What is determinism in physics?

Authors: Santiago Collado (University of Navarra) and Héctor Velázquez (Universidad Panamericana, Mexico)
Published in: Vanney C, Franck JF, eds. Determinism or Indeterminism? Big questions from the sciences to philosophy. Rosario: Logos; 2016, p. 39-66. (20-01-2017)

Throughout history various notions have been associated with determinism. Terms such as fatalism, causality, legality or predictability led to a deterministic view of the natural world, making determinism a multifaceted notion, as each of these characterisations emphasises different aspects. The interest in determinism predates the emergence of modern science and, in particular, precedes the birth of experimental physics. In its deepest dimension, it manifests the contrast we perceive between our inner experience and our experience of physical phenomena. At final, what is at stake in the discussion on determinism is nothing other than the very existence of our freedom (Loewer 2008, 328).

It was a rather modern approach that divided reality into two worlds: that of freedom and that of necessity (as proposed by Descartes and Euler); against whose opposition some attempted a reconciliation by turning freedom into another face of necessity (Spinoza and Leibniz); while others considered the physical causality of nature as a mere mental projection, which in the end implied the total negation of freedom (as in Hobbes and Hume) (Arana, 2005). Degree Under this principle, human actions would also be the result of perfectly determined causes that would condition future events to such an extent that they would be as fixed and immovable as the past.

It would seem that indeterminism or determinism is the notion that authorises or forbids us to speak of freedom from science. These questions have been, and it seems that they will always be, a challenge to our reason. They enclose a tension that manifests itself in the aporia of a freedom that wants to be conquered thanks to the exercise of complete control over the physical world, only to discover later - when it seems that we are in a position to achieve it - that this achievement snatches freedom away from us.

Fatalism appears in the history of thought as a manifestation of the longing for a freedom that is recognised, but which contrasts with other factors that leave it out of our reach, such as tragic destiny in Greek thought, or the recognition of the existence of regularities that we can perhaps predict, but which are imposed on us from an inevitable written request , making our freedom a mere appearance. Fatalism expresses the pessimism that hovers over us when we discover that our freedom is illusory. It is just as fatalistic to believe that our freedom is taken away from us by a destiny written by the gods and therefore beyond our control, as it is to conclude that our decisions and beliefs are dictated by the very nature we aspire to control.

The prior knowledge of future events (e.g. as result of divine omniscience) would make present events so determined and necessary that it would be difficult to differentiate between past, present and future. This was as much a concern in ancient thought (the Homeric fairies were described as beings with powers over the future) as it was in medieval and modern thought. Today, there are those who claim to base the existence of freedom on the indeterminacy of quantum mechanics, so that the absence of physical determinism would be an example of the possibility of the indeterminacy inherent in freedom. Leibniz had already opposed the conception of indifference as a condition of possibility for freedom (which he understood as action free of coercion), because he believed that it was not necessary to postulate the absence of reason in the choice between one option and another for the soul to be free, since there would always be a sufficient reason that would incline us in our decisions. Unlike absolute necessity (where the opposite implies contradiction, as in mathematics, metaphysics or logic), Leibniz recognised a hypothetical necessity proper to morality (Leibniz 1990). In any case, the claim that physical indeterminacy is the basis for the indeterminacy of freedom reduces the notion of causality to its quantifiable sense, inherited from mechanicism; moreover, it confuses freedom or free will with the options that are presented to choice.

Whether or not to embrace a certain neo-fatalism today will depend, to a large extent, on the enquiries we make about the scope of determinism. According to the Royal Academy of the Spanish language , determinism has two meanings. The first reads: "Theory that assumes that the development of natural phenomena is necessarily determined by initial conditions" (RAE, 23rd edition). In the second, the Dictionary states that it is a "philosophical doctrine according to which all events, and in particular human actions, are linked and determined by the chain of previous events" (RAE, 23rd edition). Obviously, both meanings propose a dual perspective on determinism: scientific and philosophical.

