” observed in many natural phenomena has formed from the very beginning the founding principle behind the “organization” and “progress” of scientific knowledge. Historically, this started from the spontaneous and growing use of “taxonomy” (observation and classification of recurrent forms) and, especially, from the instinctive and later systematic observation of the sky ( ASTRONOMY). The regular rising and setting of the sun, the moon, and the stars, and the periodic motions of the internal planets (Mercury and Venus) represent, in fact, a grandiose example of “lawful” behavior. The sky, with its beckoning to transcendence, provided the natural link between the observed lawfulness and divine authority. It offered, among other things, a certain relative contrast to terrestrial phenomena, whose regularity turned out to be difficult to discern and whose behavior was judged, at times, as changing and inconstant.

Throughout the centuries, scientists would leave, almost unaltered, this sensibility towards regularity, which comes into play in two phases of scientific research: the observation of the phenomenon, and the set up of the experiment to reproduce what has been observed ( EXPERIENCE, IV). On the experimental side, the search for regularity is almost always associated with the search for a correlation, which appears to the scientist under the guise of a regular relationship between two or more quantities (which a graph can easily transform into a mathematical expression). In this way, a correlation can be transformed into an equation and thus suggest the existence of a law.

But in an equally original way, the scientist also perceives the “problem of induction”. The essence of this problem resides in the question of whether the regularity one observes from a finite and limited number of trials is normative of the phenomenon, or whether instead, it can be invalidated from a certain moment on, thereby giving a provisory, and in a certain measure, unfounded character to scientific knowledge. The cognitive value of induction, which is a central theme of the philosophy of science, has been called into question by D. Hume (1711-1776) and by neopositivism; in more recent times, it has been defended by A.N. Whitehead (1861-1947) and J. Stuart Mill (1806-1873), but vigorously contested by K. Popper (1902-1994). It must, however, be observed that the belief in the universal, and in a certain sense, absolute, character of laws (which is needed to scientifically motivate the problem), as well as the willingness to revise them (accepting their in part conventional character), are attitudes which coexist in harmony in any scientific experience. This is nothing but the effect of the two-fold theoretical/deductive and empirical/inductive (but also idealist, and at the same time, realist) aspects present in every scientific investigation.

Recognizing the existence of a “principle of law and uniformity” as the indispensable basis of the process of scientific knowledge —a principle which, for its importance, a few authors have called “scientific faith” in the order of nature— is not equivalent to assuming necessarily a rigid “principle of determinism”. According to the latter, once the state of a system and the laws which describe the behavior of physical-mathematical quantities in space and time are known, it is always possible to know deterministically the system's configuration at all times, past and future. The “principle of lawfulness” must also be distinguished from the “principle of causality”, which states that every finite or contingent entity, in the order of being, and every change, in the order of becoming, always has a cause. The principle of causality has a metaphysical significance and is therefore much more general: it does not depend on whether the laws of nature are stable or uniform, nor on whether it is possible to predict with accuracy all effects from the knowledge of their causes. In particular, “mechanism” made an unwarranted identification between the principle of causality and the principle of determinism ( MECHANICS, IV).

2. Law and Regularity in Several Specific Fields. The search for “regularity” still guides the formulation of “statistical” and “probabilistic” laws and therefore, also in this case, one does not abandon the notion of law. By statistical laws, which originally arose in the context of social phenomena, one attempts to understand regularity exhibited by a system in its globality. This is so, because they are used when one has neither the capability nor the possibility to observe the behavior of single individuals, as if they had been observed beforehand, due to the role played by human liberty (as it so happens, for example, in sociology), to the large number of individuals (for example, the use of statistics in biology), or to the uncountability of the mathematical-physical entities involved (as it happens, for example, in thermodynamics). The probabilistic laws describing a single individual or entity, and not necessarily an entire “statistical” system, simply give the probability that a certain event occurs among many other possible events. Even these are laws because they are capable of describing rigorously, through so-called “distribution laws” (Gauss, Poisson, Bayes, etc.), what the expected outcome of a certain phenomenon should be. A probabilistic law can not be directly utilized to predict the behavior of a single event. However, it is capable of predicting such behavior for a sufficiently large and practically infinite number of actual cases (as in the law of “large numbers”). The recourse to statistical and probabilistic laws does not weaken the principle of causality both because the latter has a broader metaphysical meaning and for reasons intrinsic to the nature of these laws. Statistical and probabilistic laws, in fact, are not used to study the “causal” phenomenology of every single element of the system, whereas our incapability to predict exactly the outcome of a single event corresponds to a lack of knowledge of all the causes which determine it, and not to a lack of causation.

In quantum mechanics, due to its robust theoretical apparatus, one often speaks of “principles”, even though many of them, not only the uncertainty principle, reveal the existence of a kind of law of nature which describes “mathematical indeterminacy” or the existence of several intrinsic limits of certain phenomenological theories. Schroedinger's equation, which governs the evolution of a wavefunction of a certain quantum state, is, in the end, a correlation law relating different quantities. A correct epistemology can also show that, in this area of physics, the principle of causality ( QUANTUM MECHANICS, V-VI) is not invalidated, and that the properties of the quantum world can continue to rest, in the last analysis, on the “natural properties” of particles or their interactions (see below, V).

3. Natural Laws, Elementary Properties, and Physical Constants. In connection with natural laws, scientific observation reveals the presence of “physical constants”. Each of these, such as the constant of universal gravitation G, are intrinsically tied to differential equations which describe a certain physical law and can be extracted from ordinary constants of integration, when the equation representing this law is solved in its integral form. From Coulomb's law to Planck's law, from Boltzmann's law to Kirchoff's law, all of the main equations of physics contain important like-named constants, that is, fixed values, which are not imposed by the physical-mathematical formalism, but are in a certain way found by the scientist who “discovers” the law. With an appropriate choice of units in which one writes down the equations, many of these constants are “dimensionless”, that is, they can be transformed into pure numbers, independently of the units chosen (sec, cm, gr, or other). There are also constants which correspond to stable properties of matter, as for example the electric charge e or the electron mass m_e. The constant c , which denotes the velocity of propagation of light in the vacuum, as well as the four “interaction constants”, which can be expressed as dimensionless numbers, of the four fundamental forces of nature (gravitational, electromagnetic, weak nuclear, and strong nuclear), all are of crucial importance.

The interest in the constants of nature arises in the most part from the fact that they seem to give access to a sort of “substratum of lawfulness” present in the matter, which is independent of our particular formulations, and therefore free from any kind of anthropomorphism. Similarly, if the mathematical form of certain equations can contain a certain amount of arbitrariness, it is not so for the physical constants there involved. Taken together as a whole, the constants of nature give a working description of “our” world; they are interrelated and interdependent in such a way that changing only one of them would mean changing practically all of them, thus changing the characteristics of the entire physical world. Precisely the discovery of the delicate balance existing between the ranges of the four fundamental forces represents one of the main results which gave rise to the conceptualization of the Anthropic Principle.It is not surprising that the constants of nature have attracted the attention of the greatest scientists. Max Planck (1858-1947), who discovered the constant h named after him which regulates the scale of interaction between all phenomena of the quantum world, stated that its validity is independent, not only of space and time, but also of other epochs and cultures, and can be extended beyond our very civilization on earth.

Natural laws can be viewed as laws which manifest the existence of a philosophical form , a “formal causality”, that is “specific properties” of the material world. The law of gravity, for instance, in all of its formulations (Newtonian, relativistic, etc.), indicates the property that every mass has of attracting another mass, or, if one prefers, of curving the space-time in which it is placed. Analogously, the electromagnetic interaction “reveals” the property of an electron to possess always and everywhere, the same electric charge (be it on earth, or in the Andromeda galaxy, today or 5 billion years ago...). The phenomenology of the physical world —one could say something analogous also for the chemical and biological world, though with a certain dependence on what happens on the physical level— therefore exhibits a “formal specificity”. That is to say, a certain number of “qualities”, of which some are more independent and fundamental than the others, capable of describing ever more specific and basic forms, including the limiting case of irreducible forms. In certain areas of contemporary physics, one prefers to describe specific properties of elementary particles in terms of reciprocal interactions (“gauge principle”), according to a vision in which significant information belong to fields, interactions, or relations, instead of to the single particles as such (which are also subject to change in their properties according to the “physical environment” in which they are placed, as it so happens between electrons and photons in the presence of a “Higgs field”). Such perspectives do not contradict the necessity of letting reality rest on stable and definite properties, but simply imply that such foundation must lie on a more general and deeper level which takes into account the coordinated behavior of the properties belonging to individual entities.

