Einstein’s Theory of Theories and Mechanicism

ABSTRACT

One of the most important contributions of Einstein to the philosophy of science is the distinction between two types of scientific theories: ‘principle’ and ‘constructive’ theories. More recently, Flores proposed a more general distinction, classifying scientific theories by their functional role into ‘framework’ and ‘interaction’ theories, attempting to solve some inadequacies in Einstein’s proposal. Here, based on an epistemic criterion, we present a generalised distinction which is an improvement over Flores approach. In this work (i) we evaluate the shortcomings related to Flores’s proposal, (ii) we present an epistemological criterion that opens the door for a more general classification of any scientific theory in all of the natural science into two distinct groups, which we call ‘mechanistic theories’ and ‘structural theories’, and (iii) we show that such a criterion is connected to Flores’ proposal while overcoming issues of all previous approaches.

KEYWORDS:

• Theory classification
• scientific explanation
• mechanistic explanations
• structural explanations
• philosophy of science

1. Introduction

Every scientific theory, in all branches of science, has particularities that render it unique. Nevertheless, since at least Galileo's times, there is a widespread intuition that it is possible to define a sharp distinction between two different classes of theories, with some theories dealing with dynamical aspects of phenomena in the world, and other theories dealing with kinematic aspects. Unfortunately, these labels are somewhat ill- defined, and also would seem to apply only to physics.

Einstein (1919) proposed a classification of scientific theories which separates them into two types, which he called ‘principle theories’ and ‘constructive theories’. This distinction is, according to Howard and Giovanelli (2019), ‘Einstein's most original contribution to twentieth- century philosophy of science’. However insightful, Einstein's classification fails to be complete, something that would be desirable for any classification, even though it was not explicitly his aim. This is the case because (i) some theories cannot be assigned to any of the two categories, and (ii) the classification, which is based on ontological considerations of assumed universal validity, seems to be of application only within physics.

More recently, Flores (1999) introduces a more general distinction, between what he called framework theories, that deal with general constraints, and theories that deal explicitly with interactions. For this, he used as a classification criterion the functional role that a theory plays, distinguishing between universally valid versus interaction specific theories. Notice that Flores’ criterion is still largely focused on physical theories. The aim of Flores is to show that each kind of theory provides a particular kind of explanation: framework theories provide top-down explanations, while interaction theories provide bottom-up explanations. Also, and most importantly for our purposes, Flores’ classification intends to achieve an easier discernment between two classes, allowing for the clear-cut classification between one or the other class for any theory.

Flores’ analysis highlighted many valuable features of the distinction. Although the criterion behind theory classification is different (ontological in one case, functional in the other), the two groupings are strongly related. Flores claims that all of what Einstein called ‘principle theories’ are equivalent to Flores’ ‘framework theories’, whereas Flores’ interaction theories are a larger group than Einstein's ‘constructive theories’ with the former containing the latter. Beyond this, Flores also relates each of the two groups of physical theories to a particular ontology, theoretical function, and epistemic contents displayed in different contexts of discovery and in different kinds of explanation. In other words, the refined classification provides a powerful conceptual tool for theoretical analysis that would be relevant for science as a whole.

However, as we discuss in more detail below, Flores’ criterion, while a clear improvement over Einstein's regarding completeness, falls just short of what can be considered the ideal: a universally valid and exhaustive classification of scientific theories. The two roles, that of describing general frames and specific interactions, a priori do not exhaust the possible roles that scientific theories can have, and there is no assurance that the complement of interaction theories are framework theories or vice versa. This being so, the field is still open for a criterion that converges all the intuitions behind the kinematical/dynamical, principle/constructive, and framework/interaction distinctions in a way that is general, robust, and informative for the analysis of science.

In this work, we attempt to offer such a criterion. For this, we carefully invert Flores's argument, taking his conclusions regarding the types of explanations provided by each kind of theory as the starting point of a classification criterion; that is, we use an epistemic approach, focusing on how different theories provide diverse types of explanations for phenomena. Such a change of focus allows us to classify any theory that provides meaningful descriptions of the material world into two distinct and well-defined groups. We also discuss how, once the theories are classified using the new criterion, all the ontological, methodological and epistemic consequences of Einstein-Flores's previous distinctions also follow so that this new criterion serves as their generalisation. The kind of distinction that we argue for is especially relevant for the scientific realist, as it can inform the ontological commitment to our best theories, and to the unobservable objects, properties, and laws they postulate.

This article is organised as follows: in section 2 we give a quick overview of the improvements made by Flores to the original distinction made by Einstein. We argue that, despite its merits, Flores’ classification falls short of the ideal aim of being a complete classification of scientific theories. On that basis, in section 3 we present our approach, which consists in proposing an epistemic classification criterion. For this, we use ideas grouped under the label of mechanicism, both in the classical form of Salmon (1984) and in the renewed ‘new mechanicism’ approach (for an overview see Glennan 2017). In section 4 we give arguments for the general approach of our ideas, which even suggest the exhaustiveness of this new classification. We compare our approach to that of Flores in section 5 and show how it solves all the issues with previous classifications. We present our conclusions in section 6.

