1.

What is there in the world, and what is it like? Any generally naturalistic view tells us that the answers to those questions can be found only by consulting our best available science. Science posits entities and their features in order to explain the observable facts of the world. Whatever the methods of science are, they represent the best methods known to us to work our way out of the only direct evidence we have for how things are, our empirical data, into a general understanding of how things are that explains why the empirical data is as it is. Our inferences to “best explanations,” whatever such inferences are like, is, surely, our optimal inferential route to inferring our believed ontology for the world.

There are, of course, many reasons to be skeptical of these proposals. One might have some kind of generally anti-naturalistic perspective that places no confidence in science or its methods at all. Or one might claim that the conclusions of science are replete with arbitrariness. One might, for example, argue that scientific decision making is historically infected with numerous cases where a scientific decision went one way that could have gone in some other direction. So that our current best theory would, then, be full of arbitrariness. Perhaps scientific decisions are culturally engendered and, therefore, at best “perspectival.” Or, perhaps, purely “internal” arbitrariness, a kind of “free choice” within the methods of science itself and independent of any kind of more general contextual “bias” might have led us in one direction when other, equally suitable directions as far as the data and the internal methods of scientific theory choice were concerned, might have been followed.

Even if you think current theory is not infected with such arbitrariness, you might still be very dubious that our best theory to date ought to guide our deep ontological beliefs. After all, how long can one expect our current best theory to remain the accepted scientific doctrine? At this point the skeptic that our current science should be taken as a guide to what is in the world and what it is like will remind us of the long history of one theory after another being overthrown by some successor theory in the history of science. Then we will be presented with all the usual arguments to the effect that even taking our theory as some sort of approximate guide to the nature of the real world is dubious, given the radical changes that have occurred in posited ontologies as one theory is rejected and a successor takes its place. And here we may also get the familiar arguments that there isn't even any reasonable sense in which there is some kind of “convergence” over time in theoretical posits that could at least give us a view of the correct ontology as that posited by science in some methodological limit.

But put all these skeptical arguments to the side. The skepticism that I am concerned with here is one that will still be present even if we put on hold any doubts about the unique “bestness” of our current theory, and any doubts about its survival as an accepted theory over time.

Can we really explain what goes on in the world by using the principles of our best available foundational scientific theories? What is that theory? Well, relativistic quantum field theory I suppose. But can we use relativistic quantum field theory to explain how an internal combustion engine works, or why sunflowers turn toward the sun, or why borderline personalities are afflicted with paranoid personality traits? It seems that we cannot.

One response to this demonstrable inability to really account for what goes on in the world by using our foundational theories in most of the contexts in which we seek for explanation is to focus attention on the place played by idealization in our scientific explanatory structures. While we cannot actually account for the behavior of ordinary things by using fundamental theories, perhaps we can account for the behavior of “models” of those ordinary things—idealized, abstract structures whose behavior does fall within the realm of that which can be accounted for by the fundamental physics and whose structure bears some relationship of “partial similarity” to the actual structure of the real systems whose behavior is too “messy” to be dealt with by the fundamental theory.

Observations such as these sometimes lead to the view that the laws of the fundamental theories are “false” of real systems, being true only of the idealized models of them. Or to the view that these laws must always be understood as having implicit “ceteris paribus” clauses attached to them, clauses which state the applicability of the law only subject to certain conditions being met, where this stipulation of conditions of applicability has a vague and open-ended character that makes it impossible for us to ever state the truly applicable law in closed, explicit form.

Now such an account may work for some of the real systems whose description escapes our fundamental theory. Suppose our fundamental theory was classical mechanics. And suppose our real system was a guitar string. Then it does seem plausible that we could characterize the relationship between fundamental theory and real system by using the language of idealized models, degrees of partial similarity, and the invocation of notions of “ceteris paribus.”

The idealized model of the guitar string is the simple harmonic oscillator, an abstract model perfectly well characterized within our fundamental theory. The guitar string isn't truly such an oscillator, but for many predictive and explanatory purposes it is close enough to such a system in some of its important respects that revealing its partial similarity to the ideal model will serve to show how the fundamental theory can be explanatory of the real system's behavior.

But deeper reflection on how things “really are” in the world of scientific explanation shows us that even this modified version of how foundational theories might serve as the explanatory basis for the behavior of real systems cannot be true to the real world of things and their explanations that we encounter in real science.