To summarize, one could say that the “principle of lawfulness and regularity”, viewed under the perspective of the laws of nature, of the physical-chemical constants, or of specific natural properties (of the particles, fields, or their interactions), suggests the existence of “forms” in nature. In philosophical terms, the interactions and transformations possible in the real world imply not only an “efficient causality”, but also and necessarily, a “formal causality”.

III. The Debate over the Status of Natural Laws, Arena of Comparison between Scientific, Philosophical, and Theological Thought

The common consensus over the importance of natural laws in the sciences, seems to break down when one asks the question as to their origin and meaning. Several questions arise: whether laws have their basis in the “nature of things” or whether they are determined by the cognitive categories of the subject; whether the regularities we observe in nature correspond to real relations or they are instead, simple functional propositions; finally, the question of whether the laws of nature embody some finalism present in the world or are instead the product of the conjunction of a mere sequence of events.

1. A few Historical Clarifications. The philosophy of the Logos of classical antiquity admits the existence of universal and stable laws, responsible for the form and becoming of the cosmos (of which human beings and their destiny are part). Such a philosophy of the Logos has two main forms, Platonism and Stoicism, which embrace two different views as to one's relation to nature. The latter posits immanent laws, and the former, transcendent laws. However, in classical antiquity, both were placed within a sacred, divine context, which viewed the ratio of the law (or of laws), as a reflection of finalism, or better yet, of a fatum . According to Aristotle, the “reason” of the order and regularity of nature does not lie in abstract ideas, but in principles inherent in things, according to a finalism capable of ascending, through the chain of causes, to the First Cause: fortune and indetermination, though present in nature, do not have the same dignity as a true cause. The only philosophy of classical antiquity at odds with this scheme was the atomism of Democritus and Leucippus ( MATERIALISM, I). They claimed that fortune was the ultimate explanation of everything and consquently negated all forms of finalism: they believed in the gods, but they rejected the notion of gods as law-makers, because even the gods are made of atoms and are therefore subject to the whims of fortune.

The Judeo-Christian tradition provided a favorable climate to the development of the the notion of law and natural laws (see above, I.1). It contributed significantly to the birth of a scientific method, whose philosophical premises had already been set forth in the patristic and medieval periods ( SCIENCE, CHRISTIAN ORIGIN OF). But, one might ask, “Is recognizing in the notion of law, as it so happens in the Christian cosmos, a theological root and therefore an appeal to a Legislator, equivalent to holding a determinist vision of nature?” To answer this question, it is necessary to remember that in Christian theology the created world does not have the same attributes as the Creator ( CREATION, IV). The “necessity” of what happens in nature is not absolute, but relative with respect to God, who is the Only necessary being. Philosophical reflection on the presence of laws, and therefore of a Legislator, deduced from the regularity and lawfulness of natural phenomena, did not coincide, historically, with the affirmation of an absolute philosophical determinism. In general terms, this was so because it was common belief that what occurred under the material sphere (which in classical antiquity was called the “sublunar” world), was always subject to change and corruption and, consequently, to occasional failure. Several clarifications, however, will have to be made for the heavenly bodies. According to Aristotle, the latter belong to the sphere of the divine. Their eternal motions and their nature are incorruptible. Therefore, they are in no way comparable to what happens in the sublunar world. In the philosophy of Thomas Aquinas (1224-1274), the conviction remains that the heavenly bodies belong to a higher sphere not subject to corruption. However, he does not attribute to the heavenly bodies divine attributes, since heavenly bodies are completely distinct from God. References to the “necessary” nature of created things, which concerned beings on various levels, were, in the first place, oriented to found their autonomy and their own creaturely consistence, and not the determinism of their motions. But in a more specific and certainly more radical way, Christian theology considers absolute determinism untenable for at least two other reasons: these have to do with both the existence of human liberty, which belongs to the world of nature and interacts with it; and, above all, the existence of the liberty of God, on whose will the laws of the world, in the last analysis, depend. Only later, since the 16th century onward, the belief in an erroneous correspondence between the affirmation of God and the affirmation of an absolute determinism was favored. Responsible for this shift were the philosophy of the late Scholastic period, beginning with Francisco Suarez (1548-1617), and especially that philosophical vision which, because of the success in applying mathematical formalism to physical phenomena, wanted to deduce a close relationship between the rationality of God and the rationality of nature (NEWTON, VI).

2. The Vision of the Laws of Nature in the Modern Age. It would be from the modern era that one began to deny the epistemological significance of the laws of nature, without for this reason denying —at least in its premises but not in many of its conclusions— a theist vision of nature. This was due in large part to the line of thought initiated by the the empiricism of Locke (1632-1704) and of Berkeley (1685-1753), which would then filter into the theoretical formulation of the Scottish philosopher, David Hume. The latter maintained that the regularity of connections which seem to exist between different phenomena, including the cause-effect relation, does not correspond to real relationships existing in nature, but derive from our repeated experience of seeing the same events occurring sequentially conjoined together; a conjunction which would lead one to think of a law or a principle of causality which are merely ideas that we supposedly project onto the things observed (cf. An Enquiry Concerning Human Understanding , 1748). What we erroneously judge as laws, is supposedly nothing else but empirical invariants, confined within the unstable horizon of induction, and therefore epistemologically conditioned by the limits of sensible knowledge, a knowledge which operates through subjective habits of the mind. In the critical philosophy of Kant (1724-1804), judgments of empirical knowledge are “synthetic a posteriori” and cannot give access to universal knowledge, which is reserved instead to “synthetic a priori” knowledge, i.e., conditions of knowledge dictated by the categories of the subject (cf. Critique of Pure Reason , 1781). According to Kant, natural laws are therefore purely empirical and not universal. They are limited to the “phenomenal” world and are incapable of saying anything about the reality of things “in themselves” (“noumenon”).

The heritage of Hume and Kant come together in the neo-empiricism and phenomenism of Ernst Mach (1838-1916), according to whom, concepts, theories, and scientific laws are none other than pragmatic tools, whose study is motivated by a criterion of pragmatic economy and efficacy, without any possible implication on the objective plane, nor on the ontological one (cf. The Analysis of Sensations , 1886; Knowledge and Error , 1905). According to Mach, the regularity of nature is an unverifiable hypothesis (the problem of induction) and laws are only a reconstruction of multiple facts, without an intrinsic relation to things. But in Mach's thought, we find also an unexpected conception of the world as a whole and the suggestion of a connection between local phenomena and those which occur on the cosmic scale, with a partial revival of the idea of universality as the necessary condition for any research activity.

The critique of the objectivity of the laws of nature delineated by phenomenal empiricism and later adopted by transcendental rationalism, precludes any reference whatsoever to a “Legislator”: any such reference, if it exists, must be sought along other paths. As interpretations which espouse an epistemological skepticism towards a real knowledge of nature (and of the Absolute, deduced from nature), empiricism and critical transcendental philosophy lead to a radical agnosticism. The classical and medieval philosophical tradition, though making it clear that an analogic knowledge of a Legislator from the observation of the natural order had to be developed along metaphysical and not physical lines (think about the fifth way of Thomas Aquinas; GOD, I.3), had certainly favored a cultural climate in which the presence of laws, order, and regularity, was considered a reflection of the action of an intelligent Creator. The subsequent loss of the original conceptual coherence, both biblical and philosophical, where such correspondence had been forged, favored a certain “absorption” of the notion of “law of nature” into a deterministic and mechanistic vision, in contrast with that authentic view of the relationship between God and creation already owned by the finest Christian theology. Descartes became its main adherent: his rationalism maintained and defended the notion of law, but exalted its geometrical dimension, its mathematical flexibility, and the ease with which such a notion could be controlled and manipulated. In greater harmony with the epistemological optimism of Leibniz (1646-1716), and in opposition to the pessimism of Locke and to the skepticism of Hume, the greatest supporters of the laws of nature, be it in science, as Galileo (1564-1641), and later, in an ever more pronounced way, Newton (1642-1727) and Laplace (1749-1827), be it in philosophy, as Comte (1798-1857), would not favor the revival of the previous conception of law. The precarious reference to a Legislator, which was barely traceable in an already decomposed form in Anglican theology of the 17th and 18th centuries, and in ever more ambiguous way in the deism of the Enlightenment, would disappear entirely in the 19th century. The debate over the possibility of arriving at the existence of a Creator from creation, would become completely absorbed in a reductive way in the debate for or against determinism.