2. The Framework/Interaction Classification of Theories

Flores (1999) performs an analysis of Einstein’s ideas on theories and notices that there are three aspects to Einstein’s classification: an ontological aspect, where the focus is on what entities are at the basis of the image of the world given by the theory; an epistemic aspect, related to how theories are developed and justified; and a functional aspect, related to what role the theory plays within our full scientific image of the world, which involves several theories working in tandem.

Einstein used the ontological aspect for his classification: constructive theories hypothesise the existence of (usually microscopic) objects that by their interactions explain the behaviour of phenomena in a bottom-up way, whereas principle theories start from general hypotheses of assumed universal validity. Einstein's prime examples for these kinds of theories were the kinetic theory of gases as a constructive theory and thermodynamics as a principle theory.

The distinction has been used in one way or another within discussions in a wide range of topics, not only in the context of Special Relativity (SR), where Einstein popularised the distinction (for example within the so-called Brown-Janssen debate, see Balashov and Janssen 2003; Brown and Pooley 2001, 2006; Felline 2011; Frisch 2011; Camp 2011; Acuña 2016), but it also appears in the context of interpretations of quantum mechanics (Bub and Demopoulos 1974; Bub 2000, 2005; Clifton, Bub, and Halvorson 2003; Brown and Timpson 2006; Plotnitsky 2015; Felline 2020), Quantum Gravity (Smolin 2017), interpretations of Quantum Field Theory and the Standard Model (Author, Author), in scientific explanations (Van Camp 2011; Lange 2011, 2014). The distinction is widely used because it highlights functional, epistemic and ontological differences among theories or theoretical elements of these two groups.

What motivates Flores’ generalisation is the fact that Einstein's classification does not appear to be universally valid, as it is not clear that any given scientific theory necessarily belongs to one of the two classes. Indeed, some theories are difficult to classify using Einstein's distinction, such as Newton's law of universal gravitation.

Whereas Einstein's proposal is based on ontological criteria, Flores proposes to focus instead on the functional aspect. The two possible functions observed by Flores differ in their level of generality. On the one hand, some theories describe specific interactions between objects in the world, such as universal gravitation. These Flores called interaction theories. On the other hand, some theories provide a unified structure for all interaction theories; these framework theories deal with general constraints that all physical processes must obey independently of what specific interaction is at play—a good example being Newton's three laws of motion or special relativity.

The functional criterion attempts to solve the issues mentioned above. It generalises Einstein's ideas and makes the classification more robust. Nonetheless, some of the issues with the principle/constructive distinction remain in Flores’ approach. In particular, it is still unclear if the classification is exhaustive: the roles played by interaction and framework theories intuitively complement each other, but this is not explicitly demonstrated. As there is no argument in Flores’ work for such complementary character of the distinction, the possibility for further classes remains.

More generally, the shortcomings of Flores’ distinction stem from how it was articulated. Although one can see the principle/constructive distinction as a particular case of the framework/interaction distinction¹, the latter was constructed from the analysis of one very specific study-case, namely Newtonian gravitation, and not from general arguments, and this ends up being problematic in several ways.

A first concern is that it remains an open question whether the function of a theory depends on the level of analysis or the theoretical context at play: that is, whether an interaction theory in a particular context (such as electromagnetism in physics) might play the role of a framework in other contexts (electromagnetism being the framework for chemistry).

In a related but different concern, Flores’ distinction might rest in differences of degree rather than constituting a categorical difference, allowing theories to belong to a spectrum passing from one kind of theory to the other, and dissolving with this the valuable ontological and epistemic information encoded in the distinction. In other words, framework and interaction do not seem to be (a priori) two complementary classes.

If these kinds of concerns succeed, and the distinction fails to be universally valid, then nothing conclusive can be said about the ontological status of the theoretical objects associated with theories within a given theory class. This would constitute a major loss, as it would be extremely useful for scientists and philosophers alike to have the means for recognising those elements in our theories that likely refer to mind/description independent objects in nature from those theoretical entities that do not need to be reified for the theory to work, allowing for the early recognition of spurious metaphysical assumptions—a useful tool for realists and anti-realist alike.²

Similarly, if the distinction fails to be universally valid, then nothing conclusive can a priori be said about the kind of scientific explanations provided by a theory. Again, we claim that this would be an unfortunate loss, as it would be extremely useful for scientists and philosophers alike to know from the start what type of explanation to expect from different theories, clarifying in this way their epistemic import.

The desiderata for a refined classification criterion would then entail for the distinction to be exhaustive, and to be general enough to be relevant for all natural sciences. This would not only strengthen the ontological and epistemic derivations just mentioned, but it would also open the door to extend the distinction to domains other than fundamental physics. This would support intuitions such that the theory of evolution, for example, is a framework theory in biology. More generally, it would open a whole unexplored area of research in philosophy of the natural sciences, where this conceptual tool could now also be at the disposal of philosophers of biology or chemistry, among others.

3. An Alternative Criterion

Flores uses its classification to enlighten a different discussion within the philosophy of science—the nature of scientific explanations—claiming that interaction theories provide bottom-up explanations that cover the causal mechanisms behind phenomena, whereas framework theories provide unifying top-down explanations. Here we turn this conclusion into our starting point and employ it as a criterion for a more general classification.

