What is a physical theory? Philosophers do have an answer by distinguishing two forms of empirical adequacy

In brief, by ontological clarity I mean the semantic virtue of a theory of being clear with respect to what it says about the possible world in which it is the case. This means that, according to this condition, the referents of theoretical terms (together with predicates’ extensions) must be assigned by the theory through a well-defined ontology that has no considerable traces of semantic ambiguity. In this way, ontological clarity is a possessed virtue of some scientific theories to be unveiled by a philosophical analysis, in the sense that there are theories that satisfy (or do not satisfy) such a virtue independently from the philosopher’s will. Let us make three important remarks concerning this virtue.

Firstly, the definition of a theoretical virtue, such as ontological clarity, is not immune to further concerns associated with its normative and regulative nature: How much clarity one needs? How ontological clarity is interpreted among different theories? As is the case for any kind of theoretical virtue, ontological clarity is immanent and contextual in the sense that it is highly dependent on the kind of ontology posited by a given scientific theory, apart from the fact that there is no unique way to specify in any particular situation the precise conditions for this virtue to be satisfied. For example, some people committed with other theoretical virtues, such as simplicity, expect that some theory satisfies ontological clarity if the associated ontology is only constituted by a minimum set of theoretical posits indispensable to explain and predict the relevant phenomena, whilst others think that this theory should go deeper and characterize the metaphysical natures of such posits at the price of positing a more robust and a less simple ontology. This normative character of ontological clarity is a reflection of the fact that the way scientific realism is defined depends on a ‘second-order’ conceptual framework where regulative and normative claims are involved, such as simplicity or (metaphysical) strength. Although these claims form part of an important element to be considered, it is important to reiterate that in this contribution our focus relies on the constitutive dimension of scientific theories.

Secondly, considering the above ‘constitutive’ definition of ontological clarity, let us stress the association of this criterion with the semantic component of scientific realism. As corroborated by a proper reading of (van Fraassen, 1980), ontological clarity is, in part, a necessary condition for the semantic component because it is a condition that makes literal interpretations possible. In van Fraassen words: “a literal construal of a theory can elaborate by identifying what theoretical terms designate”, provided that “on a literal construal, the apparent statements of science really are statements, capable of being true or false (van Fraassen, 1980, p. 10).” Furthermore, ontological clarity is a virtue that makes the semantic component different from the epistemic component because a literal construal is not related to “our epistemic attitudes towards theories, nor to the aim we pursue in constructing theories, but only to the correct understanding of what a theory says” (van Fraassen, 1980, p. 11).

Finally, one might claim that the ontology of a scientific theory involved in the definition of ontological clarity not only includes the referents of theoretical terms (e.g., electrons, quarks, genes, and so on), but also certain one-place or many-place predicates satisfied by the extensions of those terms, such as their properties (e.g., charge, quark color, locus, and so on) and, specially, the corresponding laws of the theory. Although endorsed by many (but not all) scholars, the above claim presupposes the metaphysical assumption that the laws of nature are existing entities pertaining to the scientific world depicted by the theory in question. As such, they can be interpreted in the primitive, ‘theological’ or fundamental sense that they govern, determine or even produce the events of the world, enforcing the behavior of the referents of theoretical terms by means of necessitarian relations or primitive universals (Dretske, 1977; Armstrong, 1983; Tooley, 1977; Maudlin, 2007); but also they can be interpreted in the dispositional sense in which they prescribe the disposition of the alleged referents to behave in certain way (conceived of as governing powers) (Shoemaker, 1980; Mumford, 2004; Bird, 2005). However, we should take this claim with caution as it depends on a non-exclusive ontological view with respect to laws of nature. In contrast to this view, we can interpret laws in an eliminativist way as having no reason to believe they exist (Cartwright, 1983; van Fraassen, 1989; Giere, 1999); alternatively, we can interpret them in a descriptive ‘humean’ sense such that they are true generalizations that appropriately summarise the patterns displayed by a mosaic of events or matter of fact (Lewis, 1973; Loewer, 1996; Cohen & Callender, 2009; Bhogal, 2020). From this point of view, the laws of nature are non-fundamental, constructive elements arising from the fundamental ontology of the theory and, according to a particular humean account, from certain normative and regulative standards, such as simplicity and informative strength, associated with the way the theory develops.

