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Composition in metaphysics and in science

The conception of naturalized metaphysics in ETMG is based on Wilfred Sellars’s question, “How do things hang together?” (where “things” and “hang together” are understood in the broadest sense of the terms) (Sellars 1963, 1). The idea is that the role of the metaphysician is to say how the sciences as a whole hang together (which presupposes [II] above) in accordance with (III). Assuming that reductionism is not viable (VII), and that we should not be eliminativists about the ontology of the special sciences (VIII), the task is to explain the integration of the sciences and 8 There are other theses in ETMG not mentioned here, but these are certainly among the most important ones.

the relationship between them. The theses above are martialed in the attempt to do so executed in ETMG. This section addresses the more limited sense in which “things hang together," namely the fact that there are composite objects composed of parts. According to ETMG, scientific accounts of composition are unified by the fact that ontology is scale relative (IX), and that science describes interactions at different scales (X) that can be integrated with each other in accordance with (II). The leads to the idea of real patterns (XIII), which brings together two notions of things “hanging together," namely, necessary connection and composition.

Analytic metaphysicians usually approach composition via van Inwagen’s (1990) general and special composition questions. The former is, “What is composition?" and he is skeptical about whether it can be answered. Accordingly, metaphysicians have put much more effort into answering the so-called “special composition question," namely, “Under what circumstances do some objects compose a composite object?" The answers that metaphysicians generally consider to this question assume are (a) that it can be answered without reference to scientific accounts of composition; and (b) that it can be answered in synchronic but not diachronic or dynamical terms. (a) and (b) are related because scientific accounts of composition are usually given in diachronic and dynamical terms. In respect of (a), here is Kriegel:

If it is true, as I think it is, that our pre-philosophical singular intuitions about objecthood exhaust the data of the theory of composition, then being in accord with such intuitions is in some good sense not just a theoretical virtue of an account of composition (as conservatism is)—it is something more like an empirical virtue. (2008, 363)[1]

Such singular intuitions about objecthood involve objects existing at a time and lead naturally to the synchronic conception of composition (b).

The special sciences concern themselves with what metaphysicians call “sortal relative" composition. Katherine Hawley (2006, 483) explains that the composition question in which metaphysicians are interested is, “What composite objects are there?" This is supposed to be independent of the further facts about what kinds those objects belong to, so that scientific accounts of sortal relative composition are irrelevant. However, there is no reason to suppose that we can know what objects there are without science, nor that how they are composed can be understood without reference to our scientific account of the world. Indeed, Ladyman and Ross asked why we should think that there is an intelligible general question as to what it takes for some things to compose a larger thing, as well as the specific questions answered by the special sciences about when things of one kind compose things of another kind. For example, roughly speaking, chemistry says that atoms compose molecules when there are (relatively enduring) chemical bonds between them, and economics says that agents compose a market when there are financial transactions between them. In both cases, the systems in question are considered over time, and composition is a result of interactions between the parts of the whole. Hence, the answers that science gives to the special composition question make reference to causal processes, not to instantaneous facts about, for example, how close things are to each other.[2]

Up to a point we can very successfully understand the world as composed of smaller spatial parts. However, even in these contexts it is often the case that the parts only compose the whole because of their dynamics (X). For example, it is the interactions among dihydrogen oxide molecules that give aggregates of them the properties of water (see ETMG, chap. 1). Composition is diachronic because it typically involves temporal limits and/or relative temporal scales. For example, in statistical mechanics, macroscopic measurements must be carried out over time scales much greater than the mean time taken in atomic interactions. Hence, in science the part/whole relation is shorthand for a process. The scale relativity of ontology is with respect to both time and space because composition is diachronic and dynamical, and because at other length scales, the relevant entities do not exist. For example, there are no water molecules at the scale of quark interactions.

Metaphysical discussions of the special composition question are almost always voiced in the idiom of material particles with some kind of lip service paid to current physics with words like “sub-atomic particles” or “electrons and quarks” disguising the fact that the ontology of the Standard Model and the way particles are described in quantum field theory is incompatible with then wondering whether they are the kinds of things that can form composite systems. There is a whole subdiscipline called “condensed matter physics” that describes how gross matter behaves in terms of interactions between atoms, electrons, and fields. In this context (and in quantum field theory) the “Renormalisation Group” is the formalism that describes the limiting relationships between theories at different scales. Theories that are renormalizable are such that some physical quantities are independent of the exact length scale cut-off that is made justifying the elimination of some degrees of freedom. There is scale relativity of ontology (IX) because the phenomena associated with the intermediate asymptotic regime exist only at the scales associated with the limit. The universalities—the real patterns—simply do not exist at other scales. More generally, scale-relative perspectives are of vital importance to understanding asymptotic analysis.[3]

