Buchler and Natural Science:


Sketch of an Ordinal Physicalism






Traditional Paper Submission


Society for the Advancement of American Philosophy 2008












Lawrence Cahoone


College of the Holy Cross

























Justus Buchler’s “ordinal” metaphysics analyzes whatever is under consideration through its location in orders of relationships, refusing to privilege any type of being, e.g., material objects, minds, relations, processes, etc., thus providing not a “view from nowhere,” but a view from anywhere. Such pluralism might seem incompatible with physicalism, since the latter must grant metaphysical priority to the physical and science’s claims about it. However, such a physicalism can be conceived inside an ordinal metaphysics. Following the Aristotelian “metaphysics of the middle,” the ordinal perspective avoids the Democritean and Platonist analyses of complex systems in reference to an ultimate order of elementary particles or mathematical structures. Doing so provides special resources for conceiving the inter-relation of wholes and components disputed by reductionists and emergentists, e.g. complex material systems, organisms, and minds. This paper will sketch the outlines of an ordinal physicalism.



An “ordinal” metaphysics analyzes whatever is under consideration through its location in an order of relationships. It is pluralistic, accepting as equally real material objects, relations, mental events, fictive objects, processes, whatever you can name. The most complete deployment of this approach is found in the work of Justus Buchler. Such pluralism might seem incompatible with physicalism, since the latter must grant metaphysical priority to physical systems and science’s claims about them. However, such a physicalism can be conceived inside, or on the basis of, ordinal metaphysics. The motivation for doing so is that ordinalism provides special resources for conceiving the multiplicity of inter-related strata of phenomena at the heart of the argument between reductionists and anti-reductionists, whether the later be emergentists or supporters of supervenience. Buchler’s scheme has, to my knowledge, only once before been turned to such a natural scientific purpose, by Stanley Salthe. This paper will thus sketch the outlines of an ordinal physicalism.

The inquiry can be located in an ancient three-way disagreement. Democritus analyzed all things as collections of a common set of tiny, simple parts. Despite the differences between modern elementary particles and Democritean atoms, presumably little needs be said to demonstrate Atomism’s continuing scientific relevance. Platonists followed the Pythagoreans in holding that the ultimate realities are forms, structures or laws which things obey. Relativity, quantum field theory, the gauge theories of electroweak and strongly interacting particles, and quantum cosmology arguably follow Platonism in making mathematical patterns the ultimate realities. Thus the spirits of Democritus and Plato are both served in contemporary physics. 

Not so the third option in the ancient debate. For Aristotle all reals are properties or performances of a finite but very large range of independent, qualitatively different kinds of individuals. Substances have not fared as well as particles or forms in recent physics or philosophy of science, partly because they seem quantitatively un-analyzable and lacking in internal or constitutive relations to other things, not to mention their guilt by association with Aristotle’s final causes and fixity of natural kinds. But substance-like notions are not foreign to contemporary science; chemistry and biology both accept fundamental natural kinds of complex individuals, respectively, atoms and elements, and cells and species. And there is a further virtue to Aristotle’s analysis. Platonism and Atomism reflect an old philosophical tradition holding that until we come to the final term of a line of metaphysical thought, all the intermediate terms are in peril, because the analysis of the local is strongly dependent on the analysis of the ultimate. If so, we are in permanent trouble, for our knowledge of the ultimate must be less reliable than our knowledge of more familiar scales, which are, as Wimsatt put it, “robust,” accessible by multiple means. Indeed, compared to the smallest scale (elementary particles) and the largest (the spacetime structure of the universe), the middle is where the greatest complexity lies, with macroscopic ensembles and objects, their thermodynamics and chemistry, and of course, life. Aristotle’s was a metaphysics of the middle. While some of its features cannot be combined with contemporary science, it may be that we can capture its virtues with a more pluralistic, ordinal conception.

Now, the current debate between reductionism and anti-reductionists may seem almost hopelessly complex. It hangs first of all on multiple linguistic analyses of what should count as a reduction. I refer not only to the difference between “ontological reduction” of wholes to components and “theory” reductionism of the rules governing wholes to interaction rules for components, but to whether reduction “derives” or “deduces” or “constructs” or “explains” or “predicts” coarse-grained from fine-grained phenomena, each of which raises or lowers the bar for what a successful reduction entails. Simultaneously, there are multiple kinds of emergence or supervenience; the dependence of chemical properties on atomic structure is different than that of cellular life on macromolecules or of thoughts on neurons. So we have multiple meanings of reduction chasing multiple kinds of phenomena, a prescription for confusion. 