3. More Recent Views. Between the 19th and 20th centuries, the situation seemed completely overturned: the French “spiritualists”, such as Bergson (1859-1941) and Blondel (1861-1949) —in a mainly anthropological context, but also with professed implications in cosmology— were the ones to combat determinism in the name of human liberty, and in the name of the irreducibility of life and the richness of the spirit to a world made only of matter. With E. Boutroux (1845-1921), the critique of determinism was launched from the point of view of the epistemology of natural laws (cf. The Contingency of the Laws of Nature , 1874). The notion of law was thus attacked on two fronts: it was attacked by Neopositivism, heir to the empirical-phenomenic school of thought, which reduced law to pure convention, to a priori projections of the subject, or to propositional functions with a pragmatic value; by those who asserted the inadequacy of scientific induction, considered a kind of aporia if placed before the inference of universal knowledge; and by anti-determinist vitalism, which does not question laws as such, but combats the flat and rigid vision of nature and things that the idea of laws would imply and would have fostered.

Even after the decline of determinism in the second half of the 20th century, philosophers of science would remain, to a certain degree, ambivalent in the way they extracted from such a historical and conceptual development the very theme of the laws of nature, and took on again the study of their epistemological status. With Thomas Kuhn (1922-1996), attention was shifted to the great scientific-cultural paradigms which carry, in revolutionary change, every preceding conceptual picture together with its regulative vision (cf. The Structure of Scientific Revolutions , Chicago, 1962). Karl Popper would distance himself from both the conventional/instrumental vision of science and the possibility of arriving at universally valid explanations. According to him, only relations in the mathematical sense, and not essences, can explain stability and universality. Laws of nature are assertions about the structural and relational properties of the world. They cannot, however, penetrate the truths existing at the root of those relations. In a science which progresses by hypotheses and refutations, which can therefore always be discredited, in a science that Popper intentionally gives up placing in a broader theory of knowledge (cf. The Logic of Scientific Discovery , London 1959; Conjectures and Refutations , London 1963), the question of truth and of the limit to which all the cognitive process must tend, can not be fully treated. However, the question cannot be completely ignored, as it emerges in several ethical-social writings of the Wiener philosopher (cf. Unended Quest , London 1976; The Open Society and its Enemies , London 1952). In the 20th century, there was no lack of philosophers who were favorable to a more realist vision of the laws of nature ( REALISM, X). Among these, we mention J. Maritain (1882-1973) (cf. Philosophy of Nature , New York 1951) and G. Bontadini (1903-1990), the latter for the general context of realism. More recently, R. Bhaskar ( A Realist Theory of Science , Leeds 1975) and E. Agazzi ( Filosofia della natura , Casale Monferrato 1995).

4. God, the Universe and Laws: a Unique Topological Cosmology. John Barrow (1990) suggested a way of summarizing, in topological terms, the possible relations between “Laws”, “Universe”, and “God”.According to the English scientist, the relationship between the universe and its laws can be represented in five different ways. In the first way, the “set” of the universe U is a subset of the “set of laws”, L , that is U ⊂ L . . This would correspond to the Platonic conception, in which laws (their ideas ) have a certain autonomy and consistency independently from the real cosmos. This view is close to several contemporary conceptions of cosmology, which treat mathematically an ideal multiplicity of possible universes as something which is conceptually (when it is not chronologically) prior to the physical universe as such ( MANY-WORLD MODELS, III). In the opposite case, U ⊃ L , the laws of nature appear to be “islands of rationality” of perhaps local, but not universal, validity. They are changing islands originating from conventional boundaries inside the universe which maintains its own identity even without its islands. In the third case, U ≡ L , the universe coincides with its laws and is therefore reinforced in its identity and uniqueness, because it would not make sense to speak of time, of physics or models, without reference to its existence or in a way independent from it. The fourth alternative is L =  Ø, that is, only U exists and not L : there are no laws of nature because the universe does not admit neither regularity, nor law. In the case that laws do exist, they are pure mental constructs without any real foundation; this is a conception which is very much in keeping with the radical philosophy of randomness, yet elevated to the status of definitively explaining the real world. The last alternative is one in which there is no universe U =  Ø. It is equivalent to a kind of physical nihilism in which laws can exist without any need of a universe. It is a vision which radicalizes the first case described above, and is not far from those conceptions of contemporary cosmology which describe the origin of the universe as a random fluctuation of a quantum wave function, whose preexistence, with respect to every possible physical reality, is posited.

If one extends this peculiar topology to the relationship between “God” ( G ) and “Laws” ( L ), other interesting situations arise. A situation in which G  ⊃ L (the reality of laws is a subset of the reality of God) is, in essence, one of the most intuitive (but not the only) form of a Christian theology of creation: God is sovereign Creator of the laws of nature who can modify or suspend them according to His will. The other alternative, G  ⊂  L , corresponds to a reductive, if not, completely contradictory image of God, in keeping with several “process theologies”, in which the nature of God depends on the history of the world; it also practically represents classical dualism, where the divine primordial principles of Good and Evil are subservient to the cosmic Law of conflict which completely conditions their ability to create; but polytheism also falls into this category, because, according to polytheism, everything that belongs to the world of the divine follow the same law ( fatum ) of the human and material world. The identification G ≡ L between God and Laws describes the situation of pantheism in its different versions, ancient and contemporary, including the assumption of a universal cosmic Law which replaces a personal God. This is what happens in Buddhism, and, more recently, in New Age . But the identification between G and L also indicates the identity in the attributes between the philosophical image of God and laws of nature, which are held to be eternal, absolute, rational, and changeless. For reasons mentioned above (nn. 1 e 2) concerning determinism, such laws do not correspond to the Judeo-Christian God, even if certain thinkers have maintained so. Moreover, the Judeo-Christian tradition maintains a “real” distinction between God and the world (for the theological aspects of the problem, ( CREATION I.2 and III.3). In order to state, as certainly most theologians do, that “God works through the laws of nature”, there is no need to identify the two terms to each other. Finally, the two remaining possibilities, God without Laws and Laws without God, can be associated with two views which are not uncommon today: the view that God is not a source of intelligibility and providence and the atheistic view which holds that the ultimate explanation of natural laws does not refer to any other reality beyond them.

IV. Reflections in Contemporary Science on the Meaning of Natural Laws

In the past few decades, the debate over the status of natural laws has been sustained mainly by thinkers directly involved in scientific research. Scientists see with surprise the stability and mutual connection of laws. They ask why they are intelligible and why the mathematical formalism is so successful in describing them, and they seek the deeper meaning of the fundamental constants of nature. One of the reasons for such interest is our contemporary and rather satisfactory formulation of a consistent, global evolutionary picture of the universe, capable of linking the physics of the micro cosm with that of the macro cosm. «The concept of law», Paul Davies says, «is so well established in science that until recently few scientists stopped to think about the nature and origin of these laws; they were happy to simply accept them as "given". Now that physicists and cosmologists have made rapid progress toward finding what they regard as the "ultimate" laws of the universe, many old questions have resurfaced. Why do the laws have the form they do? Might they have been otherwise? Where do these laws come from? Do they exist independently of the physical universe?» (Davies, 1992, p. 73).

1. What is the Nature of the Laws of Nature? The irreducibility of the laws of nature to the idea of mere principles, so claiming their own epistemological status,was already proposed by Henri Poincaré (1854-1912), though in a somewhat conventional perspective. J. Clerk Maxwell (1831-1879), Max Planck, and Albert Einstein (1879-1955) offered a decisively realist vision of the laws of nature, insisting on the necessary faith in the lawfulness of reality as a presupposition of scientific knowledge. «In the faith that the real world is governed by laws», the founding father of the quantum theory noted, «the physicist forms a system of concepts and principles, the so-called physical view of the world, which he develops as he can best do, so that such a view, which lie on the level of the real world, gives him the same messages as the real world would» (M. Planck, Positismus und reale Aussenwelt (1931) in Wege zur physikalischen Erkenntnis , S. Hirzel, Leipzig 1933). A correct understanding of this “world view” requires, according to Einstein, that the inductive and deductive approach be inseparable: «The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them» ( The World as I See it , London 1955, p. 125). From the logical point of view, laws are free creations of the human intellect which cannot be justified a priori , but, from the view-point of experience, our intuitions turn out to follow certain norms: our free creativity is limited by the “freedom” of nature.

