We revive the idea that a deductive-nomological explanation of a scientific theory by its successor may be defensible, even in those common and troublesome cases where the theories concerned are mutually incompatible; and limiting, approximating and counterfactual assumptions may be required in order to define a logical relation between them. Our solution is based on a general characterization of limiting relations between physical theories using the method of nonstandard analysis.

Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from (...) a theory describing only finite systems? In this paper, I change the subject in order to consider the motivations behind the definability and deducibility requirements. The classical accounts of intertheoretic reduction are appealing because when the definability and deducibility requirements are satisfied there is a sense in which the reduced theory is forced upon us by the reducing theory and the reduced theory contains no more information or structure than the reducing theory. I will show that, likewise, there is a precise sense in which in statistical mechanics the properties of infinite limiting systems are forced upon us by the properties of finite systems, and the properties of infinite systems contain no information beyond the properties of finite systems. (shrink)

By moving away from the traditional reductionist reading of the quantum theory of atoms in molecules, in this paper we analyze the role played by QTAIM in the relationship between molecular chemistry and quantum mechanics from an emergentist perspective. In particular, we show that such a relationship involves two steps: an intra-domain emergence and an inter-domain emergence. Intra-domain emergence, internal to quantum mechanics, results from the fact that the electron density, from which all the other QTAIM’s concepts are defined, arises (...) from the wavefunction as a coarse-grained magnitude. Inter-domain emergence involves an analogical link, a mapping, between QTAIM’s entities, such as topological atoms and bond paths, and the entities that populate the molecular-chemistry domain, such as chemical atoms and chemical bonds. (shrink)

The purpose of this work is to discuss which relation can be established between molecular chemistry, on the one hand, and macrochemistry and nanochemistry, on the other hand. In order to do this, we will consider molecular chemistry as an underlying level, and macrochemistry and nanochemistry as emergent levels. Emergence is characterized in very different ways in the philosophical literature; we will not discuss those differences. We will address a distinction between inter-domain emergence and intra-domain emergence. It is our purpose (...) to argue that, from a basal micro-molecular level, macrochemistry and nanochemistry emerge in parallel. The emergence of macrochemistry is an inter-domain emergence, while the emergence of the nanolevel is an intra-domain one. If this is the case, therefore macrochemistry and nanochemistry are not “successive” levels, but parallel ones. This discussion will be held from an ontological point of view, instead of the classical characterization in terms of scale. (shrink)

I provide a formally precise account of diachronic emergence of properties as described within scientific theories, extending a recent account of synchronic emergence using similarity structure on the theories’ models. This similarity structure approach to emergent properties unifies the synchronic and diachronic types by revealing that they only differ in how they delineate the domains of application of theories. This allows it to apply also to cases where the synchronic/diachronic distinction is unclear, such as spacetime emergence from theories of quantum (...) gravity. In addition, I discuss two further case studies—finite periodicity in van der Pol oscillators and two-dimensional quasiparticles in the fractional quantum Hall effect—to facilitate comparison of this approach to others in the literature on concepts of emergence applicable to the sciences. My discussion of the fractional quantum Hall effect in particular may be of independent interest to philosophers of physics concerned with its interpretation. (shrink)

Scientists employ a variety of procedures to eliminate degrees of freedom from computationally and/or analytically intractable equations. In the process, they often construct new models and discover new concepts, laws and functional relations. I argue these procedures embody a central notion of reduction, namely, the containment of one structure within another. However, their inclusion in the philosophical concept of reduction necessitates a reevaluation of many standard assumptions about the ontological, epistemological and functional features of a reduction. On the basis of (...) the reevaluation, I advocate a continuum of reduction which proceeds from the eliminative to the constructive. The metaphysical aspects of theory use in constructive reductions are sketched. (shrink)

How do we characterize theoretical disagreement and how does this translate into strategies for practicing scientists? I integrate Kuhn’s (1962) notions of paradigms and problem-fields with Hull’s (1982,1988) concept of populational variation and Shapere’s (1974) characterization of domains in interpreting the Ox-Phos Controversy in bioenergetics (1961-1977). The analysis highlights the differences between intraparadigm disagreement (based on proposed solutions to shared problems) and interparadigm disagreement (based on the problems themselves and views of relevant domain).Kuhn (1959,1962) introduced the notion that a single, (...) uniform paradigm guides ‘normal science’. He further suggested that scientific communities undergo gestalt-like changes in research focus, implying that all disagreement is based on ‘incommensurable’ paradigms. Philosophers and historians of science concerned largely with how consensus is established (see Laudan 1984; Laudan and Laudan 1989) have found this problematic as a universal model (e.g., Lakatos and Musgrave 1970; Laudan 1977). (shrink)

There has been a good deal of discussion of the subject of reductionism in the literature of the history and philosophy of science. It would not be an understatement to claim that the standard or received account of the reduction of theories in science, characterized both by its close attention to the supposed connectability of terms between the theories involved in reduction, and, by the prominence assigned to derivation as the core of the reductionistic enterprise [27], has not fared well (...) in recent critical evaluations ([7], [10], [11], [16], [17], [18], [19], [26], [29], [30], [38]). The derivational view of reduction, or at least the version put forth by Ernest Nagel in his book,The Structure of Science, has been criticized as impractical, inaccurate, idealized, distorting, sterile, and even incoherent [38]. Perhaps the most decimating of all the charges brought against the Nagelian account of derivational reduction is that there is not a single instance of derivational reduction to be found anywhere in the entire annals of scientific inquiry([3], [4], [38]). (shrink)