But perhaps the confusion teaches an unintended truth. For in scientific practice reduction, hence emergence, is a matter of degree. As Shimony points out, a successful reduction often rests on special assumptions or construction of models beyond what is contained in the unadulterated theory of the components and their interactions, and may explain some but not all of the composite product’s properties or performances. As Wimsatt argues, the possibility of reduction depends on several properties of “aggregativity,” some of which can be true of a system while others are not. Combine this with Teller’s point that if a derivation of a composite system employs not only component properties and two-body interactions but specifications of global relations among the components, then it simply reads holistic complexity into the parts.  This means we have, not reduction or emergence, but reduction and emergence. Reductionism and emergentism are metaphysical positions, but reduction and emergence are scientific facts (more precisely, emergence is a fact and reduction is a program, but we may say it is a program often factual of the real world). As matters of degree, they are compatible facts present in inverse proportion to the other. Rather than a problem, this combination of reduction and emergence appears to be a characteristic feature of the kind of world we inhabit.

Now, the ordinal approach to metaphysics can be indicated with respect to Thomas Nagel’s famous denial that philosophy can seek a “view from nowhere,” devoid of perspective. Presumably his denial holds also for a view from “everywhere” or all possible perspectives. But a view from anywhere would be quite another thing. It would provide a scheme by which anything could be analyzed locally, a distributive rather than collective metaphysics.

In Buchler’s metaphysics anything that can be discriminated in any sense is a “natural complex.” The qualifier “natural” signifies that there can be no discontinuous realms of things, while “complex” means that nothing is simple, unrelated to others, incapable of analysis, wholly indeterminate or wholly determinate. Complexes include but are not limited to physical objects, events, relations, particulars, universals, fictional characters, minds, and artifacts. Every complex must be related to some other complex (which does not mean related to all other complexes). Every complex is located in one or more contexts of relations or orders, in which the complex functions and has an “integrity.” Its identity or “contour” is the continuous relation of its collection of integrities to its individual integrities. Buchler accepts “ontological parity,” under which nothing is more or less real than anything else. Stones and fairies are equally natural complexes, one obtaining in the order of physical objects, the other, as far as we know, in mythology and fiction. Thus the notions “being,” “non-being,” “real “apparent,” and “epiphenomenon” drop out of Buchler’s metaphysics.

Buchler’s metaphysics is not unobjectionable, but it is the closest thing we have to a metaphysics of any possible world. Conceive a system of disembodied spirits, a quark-plasma, a set of Platonic forms, or a world in which beings otherwise like ourselves communicate telepathically or have no biological needs. Buchler’s metaphysics would hold equally well for these “worlds,” all of whose members could be described as ordinally located natural complexes. But if that is so, then it is equally true to say that his metaphysics does not pick out our world. It underdetermines our reality, allowing all sorts of processes that cannot or do not occur in reality as far as we can tell. Whether this is a vice or virtue depends on one’s view of how far a metaphysics should go in fixing reality. Nevertheless, I suggest that Buchler’s scheme provides an indispensable background language within which we can describe the physical orders of our world.

To begin, we must analyze the “physical.” While the term belongs to all the physical sciences, physics is here “first among equals,” not because it is more fundamental, but more general. All objects of biology and chemistry must fall in some sense under physics. The privilege of physics is horizontal, not vertical.

But what is the physical? Not the material; matter is a minority concern in a universe that currently appears to be mostly dark energy. What is regarded as the most basic and reliable theory of the physical, Quantum Field Theory, has a relatively clear metaphysics: at that scale what obtains are fields and their localized, quantized excitations or energy spikes. Fields and waves, unlike fermions – for example, electrons, protons, and neutrons – do not obey the Pauli Exclusion Principle; they superpose rather than aggregate or clump as matter does. But while not spatially bounded or exclusive, fields and waves are still spatially located and extended. Space is embedded in spacetime, a dynamic physical presence, quantitatively described, causally interacting with mass-energy under the General Theory of Relativity. Then there is energy. Energy is conserved in all closed systems, and nothing with causal relevance can fail to possess it. But it is defined only in terms of the forms it takes. Energy is best conceived as a content that whatever exists must have, while spacetime is a framework for where and when what exists must be, hence what it can causally interact with. (Relativity does not banish the concept of such a framework, it makes it local and dynamic.) This might suggest a two-part definition of physicality as spacetime energy. Unfortunately, that will not strictly do, because students of Quantum Gravity assume spacetime must cease to obtain at some scale far below that of Quantum Field Theory. Still, for current purposes we can offer a tentative characterization of the physical as: a) a continuous domain, b) of energetic systems, c) capable of evolving spacetime and matter.