Why does the sunflower turn toward the sun? Assume that our foundational theory is relativistic quantum field theory. What sort of model of the sunflower situation could we construct, a model to which relativistic quantum field theory could be directly applied, and a model that would bear sufficient similarity to the real sunflower system that explanation could be carried to the real system by means of its partial similarities to the model? There is no such model. We don't even have a clear idea of how such a model could be constructed.

Indeed, our foundational theories are not invoked at all when explanations of such floral behavior are requested and when they are provided. What do our explanations look like when we explain the behavior of sunflowers, or obsessive-compulsive individuals, or socialist economies, or for that matter such purely “physical” systems as flowing water or an internal combustion engine? Do we see in the explanations we offer for such phenomena any reference to relativistic quantum fields, or quarks, or d-branes, or any of the other recherché entities with their strange, abstract properties that are the ontological commitments of current best foundational physical theories? We do not.

Our explanatory system in science is multifarious and diverse. Here we may use reference to plant cells and biological photo-receptors, there we may refer to unconscious anxieties or feelings of guilt. Somewhere else we may be talking about ordinal subjective utilities. Even in the physical cases it is often blocks of fluid or connecting rods we are talking about, not quantum fields or bosonic strings. Our explanatory structure is “dappled,” to use the piquant term of Nancy Cartwright. The “special sciences,” even the very general special sciences such as chemistry, biology, or the real physics of the macroscopic world, each have their own explanatory structures, invoking their own explanatory general principles or laws, to account for the phenomena within their domain.

But if our explanatory structure in science is “dappled,” a collection of individual and distinct different explanatory modes each with its own collection of referred to entities and properties, and if our best scientific explanation is to be our guide to our ontological commitments, then why not take our best scientific ontology as “dappled” as well? Why assume that the ontology demanded by foundational physics in those limited realms where it can really be applied for explanation and prediction is a universal structure for the world? Why not allow for a world with a wide diversity of ontologies? Why not take each portion of our grab-bag of explanatory principles as guiding us to the ontology of the realm where that portion of the collection of diverse explanatory and predictive modes is genuinely applicable?

Now there are, of course, other reasons why one might be skeptical of a claim to ontological universality for some posited fundamental physical theory. Exaggerated claims of being on the brink of discovering a “theory of everything” by the practitioners of one speculative and empirically unconfirmed project after another for a unified foundational physics are to be treated with skepticism, to be sure. And we have those special features of the world where, no matter what the foundational physics is like, some have often been skeptical that the features in question can really fall into the domain accounted for by that physics. How could phenomenal mental states, visual appearances and pains, for example, possibly be fitted into a world described by physics? Such is one part of the “mind-body” problem from the seventeenth century onward.

But these are not the grounds for skepticism of “the imperial pretensions of foundational physics” with which we are concerned. Does the seemingly ineliminable plurality of explanatory schemes imply a plurality of ontologies as well? Or is a uniform account of the ontology of the world as being the kind of world described by fundamental physics compatible with as much plurality of method as one likes?

2.

First let us all agree that the explanatory and predictive methods of science do, indeed, constitute a diverse plurality. The generalizations we invoke for explanation and prediction in sociology, anthropology, linguistics, evolutionary biology, and even in chemistry for the most part, are not the principles invoked in our foundational physics. Even in the realm of physics itself, most of our explanations are not framed in terms of the laws of the foundational theories. When we predict the behavior of falling rocks, moving fluids, or energy transforming steam engines we don't use relativistic quantum field theory. We use instead the Newtonian theory of rigid bodies, hydrodynamics, or thermodynamics.

And the multiple explanatory schemes each carry their own posited ontology: manifest and latent social functions, genes and mitochondria, rocks and continuous fluids. These are the entities referred to in our “special” sciences—not bosonic and fermionic fields, much less supersymmetric strings or d-branes.

Why are our predictive-explanatory schemes so diverse? Well it is a fact about the world in which we live that it is open to scientific understanding, and that this understanding, which demands the subsumption of individual facts under regularities, comes in a variety of forms. That many special sciences can exist, that each special science requires its own conceptual framework with which to characterize the features of the world relevant to that science, and that each such science can discover its own set of regularities appropriate to its domain of explanation and prediction, is something we discover to be true of our world. Within those special sciences, of course, it remains true that the regularities in question are applicable only modulo an only partially explicit set of background conditions holding, and it remains true that the usefulness of the laws of the special sciences is itself moderated by means of models and idealization.