Several physicists of today, such as Carl von Weizsäcker, Richard Feynman, Paul Davies, and John Barrow, seem to have thought along this line of reasoning. They have all emphasized, even if with different perspectives, the “given”, objective, and in a certain sense, founding, character of the laws of nature. One can understand the action of the laws of nature only by conceiving them on the cosmic scale, that is, only by assuming that laws are universally valid. In the introduction to his university course on Quantum Electrodynamics, Richard Feynman alerted his students, «the reason that you might think you do not understand what I am telling you is, while I am describing to you how Nature works, you won't understand why Nature works that way. But you see, nobody understands that. I can't explain why nature behaves in this peculiar way» ( QED , The Strange Theory of Light and Matter , Princeton 1985, p. 10). The fact that the laws they use are imprecise and can be revised, have led a good number of scientists, as Feynman, to emphasize that laws are descriptions and not explanations, so preferring for them the category of “relation” instead of that of “essence”, as if the “principle of lawfulness or regularity” seemed to belong more to nature than to its laws. Nature exhibits continually new and unpredictable behavior, but always in a way that does not lead to chaos or indeterminism, but to new and more general levels of understanding and law.

In his defense of the objective, epistemological status of natural laws, Paul Davies states, «it is important to understand that the regularities of nature are real. Sometimes it is argued that laws of nature, which are attempts to capture these regularities systematically, are imposed on the world by our minds in order to make sense of it. It is certainly true that the human mind does have a tendency to spot patterns, and even to imagine them where none exist. Our ancestors saw animals and gods amid the stars, and invented the constellations. And we have all looked for faces in clouds and rocks and flames. Nevertheless, I believe any suggestion that the laws of nature are similar projections of the human mind is absurd. The existence of regularities in nature is an objective mathematical fact. On the other hand, the statements called laws that are found in textbooks clearly are human inventions, but inventions designed to reflect, albeit imperfectly, actually existing properties of nature. Without this assumption that the regularities are real, science is reduced to a meaningless charade» (Davies, 1992, p. 81). One of the reasons used to support this point of view is the fact that laws can predict and explain new events that go beyond the phenomenon originally studied, allowing for a successful interpretation of new unexpected happenings.Starting from a new proposed law, one can deduce verifiable consequences to happen in other situations, which lead in turn to new and unexpected discoveries, often unrelated to the original subject of study.

As it is well known, the problem of the realist view of the laws of nature (that is other than its determinist view) has been revisited in quantum mechanics. It must however be remembered that along with tendentially idealist interpretations (Copenhagen interpretation of Bohr and Heisenberg), there have been also more realist ones, developed by such physicists as David Bohm, John Bell, Richard Feynman, and more recently, John Cramer (for a general overview, cf. J. Gribbin, Schrodinger's Kittens and the Search for Reality , Boston-New York 1995). As Polkinghorne (1988) has concisely put, in quantum physics, «we are presented with a picture of the physical world that is neither mechanical nor chaotic, but at once both open and orderly in its character» (p. 341).

2. The Intelligibility of the Laws of Nature and the Search for their Unification . The debate within the scientific realm over the laws of nature is often associated with the question as to their “intelligibility”: one wonders why they can be described by a mathematical formalism which is relatively simple, and not seldom elegant ( BEAUTY, II-III). One also wonders why there is a necessary correspondence between our mind and logic, on the one hand, and the way nature seems to behave, on the other. Such agreement is both a type of faith (we have to “accept” induction) and a result (predictability of deduction). In the philosophical perspective, the rules of the debate reproduce those between a realist and an idealist view of the natural laws, as pointed out above. In the religious-theological perspective, the possible Legislator is sometimes dressed in the robes of an Architect. In popular science books, one finds concepts such as the “cosmic code” or “cosmic blueprint”. Along with the consequences the intelligibility of the real physical world has on the level of natural religion and of the theology of the Christian Logos (already dealt with in other entries of the Dictionary, ( MYSTERY, IV. 1; JESUS CHRIST, INCARNATION AND DOCTRINE OF LOGOS, III.3-4), we will summarize here several reasons why the issue of the intelligibility of nature seems to be truly significant in the sciences.

The question cannot be addressed to the laws themselves, because these are precisely an intentional concretion of such intelligibility, which is needed to make the behavior of reality understandable and predictable. It must be directed, instead, to mathematics and to our mind. Many mathematical properties observed in nature are less obvious than they seem. Not a few laws could have been other than simple, symmetric, and equipped with convergent integrals. It is for this reason that they can be easily approximated with ideal models. Many phenomena with radial or spherical symmetry are described by equations whose variables have “simple” natural numbers as exponents, centralizing all the “problematic” of the mathematical computation in the transcendental (that is, transfinite) value of p . What would happen if these exponents were complicated rational or even irrational numbers?

If mathematics is to a large degree a projection of the human mind onto the real physical world, the physical world must also have the property of allowing such a projection “work”, showing itself apt to host a web of logical-mathematical relations which let us to interpret and predict many phenomena.The link between mathematics and nature seems to be pushed much further than what the simple construction of real numbers from natural numbers might suggest. «One might (indeed one should) expect that the world evidenced itself as lawful only so far as we grasp it in an orderly fashion. This would be a sort of order like the alphabetical order of words. On the other hand, the kind of order created, for example, by Newton's gravitational theory is of a very different character. Even if the axioms of the theory are posited by man, the success of such a procedure supposes in the objective world a high degree of order, which we are in no way entitled to expect a priori» (A. Einstein, Letter to M. Solovine , March, 30, 1952, Eng. transl. quoted by S. Jaki, The Road of Science and the Ways to God , Chicago 1978, p. 193). One of the ways to drastically reduce the problem is to make the following objection: that the laws which govern the cosmos and allow intelligent life to evolve ( ANTHROPIC PRINCIPLE) necessarily have to be the same as those which govern the behavior of our mind. The agreement between the human intellect and natural laws would then depend only on the fact that the brain operates according to physical laws, and that these laws turn out to be completely compatible with the brain. In reality, such an objection is not very convincing. The bio-chemical and physical functioning of the brain, on the one hand, whose laws are certainly in agreement with those of the cosmos to which it belongs, and, on the other hand, the rational activity of abstraction of the mind, with its ability of finding mathematical form in physics, operate on two distinct and irreducible levels ( MIND-BODY RELATIONSHIP). Justifying the fact that we live in a “mathematical” universe only because our universe is “anthropically selected” from infinite possible “non-mathematical” universes is a philosophical a priori hypothesis and not a scientific solution in the strict sense. The intelligibility of the laws of nature cannot be considered a consequence of natural selection in our biological evolution, because it is difficult to maintain that the ability to solve differential equations has been a historically relevant factor in the survival of the human species. Without wanting to solve the riddle of intelligibility, whose complete solution does not seem feasible within the scientific method only, it would seem more logical to conclude that the structure and the intelligibility of the universe are two closely tied aspects: if the scientist accepts as “given” the former, that is, the ultimate reason of why the universe is as it is, he is also obliged to accept as given the deep reason of the latter, that is, why we can know it. In principle, it would have been possible for the human race to adapt and organize in the world only biologically, that is, without any intellectual understanding of it. But this has not been the case.

A more ambitious field, in which both the intelligibility of natural laws and the ability to describe them mathematically are evident, is without doubt the project of the unification of the four fundamental forces. Scientists, who have been capable for quite some time of describing within the same formalism both electric and magnetic fields, have been able, in recent times, to unify the electro-magnetic and the weak nuclear forces, and to experimentally confirm this with the discovery of the corresponding particle/carriers of the unified field. Today, there are several satisfactory theories, usually called the “standard model” or also GUT ( Grand Unified Theories ) capable of including in the same unified picture a third force, the strong nuclear one. However, unifying the fourth remaining force (the gravitational force) has lead to much greater difficulties. The mathematical formalism used is not univocal, as evidenced by the fact that the equations involved have many free parameters, but the physical view of the cosmos which emerges from it is highly suggestive. The mathematical unification of the forces is reasonable and progresses because the universe is “susceptible to be unified”. The formulation of more general “symmetry groups” is undoubtedly the work of the creative mind of the researcher, but nature must contain, in its foundations and on some level, a closely-knit structural reality on which such rationality can rest.

Another shoot-off of the search for a unified theory is the seduction to propound a Theory of Everything (TOE). Although it is not supported by the majority of cosmologists, there have been several animated adherents such as S. Hawking ( A Brief History of Time , New York 1988) and S. Weinberg ( Dreams of a Final Theory , New York 1992). According to this dream , the definitive discovery of mathematical-physical laws which, in the first moments of life in the universe, regulated the progressive separation of the four fundamental forces through “symmetry breaking” occurring as the global temperature decreased, would contain the ultimate reason of the existence of these forces, or the single “superforce”, giving thus the ultimate explanation of everything. But the attempt to use a similar unified formalism as an exhaustive description of all of physical reality leads to obvious contradictions, not only on the philosophical level, due to the impossibility of the scientific method to treat the “problem of the whole” ( UNIVERSE, III), but also on the strictly physical level (cf. Ellis, 1991; Barrow, 1990 and 1998). This leads to the classic “problems of incompleteness”, either on the logical or ontological level, and it ends by proposing again the canons of an untenable reductionism.