What is certain is that both disciplines use different methodologies, contributing to the increasingly rich experiences we have of reality knowledge . Thus, the analysis of what physics says and what philosophy says about determinism gives us a new opportunity to discern what is methodically congruent with each of these disciplines. But it also requires us to underline the close relationship and interdependence that exists between both perspectives, since both types of knowledge come from and speak to us of the same and unique reality which, in its plural appearance as truth to our experience, obliges us to cast different nets to catch it.

1. Competing notions Who called first?

Natural determination, stability and regularity have traditionally been the subject of philosophical enquiry. Aristotelian thought described natural phenomena as a mixture of necessary processes (which could not be otherwise), regular processes (which maintained a constant structure and regularity over time), and random processes (which were difficult to explain or predict because their occurrence depended on a combination of circumstances that were totally irregular). This threefold description has been taken up with different nuances throughout the various schools of Western thought, but with one constant: to account for structure and regularity.

A first difficulty we encounter, and no small one, in the characterisation of determinism is to discern the nuances added by other notions with which it is usually associated, such as causality, legality or predictability. Some of these notions have been used since the very birth of philosophy and, throughout history, they have also changed their meaning or, at least, have incorporated new relevant perspectives. It is enough to look at the pages of The Cellars of the Universe ( cf. Arana 2012, 61 ff.) to realise the difficulties involved, for example, in trying to understand the evolution experienced by the notion of cause. To overcome this difficulty, at least in part, we are going to reflect on these notions in three contexts which, in our opinion, have brought about a real change in perspective over time.

It is interesting to note that, in contemporary philosophy of science, the interest in determinism (or indeterminism) has become particularly important. In addition to, or perhaps rather in connection with, the anthropologically resonant reasons already given, this interest stems from the new indeterministic scenarios proposed by physics at the beginning of the twentieth century, which opposed the previously dominant ones. While our interest in this chapter focuses on the study of determinism, we will see that its understanding is not independent of other notions such as cause, law and prediction. Moreover, we will see that the fate of determinism depends on that of the rest of its fellow travellers.

It is clear that several centuries of science, and many more of philosophy, have left an imprint on the language we use in our daily lives and which shapes the prevailing worldview of the time. The sensibility of each era, and the problems of each generation, also guide reflection on what both perspectives have contributed to the history of thought. In tracing the notions of cause, law and prediction in the history of thought, it can be seen that not all of them have always had the same importance. In the different historical periods, some notions have had priority over others; the priority, moreover, has changed over time; and the explanations of physical reality and, in particular, the understanding of determination and determinism, rest mainly on the notions that at each moment have assumed greater prominence.

In our opinion, there are two particularly relevant notions, which have disputed priority in the affirmation or denial of determinism: the notion of cause and the notion of law. For the answer to the question of determinism depends to a large extent on whether it is the causes that account for the laws, or whether it is the laws that explain the causes. Concretely, we will see how, depending on the priority given to these two notions, and how they are characterised, it is possible to distinguish three periods in the history of thought. Moreover, although these periods do not have totally defined limits, it is also possible to find characters who embody in a paradigmatic way the worldview reigning in them. Thus, although they are not the only or perhaps even the most important ones, we consider Aristotle, Newton and Heisenberg to be worthy representatives of each of them.

The passage from Aristotle to Newton is marked by a change of priority, which shifts from the notion of cause to the notion of law. In some authors, this change of priority goes so far as to understand that laws are the true causes that determine the behaviour of the physical world. In the terms used by Professor Arana, cause and law are categories of determination (Arana 2012, 66). Each of them is proposal to explain the movements of physical reality in different intellectual contexts. This makes it perfectly reasonable that priority can be placed on one or the other and, although this is perhaps no longer so easy to perceive, that such an alternative introduces a change in the consideration of determination in nature.

From Newton onwards, the priority of the notion of law was well established to account for physical phenomena. So the passage from Newton to Heisenberg does not imply a change of priorities between the notions of cause or law, but a change in the characteristics of physical laws. For the new laws do not allow prediction with certainty, but within a range of probability. This new step is introduced by the need to explain previously unknown phenomena, for which the laws of classical mechanics proved to be insufficient. New laws are necessary, and they impose a new vision of the problems linked to determinism. If the laws of Newtonian mechanics were formulated to explain phenomena within the reach of our direct experience of reality, the phenomena studied by quantum mechanics escape such direct observation, and even seem to defy common sense or the conclusions that come from an immediate observation of reality.