We are now in the position to present our proposal, what we call a mechanistic criterion (MC), for the classification of scientific theories in two groups. We first state our criterion and then discuss some of its details:

(MC): Those theories that allow us to trace the causal mechanisms that explain mechanistically the occurrence of a certain phenomenon we call mechanistic theories. And those theories that lack agents whose actions are causally responsible for phenomena, but that instead provide general constraints or structural elements that lead to unificationist explanations we call ‘structural theories’.

The term causal mechanism in (MC) refers to (causal) relations between two relata, A and B, instantiated by some agents and activities responsible for bringing about B from A. In the philosophical literature theories of causation are classified (among other categorizations) into two large groups: mechanistic theories of causation, where causation is analysed in terms of physical processes joining causes and effects; and difference-making theories of causation, in which it is considered that the presence of a cause ‘makes a difference’ with respect to its absence. In general, the explanatory component that a causal claim possesses is considered to be exploited by mechanistic theories of causation rather than by difference-making approaches³, and since (MC) emphasises the concept of ‘explanation’, we believe it is more appropriate to use a mechanistic causal approach for our criterion.

Note that mechanistic theories do not only involve those approaches to physical causation based on, for example, the ‘classical’ mechanist ideas of Salmon and Dowe (e.g. Salmon 1984; Dowe 2000)—which were what Flores had in mind when discussing explanations—but also include those approaches to causation that came to be known as ‘new mechanicism’, that attempt to describe how causal explanations work in e.g. biological and health science phenomena (Glennan 2017, and references therein). Very approximately, in this last type of theories, it is affirmed that A is the cause of B if there is some mechanism, understood as a series of organised entities and activities, that explains the occurrence of B from A. As the requisites needed for ‘new mechanisms’ are less restrictive than those that must be fulfilled in the case of classical mechanisms, the latter naturally become a subgroup of the former. In this way, our proposal is not restricted to theories in physics but aims to be useful in other natural sciences.

Let us now clarify the concept of tracing. The term ‘to trace’ in (MC) refers to finding and describing the sequence of causal links present between the occurrence of a phenomenon A and the occurrence of a phenomenon B, consistent with the theory under study. The characterisation of tracing that we use implies that it is not always possible to obtain the complete sequence of events within a theory. Whether or not this complete sequence is obtained depends on the characteristics of the theory that describes a particular phenomenon. That is, given the limitations of the theory, we could obtain the whole mechanism and all the causal relations allowing a complete explanation of the phenomenon under study, or only a part of them. It would be enough to describe some of the causal links involved in the explanation of phenomenon B from phenomenon A to realise that the theory that provides such explanatory statements is mechanistic.

In other words, the causal mechanism needs not to be complete to its ultimate details to be considered a mechanistic theory, in fact, a full explanation for a phenomenon might need to use several theories in tandem, some of which might not be mechanistic following (MC). For example, an explanation of a microscopic phenomenon might have to use elements from the mechanistic theory of electromagnetism, such as the Lorentz force law, as well as elements from the structural theory of relativity, such as the invariance of the speed of light. The distinction allows us to analyse each part of the explanation and identify from it interacting agents and structural features.

Finally, a brief comment about the concept of explanation in (MC). What is relevant about the causal links that lead to the occurrence of a certain phenomenon is that they can construct an explanation of this phenomenon. In this sense, our (MC) is an epistemological criterion. It should be stressed that our proposal is motivated by Flores’ conclusions regarding the connection to types of explanations. On the one hand, mechanistic theories are connected to bottom-up explanations based on the actions of agents that underlie causal chains of explanation. This connection was deliberately constructed in (MC), which paraphrases Salmon (1984) notion of ‘bottom-up’ explanation.⁴ On the other hand, we connect structural theories with top-down explanations based on general constraints. This second type we associate with what Kitcher (1989) calls unificationist explanations: explanations that unify a diversity of phenomena, usually employing some underlying structure.

Notice how this criterion constitutes also a good generalisation of the notions of kinematic and dynamic theories: whereas dynamics is traditionally conceptualised to deal with the studying the causes behind changes, kinematics is conceptualised to study the constraints to any movement independent of causes. (MC) thus fleshes out the intuitions behind this distinction, while also generalising Einstein's and Flores’ accounts, as we discuss below.

Let us finish this section with an example of the use of (MC). Consider the following situation: after rubbing a balloon against fur and approaching it with small pieces of paper, some pieces of paper are attracted to the balloon. To explain this event using thermodynamics, we could appeal to the first law to explain that the energy needed to lift the pieces of paper cannot be greater than the work done by rubbing the balloon against the fur. Note that such an explanation does not allow us to trace the causal mechanisms behind the phenomenon (the lifting of the papers), but it provides a general constraint, from which we can conclude that thermodynamics is a structural theory. Conversely, if electromagnetism is used to explain the same situation, we could appeal to the rearrangement of electric charges caused by the rubbing of the balloon and the fur, which generates an excess of charge on the insulator surface of the balloon, which generates an electric field in space, that induces a polarised distribution of charges on the conductive pieces of paper, in a way that opposed charges get closer to the balloon and, by the Lorentz force, the opposed charges attract each other doing the necessary work to lift the pieces of paper. In this second case, we can trace the causal links that explain the phenomenon mechanistically, and we conclude that electromagnetism is a mechanistic theory.