3. An Evolutionary View of the Laws of Nature: from Being to Becoming? The increasing importance attributed to the concept of evolution and the greater attention paid to the arrow of time ( TIME, II. 4), especially from thermodynamic considerations of irreversible processes, has introduced, in the last decades, important new discoveries in the way we view natural laws, placing them in a highly philosophical framework. Such new discoveries have been described by some authors in terms of a transition from the ideal, ordered and changeless cosmos governed by natural laws, to a real, disordered universe of evolutionary processes. If the scientific interpretation loses its “paradise of laws” (cf. Cini, 1994), it would also lose with it that philosophical vision which has been traditionally built on the notion of law and, consequently, on its Legislator. Strictly speaking, this philosophical view does not stem from the discovery of the mathematical unpredictability of complex phenomena (I have already alluded to how mathematical predictability is different from both the principle of causality and the principle of lawfulness, which are always at work), but from the fact that, in the origin of order, structuring, and diversification of reality, there would be no longer the idea of “natural law”, but that of “process”. This latter notion is supposed to represent better phenomena such as self-organization, functional development, the emergence of complex structures, the adaptation to and interaction with the environment, which are supposedly those things truly responsible for all the properties and morphology observed in nature. The new vision would involve physics (giving a greater emphasis on the relational-global elementary properties of matter) as well as, and above all, chemistry and biology, which are fundamentally open to the categories of “transformation”, “development”, and even of “emergence”.

The Belgian chemist and epistemologist of Russian origin, Ilya Prigogine (1917-2003) has contributed a great deal to the development of the new vision described above. The study of the evolution of thermodynamic systems far from equilibrium allows one to describe the emergence of organized structures which are morphologically more interesting and complex than the initial system (mainly Prigogine and Stengers, La Nouvelle Alliance , 1979; see Prigogine, 1980 and Prigogine and Stengers, 1984). The “non-equilibrium solutions”, which are possible near “bifurcation points” of a system, are those which are the most “undecidable”. They can, therefore, only be treated probabilistically (in orographic terms, they can be compared to the behavior of a ball on the peaks of contours) and describe the “evolutionary dimension” or the “creative development” of the system. The equilibrium solutions, instead, located far away from the bifurcations (represented by the behavior of balls in the valleys), reduce the system to a predictable and deterministic phenomenon with well-known laws. Such behavior exists in nature, where one observes a progressive diversification of chemical, biochemical, and biological laws. And it holds also when we consider the formation of rather structured physical systems (for example, the thermodynamics of a star) out of chaotic systems (the cloud of hydrogen gas from which it is formed). We are dealing with the emergence of “order from chaos” ( Order out of Chaos , is actually the title of the English translation of the La Nouvelle Alliance ). Non-equilibrium thermodynamics succeeds in describing “islands of decreasing entropy” in which the novelty of a world in evolution is contained, standing out of the background of a global law of “increasing entropy”. The latter describes, instead, the universe as a whole, as it moves very probably towards a state of progressive thermal and energetic degradation.

Due to the explicit philosophical slant given to the above scientific picture by Prigogine himself, such a picture has been used to pose the question of whether the main factor of organization (and of intepretation) of the physical universe can be represented by the laws of nature, letting now the “emergence of the unpredictable” play the key role. Since natural laws are more easily associated with the description of systems in equilibrium, with stable solutions, and with their predictable evolution, they lead to the notions of bond and eternal recurrence, whereas the idea of emergence and complexity would lead to the notion of creativity and even to that of liberty. In keeping with this change of perspective —and using the terms of a by now classical antithesis— Prigogine holds the primacy of becoming over being, of process over substance, bringing into such an antithesis the great ideas and heritages of philosophy and religion (cf. Prigogine, 1986). He cites the work of M. Heidegger, Being and Time (1927) and the philosophy of the process developed by Whitehead, as a more fitting philosophical framework. But there is more. The vision of a kind of science whose importance and interpretative power are shifted from time-reversible equations, typical of the natural laws traditionally (and reductively!) understood, to the thermodynamics of irreversible phenomena, which are responsible for the true novelty and richness of the universe and are typically closer to biology, would allow finally “a new alliance” with the world of humans and life. A less deterministic science which is freer from an excess of physical, mechanistic laws, is affirmed to be more easily in dialogue with the humanities, which are open to liberty and to creativity.

Even though the scientific merit and the epistemological novelty of non-equilibrium thermodynamics are incontestable, we do not agree with the majority of the “philosophical” consequences brought about by Prigogine's suggestion. As alluded above, these consequences stem from an unconsciously reductive view, not only of natural laws (identified by him with determinism) and of the principle of lawfulness (identified with a notion of static order that precludes any novelty), but also of science itself as a whole. The possibility of dialogue between the natural sciences, the humanities and philosophy, has certainly increased with the abandonment of mechanism, though to overcome mechanism we do not need to reject the notion of laws. However, the development of such a dialogue depends, in my opinion, on more grounded philosophically factors (CULTURE, V-VI; UNITY OF KNOWLEDGE) than the re-discovery of the open and “creative” behavior of nature, or the setting-up of a theory which better interpret that behavior.

The phenomenology of non-equilibrium thermodynamics does not constitute a negation of the value of laws of nature for at least two reasons. In the first place, any thermodynamic system, in whatever way it is represented, does not constitute the “formal cause” of the emergence of an ordered and complex structure, but simply constitutes its material and chronological, prior context: the emergence of novelty is due to an “act of nature”: if the act of nature does not have the form of a reproducible law (which is, in fact, the law describing a ball which falls from the top of a hill), it is so because of the non-reproducibility of the same boundary conditions (or initial conditions) of the system, not because of the absence of any principle of lawfulness or regularity (that in this case is the very law of gravity, which makes the ball fall, even if we do not know where). In the second place, the behavior of fluctuations and instabilities from which the system will later evolve in an unpredictable way, can be described by mathematical-physical laws, as it happens, for example, in the instabilities that occur in fluid dynamics. As a proof of it, Prigogine would inevitably continue to use the notion of law, describing the behavior of nature as a delicate balance between fortune and necessity, between fluctuations and deterministic laws, between symmetry breaking and laws which cause such breaking.

4. Special Aspects in the Field of Biology. In biology, contrary to what can happen in physics, thinking of laws of nature in terms of “processes” instead of simple regularities, does not represent a change of viewpoint. Even though one speaks seldom of “laws” in biology, their existence seems to be evident on several levels. The genetic code contained in the DNA of cellular nuclei gives rise to particular developments of a certain individual and not to others. Hereditary traits are passed on following certain rules of combinatorics. To the same interactions with the environment, living beings react in the same way, that is according to a “principle of lawfulness”, etc. From the historical point of view, the debate over the presence of a possible “Legislator”, arose along two classic lines of thought, whose opposition gave and continues to give rise to misunderstandings. They are, on the one hand, the apologetic use of the marked organization, complexity, and finalism evidenced by living beings, and on the other hand, the attempt at explaining all these features as chance outcomes, by simply appealing to the ideas of natural selection, adaptation to the environment, or other factors. We will limit ourselves to mentioning only some hints which could aid the understanding of what the term “law” might mean within a biological context (for an overview of the main interdisciplinary aspects, cf. R. Russell, W. Stoeger, F. Ayala, 1998).

A special case of “biological law” is that of the “classic” Darwinian theory of evolution, based on the “law of natural selection”, which is thought of as a process determined by two factors: random genetic mutation, with the passing of hereditary traits, and the survival of species whose mutations cause morphologies which are more fit to the environment of the living organism. Keeping the notions of adaptation and evolution, whose functioning is certainly without doubt, such a vision is today hotly debated, because the passing on of hereditary traits of mutations is not a fixed rule, and because the main origin of mutations is no longer seen as “random”, but as the action of the environment on living organisms.