According to NFEA, phenomena are not brute empirical facts of the actual world waiting to be explained by a conscious human being capable of accessing that part of the world through her best scientific theory. On the contrary, they are putative, theoretical explanations and predictions confined within a given scientific theory incapable of transcending the scope of the possible world in which such a theory is the case (where such a possible world is not necessarily the actual one). Thus, when talking about phenomena in the context of Newtonian gravitational theory we are not referring to regularities in the sky observed through the naked eye; instead, we have in mind something like immensely large particle aggregates in elliptical motion explained and predicted by Newton’s universal gravitational law, the worldview of which is no more that absolute space, external forces, point-wise particles without any external human mind capable of confirming the theory with an ingenious telescope. As such, phenomena are disassociated from the epistemological context of justification as they constrain the scope of the ‘empirical compartment’ of a theory (to be clarified below), irrespective of whether or not such phenomena are confirmed by available empirical facts in the actual world. More specifically, they serve as a reservoir of potential theoretical explanations and predictions to be actually confirmed in case there were someone capable of perceiving the actual world in some way or another. This means that in context of NFEA the phenomenological domain depends on what the theory allows to be in principle explained and predicted, independent of how we humans or any other agent assess that theory on the basis of their perceptive capabilities. Let us analyse this in more detail.

Many philosophers of empiricist spirit think of the phenomena of a scientific theory as constituted by empirical facts. Although these facts are normally interpreted as brute, self-standing elements that ultimately arise from a mind-independent world —as far as the metaphysical component of scientific realism is assumed—, they appear to us as concrete, available sense data, the structure of which is the result of a worldly-human process mediated by our perception system —sometimes called unaided sense perception. For example, the primary set of empirical facts that scientists usually read from their complicated measuring devices before any kind of systematisation process takes place is ultimately displayed in the form of some sensitive effects occurring in the manifested world, such as a ‘pointer’ heading in a certain direction. Thus, when the phenomena are interpreted as empirical facts, it seems that these phenomena are displayed in a form accessible through the human senses.

Moreover, in order to say something about empirical facts, they should be represented in some way or another. The way these facts are represented depends, of course, on an immanent representational framework capable of organising and conceptualising the available sense data. The nature of this representational framework depends, in turn, on the kind of knowledge that arises from such facts.

When ordinary people represent empirical facts —provided ordinary people are human agents with a well-functioning unaided sense perception—, the respective framework is associated with what is called perceptual knowledge.⁵⁵5For a recent comprehensive description of perceptual knowledge and its relation to scientific knowledge see (Teller, 2021). This framework organizes the available sense data in terms of certain useful and stock-in-trade concepts confined within the scope of everyday language. Although these concepts are associated with an imperfect, idealised framework incapable of capturing the nature of unaided sense perception in its full complexity, they are successfully used in everyday thinking and ordinary affairs of practical kind. For example, the motion of a $1m^{3}$-volume, grey, iron sphere in free fall is perceived by the eye as a temporal succession of extended positions possessed by a rigid object in physical space, and this sense perception is approximately represented by familiar concepts, such as “rigid object of spherical shape”, “volume”, “grey color”, “iron” and “temporal succession”. Although these concepts do not represent the perceptual situation in exact terms (as any real object of this kind is not perfectly spherical, grey and iron-made), they suffice to indicate us, for all practical purposes, that we are in the face of an acknowledgeable empirical fact.

However, the way scientific theories represent empirical facts depends on a completely different representational framework to that of everyday language. Coming back to the previous example, the iron sphere in free fall is represented by Newtonian theory (considering the appropriate idealisations and approximations) as a large configuration of point-wise particles (forming a composed spherical object of about $1m^{3}$ size), describing multiple integral curves of a vector field in a mathematical Euclidean space. As learnt from Susan Stebbing’s objection against Eddington’s famous two-tables tale, everyday language and scientific language should not be mixed; on the contrary, the framework associated with a scientific theory involves a conceptualisation of empirical facts that cannot be corrupted by the concepts used in everyday language.

Thus, once a given empirical fact is represented by a scientific theory independently of everyday language, some set of ‘empirical data’ is obtained. This resulting representation, constrained within the epistemic limits of the theory, are theoretical elements located in some region of its conceptual space. Where exactly they are located depends on the way we represent, at the metaphilosophical level, the complex structure of scientific theories. From the point of view of the orthodox version of the syntactic framework, empirical data are represented as synthetic propositions disassociated from the formal structure of the theory (i.e., analytical propositions), whist from the point of view of the (also orthodox) semantic approach, they form a family of data models (i.e., substructures contained in and related to other structures of the theory) that make ‘observable’ propositions of the theory true. Irrespective of the choice made among these alternative frameworks, they share the premise that within the limits of a certain theory there is a set of empirical data, distinguished from the rest of its elements, having the potential quality of representing the realm of empirical facts, in case such a theory were assessed through sense detection or experimentation.

But if we transcend the context of justification beyond the mere task of designing experiments to confirm the available explanations and predictions, and scientific theories are interpreted, in turn, as self-standing, conceptual constructions that take on a life of their own —through, for example, working hypotheses about a possible world whose true values are assumed to be irrelevant—, the question is whether or not some set of empirical data can still be distinguished from the rest of the elements contained in the theory. The answer, according to NFEA, is that there is in fact a distinguished set, which we shall call nomological phenomena (from here to the end of this section, let us just call it ‘phenomena’).