It is also true, as those skeptical of a universalist foundational science often remind us, that without the discovery of the domain specific, “phenomenological,” laws of the special sciences, we would never have been able to discover the appropriate concepts and laws of the foundational physical science. Nor, they also emphasize correctly, would we be able to apply those foundational laws to particular cases without making use of the phenomenological principles to characterize the conditions of those experimental situations in which we use the foundational principles to make predictions and explanations, and which count as the fundamental testing cases for the adequacy of the foundational theory.

But what are the legitimate conclusions that can be drawn about ontology from this admitted methodological pluralism? The foundational laws can be applied for explanatory and predictive purposes only in a limited domain of the world. Even allowing for idealization, allowing for the laws to hold exactly only of abstract models of the real situations, we can use the concepts and laws of foundational physics only in those highly constructed situations of the experimental laboratory. Only when we are dealing with small numbers of elementary particles, say, and only when these particles have been with enormous effort isolated from interference with their behavior by the outside world, can we really apply relativistic quantum field theory to predict how they will behave and to explain that behavior. But do we have reason to infer from that that the ontology described by that foundational theory is not a universal ontology for the world as a whole? Or should we, instead, make just such a universalizing inference?

We do, of course, speak of flowing fluids as continuous media, say. And it is certainly true that if they really are such things, where ‘continuous’ really means just that in its fullest sense, they cannot be the sorts of things described by the foundational physical theory. There is no question that our pluralistic explanatory scheme often speaks of portions of the world “as if” they were so constituted that they just couldn't have the constitution that foundational physics would ascribe to them. But there is more than one way of understanding this situation. We might take it that it really is the case that foundational physics is a domain-limited theory whose universalizing pretensions are illegitimate. Or, rather, we might take it that some of these “special” ontologies of the phenomenological sciences are to be understood not as meant to characterize “how things are” at all, but to serve as “useful fictions” in some sense. Which view is the more plausible?

3.

Prior to exploring the claims to universality of domain of foundational physics, we might first note that any program that takes plurality of conceptualization and method to entail plurality of ontology must be one of some delicacy. Certainly no one could maintain that we ought to think of each and every mode of conceptualization and explanation applied to a system as genuinely characterizing “what that system is really like.”

Many physical systems are usefully described by a variety of conceptual schemes that are incompatible with one another. If a metal object is spinning in a force field, and if all one cares about is its gross dynamical behavior, it may be useful to characterize that system as a perfectly rigid body. But if one is concerned with how the system will actually show small distortions in its shape as the dynamical forces applied to it vary, we may, instead think of the system as not rigid at all, but as made up of discrete elements joined by binding forces.

Any suggestion that we ought naively and straight-forwardly think of the multiple descriptive and explanatory schemes as applying to distinct systems will lead to a grotesque multiplication of entities that make the old “two tables” hypothesis seem innocuous! Better to understand that at least some of our conceptualizations are not meant to say “how things really are.” They are intended, rather, to present models of systems that are deliberately misrepresentative of the “true” state of affairs, but which are sufficiently similar to “how things are” for some predictive, and even genuinely explanatory, purposes.

Indeed, there will be those who would argue that every conceptualization is of this sort, and that there is no principled way of distinguishing conceptualization meant to represent how things really are with a system and those meant merely to describe “useful fictions” about the system. Indeed, those skeptical of the universal applicability to the world of foundational physics might very well be happy with such an approach. Of course if they are they might be thought of not as postulating a pluralistic ontology for the world in the sense a realist might espouse pluralism, but, rather some sort of “pragmatist” pluralism—whatever that might mean.

One thing is certain. The view that our explanatory schemes reveal to us our ontological commitments must take account of the possibility that an explanatory conceptualization might be meant to apply to a system in some way that is not naively realist. However one deals with this subtlety, though, the question will still be open: Are the pretensions of foundational physics to be a universal description of how everything is legitimate pretensions? Or, rather, does our inability to really use the concepts and laws of foundational physics to usefully describe and explain the behavior of all the systems of the world except the very special few that occur in the physicist's laboratory experiments cast grave doubt on the imperial pretensions of foundational physical theories? And is the plurality of methods of description and explanation that we find in science as it is really practiced evidence instead of some kind of genuine plurality of ontology in the world?