An ordinal physicalism begins with two claims. First, the physical is an order, or anticipating later purposes, a family of orders. Second, all physical phenomena are complexes. Thus all physical beings are complex. But the last claim requires two clarifications, one linguistic and one physical.

Linguistically, the physical and Buchlerian use of “complexity” are different. For Buchler, “complex” does not admit of degree. This is because for him complexity refers to the open-ended actual and potential ordinal locations of a complex. In science, however, complexity means the quantity of parts, properties, and organizational structure a system exhibits, hence the length of its shortest adequate description. Rather than using another term for physical complexity (e.g. “organizational complexity”), in what follows “complexity” will have its scientific meaning.

Physically, the claim of complexity may seem to be violated by “elementary particles,” or quarks and leptons (e.g. electrons). The objection is not compelling. Quarks are “confined,” meaning they appear in clusters, hence arguably are constituted by relations to things outside themselves. Indeed, all quantum particles exhibit non-locality or entanglement with others. Furthermore, quantum field theory conceives all particles as field excitations, and fields are not simples. Philosopher Tian-yu Cao and cosmologist Lee Smolin have separately warned against the search for “structureless” components or simples as the ultimate building blocks of reality. So, even if we have arrived at the most elementary particles, which is doubtful, elementary cannot mean “simple” simpliciter.

Now, the physical sciences have a term for many of its objects that is almost ordinal in its scope of application: system. Not all physical complexes are systems: states and traits like temperature and velocity, structures and processes such as a crystal lattice and oxidation, and natural kinds like Hydrogen, are not systems. We can say that the “entities” of physical science are systems. Systems have parts, which may themselves be systems, and are located in environments that are systems. This focus on systems may seem to privilege entities over events and relations. But here ordinalism makes a contribution: many systems can be simultaneously considered a set of components, a structure of relations among components, and a process that constitutes and maintains the structure. A system is its parts, is a structure, and is a process, if it has all three, which, we shall see, not all systems do. Parts, process, and structure have ontological parity. Such parity reminds that any simple form of ontological reductionism is just as objectionable as theory or explanatory reductionism. There is more in a water molecule than quarks and electrons: there are structures and processes.

We can distinguish three types of systems: fields, ensembles, and individuals. Fields are spacetime distributions of a physical quantity. They have structure but no parts, and superpose rather than aggregate. Ensembles are weakly structured, environmentally-bounded collections of components, such as volumes of gases and liquids, weather systems and ecosystems. Some exhibit complex, although unstable, self-organization. Individuals are tightly structured material aggregates, individuated independently of their environmental roles. They include nucleons, atoms, molecules, solid state macroscopic objects, cells, organisms, planets, and stars.

While there is ontological parity between fields, ensembles, and individuals, individuals play a distinctive role. They alone are capable of the modular-hierarchical organization that, Herbert Simon showed, facilitates the evolution of stable complexity; they can aggregate in a stable structured way so that their differences combine to create novel kinds of beings. Solid-state material things are not inert “stuff.” They are possible only under special circumstances (e.g. low temperature), given complex histories (e.g. gravity acting over a long period of time), and maintained by active (at least, nuclear and electromagnetic) processes, all flying in the face of the second law of thermodynamics, the tendency of systems toward simple equilibrium. They are achievements, not givens. This is what Aristotle did not know, that his substances were thermodynamically rare, improbable islands precariously maintained by fine-tuned interactions among basic forces after billions of years of cosmogenesis.

Now, there is a special kind of order we must consider besides systems: strata. A stratum is an order of comparable systems open to interaction according to a common set of causal rules. Usually called “levels,” strata are, as Wimsatt recommends, peaks of regularity, those scales of phenomena which present a particular regime of predictable behavior, some being segregated as the objects of different sciences. There are systems which occupy only one stratum, systems that cross several strata, and causal processes within and between strata (see figure 1). Macroscopic systems cross several strata; the glass of water functions at quantum, atomic, and macroscopic strata simultaneously. Ordinal physicalism makes the identity of such an individual a function of its integrities in multiple orders. The identity of the water molecule is, from Buchler’s perspective, the “contour” or continuous relation among those different roles or functional integrities, which may reside in multiple strata, not merely its properties in relative isolation. 