In this new period, in our opinion, the substitution of the priority of the notion of cause for that of law is consummated. For it would seem that in order to give a rational account of phenomena, only physical laws are required. Thus, in order to reach a better understanding of the determinism of nature, it is necessary to interrogate the laws of the new physical theories, whose formalisms also require interpretation.

The fact that the laws of science are now the protagonists, assuming the role of giving us a reason for reality, has important consequences for philosophy as well. This is possibly one of the reasons why philosophy of nature lost weight within philosophy in favour of philosophy of science during the 20th century, focusing philosophical research on the analysis of the laws used by science to describe nature.

Summarising what has been said so far, we could say that the study of 'determinism' allows for a better understanding of the physical world and our relationship with it. There are three notions on which the various answers usually given to the question of determinism mainly depend: the notion of cause, the notion of law and the notion of prediction. Finally, we claim that the notions of cause and law have historically disputed priority with respect to the understanding of physical reality; and that the fact of giving priority to one or the other has led to a change of scenery in which we can distinguish three relevant historical stages in the consideration of determinism. We have labelled them with the names of three representative figures: Aristotle (primacy of causality), Newton (primacy of the laws of nature) and Heisenberg (the interpretation of formalism).

2. Aristotle. Primacy of causality

The notions that really touch the nerve of physical reality are, for Aristotle, the notions of substance, essence and causality. There is a close relationship between them which, logically, we cannot dwell on in this work. The great caveat of the causal outline that Greece bequeathed to the West is that determination is not explained univocally. It allows us to ask about what happens as well as what simply exists, whether in a temporal sense or in a sense of order or sequence, without leaving out the qualitative or quantitative factors surrounding phenomena and their determination. The Aristotelian tetracausal outline allowed us to conclude that determination cannot be explained in isolation from the movements or processes it triggers or the results it leads to.

Material, formal, efficient and final causes are principles and, therefore, are not categories that can be reduced to each other. In particular, if formal cause is in Aristotelian philosophy a category of 'determination', material cause is a principle of 'indeterminacy'. Thus, physical movements are for Aristotle the result of an act-power duality, which combines determination and indeterminacy.

Aristotle dealt with the notion of the subject prima or material cause in different places in his work. When he describes it, his struggle with the language of his time, which is insufficient to express what he thinks about this causal principle, becomes clear. Between some of his descriptions of the subject there does not even seem to be much of a connection. In what follows we reproduce three fragments of his work in which we can guess this hard struggle (the translations are taken from Cencillo 1958):

"I call subject the first subject of every being, the immanent and non-accidental element of generation and in which, if corrupted, it ultimately resolves itself"(Physics I, 192 to 31-33).

"I call subject that which in itself is not conceptualised as something determined, neither how much, nor [affected] by any of the other [categories] by which being is determined"(Metaphysics Z 3, 1029 a 20).

"The possibility of being and of not being each one [of the generable beings], that is the subject in each one"(Metaphysics Z 7, 1032 a 21-22).

That is to say, for Aristotle the subject prima is the cause of a mode of being which we therefore call material. It is therefore a matter of thinking of the subject not as a thing itself but as a 'principle'. This is especially evident in the third characterisation, in which subject is explained as "the possibility of being and of not being". To think of this possibility as one of the causes in which our ultimate understanding of physical motion is resolved is core topic for our speech. In this 'intrinsic' possibility or potentiality consists the mode of being that we know as material.

On the other hand, determination was described and studied for centuries under the concrete of formal cause, that is, form understood as a certain proportion between the parts of a whole that is maintained as such over time; capable even of losing or incorporating elements without collapsing the stable configuration that gave rise to it and maintains its permanence. The Greek eidos or the Latin forma , sought to express, from the time of ancient and medieval thought, both the subject of existence of the parts integrated into a whole in core topic of unity, and the principles of interaction between them. The notion of formal cause or formal determination made it possible to understand why dissimilar realities, apparently unconnected, could maintain relationship, synchrony, homogeneity and stability in time.