4.

How are we to determine if the characterization of a system within science is meant to describe the real system or if, instead, it is merely intended to provide a “useful fiction” that is meant to have predictive value but not to characterize how things “really are?” How are we to determine what is the intended or appropriate domain of applicability of a conceptual and explanatory scheme in science? How are we to determine if the domain of applicability of foundational physics is universal or is merely the very restricted domain in which it can actually be used to make predictions?

These questions can only be answered, I claim, by consulting the science itself. Issues of the manner in which concepts and putative laws are intended to deal with the world cannot be decided upon a priori by the methodologist. Science is replete both with schemes intended to truly characterize “how things are” and with other schemes intended only as knowingly false but useful models of the real situation. But only the science itself can do the job of explicating the intended purpose of its own descriptive and explanatory schemes.

Science does reveal many schemes that are intended to have applicability only within restricted domains of reality. Once again, however, it is only the science itself, not philosophy, that can tell us what the intended or reasonable restrictions on applicability of a descriptive and explanatory scheme is or should be. But science also at least seems to present us with schemes whose intended domain of applicability—not for “practical” predictive purposes but for telling us “how things really are”—is everything there is. And, once again, it is only the science itself that can show us how such a claim to universal applicability can be made, and being made how it can be justified. It can often be the case, of course, that at a given stage of scientific development, the question of whether some scheme should be meant as merely “phenomenological” or “false but useful,” or whether it should be thought of as at least on the road to the characterization of “how things really are,” can itself be a matter of scientific controversy.

Suppose the scientific justification for a claim of universality for foundational physics itself relies upon using a repertoire of phenomenological laws that have not been strictly derived from the foundational physics? Would such a justification of the universality claim then be justified? Once again, the answer can only come from “science itself.” Only a reliance on the content of science will allow us the resources to answer such a question.

One thing ought to be admitted at this point: The initial burden of proof in a debate about the universality of foundational physics is on those who make the universalist claims. The world initially appears to us diverse in content and in the regularity of its phenomena. It is a bold and striking claim that some one scientific scheme of concepts and laws is universal in its application. And such a claim requires a justification if it is to be believed. Later we shall see that at a certain point the burden of proof switches to those who would deny this universality for foundational physics. But at the beginning it is the universalist who must convince us that there is reason to accept his claims.

5.

What does the foundational physics look like that has the criticized universalist pretensions? We don't need the details, just an outline of what those structural features are that generate the claim of universality of domain.

One part of the foundational theory is dynamics. This part of physics will offer a theory of motion and its causes, or, more generally a theory that tells us how the structures of the world are related to one another over time—or, possibly, over regions of spacetime. The theoretical characterization of spacetime itself will be integral to the dynamics, since various aspects of spacetime (its symmetries whether global or local) will play a role in the fundamental dynamical principles (the conservation laws). The general dynamical theory will not of itself fully characterize change, since to make it work one must plug in an additional element. In Newtonian theory this might be the forces elements of nature exert on one another. In more contemporary theories it might be the form of the Hamiltonian (energy) function or of the Lagrangian, each determined by the structure of the elements of nature whose changes are in question.

The second part of the foundational theory will be a catalogue of what are taken to be the basic constituents of nature. These might be the elementary particles, or given the nature of quantum field theory the basic fields. Here the constituents are typically characterized by intrinsic parameters—rest mass, charge, spin, “color,” “flavor,” and so on. These attributions of basic features to the elementary entities play multiple roles. On the one hand they characterize how the entities will respond dynamically to the physical situation in which they find themselves. On the other hand they characterize the way in which the situation in which the entities find themselves will itself generate the causal features that determine the dynamic changes. Electric charge, for example, will play the role of passive charge for determining the effect of the electromagnetic field on the particle and also play the role of active charge in determining the causal effect the presence of the particle will have electromagnetically on other particles.

Of course with the current fundamental theory being quantum field theory, the old-fashioned separation of the dynamical theory from the specification of the basic elements of nature is not really possible. “Particles” as quanta of a field can serve simultaneously as elements of nature and representatives of causal interactions among those elements.