For example, Newtonian mechanics can be clearly formulated as a theory of interacting point-wise particles and external forces exerted upon them. But if these tiny, idealised particles interact with each together by creating complex mereological configurations sising at the scale of about $10^{-1}m$, and these configurations interact with other configurations of the same size scale, one may obtain phenomena having the potential of being qualitatively identical (at least approximately) to macroscopic objects, such as tables and chairs, whose macroscopic properties can be observed through the human senses. Note, however, that this mapping identity between a set of microscopic particles and macroscopic tables and chairs, directly observable by the naked eye, is an anthropocentric measure or reference external to the theory that is put by hand in order to confirm (though the mediation of our visual perceptual system) Newton’s theory predictions. Thus, it seems that if we are not interested in confirming Newton’s theory, the phenomena associated with this theory should be merely interpreted as theoretical elements, such as configurations of particles, whose aggregate properties obey certain effective principles or laws associated with rigid bodies (i.e., Euler’s laws of motion) different from (although compatible with) those that govern the individual particles.

The problem with NFEA’s answer is what makes the aforementioned distinction possible in case there are no available empirical facts arising from the actual world to be represented by the corresponding phenomena. Going back to the previous example, the problem is to identify without anything external to Newton’s theory the distinguishing qualities associated with the phenomena (i.e., configurations of particles and their aggregate properties governed by Euler’s laws of motion) that are not shared by the rest of the elements contained in the theory (e.g., individual particles, forces, Newton’s laws, etc.).

One well-known answer associated with constructivist empiricism is to the bite the bullet and postulate by fiat a fundamental epistemological distinction between observable and unobservable elements of the theory. The idea is to say that there are two kinds of claims and terms posited by scientific theories: observable claims together with observable terms (e.g., tables and chairs), on the one hand, and unobservable claims together with unobservable terms (e.g., electrons and quarks), on the other. The problem with this response is that (van Fraassen, 1980) is implicitly distinguishing observables from unobservables by means of an anthropocentric criterion that gives meaning to the observability of certain phenomena. In fact, according to him, what is observable is what is in principle observable by us (throughout our past, present and future), in the sense that observables claims and terms are empirical facts that appear to us as concrete, available sense data. In this way, (van Fraassen, 1980) ends up embracing something external to the theory (i.e., the way humans perceive the world), a situation which we have denied from the start in the context of NFEA.

Another answer is to deny that there is a fundamental epistemological distinction between observable and unobservable elements of the theory; in contrast, there is a distinction but of modal nature (similar to (Chakravartty, 2007)’ distinction between detection and auxiliary properties), in the sense that observable claims/terms (as opposed to unobservables) are theoretical elements with at least two potentially-based propensities that can be realised depending on certain conditions imposed by the actual world (and, therefore, external to the theory): either being qualitatively identical to some empirical facts —in case observable claims of the theory are true and observable terms are referring terms— or being qualitatively different to them —in case those claims are false and observable terms do not refer. Although the alleged propensities serve as distinguishing qualities by means of which one clearly differentiates observable from unobservable claims/terms, as long as we stay within the context of NFEA (where something external to the theory is neglected), these propensities shall remain in potentia without being actually realised in the way just described.

There is, however, one objection that can be raised against this response. The idea is that nothing within the theory allows us to introduce the alleged metaphysical propensities associated with the way observables claims/terms are distinguished and characterised. Since those propensities are introduced by contrasting the body of theoretical elements within the theory with the available empirical facts in the actual world, we are introducing fixed metaphysical commitments (and increasing the metaphysical baggage of the theory, in turn) based on empirical data that could change as our experimental and detection capabilities are improved. In other words, what distinguishes the observable claims/terms of the theory from the rest of its elements would be fixed, and this means that the theory would be incapable of bringing some unobservable theoretical elements to the space of observables, contrary to the evidence we have from the history of science.

Considering the above critical comments, we can suggest a better response if we focus our attention to the actual process through which scientific theories are discovered. This response is based on the observation that any theoretical construction, such as a scientific theory, ultimately originates from sense data, even if it is later considered as an immanent body of working hypotheses and empirical data incapable of transcending the scope of the possible world in which such a theoretical construction is the case. As nicely claimed by Whitehead, “The true method of discovery is like the flight of an aeroplane. It starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalisation; and it again lands for renewed observation rendered acute by rational interpretation” (Whitehead, 1929, p. 5). In this way, at a given early stage during the development of scientific theories, there are some empirical facts available from which certain working hypotheses arise. For example, by a process of abductive reasoning one may be able to perceive certain evidence and try to explain that evidence in terms of some possible conjecture or hypothesis. Once the resulting hypotheses are settled, one may dispense from the empirical facts that served to produce them and only retain the theoretical counterparts of such facts, which we have called the phenomena (i.e., theoretical representations of worldly empirical facts). However, the way the theory has being constructed, according to this reasoning, involves a complex inner structure (i.e., either a hierarchical or model-based structure depending on the metaphilosophical framework endorsed) where the phenomena of the theory are distinguished from the corresponding hypotheses and the rest of theoretical elements. The available empirical facts in the actual world is like the plastic mold used to produce some shapes when cooking some cookies: once their shapes are formed, one can dispense from the mold and the cookies retain their form. In this case, the preserved form is precisely the structure that codifies the distinction between the phenomena and the rest of the theory’s elements. Thus, it seems that the phenomena can be identified and distinguished from other elements of scientific theories based on the way these theories are discovered.

