A Minimalist Ontology of the Natural World

Michael Esfeld, Dirk-Andre Deckert

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351392167
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

This book seeks to work out which commitments are minimally sufficient to obtain an ontology of the natural world that matches all of today's well-established physical theories. We propose an ontology of the natural world that is defined only by two axioms: (1) There are distance relations that individuate simple objects, namely matter points. (2) The matter points are permanent, with the distances between them changing. Everything else comes in as a means to represent the change in the distance relations in a manner that is both as simple and as informative as possible. The book works this minimalist ontology out in philosophical as well as mathematical terms and shows how one can understand classical mechanics, quantum field theory and relativistic physics on the basis of this ontology. Along the way, we seek to achieve four subsidiary aims: (a) to make a case for a holistic individuation of the basic objects (ontic structural realism); (b) to work out a new version of Humeanism, dubbed Super-Humeanism, that does without natural properties; (c) to set out an ontology of quantum physics that is an alternative to quantum state realism and that avoids any ontological dualism of particles and fields; (d) to vindicate a relationalist ontology based on point objects also in the domain of relativistic physics.

1
Introduction

1.1 The aim of the book

Physics, being the study of nature (physis in Greek), and metaphysics, being the study of the most fundamental and general traits of being (cf. Aristotle, Metaphysics IV, 1003a21-22), can together be expected to answer the following three questions:

1. What is matter? What is space and time?
2. What are the laws of nature?
3. How does matter in space and time, being subject to certain laws, explain the observable phenomena?

The question of what is matter is connected with the question of what is space and time: one’s view of matter has implications for one’s view of space and time, and vice versa. The stance that one takes with respect to laws of nature, by contrast, is largely independent of the stance that one takes with respect to matter, space and time. The question about the laws has two aspects: what their content is and what their status of being is. Finally, the position that one endorses with respect to matter, space and time as well as laws is probed by the way in which one elaborates on how this position as a whole explains the observable phenomena.

These questions are philosophical as well as scientific. Even if it may seem too optimistic to hope that one day answers to these questions can be given in full completeness, the mere attempt of finding sensible answers and weighing their successfulness is already a fruitful enterprise in building a view of nature and its workings. This enterprise can best be characterized as natural philosophy, involving physics and philosophy in a seamless manner.

This enterprise is probably as old as mankind, and possible answers range, say, from quantum mechanics to religion. This is due to the fact that it is not even clear in which sense we would be satisfied with a potential answer. Since human thought is tied to concepts, one of the first questions should be which concepts should we employ in our formulation? Are “particles, fields, strings, genes, trees, souls, devils, angels, and gods” good choices?

Obviously, the story we will attempt to tell in finding answers to the aforementioned questions will depend heavily on this choice, and some of the chosen words should better relate to some of the natural things that exist independently of our thoughts and language; otherwise, the aforementioned enterprise will be futile. On the one hand, the larger the vocabulary that has to be taken as basic, the shorter the potential stories, but also the weaker is their explanatory power as the many concepts in the vocabulary cannot be scrutinized. On the other hand, the smaller the basic vocabulary, the more can be scrutinized, but also the longer will the stories be that we have to tell. Consider how Jackson (1994) describes the enterprise of metaphysics:

Metaphysics, we said, is about what there is and what it is like. But of course it is concerned not with any old shopping list of what there is and what it is like. Metaphysicians seek a comprehensive account of some subject matter—the mind, the semantic, or, most ambitiously, everything—in terms of a limited number of more or less basic notions. In doing this they are following the good example of physicists. The methodology is not that of letting a thousand flowers bloom but rather that of making do with as meagre a diet as possible. … Because the ingredients are limited, some putative features of the world are not going to appear explicitly in the story. The question then will be whether they, nevertheless, figure implicitly in the story. Serious metaphysics is simultaneously discriminatory and putatively complete, and the combination of these two facts means that there is bound to be a whole range of putative features of our world up for either elimination or location.

(Jackson (1994), p. 25)

The same goes for the scientific enterprise in general. The sciences seek a good balance between the complexity of the vocabulary and the length of their explanations that should of course depend on the natural phenomena under study. For instance, while molecules may be well described by using the notion of atoms, it would be a tiresome endeavour to explain the functions of a cell in terms of only the atomistic vocabulary. Such switches in the basic concepts that are employed are quite common, even in mathematics. However, they often make it difficult to relate one well-established theory to another one. Consider, to mention just one example, how difficult it is to specify how and when quantum mechanics can be well approximated by Newtonian mechanics.

Nevertheless, all these theories have a common goal—namely, to describe what there is. As it would be outrageous to think that what there is depends on our theories about the world, there must be a sense in which all these vocabularies have a, in some sense minimal, common set relating to the things that exist. One convincing example that such a common set can be found comes from statistical mechanics, which is able to relate the concepts “temperature, pressure, volume and entropy” used in thermodynamics to the concept “particle motion” used in Newtonian mechanics. A common set of concepts must contain good candidates for building an ontology of the natural world. Although we humans may never be able to fully infer what there really is, we can at least ask the following question. What is a minimal set of entities that form an ontology that matches today’s well-established physical theories? In answering this question, we will carefully distinguish within the vocabulary used in these physical theories between, on the one hand, the concepts that relate to what there is in the sense of this minimal set of entities and, on the other hand, the concepts that make up what we call the dynamical structure of a physical theory, providing an economic means of telling the necessary scientific stories.