The foundational theory contains elements that deal with the problem of complex systems. How will a system made up of a number of the basic components of nature behave? One may need some principles that govern how forces combine, so that one has rules for stipulating how a number of particles that may interact pairwise by means of some force law will interact when more than two particles are involved. One might, for example, posit some linearity condition so that the forces among the particles in a pair remain the same even if the members of the pairs have entered into other interactions. Or there may be some principle for generating evolution-determining functions (Hamiltonians) for multiple particle systems. In the quantum mechanical case there will also be the subtle principles that tell us how wave-functions of multiple particle systems behave given the nature (boson or fermion) of the individual particles in the system.

But where in all of this do claims for universal applicability lie? Here one must invoke an additional element. This is the claim that all of the things of the world are composed of the elementary constituents described by the fundamental theory. It is because they believe that trees and rocks, stars and planets, monkeys and galaxies are made up out of the elementary particles that those who claim a universal domain for fundamental physics make such a claim.

The claim, of course, is not that one can expect to find useful predictions or illuminating explanations for the familiar behaviors of all of those things of the world by tracing out derivations from fundamental physics through the route of the composition of the macroscopic things out of their elementary constituents. That, admittedly, is not the way the pluralistic methodology of science works when real predictions and illuminating explanations for such objects are sought. The claim is, rather, that the concepts of the fundamental theory still are applicable “in principle” to complex, compound objects and that the laws of the fundamental theory are as true of these objects as they are of the carefully isolated systems of small numbers of particles constructed in the laboratory, for which the foundational concepts and laws do provide useful predictions and illuminating explanations.

If the foundational theory contains, as it does, principles governing how it can be legitimately applied to systems compounded out of any number of the fundamental constituents of the world whose dynamics it stipulates, and if we believe that there is a universal composition of the things of the world out of these constituents, then why shouldn't we believe that the domain of applicability of the foundational laws is universal?

6.

Now there certainly could be doubts founded upon some denial of the universal composition of things out of the basic constituents. The existence of mental states whose nature seems to find no place in the overall compositional structure of things, of sensory qualia in particular, casts doubt now, as it always has, on the truth of physicalism in general. And since the foundational physical principles never purport to govern anything but the realm of the physical world, the existence of qualia could very well be a ground for doubting the universality of their domain.

I suppose that late-nineteenth- and early-twentieth-century vitalists might also have had doubts about the universality of the foundational laws of physics based on doubts about the universality of compositionality. It is hard to know what was meant by “life force” or other versions of the claims to the effect that biological phenomena were outside the realm of physical explanation, but some claim to the effect that some element of a living thing was not “composed” of the elementary constituents of the world seems to be necessary for the antireductionist claims of the vitalists as they meant those claims.

But, as we noted earlier, those grounds for skepticism of the universality of the fundamental laws are not the grounds we are concerned with here. We are concerned, rather, with the skeptic who notes both our inability actually to use the foundational laws for predictive and explanatory purposes outside extremely limited laboratory situations and our ability to make predictions and offer explanations for the behavior of the systems outside the scope of foundational physics for these purposes by using autonomous conceptual schemes and lawlike regularities appropriate to the systems in question.

What can science itself tell us about the domain of applicability of its foundational laws, applicability not for “practical” purposes of prediction and explanation, but applicability in the sense of truly governing the behavior of a system. Suppose the system is one composed of a vast number of elementary constituents. And suppose that those constituents are related to one another in a manner that is highly complex. Suppose, indeed, that it would be both hopeless and pointless to try and deal with the system by means of foundational physics for predictive and explanatory purposes. What right, then, does “science itself” give us to think that the system is governed by the foundational laws?

Well, there are some relevant experiments. The foundational laws are quantum mechanical. Such laws demand the possibility of constructing systems that exist in the superposition of classically described states. Finding systems in such superposition states and demonstrating their superposition is easy for systems composed of a very small number of elementary particles and systems kept in ideal conditions. But we certainly don't see rocks and trees or, to use the famous Einstein-Schrödinger example, cats in superposition states. Why believe then that such a fundamental property of systems characterized by the foundational laws really can hold of macroscopic objects?

The experimenter seeks larger-scale superpositions than those commonly found in the laboratory. If photons, electrons, and neutrons can show the interference that reveals superposition, can we demonstrate interference using beams of whole atoms or molecules as well? Can we really construct macroscopically sized systems all of whose components are in the same degenerate lowest energy state predicted for bosonic particles by quantum statistical mechanics? The answer is now known to be affirmative. The demonstration of superposition between counter-rotating superconducting currents in SQUID rings, for example, is considered important as showing, once again, that superposition is not confined to the simplest systems but can be show to exist even in the macroscopic realm.