Let us come back to the previous Newtonian example to explain the proposed response. Newton’s theory was discovered, in part, through regular observations of a multiplicity of empirical facts, such as Galileo’s famous experiments or the precise experimental data obtained by Tycho Brahe. Once the laws of Newton were established, together with other theoretical elements (e.g., absolute space, Newtonian forces, Newtonian particles, etc.), the theory was completed as we approximately know it today. More specifically, it turned out to be a selfstanding body of working hypotheses that could be disassociated from the above empirical facts and generate a multiplicity of nomological possibilities independent of these facts, such as idealised friction-free models of inertial motion. Note that from the immanent standpoint of the completed theory, the phenomena that initially represented the available empirical facts as observed through our senses, such as the real motion of a 10-cm-diameter iron ball moving down an inclined wood plane, were (strictly speaking) no more than configurations of particles whose aggregate properties obey Euler’s laws of motion. However, the ‘mold’ left by the Newtonian explanation of the actual iron ball’s motion in terms of the ontology of the theory (and, therefore, the distinction between microscopic particles and macroscopic rigid bodies) did not evaporate; rather, it was preserved to the extent that the physics of rigid bodies emerged as an effective theory of large configurations of particles, each of which obeys Newton’s laws.

This alternative response opens the possibility of having a distinction which is not epistemologically fundamental, as van Fraassen claims, but does not have to increase the metaphysical baggage of the theory at the price of drawing a once-and-for-all distinction, as the modal response seems to suggest. Rather, it is a relativised distinction, defined with respect to a certain stage of knowledge, that can change as scientific theories develop. From our point of view, what ultimately distinguishes the phenomena from the rest of the elements of a scientific theory are the multiple nomological possibilities generated by a family of working hypotheses compatible with some set of empirical facts available at a certain stage of knowledge. As a result, we endorse a nomological conception of the phenomena, the central role of which is to focus on the multiple possibilities of a theory to generate novel predictions and explanations independent of the epistemological task of confirming such predictions and explanations though the mediation of our sense perceptions.

This view is reinforced by the observation that scientific theories are more complex structures than sense-based machineries whose sole function is to represent empirical facts, as perceived by the human senses, in terms of a theoretical calculus. On the contrary, scientific theories frequently posit entities that generate and predict novel phenomena, some of which transcend the human-based domain of sense data. Thus, the phenomena may comprise not only empirical data that have been experimentally detected, but also scientifically possible data that cannot be (or have not been) displayed in a form accessible through the human senses. Illustrative examples are idealised models, such as friction-free inertial motion of point-wise particles (already mentioned above), and thought experiments seen throughout the history of science: without inquiring into the extensive literature on this issue, some of these experiments are phenomena that have not been experimentally detected, but are in principle detectable by any possible perceptual system capable to be described as any other constitutive element of a theory (whose properties supervene on some properties of such a theory). It follows from this last example that in the context of a given theory nomological phenomena are in principle detectable by any agent (human, non-human, or whatever entity or property) living in a possible world where such a theory is the case.

In his famous first chapter of Process and Reality, Alfred N. Whitehead defines ‘speculative philosophy’ as

“[…] the endeavor to frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted.” (Whitehead, 1929, p. 3)

provided this system is applicable and adequate with respect to its interpretation, in the sense that “some items of experience are thus interpretable” and that “there are no items of experience incapable of such interpretation.” (Whitehead, 1929, p. 3).

Inspired by pragmatist ideas of his time, Whitehead acknowledges that such an endeavor is never final, but it is an adventure in “the clarification of thought […] in which even partial success has importance” (Whitehead, 1929, p. 9). As a result, he is in some way committing himself to a fallible (but still objective) stance towards any system of philosophical ideas, where some pragmatic criteria associated with this system (i.e., coherence, logical consistency, generality, necessity, applicability and adequacy) should be satisfied, irrespective of whether or not it leads to objective true. According to this stance, these criteria are pragmatic as they are associated with immanent, contextual and normative standards defined with respect to a given stage of knowledge and confined within the limits of the empirical facts that are epistemically accessible at that stage (what he understands as the “system’s sphere of validity”). This is clear when Whitehead says that the alleged system “[…] is a matrix from which true propositions applicable to particular circumstances can be derived.” (Whitehead, 1929, p. 8). Contrary to objective truth, the aim of any philosophical theory is, according to him, the mere process of understanding, which is

“[…] never a completed static state of mind. It always bears the character of a process of penetration, incomplete and partial. …Of course in a sense, there is a completion. But it is a completion presupposing relation to some given undefined environment, imposing a perspective and awaiting exploration.” (Whitehead, 1938, p. 43).