4. Towards a General Classification

(MC) constitutes a new criterion for theory classification, based on how theories explain phenomena. We claim that this criterion solves the issues affecting Flores's functional distinction. In this section, we explore whether our criterion is generalisable to scientific theories outside of physics.

Theories that are classified as mechanistic deal with objects (or agents) acting on one another i.e. interacting: therefore, mechanistic theories are a generalisation of interaction theories that goes beyond physics. All mechanisms require interactions among agents, and therefore all mechanistic explanations involve interaction theories.⁵ What is not a priori clear is that every theory (or theoretical element) that cannot be classified as mechanistic will always provide structural constraints, i.e. it is not clear if every time a theory is not mechanistic then it will belong to what we called structural theories. Note that structural theories resemble what Flores called framework theories: general descriptions dealing with constraints and regularities that provide global structure to interaction theories. Only if this is the case the classification provided by (MC) would exhaust all scientific theories in a non-trivial way, generalising Flores criterion.

We provide two arguments that strongly suggest, although unfortunately do not amount to, a full proof of exhaustiveness. These are (i) a consequence of the semantic view on scientific theories, (ii) a conclusion from a review of the main theories of explanation.

Given that the two arguments are independent, and the scenario in which both fail is implausible, we conclude that the most rational standpoint is to acknowledge the general and exhaustive character of the distinction.

4.1. The Semantic View on Theories

It is possible to argue for the exhaustiveness of our classification by considering the semantic view on scientific theories (Suppes 1967, 2002; Suppe 1977; Van Fraassen 1989). This is particularly true from the perspective of what is known as the state-space approach, which connects with ease with (MC). A scientific theory or model generically can be described as a set (in the sense of set theory) of objects and relations governed by certain laws, sets which purportedly represent or correspond to phenomena in the real world. This correspondence could work at the level of whole theories or—in aligning with the spirit of the new mechanicists—at the level of individual models of phenomena. The set of all possible configurations or states that a model can take defines the state-space of the model, and its structure yields information about what phenomena are possible in the world if the model is true.

Generally speaking, the laws which connect the diverse elements of our theoretical model within their state-space correspond to one out of three classes (Suppe 1977; Lloyd 1994; Weisberg 2013) viz., laws of succession determining possible trajectories through that space (e.g. Newtonian kinematic laws); laws of co-existence specifying the permitted regions of the total state-space (e.g. Boyle's law); and laws of interaction (e.g. Newtonian gravity, or population genetic models combining mechanisms of gene mutation and natural selection).

If we go over these three types of laws, we can observe that laws of interaction are associated with mechanistic explanations: they offer the links of the mechanistic chain of objects (or agents) acting on other objects to connect causes and effects. Newton's universal law of gravitation constitutes an excellent example of a law of interaction, and explanations that use this law are always mechanistic: planets describe ellipses around the sun because of this inverse square law, which describes the attractive force the sun and the planets exert on each other.

Conversely, laws of co-existence are non-mechanistic, and align with structural or unificationist types of explanations: there is no explicit mechanism behind the constraints obeyed by the state-space of a theory. By way of an example, consider the axioms of standard quantum mechanics that require the description of a quantum state as a vector (or a ray) in a Hilbert space determined by the degrees of freedom of the system. There is no mechanism behind this requirement, but instead a general structural constraint.

The case of laws of succession is more subtle. Laws that describe the time evolution (e.g. Newton's second law, or the Schrödinger equation) are naturally what Flores would call framework laws: they do not refer to any interaction. Nonetheless, for these laws to enter a scientific explanation they must be complemented by an interaction law. For example, if an explanation about planetary movement makes use of Newton's second law F = ma, the explicit form of the gravitational interaction must take the place of the F term, which acts as a placeholder for any interaction within the Newtonian law of succession. Thus, when laws of succession enter an explanation an interaction law must also be at play, making the explanation mechanistic.

This underlines an important aspect of the framework/interaction distinction, which remains unaltered when classifying theories following (MC). Interaction theories are always embedded within a framework theory, as frameworks have the role of providing the ‘playing field’ where interactions take place. Otherwise said, the general constraints of structural theories are found by analysing the behaviour of many mechanistic interactions–potentially all the interactions within a certain area of research. When Einstein developed special relativity, he did so by taking as starting points two general constraints obeyed by electromagnetism, that the success of his theory helped to show were universal.

By way of this three-lemma we exhaust all possible explanations within a semantic view of scientific theories between two classes. All theories or laws that are not mechanistic following (MC) provide structural explanations (justifying the naming convention we use in (MC)), and there are no more types of explanation.

This would constitute proof of the exhaustiveness of (MC) within the semantic view on theories. What makes this proof incomplete, of course, is that one can deny the semantic view and defend/adopt the syntactic or the pragmatic view of scientific theories. In such cases, a defence of the exhaustiveness of our criterion is less clear. The syntactic view has little support nowadays (for notable exceptions see Friedman 2001; Halvorson 2013), and even then, an argument for the exhaustiveness of the mechanistic/structural divide could be constructed in this case along similar lines by analysing how laws depend on specific relations between particulars–a tell-tale sign of a causal mechanism, or if it applies in an unspecified generalised way, which would signal structural constraints.