Form thus became a truly fortunate notion, for once the presence of interacting parts within a whole showed stability over time, that form or formal cause required for a better understanding to be associated with the other causal factors: the composition (material cause), the factors that produced it (efficient cause) and the tendencies arising from its existence and determination (final cause).

Aristotle recognised in the physical reality of the world around us (the sublunar world in his worldview) and in its movements the influence of the material cause, and because the latter is regarded as a principle, material reality is intrinsically indeterminate. That is, one could say that physical reality is ontologically indeterministic, meaning that it possesses indeterminacy or real, and not only logical, potentiality. In other words, things can become this, but they can also become something else: to be (this) or not to be. In the physical realm there would therefore be no necessity.

For Aristotle, necessity is to be found in thought and, more specifically, in the axioms proper to thinking. Necessity properly belongs to the first principles of thinking, such as the principle of non-contradiction. This aspect of Aristotelian thought is very remarkable, for it clearly delimits the realm of the necessary and the contingent. Everything that is subject to the influence of the material cause escapes necessity. Geometry, on the other hand, with the perfection of its forms and its necessity, does not seem to be the most adequate description of what possesses the imperfection and potentiality proper to subject. Thus, none of the four causes, insofar as they are principles, is trapped either by the perfection of geometrical figures or by the exactness of numbers. The bodies of the celestial world admit the necessity and, therefore, the prediction of their trajectories, described by means of circular movements. Prediction, in the Greek world, is possible in the region of the cosmos whose substance is ether. It is the motion of the celestial world, because of its proximity to the motion of the immobile motor, which can be described numerically and geometrically and which, consequently, admits of prediction. In the Greek world, mathematics is used where regularity and necessity are discovered.

On the other hand, in ancient Greece science was not clearly distinguished from philosophy, of which physics, biology and metaphysics were also part. Physics was therefore a philosophical knowledge, although it also included subject areas that could today be described as scientific. Aristotle devoted special attention to biology, and the observation of living things was one of his main sources of inspiration. Some of his experiments - such as his studies on the embryology of the chick (Harré 1981: 25-31) - are models of their kind also for the scientist of today.

For Aristotle the most interesting movements were not the movements of inanimate beings, but the movements of living beings (beings possessing a 'soul'): being born, growing, feeding, dying.... But the Aristotelian distinction between the qualitative (belonging to the accident quality) and the quantitative (belonging to the accident quantity) prevented the pretension of expressing them in mathematical terms, since it would have implied renouncing the 'true' knowledge of reality. Mathematics, and in particular arithmetic, is a knowledge that refers to one of the Aristotelian categories: the accident quantity. The Aristotelian category of substance, for example, cannot be expressed mathematically.

Thus, in his research on movement and on the basis of the real, Aristotle did not favour mathematical language, nor did he seek to formulate mathematically the laws of nature, as modernity would later do. For the Aristotelians, law was the rule that should guide human action. Its fulfilment improves the human being, while its rejection and non-fulfilment degrades him. It is clear that the notion of law, as we understand it today, did not apply then to the field of physics. Even less so if one considers that mathematically formulated physical laws can only express aspects of reality related to extension and quantity, insofar as they are accidents of substance.

However, for the study of some subjects, the methodical approach of Greek thought came close to modern science. For example, the Greek distinction between astronomy and philosophy - although there were also thinkers who united both professions - bears a certain resemblance, at the methodical level, to the current distinction between philosophy and science, and more particularly with physical science.

According to Artigas, the intrinsic and inseparable objectives of experimental science are twofold (Artigas 1999, 15). One theoretical, which is the knowledge of nature. The other practical, which is its controlled mastery. The aspiration to exercise some control subject is what links the scientific knowledge with experiment. The experiment thus achieves its greatest effectiveness, and becomes an element core topic of science by allowing its results to be contrasted in a precise way. But this is facilitated by the mathematical formulation of laws. In Greek thought, mathematics has its home mainly in astronomy. The reasons for this have already been stated. With modernity, mathematics becomes the guest of honour of any science. Although not all of them have managed to accommodate it in a satisfactory way. In Newtonian physics, and we could say even more so today, mathematics is not just any guest but, without a doubt, the master of the house. The methodical use of mathematics, present in both ancient astronomy and modern science, allows us now to jump to our next character: Newton.