Today, implicit reference is made to the principle of lawfulness in two new areas of research which are becoming more and more important. The first of these involves the idea that there are processes of “steering” or “confluence”, through which structural or thermodynamic principles intrinsic in molecular or cellular organization are manifested during the evolution of living organisms and when circumstances make it possible (cf. Webster and Goodwin, 1996). It is as if biological evolution did not have to “make way for itself”, but simply “follow the shapes of the landscape” that have already determined the path to take. The second is the re-evaluation of the “specific individual formality” of the living organism, be it a cell or a complex organism, as a unity and a subject of functions which cannot be reductively interpreted as a simple sum or combination of the properties of the component parts. Such a behavior indicates, in essence, the ability of the organism to maintain and develop in a consistent way invariant characteristics, as, for example, homeostasis, functional symmetries, immunity to external agents, etc.. According to the “Gaia hypothesis”, a similar behavior is in a certain way applicable, on the planetary scale, to the entire biosphere, now seen as a sort of living organism that tries to maintain and develop its own life (cf. J.E. Lovelock, A New Look of Life on Earth , Oxford 1979; The Ages of Gaia. A Biography of our Living Earth , London 1988). It is interesting to mention that both areas of research had already been theorized in the middle of the 20th century by Teilhard de Chardin (cf. L. Galleni, How does the Teilhardian Vision of Evolution compare with Contemporary Theories? , “Zygon” 30 (1995), pp. 23-43).

From the most traditional point of view, the recourse to the idea of law and regularity has always accompanied the description of the phenomenology of life. There is a well recognized “functional regularity of living organisms”, in virtue of which every part serves the good of the whole and the whole defends its parts, according to a logic which transcends the individual and works towards the good of the species. There is a certain “constant in existence”, manifested by the replication of the same structures, which provides a certain morphological, functional, but also reproductive regularity. Analogously with what happens in the variational principles of mathematical physics, in biology, there also seems to operate a kind of “law of simplicity”, a fundamental law which leads the living organisms to act with minimal work (i.e, with a simple and sure way of proceeding which avoids useless complications).

V. Towards an Ontological Analysis of the Laws of Nature: Scientific Laws, Natural Laws, and the Metaphysical Notion of “Nature”

Resuming the questions put forth by Paul Davies «where do natural laws come from» or, also «could they have been different?», implies shifting one's attention from their epistemological to ontological status. The need to access, sooner or later, this level was addressed from a historical viewpoint by Pierre Duhem: «Theoretical physics can never give us the explanation of experimental laws, it does not reveal to us the reality which is hidden beneath sensible appearance. But the more it is perfected, the more we sense that the logical order in which it places the experimental laws is a reflection of an ontological order; the more we doubt that the relations it establishes between observational data corresponds to relationships between things, the more we discover that it tends to be a natural classification [...]. Nevertheless, if the physicists is incapable of motivating such a belief, he is no less incapable of taking away its reason of being» ( La théorie physique , Paris 1914, pp. 35-36). Another epistemologist and scientist, Henri Poincaré, wondered, though recognizing that scientific laws are conventional, if, as a whole, laws could be independent from their conventions, if they could be considered “invariant”. He concluded later, however, that the existence of invariants is, in essence, required by the role of the “translator” of science: the relations between scientific facts —inevitably expressed through conventions—do exist because invariant laws exist.Such laws are relations between facts in themselves and by themselves, of which scientific laws are precisely a “translation” (cf. The Value of Science , 1911, ch. X, § 4).

We are therefore led to a necessary distinction between “natural laws” and “scientific laws”. The two are not identical (cf. Artigas and Sanguineti, 1984). We can work only with the latter, and not with the former. Scientific laws have a limited cognitive scope and are always subject to experimental revision; their knowability and intelligibility rest on an “invariant” substrate of a thoroughly meta -physical character, which, in first approximation, would be representative of the “laws of nature”; we will see later that they rest on the “metaphysical nature of each entity”, that is, on that operative principle describing the formal properties and the possibilities of active and passive interaction of a physical being, and manifesting its essence.

Richard Feynman loved to associate the image of musical rhythm to experimental laws which relate different phenomena with each other. Going back to the preceding distinction, laws of nature are what makes the regularity and cadence of “rhythm” possible, and which permits scientific laws to be discovered and described with mathematical formulas. The latter have a necessarily conventional character, and allow for a multiplicity of approaches and formulations, whose freedom is however limited by the responses received “from nature” through an experimental method open to reality. Once understood in this way, laws of nature are a kind of “asymptote” which the scientific laws approach. We are dealing with a “philosophical”, rather than “mathematical” asymptote. Science, in fact, cannot “supply the reason” for the laws of nature: they have a character of givenness, they are something given and received. Although the ultimate “why” they embody escapes the scrutiny of science, it is precisely in virtue of the laws of nature that science is possible. Scientific laws describe the world without being able to “explain” it, whereas the laws of nature furnish the reason as to how the world is, without being able to describe it directly.

A realist epistemology of natural laws does not imply that the mathematical expressions which describe physical processes “are there, inside things”, nor any less that the regularity and symmetry, in virtue of which we can arrive at a formulation of a law, constitute the “real and concrete” structure of that phenomenon. A realist vision of natural laws states only that the “principle of lawfulness”, the point of departure for the structuring of scientific knowledge, is a principle that responds to the nature of things. Its cognitive validity does not turn out to be genetically compromised by the problem of induction; its existence is the consequence of natural, stable, and intelligible properties, whose ultimate explanation science receives from reality, as something “given”.

It is interesting to note that in metaphysics every being has its own “nature”. In his Commentary on Book II of the Physics of Aristotle, Thomas Aquinas defines “nature” as an operative principle in virtue of which every being, because it has a specific “essence”, acts according to what it is. Nature is a natural inclination which regulates the ways in which a certain being can interact with what surrounds it. Nature is a principle of motion but also of rest: that is, it refers not only to the regularity of the interactions, but also to the stability of the intrinsic properties (cf. In II Physicorum , lec. 1, nn. 145-146; lec. 14, n. 267; cf. also Summa Theologiae , I-II, q. 6, a . 5, ad 2^um ). “Nature”, however, turns out to be related to “formal causality” of the being, but with interesting relations to “final causality”. The First Cause, in fact, which is responsible for being and the project of all that exists, is the ultimate explanation of the “why” of the specific nature of every being. In the cosmos of Thomas Aquinas (who added to the Aristotelian vision the theological perspective of creation and the important philosophical intuition of the “act of being”), finality or the global design of the universe —and therefore, indirectly, also the act of the Legislator— is not something imposed on the physical world from outside, but is the result of a harmonious operation of all created beings according to their nature, an operation which leads every thing towards its final end.

Several thinkers have suggested a certain convergence between the metaphysical notion of nature and the elementary and founding properties of physical reality. According to these thinkers, an analysis of greater ontological depth shows that the latter have to, on a certain level, rest on the former (cf. R.J. Connell, Matter and Becoming , Chicago 1966; P. Durbin, Philosophy of Science. An Introduction , New York 1968; cf. also W.A. Wallace, The Modeling of Nature , Washington 1996). I have proposed the idea that such a convergence can also be found in the notion of “laws of nature” (cf. Tanzella-Nitti, 1997). This has two advantages: first, it gives reason of the intelligibility of scientific laws and, second, it affords an understanding in a non-conflicting way of the relationship between divine action (or divine project of the world) and natural phenomena. The latter relation can in fact rest on the rather close relation between formal and final causality. Even though a certain finalism has a regulative value in the formulation of sciences ( MECHANICS, VI), the scientific method typically meets the idea of final cause with suspicion, whereas it is instead constitutively open to the formal cause.

On the subject of the new experimental and theoretical fields which contemporary scientists are bringing to the attention of the philosopher (see above, IV), we also note that the distinction between scientific laws and natural laws aids our understanding of how true laws of nature are still compatible with the unusual and complex phenomenology of quantum mechanics. At first sight, it seems more problematic to harmonize the metaphysical notion of nature with an interpretative picture, as that of a good part of contemporary science, in which properties are always understood in terms of relations, connections, and interactions, and not as intrinsic characteristics of beings as such. However, the metaphysical notion of nature is a notion which is “open to the relation” in that it denotes not only an active principle of operation, but also a passive principle, the specific ability of receiving new forms, of giving rise to specific interactions (cf. Summa Theologiae , I-II, q. 6, q. 5, ad 2^um ; De spiritualibus creaturis , a. 2., ad 8^umm ). It does not, however, contradict the notion of relation, emergence, and process, but simply regulates their operative modes along a specific and non-random path.