As for the pragmatic view of theories (see e.g. Cartwright and McMullin 1984; Cartwright et al. 1999; Hacking 2009), it proposes a pluralistic take on theory structure and typology. But even more, it puts the emphasis, when studying the scientific process, not on theories, but on scientific models. This focus on models makes it more difficult to extract general claims about theories in the pragmatist literature, besides their purported lack of importance for philosophical analysis.

When considering individual models, in general they will include elements of several theories. If and when the model includes the interactions of agents, it will always be possible to claim that there is a mechanistic theory at play following (MC). Once again, using the ideas of the new mechanicists puts us at an advantage here with respect to previous criteria, as mechanism are also defined at the level of models of specific phenomena.

The question of exhaustivity then becomes the question of what kinds of non-mechanistic explanations do scientific models provide. If a certain explanation is non-mechanistic, then it does not involve the actions of agents, which means that the explanation exploits some general non-localised rule of behaviour–in other words a structural constraint. We can go further and add that an explanation that is not bottom-up (that is, from the behaviour of the agents composing the system), must be top-down (that is, starting from general principles that transcend any mechanism). We explore this in the following section.

4.2. Bottom-up and Top-down Explanations

The distinction between top-down and bottom-up explanations is covered in detail by De Regt (2006), section 2, which describes the origin of the distinction as taking place in the works of Salmon, Friedman and Kitcher.

On the one hand, top-down explanations involve unification or reduction in the number of phenomena or facts that we must accept as ultimate or brute (Friedman 1974; Kitcher 1989). De Regt (2006) gives a characterisation of Kitcher's ideas regarding unificationist explanations in the following way: ‘Any candidate explanation is a derivation of a specific conclusion from a set of premises, which can be viewed as an instantiation of some general argument pattern.’ (our emphasis). This description is almost verbatim Einstein's characterisation of principle theories, which following Flores can be considered as equivalent to framework theories. The kinds of explanations delivered by framework theories are top-down explanations, almost by definition.

On the other hand, bottom-up explanations are those that involve causal mechanisms, for as Salmon says: ‘Causal processes, causal interactions, and causal laws provide the mechanisms by which the world works; to understand why certain things happen, we need to see how they are produced by these mechanisms’ (Salmon 1984). Such a description is almost verbatim to our proposal as resumed in (MC), and it follows that mechanistic theories naturally provide bottom-up explanations.

It should be stressed that the bottom-up versus top-down distinction has been conceptualised in different ways in the literature. The distinction has been related to the idea of unificationist versus causal explanations as presented here, but it has also been connected to the notion of global versus local explanations. Shortly stated, local explanations would focus (only) on the specific phenomenon being explained, as opposed to global explanations that entail generalisations connecting many phenomena. The global versus local conceptualisation of top-down versus bottom-up is very prominent in Friedman's approach to the topic.

Instead of this restrictive notion of locality, in this work, we favour a distinction based on causal tracing via mechanisms. Mechanisms are local in the sense that the interactions and actions performed by agents take place locally in space–time. However, nothing stops us from recognising the same patterns whenever agents of the same kind act in the same way; nothing in the mechanicist approach prevents us from generalising a given mechanism to several related phenomena. For example, the mechanism behind ATP production through photosynthesis can be generalised to all plants in the world without stopping being a ‘local’ explanation (in the sense of requiring agents that perform actions in confined regions of space–time).

Using this notion of spatiotemporal locality, the unificationist account of explanations also becomes clear-cut, because the reduction in the number of phenomena or type of facts that we must accept as ultimate or brute must exceed a particular mechanism to constitute a global conceptual unification, and when this happens, no specific agents or actions are considered, but instead general, structural properties of the natural world.

Take for example ‘energy conservation’ or ‘natural selection’ as such unifying concepts: both apply to several (in the first case, probably to all) mechanisms in nature, where different agents perform a diversity of actions while nonetheless being required to obey the unifying constraints imposed by those general structures.

A richer form of ‘global’ or ‘non-local’ is in place here, one that separates one kind of theory from the other, and that highlights the categorical difference between the two types of explanations. It is the most fruitful to talk about local whenever interacting agents play the explanatory role because such agents in the material world are spatio- temporal objects, and to talk about global whenever the theoretical elements playing the explanatory role do not require specific agents performing any specific actions, and in this sense, they work as global constraints over whatever mechanistic interactions are at work.

Using these definitions, we can determine whether our distinction is exhaustive by exploring the possible alternatives, to see whether they open the way to new forms of explanations that would be relevant for science. The bottom-up and top-down classification would not be exhaustive in two cases: (a) if there are explanations that do not contain agents nor actions (and in this sense are similar to top-down explanations, let us call them top-down*), but that explain without unifying different phenomena and therefore do not corresponds to ‘genuine’ top-down explanation, or (b) if there are explanations constructed with agents and actions (therefore similar to bottom-up explanations, let us call them bottom-up*) that do not participate in the causal mechanisms behind the phenomenon under study, therefore not being ‘genuine’ bottom-up explanations.