Newton. Primacy of the laws of nature  

We cannot dwell on the very complex and articulated historical process that leads to the notion of cause losing its prominent place, and yielding its primacy to the notion of law (Olson 2004: 25-56; Shapin 2000: 66ff, Carroll 2011). For example, the crisis of scholastic philosophy, which led to Ockham's nominalism, was one of the levers that led Renaissance thinkers to seek alternatives to classical approaches. The new context favoured experimentation, the finding of natural regularities and their formulation in mathematical terms, opening the way to a new way of knowing that, at last, enjoyed a longed-for certainty. Modernity thus aspired to regain confidence in reason, and the laws of science - new categories of determination - together with experimentation were the key that opened the door to a new rationality.

Newton managed to quantify the sublunar world in a similar way as the Greeks had done with the celestial world, and this quantification was the core topic of the success of a process that culminated in the formulation of mechanics, disappearing forever the distinction between the two worlds. Thanks to the use of mathematics, Newton was able to link natural physical laws with experimental results in an extraordinarily successful way (Collado 2007). But every success has its price, and in this case the price was the important change of perspective of making natural law a priority category of determination. Thus, instructions was set up so that the laws of nature could assume the role that causes had occupied in the Aristotelian perspective.

Newton's work has been the subject of numerous research works, in which the complexity of his personality and thought is evident. He dealt with a plurality of subjects, with his scientific writings, such as the monumental Mathematical Principles of Natural Philosophy, standing out. While some authors highlight the separation of the different fields that Newton dealt with (natural philosophy, mathematics, alchemy, natural theology, Sacred Scripture,...), others see a common interest in all of them and try to establish their relationship and mutual influence. John Henry, for example, argues that Newton's main interest is theological, and that it is his physics - his natural philosophy - that shapes his particular theology (Henry 2008, 69-101; Velázquez 2007). The aspect we are interested in highlighting now is the importance Newton attached to the method he deployed in his natural philosophy. In continuity with Galileo, he thought that mathematics is no longer just another language to express natural regularities, but reveals to us the true being of reality. Moreover, they give us access even to God himself, who is the creator of nature and through whom he makes himself known to us.

This perspective is manifested in the way Newton expresses his understanding of space and time in the Principia. In the first scholium, after defining "the lesser known words" that he is going to use in his work, he is obliged to specify the meaning of the words that are better known, distinguishing in the understanding of them "between the absolute and the relative, the true and the apparent, the mathematical and the vulgar" (Newton 2011, 32). It is clear from this passage how Newton associates mathematical understanding with true and absolute understanding. Regarding his intended understanding of space and time he states: "Absolute time, true and mathematical in itself and by its nature, and without relation to anything external, flows uniformly (...) Absolute space, taken in its nature, without relation to anything external, remains always similar and motionless" (Newton 2011, 32-33).

Newton did not claim to exhaust the knowledge of reality with his natural philosophy, not because he considered his method insufficient, but because, for him, reality itself - which makes its mechanics known to us - requires the assistance of the divinity to preserve the order and harmony that we observe in the Universe. In other words, there are implications in his physics that are proper to natural theology. Newtonian mechanics is not only a physical theory in the modern sense of the word, but, because of its claim to truth and comprehensiveness (absolute time and space), it also offers the elements of a natural philosophy, later known as mechanical philosophy.

In Newtonian natural philosophy, measured quantities, mathematically formulated laws and experimentation aspired to know reality as it is. Although they could not encompass the whole of reality knowledge , they opened the way to the idea that it was only a matter of time before this could be achieved. Thus, as Newtonian natural philosophy attributed an ontological scope to physical theory, the question of the determinism of nature soon translated into the question of whether the laws governing the motions of physical bodies were deterministic or not.