In this sense, using parsimony as the guide for ontology, the aim of this book is to develop a minimalist answer to the aforementioned questions: we seek to work out which commitments are minimally sufficient to obtain an ontology of the natural world that is empirically adequate. Generally speaking, the reason for employing parsimony as the guide for ontology is that for any candidate entity stemming from science—or common sense, or intuitions—we need an argument for why one should endorse an ontological commitment to that entity. Its being part of what is minimally sufficient to obtain an ontology of the natural world that is empirically adequate is the best argument for an ontological commitment. It is an illusion to think that by abandoning parsimony and enriching the ontology, one achieves explanations that are deeper than those that a parsimonious ontology can yield; one thereby runs only into artificial problems and impasses, as we shall show in this book.

In this vein, we start from the idea that given a plurality of objects, there has to be a certain type of relations in virtue of which these objects make up a world. The minimalist hypothesis then is that these relations also individuate the objects, thus paving the way for the claim that there is nothing more to these objects than standing in these relations. The objects thus are simple, having no parts or any other internal structure. When it comes to the natural world, relations providing for extension—namely, distances—are the first and foremost candidate for the type of relations that fulfills this task. Distances connect unextended and thus point-sized objects. If they individuate these objects, they provide for variation within a configuration of point-sized objects, with each of these objects being distinct from all the other ones by at least one distance relation that it bears to another object. In virtue of standing in distance relations, these objects then are matter points (recall the sparse Cartesian conception of the natural world as res extensa). In order to achieve empirical adequacy, we furthermore have to stipulate that these relations change. We thus propose an ontology of the natural world that is defined by the following two axioms, and only by these two axioms:

• (1) There are distance relations that individuate simple objects—namely, matter points.
• (2) The matter points are permanent, with the distances between them changing.

We submit that these two axioms prescribe the diet that is as meagre as possible in accounting for the natural world, to come back to the citation from Jackson earlier. Everything else then comes in as a means to represent the change in the distance relations that actually occurs in a manner that is both as simple and as informative as possible.

We thus take up atomism and seek to develop it into a minimalist ontology of the natural world. Atomism is the oldest and most influential tradition in natural philosophy, going back to the pre-Socratic philosophers Leucippus and Democritus. The latter is reported as maintaining that

substances infinite in number and indestructible, and moreover without action or affection, travel scattered about in the void. When they encounter each other, collide, or become entangled, collections of them appear as water or fire, plant or man.

(fragment Diels-Kranz 68 A57, quoted from Graham (2010), p. 537)

In a similar vein, Newton writes at the end of the Opticks,

It seems probable to me, that God in the Beginning form’d Matter in solid, massy, hard, impenetrable, moveable Particles … the Changes of corporeal Things are to be placed only in the various Separations and new Associations and motions of these permanent Particles.

(Newton (1952), question 31, p. 400)

The attractiveness of atomism is evident from these quotations: on the one hand, it is a proposal for a fundamental ontology that is most parsimonious and most general. On the other hand, it offers a clear and simple explanation of the realm of our experience. Macroscopic objects are composed of indivisible particles. All the differences between the macroscopic objects—at a time as well as in time—are accounted for in terms of the spatial configuration of these particles and its change, which is subject to certain laws. That is why Feynman famously writes at the beginning of the Feynman lectures on physics,

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.

(Feynman et al. (1963), ch. 1–2)

Whereas atomism is a purely philosophical proposal in Leucippus and Democritus, it is turned into a precise physical theory by Newton. Accordingly, classical mechanics—and classical statistical physics—are usually seen as the greatest triumph of atomism. Nonetheless, atomism loses nothing of its attractiveness when it comes to quantum physics. In the first place, also in this domain, all experimental evidence is evidence of discrete objects (i.e. particles)—from dots on a display to traces in a cloud chamber. Entities that are not particles—such as waves or fields—come in as figuring in the explanation of the behaviour of the particles, but they are not themselves part of the experimental evidence: an electric field is probed by the motion of a test charge subject to it (such as the electron in the wire); the double slit experiment is made apparent by sufficiently many particles hitting on a screen, etc.

Moreover, in quantum as in classical physics, there are good arguments to maintain that we need an account of macroscopic objects—such as, for instance, a cat or an apparatus with a pointer that points in a certain direction—in terms of matter being arranged in a certain manner in physical space. In order to achieve such an account, one cannot only endorse the quantum state, which is defined on a very high-dimensional mathematical space (namely, the configuration space of the universe), but one has to conceive that state as being the state of matter arranged in three-dimensional space or four-dimensional space-time: we take the arguments to this effect going back to Bell (2004, ch. 7) and elaborated on notably by Maudlin (2010, 2015) to be convincing. In brief, according to these arguments, it is not sufficient that one can find something in the quantum state of the universe that functionally corresponds to cat-like or pointer-like behaviour; for there to be a cat, or a pointer, there have to be basic objects that compose a cat, or a pointer, if they are arranged in the right manner in physical space such that the evolution of such a configuration of basic objects then amounts to the motion of a cat, or a pointer, in space.