Furthermore, he insists that we should refrain from committing ourselves to what he calls the ‘fallacy of misplaced concreteness’, which happens when one mistakes an abstract and working hypothesis about the way things are for concrete reality.

Considering these well-known observations, we would like to focus on Whitehead’s pragmatic notion of ‘experience’ (as part of his definition of a speculative scheme), as it retains the spirit of what we define as ‘phenomena’ in our definition of NFEA. Once this correspondence is established, we shall see that his notion of ‘interpretation’ is directly associated with our notion of ‘explanation’ (to be defined here in more precise terms), except from the fact that in the latter case the associated scheme is contextualised to scientific theories —as if it were the worldview depicted by a scientific theory. As a consequence of this association, we shall be able to motivate our definition of NFEA in terms of a reconceptualisation of Whitehead’s speculative scheme in the context of scientific theories.

As already said above, Whitehead sustains that the root of any system of philosophical ideas arises from a restricted set of available empirical facts. However, once this system is settled and takes on a life of its own, its functional role merely consists in the “clarification of thought” by constructing a theoretical edifice of working hypotheses and empirical data governed by the rules of logic and other pragmatic criteria. Analogous to the already established distinction between phenomena and other theoretical elements of a theory, Whitehead argues that this theoretical edifice has its rational side and its empirical side. The rational side is expressed by the regulative criteria of coherence and logical consistency, whilst the empirical side is expressed by those of applicability and adequacy. Furthermore, the relativised nature of such a distinction is also illustrated by Whitehead’s insistence that the rational and empirical sides are bound together by virtue of the fact that any coherent, logical and necessary system of general ideas located in the rational side should be applicable and adequate with respect to the empirical side, provided “the texture of observed experience, as illustrating the philosophic scheme, is such that all related experience must exhibit the same texture.” (Whitehead, 1929, p. 4). This quotation presupposes an interpretative-laden notion of experience that points towards the impossibility of perceiving brute empirical facts disassociated from the theoretical framework used to represent them; instead, all “elements of experience” conceptualize and represent the available empirical facts, provided they are immanently associated with a theory in an way that cannot be abstracted from it. In his own words:

“[…] there are no brute, self-contained matters of fact, capable of being understood apart from interpretation as an element in a system. […] Thus the understanding of the immediate brute fact requires its metaphysical interpretation as an item in a world with some systematic relation to it. When thought comes upon the scene, it finds the interpretations as matters of practice. Philosophy does not initiate interpretations. Its search for a rationalistic scheme is the search for more adequate criticism, and for more adequate justification, of the interpretations which we perforce employ. Our habitual experience is a complex of failure and success in the enterprise of interpretation. If we desire a record of uninterpreted experience, we must ask a stone to record its autobiography.” (Whitehead, 1929, p. 14-15)

Considering this observation in the context of scientific theories, it follows that Whitehead’s notion of experience can be nicely associated with the notion of nomological phenomena defined above. Along Whitehead’s lines, we are interpreting phenomena as distinguished elements of a theory capable of representing —in case such a theory is confirmed— some confined set of empirical facts in a way that illustrates and exhibits a possible world in which such a theory is the case. As he put it, “Every scientific memoir in its record of the ‘facts’ is shot through and through with interpretation.” (Whitehead, 1929, p. 15).

Granted this association, let us finally demonstrate how Whitehead’s notion of ‘interpretation’ directly motivates the notion of ‘explanation’ involved in the definition of NFEA. In so doing, let us remind the reader that the way scientific theories say something about the available empirical facts is by representing them in terms of some set of phenomena immanently incorporated into its theoretical edifice. However, when the worldview depicted by a scientific theory is regarded as an instantiation of a system of philosophical ideas concerning the world —provided some sort of naturalistic criterion towards philosophy is endorsed—, it is not hard to see that this notion of representation can be directly linked to Whitehead’s notion of interpretation, and since the latter can be conceived as explanatory in the ontological sense, it is therefore linked to a notion of metaphysical explanation. Let us inquire into some details of this claim.