The thinker who embodied in a paradigmatic way the defence of the determinism of nature was Laplace. One of the most widely reproduced texts of his works referring to the problem of determinism is found in the book Essai philosophique sur les probabilités, published in 1840. It is paradoxical, although perfectly coherent, that Laplace formulates the strictest physical determinism in a essay on probabilities. The oft-quoted text is the following:

"Thus we must regard the present state of the universe as the effect of its former state and as the cause of the state which is to follow it. An intelligence which at a given moment knew all the forces that animate nature, as well as the respective situation of the beings that compose it, if it were also broad enough to submit such data to analysis, could embrace in a single formula the movements of the largest bodies in the universe and those of the lightest atom; nothing would be uncertain to it, and both the future and the past would be present before its eyes" (Laplace 1985, 25).

Laplacian thought, as presented in this well-known text, is openly deterministic. The dynamical equations impose necessity on the evolution of a physical system, since its evolution is determined by Newton's laws and necessarily conditioned by previous states. It is important to mention that, in Laplace's time, on the one hand, Newtonian mechanics was unrivalled as a rationality for knowing the truth about nature and, on the other hand, mechanical laws were not separated from the ontology of mechanical philosophy.

In this context, the causes of the motions are the interactions and the states of the previous motions of each of the bodies: forces, masses, velocities. But although Laplace uses the word 'cause', the notion of cause he employs is obviously no longer the classical one. It is now a cause that refers only to the dynamics of the system. That is to say, we identify it as a cause only in so far as it is the expression of a regularity, which can be expressed by a mathematical law and which can be experimentally contrasted. Thus we see that the subversion of the order of priorities has been consummated in practice: natural law is now the priority category of determination.

Also illuminating are Laplace's statements about our predictive ability following the text quoted above:

"The human spirit offers, in the perfection which it has been able to give to astronomy, a faint outline of this intelligence. His discoveries in mechanics and geometry, together with that of universal gravitation, have enabled him to embrace in the same analytical expressions the past and future states of the system of the world. Applying the same method to some other objects of his knowledge, he has succeeded in reducing observed phenomena to general laws and in foreseeing those phenomena which must occur under certain circumstances. All his efforts to seek the truth tend to bring him continually nearer to the intelligence we have just imagined, but from which he will always remain infinitely distant. It is this tendency, peculiar to the human species, which makes it superior to animals, and its progress in this field, which distinguishes nations and centuries and cements its true glory" (Laplace 1985, 25-26).

As a representative author of mechanical philosophy, Laplace maintains an ontological determinism. However, from a practical point of view, he also admits a gnoseological indeterminism, since he indicates that due to the limitation of our knowledge we cannot completely know the evolution of the system. Consistent with the practice and experience of the mechanics of the time, Laplace considers that there is an infinite distance between our knowledge and that necessary for an absolute prediction average , since it is impossible to fully determine the initial state of a dynamical system, which is always determined with a margin of error. To know completely the state of the system at a given time requires super-intelligence.

A paradigmatic case is found in fluid mechanics, where only a statistical estimation of the range of position in which its particles would find themselves after a certain time is possible, so that position and time have statistical uncertainty. However, this indeterminacy of the values of the elements of a system could be interpreted as a technical impossibility of means to calculate them, not as an ontological indeterminacy of those values. If the indeterminacy were only cognitive, determinism as an essential characteristic of natural systems would still be valid.

Bishop points out the two sources of 'error' that lead to indeterminism in prediction. "The first source of error is due to limitations in the precision of measurements (...) A second source of error is due to limitations in representing the initial values of a variable (e.g., velocity) to achieve full precision when the value is an irrational number" (Bishop 2003, 181-183). It is important to note here that imprecision is not considered a property of nature, but is due to the limitation of our knowledge.

At summary, mechanistic determinism assumes that, when the initial conditions of the physical system are known, the laws governing its dynamic evolution impose a determinate evolution on it. This is the core of Laplacian determinism (Bishop 2006, 30). However, since the initial conditions can only be established with a certain margin of error, it is not possible to predict this evolution with complete accuracy. This dichotomy gives rise to an awkward situation. One accepts an ontology that is supported by a physics that, in turn, cannot justify such an ontology: mechanics cannot overcome indeterminism in prediction, which would be the experimental confirmation of determinism. Strictly logically, the assertion of determinism is not a scientific conclusion, but responds to the ontology proposal by the theoretical framework of classical mechanics. In particular, mechanistic determinism rests on the determinism of Newtonian laws. As long as Newtonian mechanics was the dominant physical theory, this way of looking at the physical world did not involve serious difficulties. When the law imposes its hegemony as a category of determination, the corresponding ontology is that of the law itself and, in this case, it is a closed ontology: installed in Newton, one could hardly arrive at a port other than Newton himself. The predictive success of mechanics and the closeness of its explanations to our ordinary experience reinforced the acceptance of a mechanistic ontology until the end of the 19th century, but the picture changed at the beginning of the last century, when new experimental results challenged the interpretations of our common sense.