But, of course, it remains true that rocks, trees, and cats are dealt with by classical dynamics and not quantum mechanics for many predictive and explanatory purposes, and by quantum mechanics for none. So why should we believe the foundational quantum theory is true of them?

General attempts at relating the theoretical descriptions that are used for practical purposes in characterizing some domain of macroscopic systems to the theoretical descriptions within the purview of the foundational theories are more important than the limited range of experiments by which one tries to extend the possibility for practical demonstrations of prediction and explanation by the foundational theory to systems usually outside the range of practical applicability of that foundational theory,.

Our fundamental theories are relativistic. But we are usually perfectly satisfied with predictions and explanations of the dynamics of objects that utilize Newtonian dynamical laws. Our fundamental theories are quantum mechanical. But when we make our predictions and give our explanations of the behavior of macroscopic things it is rare indeed that we will have any interest in the strange possibilities of superpositions or of noncausal distant correlations that are so endemic to quantum mechanics. We are sure that our fundamental theory of light will involve its wave-like aspects of diffraction and interference. But for many purposes, say most aspects of ordinary lens design, we are happy to apply the geometric optics of the seventeenth century. Standard thermodynamics works like a charm when we design our heat engines, even if statistical mechanics tells us that it blatantly ignores such fundamental facts about the world as statistical fluctuations away from equilibrium.

But there are major programs of science itself that are specifically designed to account for the fact that we are so successful in meeting our aims of prediction and explanation when we use theories that the fundamental science tells us cannot possibly be really correct in the contexts in which they are applied.

These are the programs that seek for the true nature of the relationship between the theories we use “for practical purposes” and the foundational physical theories. Methodologists are well aware that this problem of “inter-theoretic reduction” is one of great subtlety. Simpleminded claims to the effect that the older “practical” theories can be simply derived from the newer foundational theories have been long understood to be too easy. But it is also true that radical claims of “incommensurability” that deny that anything useful can be said about the relations between these theories of a subsuming or explanatory sort are gravely misleading. There are explanatory relations between foundational theory and practical surrogate, but these relations vary from theory to theory and often can be discerned only through serious scientific and philosophical investigation.

Sometimes the relation of one theory to the other can be neatly characterized in terms of a limiting relationship governed by some parameter of the more fundamental theory. Such is the case between the Minkowski spacetime of special relativity and the Galilean (neo-Newtonian) spacetime of Newtonian dynamics. But in other cases naive hopes for such a simple “in the limit” relationship won't do. For example it is quite misleading to say that Newtonian theory falls out of quantum theory “in the limit as Planck's constant goes to zero.” Here the radical structural change from classical dynamics with its determinate particle trajectories to a quantum mechanics of “waves” of probabilities that can be superimposed upon one another makes the relation between the older and the newer theory one that requires a subtle and sometimes quite complex characterization.

Yet that doesn't mean that there is no possibility of finding out what the real structure of the quantum theory is that allows for an explanation, internal to that theory, of why it is that in the appropriate circumstances nonquantum concepts may be applicable and the earlier Newtonian laws useful for prediction and explanation. All the ongoing work on “decoherence” is designed to provide just such an account of why it is that we can “pretend” to live in a nonquantum world when, according to the foundational theory, we do not.

Now it is certainly true that in probing the relationship between the foundational theory and some higher-level, phenomenological theory one may need to work “from the top down.” Even taking limits into account, it may be well-nigh impossible from a practical standpoint to work upward from the foundational theory alone in establishing the connections between the theories. Sometimes the only fruitful procedure is to use the known laws of the upper level theory to discover the connections of those laws to those of the foundational theory. For example in trying to establish the connection between geometric optics and the underlying wave theory of physical optics it is sometimes the case that the only hope of success comes about by assuming various principles of geometric optics true and using these known truths to find the resources that will provide the insights into structures lying at the physical optical level that can connect the two theories together (Batterman Reference Batterman2002, chapter 6).