Figure 1

(Strata in gray, systems in black)


We can now see the most significant impact of ordinalism, which lies less in what it adds than subtracts from the debate, namely, questions of which strata are more real or fundamental. “Real” as a comparative term, we have seen, is thrown out entirely. “Basic” or “fundamental” are legitimate but ordinal terms; something is more fundamental only relative to its role in a system. Are the rules governing the proton itself more fundamental than the rules governing, say, oxidation or eutrification, as Steven Weinberg argued against Philip Anderson? More general, yes, because the laws governing isolated protons make some contribution to understanding all occurrences of protons, hence to all matter. But that contribution may well be swamped by the role dictated to the proton by the order in which it functions. To use a geometric illustration, suppose we compare three figures each made of nine components (see figure 2). A and B are triangles identical in size and corresponding angles, although none of their components are the same. A and C have identical components, but form different arrays. Suppose that asterisks and plus-signs obey different interaction rules. Are the properties of asterisks and plus-signs, and their interaction rules, more fundamental than the properties of the arrays, like 3 or 4-sidedness? Even if they were a cause of the constitution of these figures, it is dubious that they are more decisive in determining a figure’s properties or interactions than sidedness. From an ordinal perspective there is no need to distinguish one fundamental stratum, relegating the others to epiphenomenal, secondary or even subjective status; there is only the need to specify the causal relations of these integrities in the systems they impact.

            *                                           +                                     *     *     *

        *      *                                   +      +                                 *     *     *

    *              *                          +              +                              *     *     *

*      *      *     *                   +      +     +     +                         

                        A                                          B                                            C


Figure 2


            Such are the outlines of an ordinal physicalism. But note what has not been said: that all complexes are physical or determined by the physical. All that has been said is that there is an order of physical orders. To anticipate perhaps the most difficult subject, and the philosophically most potent objection to physicalism, ordinal or not, an intentionality or consciousness constitutes an order which, as far as we can tell, is a trait of some biological individuals in social context. Let us say, for the purposes of discussion, that consciousness or intentionality includes feelings, images, and representations, or whatever is internal to the process of first-person experience. Presumably this process, or some version of it, is characteristic not only of humans, but of primates and cetaceans, probably mammals, and perhaps many vertebrates and cephalopods as well. Wherever we find brains and sensory-motor neurology, along with behavior, similar to the subjectivity-implying structures and behavior of our own, we must suspect the presence of such subjectivity. In evolutionary terms, we may imagine that it conferred advantages on organisms possessing it, meaning that feeling hunger or having images of an environment and one’s own physical state bestowed on creatures naturally selectable advantages beyond those of more direct sensori-motor connections.

Particular intentional complexes are not physical, because their semantic contents are not spatial and have no measurable energy content. They are non-physical performances of a physical system, dependent on and arising from electrical patterns of a somatically integrated brain in its behavioral context. However this is possible, it certainly appears actual. In ordinal perspective, such a performance is not less real or significant than the system achieving it, for there is no reason to deny physical complexes can have non-physical properties or performances, that is, function in non-physical (e.g. semantic) orders. Such an ordinal analysis does not solve problems for the philosophy of mind, but it does shift the mind-body problem from questions of reality, existence, and the nature of orders to the question the type of relation holding among orders.

 One final implication of ordinal physicalism can best be seen in relation to Peirce. In his pragmatism essays Peirce conceived mind naturalistically, as a means by which an organism accomplishes its tasks. But, despairing that mind could be derived from matter, in his metaphysical essays he concluded that matter could be “frozen” or “coarse” mind, mind whose capacity for new habits was exhausted. Hence he endorsed “panpsychism.” What enabled him to do so is that he did not take the view of most idealists that the human mind makes an end run around physical law to be continuous with a Divine or Absolute mind. Peirce put human minds in nature, but then derived nature from inchoate mind. We can learn from this example without endorsing his panpsychism. It reminds us that even if one were to locate the physical in a broader non-physical context, one would still have to explain how the minds we know emerge within or from their physical neighborhood. Ordinal physicalism takes such local relationships as its subject, leaving open the question whether the physical universe stands within, or derives from, some non-physical order.

In conclusion, while any complex individual is a product of the interactions of its simplest components, it is also a set of integrities functioning at different strata. This hierarchical dependence/emergence is seconded by the facts of history, for the more complex has generally come later in cosmogenesis, enabled by the fine-tuning of physical forces and pockets of non-equilibrium thermodynamics. Such history teaches metaphysical lessons. For both a strong Atomistic reductionism and a severe Platonism would be forced to say that nothing metaphysically interesting has happened since the universe’s first second, since its simplest components and laws presumably have not changed since then. The evolution of stars, galaxies, solar systems, heavy elements, planets, life, and mind in the past 15 billion years would therefore make no difference to metaphysics. But one would rather say it is such a metaphysics that makes no difference. For stratified dependence and emergence is a – I do not presume to say the – moral of the story of the universe. It makes ours a world of not one, but of multiple, mutually influencing inquiries, a world that invites the unity of science, or better, the unity of sciences. An ordinal approach seems tailor-made for such a world, as long as we accept that the aim of metaphysics with respect to science is to understand, extend and channel it, rather than pre-empt it.




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