4. Heisenberg. Interpretation of the formalism

At the beginning of the 20th century, the ontology proposal of classical mechanics (mechanical philosophy) suffered a deep, perhaps even mortal wound with the development of chaos physics and, above all, with the irruption of quantum mechanics (paradigmatically represented by Heisenberg), giving rise to a new scientific rationality.

With the study of deterministic chaos, a new, holistic view of the world was initiated in which it is no longer possible to sustain a reductionist proposal . According to Prigogine, the science of chaos is a science of processes rather than of states; a science of becoming rather than a science of being. Controlled disorder and deterministic chaos are creative and bearers of novelty. The beautiful and varied forms that nature brings forth are no longer represented by straight lines or simple geometric figures. Familiar curves such as the ellipse and the circle give rise to complex Structures (fractals), which show how the subject self-organises according to the principles of complexity, and acquires emergent properties that cannot be deduced from the study of its components. From the complex study of chaos, the natural sciences freed themselves - according to Prigogine - from the stagnant mechanistic and deterministic conception in which novelty and diversity were denied in the name of immutable laws (Prigogine 1996). On the other hand, some laws of quantum mechanics - such as Heisenberg's principle of indeterminacy - affirmed an indeterminism for which not only our lack of knowledge is responsible, but also nature itself (Foster 2008).

The crisis of the deterministic worldview affected rationality as a whole, giving rise to what Thomas Kuhn called a 'paradigm shift' (Kuhn 1971). The repercussions of this 'scientific revolution' were such that they led to the emergence of a new academic discipline : philosophy of science. When we speak nowadays of philosophy of science, for example, we refer to a kind of meta-science (a reflection on science itself) about method (various unordered notions), logic (logical procedures), theory, model, demonstration, counterfactuality, possible worlds, state space or phases, probability, supervenience, emergence, law, prediction, chance, causation, and so on. All of them notions core topic in the method of the philosophy of science. In this new context, the relationship between science and reality was questioned again, seeking to establish the veritative value and ontological scope of the scientific knowledge .

In the last century, much thought was given to the concepts of law of nature, causation and determinism. The concept of law - understood as a category of determination of the physical world - did not lose its hegemony in the new perspective, as the ultimate questions about natural reality continued to be directed, directly or indirectly, towards it. But in contrast to earlier times, the very concept of law became an object of study. While laws of nature were recognised as the most significant notion to characterise determinism, a broad reflection on the types of generalisation used in scientific explanations also began, as not all true generalisations are or are associated with a law (Loewer 2008, 327).

Some authors, such as Butterfield, considered that the concepts of causation and prediction are insufficient to deal with the problem of determinism, and tried to specify it without resorting to them. To investigate determinism, they have thus proposed using concepts closer to current physical theories and closely linked to the logical treatment of laws -such as those of system, state, model or scientific theory-, suggesting to avoid classical positions that can be ambiguous and have not been able to shed much light on the problem so far (Butterfield 2005). But, paradoxically, this proposal encountered problems similar to those it sought to avoid. The notion of state, for example, turned out to be particularly problematic, because in order to use it for this purpose, a number of conditions must be attached to it that make it less precise than it was originally intended to be.

Hitchcock's study of causation is an interesting example of the various ways in which the notion of cause can be understood and the problems presented by each of them (Hitchcock 2008). It is a fairly exhaustive study, but not very conclusive, except for the fact that it recognises that the notion of cause is not as useless and outdated as Russell claimed (Russell 1913). The greatest problems that this author encounters arise when he tries to specify the notion of cause and to give a reason for it in terms of a temporal dynamic that can be expressed, in the last analysis, by laws and logical formalisations. In this situation, resource is forced to probability.