Again, in connecting thermodynamic descriptions with those of the more foundational statistical mechanics, it is often the case that one must first presuppose the truth of some thermodynamic description in order to be able to apply the statistical mechanical methods. Such is the case in the work of Chapman and Enskog in solving the Boltzmann equation (where a thermodynamic solution's existence is presupposed and the reduction is then used to calculate such values as the transport coefficients), and more generally in finding the right macroscopic parameters under which to place statistical distributions of microscopic conditions in nonequilibrium statistical mechanics (Sklar Reference Sklar1993, chapter 9).

So methodologically even in the cases where reduction of some sort is possible, one cannot expect to find simple, one-way derivations of phenomenological theory from foundational theory. But that in no way need vitiate the claim that the connections between the theories so established provide evidence of the truth of the claim that the foundational theory includes within its domain of applicability, as a describer of what things there are and how they are, all the things and features within the domain of the phenomenological theory. That the phenomenological theory might in practice be the only epistemic route into finding the connecting links between the theories doesn't in any way entail some autonomous ontological domain for its application.

The subtle and varied ways in which the phenomenological theories relate to the foundational are currently areas of intense interest within science. Some of the most important work deals with the way in which certain overall structures of the systems in question can determine “universal” features that are independent of much of what goes on at the foundational level. Renormalization group theory, for example, tells us that many system composed of large numbers of microscopic components will have features at the phenomenological level that depend primarily on the dimensions of the system and the degrees of freedom of the microscopic components, and on the details of the dynamic interactions of those components only to the extent that such dynamical interactions obey appropriate bounding principles—aren't long-range, for example, or don't diverge at short ranges (Batterman Reference Batterman2002, chapter 4).

Work of this kind can show us why systems apparently quite unlike one another when described at the foundational level can behave alike at the phenomenological level. So phase transitions in ferromagnetic systems can look like phase transitions of a more familiar thermodynamic sort, even though the spin couplings of the atoms in iron are quite unlike the van der Waals forces between atoms in gases and liquids.

In a way, then, this work shows us why it is that certain details of the foundational description of the system may be irrelevant to predicting and explaining its macroscopic behavior. But, once again, such work in no way tells us that the foundational laws do not truly apply to the systems in question. Indeed, if they didn't then one couldn't use the features of the foundational interactions that do matter in one's explanations or explain the irrelevance of the features that don't matter.

7.

But most of the special sciences are not like Newtonian dynamics, geometrical optics, thermodynamics, or renormalization group theory. Freudian personality theory has its concepts and regularities. So does the theory of cooperative games. So does ecological dynamics. Where is even the loosest connection to be found between the concepts and laws of these theories and those of foundational physics?

Much of the time there will be very little connection indeed. But why should there be? Often the very physical nature of the systems involved will play at best only a background role in the science, with the useful conceptualization leading to finding interesting predictive and explanatory relations depending on such things as the complexity of the systems and on various structural features of construction or operation that are characteristic of the systems in question. Finding the right concepts and the right laws will depend on observation and insight that has little or nothing to do with the ways in which the world is composed of its elementary particles or with the laws governing the interactions of those particles.

This is something we have all known for a long time. The special sciences are special and there is no hope, and no need, for deriving all of their concepts or all of their generalizations from foundational physics. But concepts such as “supervenience” became popular in the philosophy of science to cover just such cases. And it is the applicability, in the sense of truth, of foundational physics to such systems that our skeptic has denied. But it is hard to see any positive reason for such skepticism in the existence of these independent schemes of conceptualization and explanation.

Other ways of characterizing systems in our higher-level sciences do seem incompatible with foundational physics. If we treat a physical system as being a continuous fluid, we can't be at the same time treating it as made up of discrete particles. But we have already emphasized the fact that we simply cannot take all of the conceptual schemes under which we subsume systems as applying to it “really” in any naively realistic way. Multiple incompatible schemes applied to one and the same system, each one of which has its legitimate descriptive and explanatory use, cannot all be intended to be genuinely “true” of the system. We must allow for “convenient fictions” in our characterization of our methods even if we are realists and not the kind of very radical pragmatist that views all such conceptualizations as equally “fictional” (whatever that would mean).

Once again there is no a priori way of deciding which descriptive schemes are to be taken as straightforward and which as useful fictive modes of characterizing the world. Deciding those questions is part and parcel of science itself. And much useful and sometime very hard and very brilliant science is devoted to just that question. Figuring out which “fictional” schemes to apply and understanding why, in the light of the nonfictive science they can work so well, is quite often an ongoing scientific project.