Jessica Wilson (2010) argues that the idea of emergent degrees of freedom, in the sense of the parameters needed to specify a state on which the laws depend, is central to the scientific account of ontologies in different sciences.[4] There are numerous examples of emergence in the form of descriptions based on coarse graining with respect to the underlying degrees of freedom that allow a reduction in the effective number of degrees of freedom that we need to use to track the collective behavior of the underlying degrees of freedom. The ideal gas laws use only three degrees of freedom to give a pretty good description of the behavior of systems that have of the order of юл2з degrees of freedom. The reduction in the number of parameters needed effectively to describe systems is exactly what the theory of real patterns (XIII) aims to capture. It provides a criterion of ontological commitment: real patterns are those that indispensibly figure in projectible generalizations that allow us to predict and explain the behavior of the world.[5] The sciences (and common sense) posit such objects, properties, relations, and processes that allow the formulation of such projections. This is why we should say,pace mereological nihilists like Trenton Merricks (2003), that ordinary objects such as tables exist, and why we should deny,

pace defenders of unrestricted composition, that arbitrary sums of ordinary objects exist. On this view, there are no real things that do not figure in projectible general- izations/causal laws.

Higher-level laws describe causes that are difference making with respect to the coarse-grained ontology (for example, we may say that the kettle would not have boiled if the gas had not been lit). It is a fact about the world (for all we know a contingent one) that it is ordered on many levels (VII). Science includes theories that link the levels (II), but in almost all cases the higher-level description is coarsegrained, approximate, and aggregative with respect to the underlying levels, so reduction is not plausible (VII). Furthermore, we have learned that reality is not scale invariant. The microworld is not just a smaller version of the macroworld in the sense that the laws of nature seem to care about length scales, energy scale, and velocity. Quantum physics and putatively more fundamental theories describe realms to which the metaphysics of everyday things is not applicable.

Fields can exist in states other than those that can be identified with definite numbers of particles. Indeed, Doreen Fraser (2008) argues that, strictly speaking, there are no particles in quantum field theory. On the other hand, David Wallace (2011) argues that particles are emergent entities. On his account, that there are particles of some kind means that there is an effective quantum field theory involving a Lagrangian for interactions written in terms of particle degrees of freedom. So all particles are really like “quasi-particles.” The latter have finite lifetimes, and therefore their existence perfectly exemplifies the scale-relativity of ontology. Physicists describe the world in terms of particles when there are effective degrees of freedom that behave like particles at some scale. Particles such as electrons and quarks are elementary in the sense that they are thought not to decay, but they are not elementary in the metaphysical sense of being excitation states of quantum fields. They also have features that make it quite absurd to wonder a priori under what circumstances if any they form composites aside from the entangled states of electrons. The relationship between quarks and hadrons such as protons and neutrons (nucleons) also illustrates the scale relativity of ontology and the real patterns criterion of existence. The puzzle about quarks is that three quarks can compose baryons, and a quark and antiquark pair can compose mesons, but quarks are never found free, and this is a lawlike fact. In high-energy collisions of electrons and nucleons, it seems that quarks hardly interact, yet they are tightly bound together in nucleons. It is posited that the coupling of the strong force in the low-energy limit is infinitely strong, and in the high-energy limit is zero. The “bound state” of quarks that we call the proton has a mass of 938.27MeV even though the component quarks have a combined mass of about 15MeV. Hence, most of the mass, that is the “substance” of protons, is due to the energy associated with the gluons that hold the quarks together. The explanations of all of this have to do with how quarks interact and with scale and the energy regime.

  • [1] Note that this is a clear expression of (1) above.
  • [2] The obvious arbitrariness of criteria such as proximity in determining composition is one motivation for nihilism, on the one hand, and unrestricted composition, on the other. Both those positions clearly conflict with thescientific image of what there is. Instead of seeking a general conception of composition a priori, those in favorof special composition should draw upon scientific accounts of composition, of which more below. What theyhave in common is that they explain how a real pattern at the composite level emerges from the real patternsat the level of the parts, so in that sense the theory of real patterns can be thought of as the naturalistic answerto both composition questions.
  • [3] This is a ubiquitous feature of physical models, e.g., in the application of the Navier-Stokes equation to theviscosity of the ocean, where the relevant scale is assumed to be small relative to the depth of the ocean so thatan infinite limit can be taken. For Bob Batterman (2002), while composition may play a role in the relationshipbetween lower- and higher-level theories, the idea of composition giving rise to novel properties with novelcausal powers as considered in much of the literature is a red herring. His analysis of emergence is focusedon the existence of a singular limit. In Batterman’s example of the caustic singularities in wave optics, there isemergence but no part/whole relation.
  • [4] Michael Strevens (this volume, chap. 2) defends an account of emergence in terms of reduction in the numberof effective degrees of freedom that is similar to the theory of real patterns.
  • [5] The idea of real patterns is introduced by Daniel Dennett with the example of John Conways “Game of Life,”as explained in ETMG chapter 4, in which it is also counseled that various features of the example make itmisleading if taken as a metaphysical model of the universe. In particular, in the Game of Life there is clearlya privileged fundamental level of description composed of the aggregation of a finite number of little things,and there is no cross-classification with respect to it at higher levels. However, the example makes it vivid howpatterns can emerge at higher levels of description.
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