In other words, then, what has become known as a primitive ontology of matter distributed in three-dimensional space or four-dimensional space-time is a necessary condition to avoid the famous measurement problem of quantum physics.¹ To turn that necessary condition into a sufficient one, one has to formulate a dynamic for the primitive ontology that excludes superpositions of matter in space so that there always is a definite configuration of matter and Schrödinger’s cat paradox, among others, is avoided, but that dynamic has to include entanglement to account for the non-local correlations that are manifest, for instance, in the Einstein Podolsky Rosen (EPR) experiment (for recent elaborations, see, notably, Allori et al. (2008), Belot (2012) and Esfeld et al. (2014)). This reasoning applies not only to non-relativistic quantum mechanics but also to quantum field theory (QFT)—as well as a future theory of quantum gravity—since any quantum theory is plagued by the measurement problem (cf. Barrett (2014)).

Its success notwithstanding, atomism faces three major problems. Our transformation of atomism into a truly minimalist ontology of the natural world seeks to address these problems.

(1) In the first place, Democritus as well as Newton set out atomism in terms of a dualism of matter on the one hand and space and time on the other: matter is conceived as being inserted in an absolute background space and as evolving in an absolute background time. However, the justification of absolute space and time is debatable, and their ontological status remains unclear in classical atomism. The commitment to absolute space and time implies in any case a commitment to a surplus structure, because absolute space and time reach, in any case, far beyond the actual configuration of matter, with its being doubtful whether one obtains a gain in explanation through that commitment.

Since Leibniz, relationalism about space and time is put forward to avoid that dualism. We follow this tradition. We set out an ontology of the natural world in relationalist terms, being committed only to distance relations among the atoms and deriving time from the change in these relations as the order of that change. We show how such an ontology can match both classical and quantum mechanics and how it remains a viable option in relativistic physics.

(2) Nonetheless, even if the dualism of matter on the one hand and space and time on the other is removed, the question of what characterizes the atoms as material substances remains. Democritus and Newton conceive them as being equipped with a few basic intrinsic properties—that is, properties that belong to each atom taken individually, independently of all the other ones, thus making up an intrinsic essence of each atom. The paradigmatic example is mass in Newtonian mechanics. However, also in Newtonian mechanics, both inertial and gravitational mass are introduced through their dynamical role—namely, as a dynamical parameter that couples the motions of the particles to one another, as was pointed out by Mach (1919, p. 241) among others. The same goes for charge, energy, etc. When it comes to quantum mechanics, despite first appearances, properties such as mass and charge cannot be conceived as intrinsic properties of the particles, but are situated on the level of their quantum state as represented by the wave function. In sum, as soon as atomism is worked out as a precise physical theory, it turns out that anything that one might regard as constituting an intrinsic essence of the atoms is in fact a dynamical parameter, expressing a dynamical relation that couples the motions of the atoms to one another. Hence, the question is what is the essence of the atoms qua material entities?

We bring in ontic structural realism to answer this question: instead of having an intrinsic essence, the atoms have a structural one. Standing in distance relations is their essence. Hence, although we propose an ontology of atomism, we draw on holism to work that ontology out: the atoms are holistically individuated in terms of the distances among them. We conceive the distance relations as establishing the order of what coexists, thereby taking up Leibniz’s relationalist definition of space: these relations are able to distinguish the objects, thereby satisfying the principle of the identity of indiscernibles. There thus is a configuration of objects that is constituted by distance relations: by individuating the atoms, the distance relations provide for variation within a given configuration of matter.

Over and above variation making up for a configuration of objects, there is change, which hence is change in the relations that constitute the configuration—that is, the distances. We follow Leibniz in conceiving time as the order of that change, with that order being unique and having a direction. Mass, charge, energy, spin, wave function, etc., then, are dynamical parameters that a physical theory introduces in order to obtain a law that describes that change in a simple and informative manner. These parameters sort the atoms into different particle species on the basis of salient patterns in their relative motion. Consequently, the atoms are not intrinsically protons, electrons, neutrons, etc., but are so described because their motion exhibits certain contingent regularities. In a nutshell, some atoms do not move electronwise because they are electrons, but they can be classified as electrons because they move electronwise.

Indeed, there is no need to admit physical properties at all. Relations do all the work. It is a misconception to set out ontic structural realism as a stance that is directed against object-oriented metaphysics (cf. Ladyman and Ross (2007) and French (2014)). Ontic structural realism is opposed to the property-oriented metaphysics that has dominated philosophy from Aristotle to today’s analytic metaphysics. Of course, if there are relations, there ar...

Table of contents

• Cover
• Title
• Copyright
• Contents
• 1 Introduction
• 2 Matter points and their dynamics
• 3 Minimalist ontology and dynamical structure in classical and quantum mechanics
• 4 A persistent particle ontology for quantum field theory
• 5 Relationalism for relativistic physics
• Bibliography
• Index