The very distinction between a descriptive scheme as “straightforward” and one as “merely fictive” is, to be sure problematic. How, in detail, such a way of thinking about things is to be made clear is an open matter. Yet there is something very different between characterizing an atomic nucleus as a complex system of neutrons and protons, with these composed of quarks bound by gluons, and with the neutrons and protons bound by a van der Waals residual effect of the quark-quark binding, and a characterization of a fissionable nucleus as a “liquid drop” held together by a “surface tension.”

The former description is at least a part of a structure “on the road” to our desired ultimate theory. The latter is intended, from the start, as nothing more than a weak model adequate only in the most restricted ways to characterizing what is really going on.

Much more needs to be said about such distinctions, and making all of this clear is, again, by no means a trivial matter. But that need not reduce us immediately to an “its all a bunch of fictional models” approach to our understanding of the aims of theory.

8.

So we have some experimental evidence that foundational physics has as its domain of applicability a range of phenomena that outruns the simplest cases of small numbers of elementary particles carefully isolated in the laboratory. And we have some theoretical ways of linking the concepts and generalizations of non-foundational theories to those of foundational physics. Of course it may very well be the case that in both the experimental and theoretical programs here we make use of nonfoundational rules we have empirically discovered to be true. But nothing in that should make us skeptical of the legitimacy of the inferences made about the domain of the foundational theoretical scheme.

In the wider world of complex systems and the science we have developed to deal with them, we have much less in the way of direct evidence that these systems and their behaviors still fall within the domain of fundamental physics. But we do have the strong evidence that complex as the systems may be, they are still composed of the basic components of the world treated by foundational physics. We still have the claim of that physics to deal with things compounded of the basic elements no matter how many such basic things are needed to make up the complex, macroscopic whole. And we still have the fact that many of the phenomenological or approximative theories that have been connected to the foundational theory in the manners we have noted still are usefully descriptive of the behavior of these complex things.

But without some direct demonstration that the domain of the foundational physics truly extends to the complex—to sunflowers and people—couldn't we still deny that there is good reason to think that it does reach that far?

It is here, I think, that the burden of proof changes hands. In our world of great diversity, it is, initially, a surprising and implausible claim that some one set of fundamental concepts and laws is universally applicable to all that there is. The burden of proof is initially on the universalist. But once our foundational theories have been constructed, and once the raft of positive arguments for the universality of the domain of their concepts and laws have been given, the burden of proof against universalism rests with the skeptic.

Here one may remember Newton's Rule IV of his “Rules of Reasoning in Philosophy,” in Book III of the Principia:

The case isn't quite that here, but the analogy is sound. Given all our positive evidence for the universality of the domain of the foundational theory, we ought not to take it that there are any restrictions on that domain without good reasons. I have argued that the mere existence of modes of conceptualization and generalization independent of the foundational theory is no such good reason. I have argued, further, that even successful conceptualizations that seem contrary to that of the foundational theory may not be taken as good reasons for denying the universality of the foundational theory if within that theory and within our general picture of the world we have good reasons for taking these incompatible conceptualizations as merely convenient fictions.

The mere fact that our science is irremediably “dappled” is not in itself the slightest reason for thinking that we live in a “dappled world,” if that is meant to deny that there is some conceptual characterization of the nature of things that is universal in its applicability.

Do I believe that our current best foundational theory is universal in its domain? No, because I don't believe that it is true of any phenomena at all. Our current foundational theory is replete with enough problematic aspects that there seems quite good reason to think that it is far from the final word on what the world is like. We are not in the position of those who believed, wrongly but with good reason, that their Newtonian picture was the end of science.

Are there some arguments that foundational physics, whatever it turns out to be, cannot be universal in its domain. I suppose so. The existence of pure phenomenal contents, “being appeared to redly,” remains as puzzling now as in the past. Perhaps there are other positive arguments we need to take seriously that argue against the universality of the domain of any possible foundational physics whatever.

But whatever these arguments are, they are not the argument from dappled methods to dappled world. Nothing in the admitted variety of our conceptual and explanatory schemes, even if that variety is admitted to be intrinsically ineliminable for adequate description and explanation of the world, by itself is good reason for denying the universal domain as the appropriate domain for the truth of foundational physics. And, as we have seen, there are good arguments for that universalist claim—not in a priori philosophy, but in the contents of our best science itself.