I begin to develop a framework for emergence in the physical sciences. Namely, I propose to explicate ontological emergence in terms of the notion of ‘novel reference’, and of an account of interpretation as a map from theory to world. I then construe ontological emergence as the “failure of the interpretation to mesh” with an appropriate linkage map between theories. Ontological emergence can obtain between theories that have the same extension but different intensions, and between theories that have both different (...) extensions and intensions. I illustrate the framework in three examples: the emergence of spontaneous magnetisation in a ferromagnet, the emergence of masslessness, and the emergence of space, in specific models of physics. The account explains why ontological emergence is independent of reduction: namely, because emergence is primarily concerned with adequate interpretation, while the sense of reduction that is relevant here is concerned with inter-theoretic relations between uninterpreted theories. (shrink)

This paper challenges a popular thesis which we call the explanatory primitiveness thesis (for short, EPT), namely, the thesis that identities leave no logical space wherein explanatory questions may be formulated and explanatory gaps may reside. We argue that while EPT is, in all likelihood, flawless when the relevant domain consists of identity statements flanked by proper names of individuals it is a mistake to hold that the thesis generalizes to cover all identity statements. In particular, we argue that EPT (...) fails decisively with respect to an important class of identity statements, viz., those in which natural kinds are identified across different theoretical levels (i.e., the so-called inter-level type-identities). If correct, our result shows EPT to be much more limited in scope than is usually supposed. Moreover, and perhaps more significantly, it shows that there is no inherent absurdity in the idea that certain type-identity statements, in particular psychophysical type-identity statements, suffer from an explanatory gap. (shrink)

I begin to develop a framework for emergence in the physical sciences. Namely, I propose to explicate ontological emergence in terms of the notion of ‘novel reference’, and of an account of interpretation as a map from theory to world. I then construe ontological emergence as the “failure of the interpretation to mesh” with an appropriate linkage map between theories. Ontological emergence can obtain between theories that have the same extension but different intensions, and between theories that have both different (...) extensions and intensions. I illustrate the framework in three examples: the emergence of spontaneous magnetisation in a ferromagnet, the emergence of masslessness, and the emergence of space, in specific models of physics. The account explains why ontological emergence is independent of reduction: namely, because emergence is primarily concerned with adequate interpretation, while the sense of reduction that is relevant here is concerned with inter-theoretic relations between uninterpreted theories. (shrink)

In this paper, I explore the possibilities for arriving at a useful conception of methodological reductionism. Some participants in the debate talk about methodological reductionism as a research program. I argue that the concept of a research program, at least in Lakatos’ sense, cannot account for the diverse nature of methodological reductionism. I then present my own concept of a research directive as a useful alternative and elaborate on this by drawing on Hasok Chang’s theory of ontological principles and epistemic (...) activities. According to my view, the reductionist research directive can be characterized as consisting of the principles fundamental ontological homogeneity, part-whole asymmetry, and orderliness, together with the corresponding activities construction of identities, decomposition, and unification. I suggest that looking at reductionism in this way enables us to understand it as a gradual concept and thus go beyond the simplistic yes-or-no-questions that dominate many current debates on this topic. (shrink)

One of the recurrent problems in the foundations of physics is to explain why we rarely observe certain phenomena that are allowed by our theories and laws. In thermodynamics, for example, the spontaneous approach towards equilibrium is ubiquitous yet the time-reversal-invariant laws that presumably govern thermal behaviour in the microscopic level equally allow spontaneous departure from equilibrium to occur. Why are the former processes frequently observed while the latter are almost never reported? Another example comes from quantum mechanics where the (...) formalism, if considered complete and universally applicable, predicts the existence of macroscopic superpositions—monstrous Schr¨odinger cats—and these are never observed: while electrons and atoms enjoy the cloudiness of waves, macroscopic objects are always localized to definite positions. (shrink)

This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of (...) reduction and emergence. (shrink)

Reduction and reductionism have been central philosophical topics in analytic philosophy of science for more than six decades. Together they encompass a diversity of issues from metaphysics and epistemology. This article provides an introduction to the topic that illuminates how contemporary epistemological discussions took their shape historically and limns the contours of concrete cases of reduction in specific natural sciences. The unity of science and the impulse to accomplish compositional reduction in accord with a layer-cake vision of the sciences, the (...) seminal contributions of Ernest Nagel on theory reduction and how they strongly conditioned subsequent philosophical discussions, and the detailed issues pertaining to different accounts of reduction that arise in both physical and biological science (e.g., limit-case and part-whole reduction in physics, the difference-making principle in genetics, and mechanisms in molecular biology) are explored. The conclusion argues that the epistemological heterogeneity and patchwork organization of the natural sciences encourages a pluralist stance about reduction. (shrink)