By ‘interpretation’ Whitehead means “that everything of which we are conscious, as enjoyed, perceived, willed, or thought, shall have the character of a particular instance of the general scheme” (Whitehead, 1929, p. 3). Considering that “everything of which we are conscious, as enjoyed, perceived, willed, or thought” is associated with theoretical or perceptual representations of available empirical facts (and not with facts themselves), this quote seems to suggest that the task of interpreting these representations (which we have called ‘the phenomena’) can be associated with an ontological, albeit putative, notion of explanation (hereinafter, purported explanation), the role of which is to account for these phenomena, as explanandum, in terms of more fundamental principles or hypotheses, as explananda, immanently confined within the theoretical edifice of the theory in question. In more precise terms, this notion of purported explanation has to do with the metaphysical problem of accounting for how the the phenomena within a scientific theory are recovered from the fundamental ontology of that theory. This means that with the help of certain theoretical resources —and perhaps an ingenious metaphysical toolbox (e.g., supervenience, grounding and/or metaphysical dependence)— the empirical counterpart of the theory must be cashed out in terms of its underlying fundamental ontology, whose entities and qualities pertain to the possible world in which such a theory is the case. Let us finally make three important remarks concerning this purported notion of explanation.

Firstly, purported explanations involve a non-factive, pragmatic notion of explanation associated with the semantic component of scientific realism. To see why, let us remind the reader that this component requires that scientific theories should tell a literal story about the possible world in which these theories are the case. It follows from this requirement that this story is purportedly explanatory in the sense that it explains the phenomena in a way that some theoretical virtues are exhibited (e.g., ontological clarity, coherence, logical consistency, generality, necessity, applicability and adequacy) although it could be wrong. In other words, purported (as opposed to factive) explanations of the phenomena are putative propositions capable of ensuring predictive success on account of the ontology of the theory, without being compromised with their truth values.

Secondly, purported explanations are interpretative-dependent. This is clear when one associates this notion of explanation with the metaphysical problem of accounting for the phenomena in terms of the ontology of the theory. Associated in this way, the ontological clarity criterion is a necessary condition for having purported explanations as the ontology of the theory must be clearly specified before indicating the way this ontology recovers the observed phenomena. If a precise ontology is not specified, there is no way to tell a literal story of how the scientific world is according to this theory.

Finally, our third remark has to do with the universality ascribed to this purported notion of explanation. As argued by Whitehead, “[…] the philosophic scheme should be ‘necessary’, in the sense of bearing in itself its own warrant of universality throughout all experience” (Whitehead, 1929, p. 4). And based on this claim, he later concludes that ‘[…] The metaphysical first principles [associated with this scheme] can never fail of exemplification” (Whitehead, 1929, p. 4). In this way, the notion of purported explanation involves a criterion of universality according to which the nomological phenomena explained by a theory is like a hologram, where each point of it exemplifies the whole theory and its fundamental laws and principles. For example, when planetary motions are interpreted by Newton’s worldview, they are conceived as phenomena governed by the same laws and principles to that of an idealised ball in friction-free inertial motion. In this way, we say that the idealised ball’s behavior exemplifies the underlying laws and principles of the Newtonian universe.

As opposed to nomological phenomena, empirical facts are constitutive elements of the actual world displayed in a form accessible through the human senses. Considering that a comprehensive definition of ‘empirical facts’ has been already established (as it was required to arrive at the notion of nomological phenomena), we only wish to mention the most important elements associated with it. Indeed, by empirical facts we mean those parts of the actual world which are epistemically accessible by some living agent capable of perceiving that world in some way or another. As such, empirical facts are necessarily associated with the epistemological context of justification as they form the epistemic basis of our scientific theories and rational beliefs. This means that, contrary to NFEA, the phenomenological domain does not depend on what a theory allows to be in principle explained and predicted, but on the way the actual world is and how we humans or any other agent assess that theory on the basis of their perceptive and detection capabilities.

As opposed to purported explanations defined above, FEA involves a factive notion of explanation the role of which to account for the phenomena by means of true propositions ensuring predictive success on account of what the actual world is really like. Defined in this way, factive explanations are associated with the epistemic component of scientific realism (as opposed to purported explanations, which are associated with the semantic one). Indeed, once we assume that the literal story told by scientific theories is approximately true, the notion of explanation changes from being pragmatic to being factual in the sense that this story involves true propositions, all of which are (part of) the reason why some empirical facts occur.

Furthermore, contrasted to purported explanations, this factive notion of explanation is neither interpretative-dependent nor universal. One the one hand, it is not dependent on the interpretation of the theory because it accounts for the available empirical facts in terms of true propositions concerning what the actual world is really like. As such, the ontology of the theory in terms of which empirical phenomena are explained is constituted by entities and qualities pertaining to the actual world, provided there is only one true and literal interpretation. On the other hand, it is not universal in the strict sense as it is not necessary with respect to all the phenomena associated with the theory in question; on the contrary, factive explanations contingently depend on what empirical facts are capable of being detected through unaided sense perception. For example, predictions obtained by the theory that cannot be detected by sense perception, such as friction-free inertial motion or certain thought experiments, are excluded from what we define as factive explanations. This means that factive explanations are confined to that which communicates with knowable, immediate matter of fact and excludes, therefore, scientifically possible data that cannot be (or have not been) displayed in a form accessible through the human senses. It follows that in the context of a given theory factive explanations account for empirical facts that are detectable by any agent with unaided sense perception living in the actual world.