The problem with these alternatives is that they seem to constitute either an empty set or to have no explanatory power and are therefore uninteresting from the point of view of the desiderata for a scientific explanation. Let us start with top-down*, an explanation that is not mechanistic, but that is not unificationist. Here we take for granted that the natural world is ontologically composed (solely) of material entities or agents that perform actions upon other material entities, that is, we rule out ghosts or miracles. Then, any top-down constraint that is not mechanistically explained by the actions of the material agents involved in a phenomenon must affect several different mechanisms—otherwise, it would be impossible to categorically claim that the constraint is not a characteristic of the mechanism under study. However, if any structural constraint affects more than one mechanism, then the explanatory role it plays is unificationist, that is to say, it is a genuine top-down explanation. In this sense case (a) seems to describe mis-characterised explanations or no explanation at all.

Conversely, the problem with bottom-up* is that agents and actions that are not part of the causal mechanisms behind phenomena can safely be removed from our explanations of said phenomena–without them these phenomena would occur anyway (those agents or actions have no causal power on the phenomenon at hand by definition). If such elements exist, they are spurious. In this sense (b) is uninteresting when considering scientific explanations.

Summarising, perhaps the most direct way of ensuring the exhaustiveness of a classification is by considering the group that satisfies a specific criterion and its complement, namely the group that does not satisfy said criterion. Clearly, the group of ‘mechanistic’ explanations is not the complement of the group of ‘unificationist’ explanations, one is not the negation nor the opposite of the other, and it is not obvious that both groups together comprise all possible explanations. However, if we consider the negation of bottom-up explanations—the group that we called bottom-up*—and the negation of top-down explanations—which we called top-down*—then we recognise that these alternatives are either empty or uninteresting, and we conclude that our distinction is, effectively, exhaustive.

Before moving on, we would like to highlight an additional fact that plays in favour of the exhaustiveness of the bottom-up/top-down distinction: a general sweep of the philosophical literature about the problem of explanation seems to indicate that each of the theories of scientific explanation existing to date can be classified either as bottom-up or top-down. As an example, in the philosophical literature we first come across the Hempelian deductive nomological model (Hempel and Oppenheim 1948) and its variants, and the statistical relevance model of Salmon (1971). These theories of explanation comply with the unificationist ideals by proposing a general explanatory structure through an explanandum, an explanans and their logical deductions, which can be applied to a variety of natural phenomena. This is also seen by De Regt, who affirms that the unificationist model of Kitcher can be seen as a sophisticated version of the Hempelian theory of explanation De Regt (2006, 132).⁶ On the other hand, as a counterpart, we find the theory of Salmon (1984). As we have seen, for Salmon it is not only important to provide explanations that unify different phenomena, but also to offer explanations that allow us to glimpse the causal mechanism that allows them to occur. We sweep over the literature to highlight our intuition that the inventory of theories of explanation available to date agrees with Salmon, since all of them, in one way or another, can be classified either as a bottom-up approach or as a top-down approach.⁷

4.3. Summary on Exhaustiveness

The arguments presented in this section, while not final, give credence to our claim about the exhaustiveness of (MC). If we are right, given a scientific theory one of three options is necessarily the case: either it is a mechanistic (or interaction) theory, dealing with causal mechanical explanations, or it is a structural (or framework) theory, dealing with structural (unificationist) explanations, or else it can be neatly divided into self-contained theories of each kind. Although historically the discussion refers to theories and we have kept this nomenclature, it should be noted that to use (MC) one must focus on the use of specific models for explaining phenomena, and not on theories in a global way. This is in going with the ideas of the new mechanicists, and it implies that for a given phenomenon under study we must generally make use of several theories, some of which will be mechanistic, whereas others will be structural. If we have two models, and a theory models agents and their action on other agents in one model, but it models structural constraints in another model, then the argument is that in fact we can split the theory in two: one theory that speaks about agents interacting, and another that speaks of general constraints. See Benitez (2019) for examples of similar ideas.

Note that these divisions are not arbitrary, as they depend on the kinds of explanations that one obtains from theories. Thus, it is not merely a matter of interpersonal agreement to decide if a theory is mechanistic or not, as there is no way in which a structural explanation that works without the action of any agents would turn to be a mechanistic explanation without deep changes to the underlying theory.

Generally speaking, there is still the question of how to disentangle the structural theory from the (possibly several) mechanistic theories participating in the explanation of a phenomenon. But this is easily done by considering what parts of the explanation depend on the existence of any agent acting in the world; that is, looking for all the mechanisms at play in the explanation on one hand, and considering the complementary aspects in the other, which will be general principles. Once the interaction laws, which describe the action of specific agents or objects on each other, are taken out, all the remaining aspects of the phenomenon must be explained by general principles, governed by structural theories.

5. Advantages of the New Classification

In this section, we explore some advantages of our proposal and show how our criterion solves the issues with Flores's distinction identified in section 2. Additionally, we argue for the validity of this classification beyond physics, particularly in chemistry and biology, providing some examples.

5.1. Issues with Flores's Distinction

The first point exposed in section 2 is the worry that the distinction may be dependent on the level of analysis or the theoretical context at play, with the example of electromagnetism being interaction theory in physics but arguably a framework for chemistry. From the point of view of this work, the problem here is related to the degree of generality of framework theories as defined by Flores.⁸ Flores’ definition of a framework leads to ambiguous situations, in which a theory provides elements for other theories to be built (filling the function of a framework theory) while being at the same time a theory that deals with interactions.