The concept of the metaphysical nature of a being is a notion open to the multiplicity and richness of the phenomenal world, because it is capable of inducing (or receiving) a practically infinite number of connections with other beings and with the environment as a whole. It is a relative (as opposed to absolute) notion, a principle of operative formality in a world of subjects where one is ordered to the other: in natura est alterum propter alterum, sicut et in arte – in nature, one thing exists for another, as it is even in art ( In II Physicorum , lec. 13, n. 257). In the ordered “cosmos”, which emerges from the metaphysical vision of Thomas Aquinas, the causal role of the whole is not weakened, nor is the relational value of the properties of the various components, which springs from their mutual dependence, undervalued. Only the organicity and the harmony of the parts are emphasized in relation to the global end. Moreover, in this cosmos there is a place not only for the substance, but also for the process: one requires only that the multiple levels of the process have an ultimate subject of attribution which is not itself a process.

VI. For a Theology of Natural Laws

1. The Cosmos, Place of the Covenant between God and Human Beings. The biblical message presents a natural world governed by laws. These laws are willed by the providence of a unique Creator, and they are obeyed by the entire inanimate and animate world. Their action is described in a language which is not, primarily, philosophical or speculative. It is described instead in a narrative, wisdom style, which is not seldom highly artistic, even though such narratives contain metaphysical consequences concerning the relationship of God and nature. A “created” world manifests itself with the characteristics of law, order, regularity, because it is an effect of the Divine Word. It is a personal, intentional, intelligent, but also good, provident, and faithful word: the wise word of God created and maintains in existence all things, leading the entire universe towards its final end (cf. Wis 8,1; 11, 24-26; Ps 33, 4-9; Ps 104, 24-29). Human beings, with the help of divine wisdom, can recognize the laws of nature and understand the truth there contained (cf. Wis 7,17-21). The principal contexts which call for the presence of laws are that of celestial phenomena SKY, III), the behavior of living beings even in relation to their habitat, and finally, the human person and his moral life. The biblical passages in this regard are numerous. The most celebrated ones are the first pages of Genesis , Psalms 19 and 104, chapters 36-29 of the Book of Job , and chapter 43 of Sirach . Cues to the “rationality” of the creative project of God and to the “lawfulness” in the behavior of nature can be found almost everywhere in the Wisdom books (cf. Prv 3,19-20 and 8,22-31; Sir 16,24-26; 42,15 - 43,33; Ps 119,89-91), and a few times in the prophetic books (cf. Jer 31,35-37).

The main idea which emerges from a reading of these passages is that the stability of the natural laws is the image and expression of the God's faithfulness and the truth of His covenant, in which creation participates as its first primordial step. It is the faithfulness of God to Himself, to the truth and goodness of His project, but it is also the faithfulness to men and women, because the laws will never be revoked and are constantly in action as a sign of God's favor and love. The stability of the heavens is the image of God's faithful love for the people He has chosen: «Thus says the Lord, He who gives the sun to light the day, moon and stars to light the night; Who stirs up the sea till its waves roar, whose name is Lord of hosts: “If ever these natural laws give way in spite of me, says the Lord, then shall the race of Israel cease as a nation before me forever”» ( Jer 31,35-36).

In the context of natural laws, it seems difficult to separate what is inscribed in nature, from what is inscribed in the heart of man: the “law” by antonomasia is the moral law inscribed by God in the human conscience. To live according to this law is a sign of wisdom and a source of happiness. The laws of nature play the role of “accompanying” and “favoring” human understanding of the moral law. They also offer a certain “guarantee” of truthfulness and goodness, relating the provident truth of the moral law to the truth of the laws of the cosmos, the latter being “in the face” of everyone. A good example in this regard is Psalm 19.

Natural laws have, finally, the function of inspiring the human being to give glory to God, to help him and her recognize the existence of the Creator through the order and regularity with which creation is governed. «The moon, too, that marks the changing times, governing the seasons, their lasting sign[...]. The beauty, the glory, of the heavens are the stars that adorn with their sparkling the heights of God, at whose command they keep their place and never relax in their vigils. A weapon against the flood waters stored on high, lighting up the firmament by its brilliance: behold the rainbow! Then bless its Maker, for majestic indeed is its splendor [...]. Lift up your voices to glorify the Lord, though he is still beyond your power to praise. Extol him with renewed strength, and weary not, though you cannot reach the end» (Sir 43,6; 9-11 and 31-32).

Theology and Christian tradition have received this biblical heritage, often associating natural laws with the idea of a “government of the world”: «Those who engage in scientific and technological research admit, as the premise of its progress, that the world is not a chaos but a cosmos; that is to say, that there exist order and natural laws which can be grasped and examined, and which, for this reason, have a certain affinity with the spirit» (John Paul II, Discourse to the Pontifical Academy of Sciences , 31.10.1992, in Papal Addresses to the Pontifical Academy of Sciences (1917-2002), “Pontificiae Academiae Scientiarum Scripta Varia”, n. 100. Vatican City 2003, p. 343. On the theme of natural laws, though in a different historical context, cf. also Pius XII, The Laws that Govern the World: Address to the Plenary Session of the Academy , 3.2.1943, in ibidem , pp. 100-109).

2. Stability of the Laws of Nature and God's Faithfulness. If we had to say what image of God the biblical beckoning to a Legislator corresponds, we would have to respond that his most salient traits are not those of an architect, nor of a watchmaker or musician, but of a faithful Creator. In Holy Scripture, the notion of “natural law” is synonymous with “faithfulness” and “truth” (these two concepts derive from the same Hebrew word ‘ emet ). Only secondarily does it refer to the notions of rationality and of order. Faithfulness does not mean determinism, but the will and ability to fulfill what has been promised, and in ways that only God knows. If Christianity, with the guide of biblical Revelation, has certainly favored a climate of “trust” in the existence of the laws of nature and in the rationality of the world, this cannot be translated, in epistemological terms, into a flat affirmation of determinism. Nature rests on stability, not on chaos or on eternal change, because God is “faithful”, that is, “true”. Lawfulness and faithfulness, both reveal an order towards an end. God does not “take back” His gifts: the world He has placed in the hands of human beings does not completely escape their “grasp”, because the world is just as true and real, and therefore knowable. As Creator, God maintains His complete transcendence over the world and His complete separation from it (He is “holy”, heb. qodes , that is, “separated”); but even as Creator, He founds, in an immanent way, the truth and autonomy of all things, and directs His provident gaze towards what He has always loved and willed as it is. The biblical image of God is not that of a Legislator who imposes from the outside His laws on a nature which He forms in the manner of a demiurge. These are not “external” to the world, lying only in the mind of God (as Platonism would have it), but are “consigned to the truth of what was created”, even though the plan of the world and the plan of its salvation certainly lie in God's wisdom.

The correct relationship between God and the laws of nature can be understood by considering God's transcendence over, and immanence in, the created world ( CREATION, IV). God works through laws, because He is the ultimate explanation of their specificity and existence, but He also exists over and beyond the laws, since the fact that they originated in the divine plan does not imply that the Creator identifies Himself with them. In this regard, a correct “theology of the laws of nature” must explicitly clarify that it is just as far from pantheism as it is from deism. It must not be forgotten that deism of the 17th and 18th centuries claimed to be a kind of rational religion and is therefore not open, by definition, to the notion of Revelation. Thus, the notion of God (or of Logos ) to which the scientist seems at times to refer when dealing with the question of the laws of nature, can be utilized legitimately by the theologian only insofar as it remains “open” to a revealed image of God. Analogously, to avoid the mire of pantheism, it is necessary that the divine Logos perceived in philosophy of nature, be able to point “beyond the laws”. If the laws are themselves “the Divine”, and the scientist's wonder stops at the “cosmic code” without enquiring for its Author, Christian theology cannot but judge all that as one more example of pantheism.

Finally, the clarification made above about determinism can also help us understand the ambiguity of those speculations which hypothesize a world without laws and investigate both the relationship between God and an undetermined universe, and, on the philosophical level, the relationship between God and chance. Whereas the negation of every law in nature is used by some to argue against the existence of God (Monod), others think that randomness and indetermination represent the space, or perhaps the “action”, that would allow an original and creative intervention of God (Peacocke, Bartholomew). We maintain that at the origin of such interpretations there is always the difficulty of grasping the simultaneous transcendence and immanence of God, which becomes comprehensible within a metaphysics of creation based on the philosophical properties of the “act of being”. When pondering on the laws of nature, scientists rightly want to avoid the dangerous idea of a “controlling” God, who programs nature or competes with its behavior. At the same time, they positively perceive the unconditioned and gratuitous character of the laws of nature —if they want to avoid the risk of self-reference: «where do they come from?» (Davies), «who gave these equations life, who breathed fire in them?» (Hawking). If a Creator exists, on one hand, we require His transcendence over this world, and on the other hand, we are aware that He must sustain the world as an immanent cause, being the innermost life and the ultimate explanation of the universe. The possibility of a simultaneous affirmation of these two poles, the transcendence and immanence of God, and the guarantee of being able to harmonize such a dialectic, seems to come from the revealed image of God only as we receive it by the Judeo-Christian tradition.