As argued in the last section, the semantic and epistemic components of scientific realism are associated with certain criteria involved in the definition of NFEA and FEA, respectively. For sake of precision, however, let us again explain this association.

On the one hand, the semantic component is constitutively identified with NFEA for the following reasons. According to this component, scientific theories should be interpreted literally, provided they are clear with respect to what they say about the possible world in which they are the case (even though such a possible world might differ from the actual one). Defined as such, this semantic commitment can be directly linked to certain capability of our best scientific theories of purportedly explaining by means of a clear ontology the nomological phenomena associated with a possible world in which they are the case. The important point to be emphasised from this link is that, apart from the well-established notion of ontological clarity, the notions of explanation and phenomena involved in this definition of NFEA are interpreted in a particular way, leading to their compatibility with the semantic component of scientific realism. Indeed, we are talking here of nomological phenomena and purported explanations, both of which are defined as non-factive, pragmatic notions that are immanently associated with the theory in question, independently of its epistemic justification. As regards purported explanations, this means that they are not compromised with the question of truth but with satisfying certain pragmatic and regulative criteria, such as ontological clarity, coherence, logical consistency, generality, necessity, applicability and adequacy.

On the other hand, the epistemic component is constitutively identified with FEA for other reasons. According to this component, scientific theories should not only be interpreted literally but also factually, in the sense that their posited theoretical terms refer to existing entities of the actual world, provided what these theories say about this world is approximately true. Defined as such, this epistemic commitment can be directly linked to certain capability of our best scientific theories of factually explaining by means of a clear ontology the available empirical facts associated with the actual world. As above, the important point to be emphasised from this link is that, apart from the well-established notion of ontological clarity, the notions of explanation and phenomena involved in this definition of FEA are interpreted in a particular way, leading to their compatibility with the epistemic component of scientific realism. Indeed, we are talking here of empirical facts (as opposed to phenomena) and factive (as opposed to purported) explanations. In contrast to NFEA, both notions are associated with the context of epistemic justification and, therefore, they are compromised with the question of truth. In particular, empirical facts are regarded as brute, contingent facts of the actual world epistemically accessible by means of unaided sense perception, whilst factive explanations are true propositions accounting for the available empirical facts.

Let us note, however, that the commitment to the epistemic component of scientific realism involves the necessary commitment to the semantic one. Indeed, although literal interpretations are not the same as true interpretations, it is necessary to have a literal, clear and empirically adequate interpretation of a theory just to specify its true values. Thus, the semantic component is a necessary (but non-sufficient) condition for the epistemic component. Furthermore, since fully-fledged scientific realism necessarily assumes the metaphysical, semantic and epistemic components, it follows from the above observation that endorsing the epistemic component is the same as endorsing fully-fledged scientific realism. In the context of the previous discussion, this means that if the epistemic component is identified with FEA, it turns out that fully-fledged scientific realism can also be identified with FEA.

Considering that the semantic component of scientific realism is constitutively identified with NFEA and fully-fledged scientific realism with FEA, let us see how these identifications serve us to locate Maudlin’s definition of a physical theory in the realism-antirealism context. As we shall see, this philosophical contextualisation opposes Maudlin’s foundational view; instead, it endorses an alternative view in which the task of doing foundations and the task of doing philosophy are intertwined.

It is clear from the above discussion that Maudlin’s canonical definition of a physical theory already presupposes some philosophical commitments shared by the semantic component of scientific realism. As we shall see, these commitments are precisely those involved in the definition of NFEA.

Let us recall that, according to Maudlin, physics can be canonically defined as the most general account of what there is and what it does, at the fundamental level of physical reality. This definition is, of course, related to the semantic component of scientific realism as it embraces a commitment to ontological clarity and other criteria associated with a literal interpretation that takes scientific theories at face-value. In more precise terms, behind Mauldin’s definition there is a commitment to clearly posit entities (i.e., local and non-local beables) that behave according to some preestablished rules (i.e., probabilistic or deterministic physical principles and laws), the physical form of which are trajectories traveling through space-time. Granted this observation, let us see how Maudlin’s definition is associated with our definition of NFEA.

First of all, the criterion of ontological clarity is clearly endorsed by Maudlin’s definition as it embraces the requirement of any physical theory to posit a clear and well-defined ontology in terms of which the referents of theoretical terms (together with predicates’ extensions) are assigned. One might argue that Maudlin is assuming in his definition not only the requirement of being clear with respect to the ontology of the theory, but also the task of settling its dynamics through the postulation of a set of fundamental laws in terms of which the ontology evolves. If this were the case, one might argue that there is in fact some difference between his definition and NFEA. However, although not explicitly expressed in (Maudlin, 2018, 2019), we have already mentioned above (when characterising the notion of ontological clarity in the realist context) that Maudlin’s ontological view towards natural laws involves the assumption that the ontology of the theory not only comprises the referents of theoretical terms but also certain many-place predicates satisfied by the extensions of those terms, such as its fundamental laws. In this way, the fundamental principles and laws can be said to be part of the ontology of the theory, rendering the association between his definition and NFEA well-suited (at least, as far as the ontological clarity criterion is concerned).