Because framework theories attempt to capture general regularities and not particular phenomena, such regularities tend to rule over several diverse kinds of events. This tendency is exemplified by the universal validity of framework theories in fundamental physics (such as the paradigmatic examples of thermodynamics or special relativity), but it is not a necessary requirement. This becomes clear when we use (MC), which is compatible with ideas of the new mechanical philosophy, originally designed to treat natural sciences other than physics—where such levels of generality cannot be expected.

The problem of misidentifying a theory in this way does not appear when using (MC), as a theory that traces the causal links between events A and B can be regarded as an interaction theory, independently of its degree of generality. Even though electromagnetism is more fundamental and, in some sense, ‘frames’ processes in chemistry, electromagnetic explanations of phenomena are as much mechanistic when considering chemical bonds as they are in physics; electromagnetism is an interaction theory in any theoretical context. In this sense, it is useful to differentiate a background theory from a framework theory: electromagnetism and thermodynamics are background theories for chemistry, however, only thermodynamics is a framework theory. Flores’ functional criterion is unable to highlight the difference, which is clear under having MC in mind.

Another problem identified in section 2 is that Flores's distinction fails to be exhaustive, related to two factors: (i) the generality of the classification in terms of its applicability to the so-called special sciences, and (ii) the universality of the classification in terms of it being able to encompass any and all scientific theories. As for the latter point, we gave our best arguments for it in the last section. As for (i), our criterion does extend to chemistry and biology, which we discuss in detail in what follows.

But before departing from fundamental physics, let us emphasise that our criterion and Flores’ fuse together within that realm, where classical mechanisms form the backbone of bottom-up explanations. Our discussion up to now would show that the interaction/framework classification is plausibly exhaustive when considering fundamental physical theories.

5.2. A Classification for All Theories Referring to the Material World

Unlike the case of previous criteria, all natural sciences can be classified by our exhaustive criterion. An explanation can be mechanistic in the sense of Salmon, or in the sense of the new mechanicists. The first class is more restrictive than the second, which includes it: a new mechanicist would accept a Salmon-like mechanistic explanation as indeed mechanistic for him/her, but not the other way around.

Already at the level of fundamental physics our classification provides relevant, not often seen facts about well-known theories. As an example, quantum mechanics famously resists a mechanistic view–see Salmon (1984) for a discussion of the possibility of the lack of causal mechanisms in quantum mechanics. This is straightforward from our point of view: quantum mechanics is a top-down structural theory, providing constraints for all interactions for all of matter. Thus, it is misguided to look for mechanistic explanations in quantum mechanics–irrespective of its historical name. For a more detailed discussion about the character of quantum mechanics see Bub (2004, 2005), Hagar and Hemmo (2006), Felline (2011, 2021), Benitez (2019).

Beyond physics, our approach extends Flores’ in two important ways. First, as mentioned already, it is based on the ideas of the new mechanicism, which were developed precisely with the aim of extending notions of mechanical explanations to the so-called special sciences. This ensures that (MC) can correctly classify mechanistic theories in these domains. Secondly, our notion of structure is more inclusive than the notion of framework in Flores. Indeed, framework theories are assumed by Flores to be of universal generality, whereas structural theories are only as general as needed, in the sense of including all the constraints needed within a given domain–as opposed to universally valid ones.

This is not the place for a detailed analysis of theories in biology and chemistry, as such a project exceeds the scope of this first proposal. We expect to carry a detailed analysis in future works; nonetheless, here we provide a couple of examples of how this distinction could be applied within biology or chemistry.

Let us consider the astonishing biodiversity on our planet. A possible way to explain it is through the theory of evolution. This theory allows us to explain that different living organisms have common ancestors and that the differences observed correspond to different adaptations to the environment that were selected during extended periods of time, with adaptations improving the fitness of organisms (its chances of reproducing and surviving). This explanation does not allow to trace causal links behind these phenomena, and therefore this theory can be considered a framework theory. We could alternatively evoke the genetic theory to explain the same biodiversity within an evolutionary framework, which allows explaining how information is stored in RNA or DNA, how such information encodes the anatomical characteristics of living creatures, how such information is replicated, and how small errors in the process of copy, or mechanical alterations to the molecule of DNA due to radiation or other external influences, may lead to mutations, and how the sum of such mutations could end up with a stable organism different enough to the original ancestor to be considered a different species, explaining in this way the observed biodiversity. The genetic theory is mechanistic following (MC) as it allows to trace the causal links behind phenomena, therefore constituting an interaction theory.

In chemistry, the basics laws of stoichiometry (the law of multiple proportions or Dalton's law, the law of definite proportion or Proust's law, and the law of reciprocal proportions) can be used to explain the relative proportions of the final results of a chemical reaction (be it compounds or residual elements) after the combination of initial elements. All these laws are structural, as they do not allow to trace causal links behind the observed results and therefore, they correspond to generalised frameworks. The same phenomena (the mix of elements and the final proportion of resultant substances) can be explained using the atomic theory; with it, it is possible to trace the causal links behind the combination of initial substances, constituting a mechanistic theory.