3. The Inexorability of Natural Laws and the Problem of Physical Evil. In the theological perspective, the theme of the laws of nature indirectly involves the problem of evil, when their inexorability becomes a cause of harm, destruction and death. This is the problem of “physical evil”, thus called to distinguish it from the term “moral evil”, which theology reserves for human sin. The possibility of a “suspension” of the laws of nature is usually invoked within the context of the theology of the miracle. Here, one asks why God, the Author of the laws of nature, allows that some natural actions have effects that destroy the environment or damage the life of human beings. In other words, one wonders how such a situation can be still “in tune” with a biblical vision which considers natural laws as a manifestation of the faith and love of the Creator.

Having put forth the necessary premise that everything in the world is involved in suffering, that it participates in the mystery of the humanity and death of Jesus Christ and of his capitality over the first and the new creation ( JESUS CHRIST, INCARNATION AND DOCTRINE OF LOGOS, II, III.1), and that therefore, from the theological standpoint, suffering can be completely understood only in the context of such a mystery, and not outside of it, one can equally suggest some paths of reflection which might render the problem of physical evil more comprehensible.

In the first place, it must be remembered that the action of the laws of nature which can cause a physical evil (earthquakes, floods, cancer, viral pathologies, etc.) is the same action that allows for the stability and the preservation of the world, or the growth and reproduction of living beings. Without these physical phenomena (for example, gravity that might cause a physical disaster) or this biological behavior (for example chemical and biochemical processes that might also let a cancer grow), the universe and life cannot subsist. The fact that such causes, forces, or processes are not removed by a Law-maker in whose Providence one trusts, can lead to two conclusions. First, it allows one to understand the radicalness of the relation between God and his creation; faithfulness to the created laws (which is, we recall, faithfulness to Himself) seems to have a greater value for the good of the world and its inhabitants, than their suspension, transformation, and alteration. Second, we are led to believe that since the relationship between God and creation “involves” the humanity of the Incarnate Word, the mystery of his death and resurrection, then this same mystery is expected to contain and unfold the meaning of the transitory, limited and fragile nature of created things, and of the suffering this vulnerability necessarily implies, suggesting to understand it in the light of a future transfiguration.

In the second place, it is the very order and stability of the natural laws, whose action can become at times a source of anguish and despair, to inspire in human beings feelings of surrender and trust in the Creator. The stability and faithfulness of those laws strengthen one's hope in divine Providence, a hope capable of overcoming the suffering caused by those same natural laws, helping the subject's faith in a final renewal, transfiguration, and restoration of justice. It is interesting to note that a Biblical account which treats human suffering with great drama and vividness, found in the Book of Job , is perhaps the most beautiful appeal to faithfulness in the goodness of the Creator, in spite of everything. Job, who asks why physical evil has put him to so bitter a test, even to the point of passing sentence on God for the horrible justice inflicted on him, is asked by God to go out into the open and contemplate the beauty of creation, its laws, and its harmony (cf. collected speeches of Job 37, 14 to 40,4). The human being cannot explain physical evil, but the contemplation of nature, governed by those same laws which can, at times, cause sorrow and calamity, helps to understand that such an explanation does exist in the wisdom and power of God the Creator.

Giuseppe Tanzella-Nitti
(translated by Eric Chang)

See also: AUTONOMY; COMPLEXITY; CREATION; DETERMINISM/INTEDERMINISM; EPISTEMOLOGY; FINALITY; NATURE; REALISM; TIME.

Documents of the Catholic Church related to the subject

Bibliography

History and Philosophy of Science: J. STUART MILL , A System of Logic, Ratiocinative and Inductive (1843), Univ. of Toronto Press, Toronto 1973; P. DUHEM , La théorie physique: son objet, et sa structure (1906), M. Rivière, Paris 1914 2 ; E. BOUTROUX , De l'idée de loi naturelle dans la science et la philosophie contemporaines (1895, 1925² ), J. Vrin, Paris 1925; R. WESTFALL , The Concept of Order , Univ. of Washington Press, Seattle-London 1968; J. MARITAIN , Philosophy of Nature , Philosophical Library, New York 1951; N. Cartwright , How the Laws of Physics Lie , Oxford Univ. Press, Oxford 1983; D.M. ARMSTRONG , What is a Law of Nature? , Cambridge Univ. Press, Cambridge 1983; M. ARTIGAS, J. SANGUINETI, Filosofía de la naturaleza, Eunsa, Pamplona 1984; M. ARTIGAS , La intelegibilidad de la naturaleza, Eunsa, Pamplona 1992; F. SELVAGGI , Filosofia del mondo , Pont. Univ. Gregoriana, Roma 1993, cap. 17: “Le leggi della natura”, pp. 401-433; G. DEL RE , Una chiave di lettura: l'essere e la verità come fondamenti della scienza , in T. Torrance, Senso del divino e scienza moderna , LEV, Città del Vaticano 1992, pp. 5-37; M. CINI , Un paradiso perduto. Dall'universo delle leggi naturali al mondo dei processi evolutivi , Feltrinelli, Milano 1994; G.C. WEBSTER, B.C. GOODWIN , Form and Transformation. Generative and Relational Principles in Biology , Cambridge University Press, Cambridge 1996.

Scientists' Reflections on the Laws of Nature: H. POINCARE' , The Value of Science (1911) . Essential Writings of Henri Poincaré , Modern Library, New York 2001; M. PLANCK , Wege zur physikalischen Erkenntnis. Reden und Vorträge, S. Hirzel, Leipzig 1933; R. THOM , Structural Stability and Morphogenesis. An Outline of a General Theory of Models , Benjamin, Reading (MA) - London 1975; G. NICOLIS, I. PRIGOGINE , Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations, Wiley, New York 1977; F. DYSON , Disturbing the universe , Harper & Row, New York 1979; I.  PRIGOGINE , From Being to Becoming. Time and Complexity in the Physical Sciences , W. H. FREEMAN, San Francisco 1980; C. von Weizsäcker , Die Einheit der Natur , Hanser, München 1981; P. DAVIES , Superforce. The Search for a Grand Unified Theory of Nature , Simon and Schuster, New York 1984; I. PRIGOGINE , I. STENGERS , Order Out of Chaos. Man's new Dialogue with Nature , Heinemann, London 1984; P. DAVIES , The Cosmic Blueprint , Heinemann, London 1987; J.  POLKINGHORNE , The Quantum World , in “Physics, Philosophy and Theology. A Common Quest for Understanding”, edited by R. RUSSELL, W.R. STOEGER, G.V. COYNE, LEV and Univ. of Notre Dame Press, Città del Vaticano 1988, pp. 333-342; J. BARROW , The World within the World , Clarendon, Oxford 1988; J. BARROW , Theories of Everything. The Quest for Ultimate Explanation , Clarendon, Oxford 1990; G. ELLIS , Major Themes in the Relation between Philosophy and Cosmology , “Memorie della Società Astronomica Italiana” 62 (1991), pp. 553-605; P. DAVIES , The Mind of God . Science and the Search for Ultimate Meaning , Simon & Schuster, London 1992; S.A. KAUFFMANN , The Origins of Order. Self-organization and Selection in Evolution , Oxford Univ. Press, New York 1993; R. RUSSELLL, N. MURPHY, C. ISHAM (eds.), Quantum Cosmology and the Laws of Nature , Vatican Observatory Publications and The Center for Theology and Natural Sciences, Città del Vaticano 1993; P. DAVIES , The Intelligibility of Nature , in ibidem , pp. 145-161; W.R. STOEGER , Contemporary Physics and the Ontological Status of the Laws of Nature , in ibidem , pp. 209-234; R. FEYNMAN , The Character of Physical Law , Modern Library, New York 1994; G. TANZELLA-NITTI , The Aristotelian-thomistic Concept of Nature and the Contemporary Scientific Debate on the Meaning of Natural Laws , in “Acta Philosophica”, 6 (1997) 237-264; R. RUSSELLL, W. STOEGER, F. AYALA (eds.), Evolutionary and Molecular Biology , Vatican Observatory and Center for Theology and Natural Sciences, Città del Vaticano - Berkeley 1998; J.  BARROW , Impossibility. The Limits of Science and the Science of Limits , Oxford University Press, Oxford - New York 1998; J. FOSTER, The Divine Lawmaker. Lectures on Induction, Laws of Nature and the Existence of God , Clarendon Press, Oxford 2004.