Furthermore, Maudlin expands on the definition of ontological clarity in the context of physics by establishing the condition that any physical theory should provide a sharp mathematical description of the posited ontology, its dynamics and the corresponding space-time structure in which it is located. In his own words: “In presenting a clear and precisely articulated physical theory, then, one ought to specify the fundamental physical ontology and how the fundamental physical ontology is to be represented mathematically.” (Maudlin, 2018, 7). This presupposes, of course, a (frequently ignored) distinction between the alleged physical entities and their mathematical representation. Granted this distinction, the way physical theories provide this mathematical description depends on what Maudlin calls ‘a commentary’, which merely consists in relating by means of appropriate approximations and idealisations the mathematical representation to the represented physical entities. These approximations and idealisations are, in his own terminology, mathematical fictions employed for certain practical purposes associated with the alleged representation, such as calculating predictions. Considering that there is no canonical way for establishing such a relation, this commentary should make clear whether or not the mathematical objects representing the physical system in question denote something in the physical world, and if they do, what kind of entities they are supposed to be denoting. In his own words, the alleged commentary clarifies which mathematical degrees of freedom correspond to the represented physical system and which rather are ‘gauge’, in the sense that have no physical counterpart in the degrees of freedom of the represented system (i.e., they form surplus mathematical structure).

Secondly, the phenomena associated with any physical theory is, according to Maudlin’s definition, physical events occurring in space-time. Indeed, the phenomena in this case are not associated with empirical facts perceived through unaided sense perception but with space-time trajectories predicted by the physical theory. Of course, a single space-time trajectory is not sufficient to obtain the phenomena associated with any physical theory; rather, there must be a considerable number of space-time trajectories all of which compose a rigid space-time object of the order of about $10^{-1}$ m (in the spatial dimension), provided this object obeys certain effective principles and laws that equally apply in the classical and macroscopic domain of unaided sense perception. Of course, the way each these effective principles and laws arise from the dynamics of the multiple trajectories shall depend on the theory in question as it has to explain how they are recovered from actual laws and principles obeyed by the posited ontology. This is the requirement presupposed by a purported notion of explanation, as we shall see next.

Thirdly, the notion of explanation presupposed by Maudlin’s definition is associated with the capability of physical theories of purportedly explaining by means of a clear fundamental ontology the phenomena associated with complex compounds of space-time trajectories. These phenomena are, in his own terminology, derivative ontology, which mainly comprise physically-possible entities composed of more fundamental entities. As such, phenomena are physically real entities, according to the possible world in which the theory is the case, but they are not fundamental as they are definable in terms of the fundamental ontology and its dynamics. Furthermore, the effective principles and laws that apply to the phenomena are sui generis in the sense that their predictive effectiveness are explained by means of fundamental laws. After all, fundamental laws do not influence the phenomena as such but the fundamental entities in terms of which these phenomena are composed. In more precise terms, there can be no fundamental physical laws that refer to composed entities whose qualities are identical to classical and macroscopic objects accessible through unaided sense perception; on the contrary, fundamental laws refer to trajectories in space-time, whilst effective laws refer to complex compounds of these trajectories.

Let us finally propose a general definition of a physical theory based on this philosophical contextualisation of Maudlin’s work but which broadens its scope in a way that can be applied to any theory of this kind.

Considering the above link between Maudlin’s definition of a physical theory and our definition of NFEA, let us note that this link is not symmetric. Although Maudlin’s definition implies NFEA, the converse is not true. This is because his definition of a physical theory does not exhaust all possibilities associated with all ever-known physical theories. As already said above, local beables are, according to him, associated with a concept of ‘matter in motion’ whose main feature is to be located in regions of space-time in the form of well-defined trajectories. However, this is not entirely true for posited entities in general as there can be space-time entities without having trajectories (e.g., physical fields, distributions of mass, and so on), something which he surely acknowledges, or entities that are not defined in space-time (e.g., events and causal relations in causal set theory).

Under these circumstances, instead of endorsing Maudlin’s definition of a physical theory, we prefer to endorse the one associated with NFEA. The advantage of endorsing the latter is that it is a more general definition that embraces not only the above theoretical possibilities but that can be applied to any past, present and future physical theory capable of positing a clear and well-defined ontology in terms of which the phenomena associated with that theory are explained. Although the notions of ontological clarity, purported explanation and nomological phenomena involved in NFEA are dependent on the stage of knowledge associated with the theory, the definition of NFEA itself does not depend on such epistemic contingencies. On the contrary, it is an objective definition that applies to any physical theory that have been (and will be) developed, irrespective of any historical revision we could have with respect to already-established physical theories.