6. Conclusions

In this work, we argue that every scientific theory belongs to one out of two different kinds, which generalise what Flores labelled as interaction/framework theories. Our distinction rests on an epistemic criterion that emphasises causal links and explanations. We argue that any scientific theory that provides causal mechanistic explanations of phenomena is a generalised interaction theory; whereas the set of scientific theories that do not provide such types of explanations always play the role of a generalised framework, providing structural accounts of phenomena. Even though it is not a priori clear that these two sets are complementary, we found evidence for this to be the case. Irrespective of this, our criterion represents a clear generalisation of Einstein's and Flores’ ideas beyond the realm of fundamental physics, thus embracing a more pluralistic view of science, epistemology, and potentially metaphysics.

The ingredients we use for our classification are then the epistemic conclusions stemming from Flores’ classification, the ongoing discussion on the nature of scientific theories, the discussion between Salmon, Kitcher and Friedman on the nature of scientific explanation, the modern ideas on mechanistic causal explanations, and some bare-bones assumptions about the regularity of nature. Put together, these show that it is reasonable to try to classify scientific theories as belonging either to the framework (structural) or to the interaction (mechanistic) kind.

In complex explanations where both types of theories are involved, the mechanistic steps are filled by interaction theories, whereas the holes in the mechanistic explanations are filled by the constraints belonging to structural theories. A tell-tale sign of a mechanistic theory is the existence of agents that participate in the interactions that allow for causal tracing–when no agents are present, the explanation must depend on structural factors.

By standing on top of a modern account of mechanisms as the basis for our criterion, we can extend the ideas of Einstein and Flores to the realm of non-fundamental science. The structural ‘frameworks’ of chemistry or biology are not all-encompassing, and our mechanistic criterion opens the door for the classification to work also in these cases. Conversely, fundamental interactions such as electromagnetism can play the role of framing other theories without ceasing to provide mechanistic explanations, which implies that in these cases our epistemic criterion is more relevant than the functional one used by Flores. Thus, our classification gains in generality with respect to previous attempts.

Additionally, our focus on explanations allows us to discern strong indications of the exhaustiveness of the distinction. Based on arguments from theories of scientific explanation, scientific understanding, and on structural properties of scientific theories, we show how our current understanding on these topics leads us to see the distinction between mechanistic (or interaction) theories and structural (or framework) theories as complementary so that any scientific theory would necessarily belong to one of the two classes. Einstein's original proposal about a distinction between general principles and interacting entities reaches in this way its full potential, and a door opens for the analysis of science from the perspective brought about by this classification.

Our classification dissolves some problems in other philosophical arenas. For instance, in the new mechanicism literature there has been a certain struggle with the fact that some explanations in fundamental physics do not seem to be causal, opposing thus the universality of mechanical explanations (see, e.g. Kuhlmann and Glennan 2014; also, Felline 2021). Notice that this is completely normal from the point of view of some theories being mechanistic and some theories being structural.

As the framework/interaction (or mechanistic/structural) distinction implies different ontological commitments, different approaches to explanation, and different functional roles of theories, to take the distinction seriously implies embracing some kind of pluralism regarding the problem of explanations in philosophy, and a selective form of scientific realism. We do not see a difficulty in this, since this adjusts to the diversity of the scientific endeavour, both in the face of the different nature of scientific theories and of the diversity of scientific disciplines. We expect to develop these ideas further in future works.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by CONICET; Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung.

Notes

1 In Flores words: ‘ … all principle theories are framework theories and vice versa; all constructive theories are interaction theories but not vice versa. Thus, Einstein's distinction is a ‘special case’ of the distinction I have introduced’. (Flores 1999, 129).

2 An example of this can be found in (Romero-Maltrana, Benitez, and Soto 2018), where an argument based on the framework/interaction distinction is put forward, favouring particles over fields as the fundamental objects in nature.

3 See Russo and Williamson (2007), Williamson (2011), Russo and Williamson (2011), Psillos and Ioannidis (2019) for more details on the debates around the mechanistic and difference-making approaches.

4 Remember that Salmon's conception of mechanism is more stringent than ours.

5 There are people that prefer to talk about activities instead of interactions (see Machamer, Darden, and Craver 2000), however, they define activities as ‘the producer of change’, which is precisely what we have in mind when talking about interactions. Briefly, objects are detected because they interact with detectors, changing the state of the detector to some degree. In this fundamental sense, interactions are the producers of observable change.

6 Note, however, that if the law inside the nomological model corresponds to an interaction law, then it provides bottom-up explanations.

7 In the philosophical literature we also find the pragmatic theories of explanation, which incorporate some additional elements such as certain psychological characteristics (e.g., interests or beliefs) of the rational agents involved in the explanations, and the context in which the explanation is made. We affirm that even explanations of this type can be categorised as top-down or bottom-up, since pragmatic explanations maintain the structure of traditional explanations while adding some psychological elements such as those mentioned above.

8 Flores explicitly claims: ‘ … from the physical principles that constitute a framework theory one can only derive other laws which must be satisfied by all physical processes.’ (…) ‘whenever one has a result that applies to any physical process whatsoever, one should look for a derivation at the level of the framework theory’ (Flores 1999, 132–133, emphasis in the original).