Contemporary physics is not conclusive in its investigation of the determinism of nature. In order to account for the same empirical results, it often uses different, irreducible theories. The scenario has now become considerably more complicated. Thus, "it is very likely that if there were an empirically adequate complete theory proposal whose dynamical laws are probabilistic, there would also be an empirically equivalent explanation in which the laws would be deterministic. The result is that we will probably never know whether or not determinism is true; but what is certain is that if it were true, then we will not be able to make predictions about the future with certainty" (Loewer 2008, 335-336).

Some authors call for a broadening of the theoretical framework to get out of this situation, reopening the game to philosophy. A recent example is Nagel, who points to Aristotle as a thinker to whom we should look for 'new' inspirations (Nagel 2014). Nagel argues for the need to combine the laws of current particle physics with supposed teleological laws that would have to be formulated and that would only be sustainable if the laws of basic physics are indeterministic, although he makes it clear that he does not know what subject such laws would be. Nagel's proposal is suggestive but does not seem to have been able to transcend the priority of the law.

5. Science and philosophy in the face of the problem of interpretation

It seems necessary to accept that contemporary science does not provide an exhaustive knowledge of reality, but that its theories require interpretation. When we speak of interpreting, in general, we refer to the act of establishing a relationship between two different cognitive levels. In interpreting, we try to explain (or sometimes we think we explain) from a level of knowledge that is more immediate, or more controllable, that which appears to us or of which we have experience at a certain level of knowledge different. Correspondence is achieved when what happens at the interpreted level is explained by what happens at the level that we take for granted or that we can better control from an operational and calculative point of view, i.e. from the point of view of prediction.

A very clear example of this can be seen in the attempt to understand what happens in microphysics (as it is a knowledge of experiments interpreted by mathematical theories). One interpretation, for example, was given by the atomists, although one could also cite Empedocles' theory of the four elements. This theory attempted to account for the innermost composition of the subject on the basis of four elements known to ordinary experience and possessing well-known properties. This interpretation explained things on the basis of theory, but we know today that it was an interpretation which later proved to be wrong. It is less true than the ones we have today. Today we have better interpretations, but the current ones follow the same outline changing the level at which they are interpreted, because they know many more phenomena, as well as incorporating the ability to calculate. This is a step core topic in relation to experimental control. 

Moreover, we could say that the more theoretical a science is, the more interpretative it is. Theoretical physics today is profoundly interpretative. What are the planes between which the relationship is established? That of the phenomena observed in experiments, and the mathematical models. The relationship between the planes is, in one sense, more distant than the old interpretations, but from another point of view it is more 'faithful' to reality because they allow better control. This opens up more questions.

Interpretation is completely inescapable in modern science. This is the reason, or at least one of the reasons why modern science is under continuous revision. Some authors judge the present moment with a certain epistemological pessimism, considering that interpretation implies introducing a certain Degree of arbitrariness, or rather of conventionality. We have to revise our interpretations, and it is easy to understand that we will never be able to reach an interpretation final. For that would mean a relationship between the two levels involved in interpretation, which could be described as identity. Is it possible to speak of truth under these conditions? Mariano Artigas spoke of a contextual truth (Artigas 1999, 260-295). In this notion, it is precisely the fact that the scientific knowledge is interpretative.

But we can go a step further and ask whether there is any subject of knowledge that is not interpretative or representational. The sensibles proper in the realm of sensibility, for example, seem to have this characteristic. But in the intellectual realm we possess knowledge that is clearly not interpretative: as is the case with number. Three as a pure numerical object is no interpretation at all. What is the advantage of exercising a non-representational knowledge ? The three that Plato thought of is the same three that I think of. We don't have to interpret the numbers they thought two thousand years ago. There could be no interpretation if there were no knowledge not interpreted.

One of the important questions then is to clarify whether the notions that physics uses are interpretations or not. The fact that it is an interpretation implies that what is said about the reality we refer to may be a property of the cognitive level at which we interpret. We can specify mathematically what determinism, legality, causation mean, but how does this relate to reality? This is where we need to pay attention to the method we are using. And this distinction is not often made explicit.

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