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)

We investigate the fate of determinism in general relativity, comparing the philosopher’s account with the physicist’s well-posed initial value formulations. The fate of determinism is interwoven with the question of what it is for a spacetime to be ‘physically reasonable’. A central concern is the status of global hyperbolicity, a putatively necessary condition for determinism in GR. While global hyperbolicity may fail to be true of all physically reasonable models, we analyze whether global hyperbolicity should be imposed by fiat; established (...) from weaker assumptions, as in cosmic censorship theorems; or justified by beyond-GR physics. (shrink)

I discuss the formal implementation, interpretation, and justification of likelihood attributions in cosmology. I show that likelihood arguments in cosmology suffer from significant conceptual and formal problems that undermine their applicability in this context.

We show a sense in which the spacetime property of effective completeness—a type of “local hole-freeness” or “local inextendibility”—is not stable.

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 essay revisits some classic problems in the philosophy of space and time concerning the counting of possibilities. I argue that we should think that two Newtonian worlds can differ only as to when or where things happen and that general relativistic worlds can differ in something like the same way—the first of these theses being quaintly heterodox, the second baldly heretical, according to the mores of contemporary philosophy of physics.

The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Jeremy Butterfield, I provide precise definitions of emergence concepts as they pertain to properties represented in models, applying them to some basic examples from space-time and thermostatistical physics. The chief formal innovation I employ, similarity structure, consists in a structured set of similarity relations among those models under analysis—and their properties—and is a generalization of topological structure. Although motivated from physics, this (...) similarity-structure-based account of emergence applies to any science that represents its possibilia with models. (shrink)

Merely approximate symmetry is mundane enough in physics that one rarely finds any explication of it. Among philosophers it has also received scant attention compared to exact symmetries. Herein I invite further consideration of this concept that is so essential to the practice of physics and interpretation of physical theory. After motivating why it deserves such scrutiny, I propose a minimal definition of approximate symmetry—that is, one that presupposes as little structure on a physical theory to which it is applied (...) as seems needed. Then I apply this definition to three topics: first, accounting for or explaining the symmetries of a theory emeritus in intertheoretic reduction; second, explicating and evaluating the Curie-Post principle; and third, a new account of accidental symmetry. (shrink)

Ruetsche claims that an abstract C*-algebra of observables will not contain all of the physically significant observables for a quantum system with infinitely many degrees of freedom. This would signal that in addition to the abstract algebra, one must use Hilbert space representations for some purposes. I argue to the contrary that there is a way to recover all of the physically significant observables by purely algebraic methods. 1 Introduction2 Preliminaries3 Three Extremist Interpretations3.1 Algebraic imperialism3.2 Hilbert space conservatism3.3 Universalism4 Parochial (...) Observables4.1 Parochial observables for the imperialist4.2 Parochial observables for the universalist5 Conclusion. (shrink)

I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states. 1Introduction2Background2.1 Physical states2.2 Reductive explanations3The Proposed ‘Correspondence Principle’4Example: Regularity5Example: Symmetry-Invariance6Conclusion: Heuristics and Discovery.

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)

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)

Two interesting “no hole” spacetime properties, not being future nakedly singular) are unstable in the fine topology.

Determinism fails easily if spacetimes with points removed from the spacetime manifold are taken to be physically reasonable representations of a way the world could be according to classical general relativity. I discuss a recently proposed condition for determining which spacetimes have holes—epistemic hole freeness—and show that epistemic hole freeness gives the correct verdict in some non-globally hyperbolic spacetimes with a closed subset removed, certain spacetimes with genuinely indeterministic features count as having an epistemic hole, which implies that the requirement (...) of epistemic hole freeness enforces a form of determinism, and there is a large class of spacetimes that intuitively are radically indeterministic and unphysical due to containing a hole, but are free from epistemic holes. I show that a few natural ways of remedying are not satisfactory. (shrink)

This article considers the following question: What is the relationship between supervenience and reduction? I investigate this formally: first, by introducing a recent argument by Christian List to the effect that one can have supervenience without reduction; then, by considering how the notion of Nagelian reduction can be related to the formal apparatus of definability and translation theory; then, by showing how, in the context of propositional theories, topological constraints on supervenience serve to enforce reducibility; and, finally, by showing how (...) constraints derived from the theory of ultraproducts can enforce reducibility in the context of first-order theories. (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)

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)

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 essay, written on the occasion of the 10th anniversary of Mariano Artigas’s death, examines Artigas’s engagement with analytic philosophy in his philosophy of science. I argue that, overall, Artigas’s project in the philosophy of science is one of—using his own metaphor—‘building bridges’ between distinct areas of knowledge. After reviewing the function of Artigas’s philosophy of science as a bridge between science and philosophy, I analyse how he moved from classical to analytic philosophy. I then assess the extent to which (...) Artigas’s work conforms to reasonable analytic standards of clarity and precision, which can be expected from work in the philosophy of science. I conclude that, while Artigas’s dedication and production were admirable, his work remains essentially unfinished, thus inviting further research that should develop and clarify his conception of science, of its aims, its methods, progress, and of how science leads to knowledge. I attempt to assess Artigas’s philosophy of science from an objective and detached perspective. Thus the essay should be of interest to both scholars in the philosophy of science, as well as to those generally interested in Artigas-scholarship. (shrink)

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.

We discuss ways in which category theory might be useful in philosophy of science, in particular for articulating the structure of scientific theories. We argue, moreover, that a categorical approach transcends the syntax-semantics dichotomy in 20th century analytic philosophy of science.

I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects living in infinite-dimensional spaces, working through many examples from cosmology. I focus on the relation of topological to measure-theoretic notions of and relating to probability, how they diverge in unpleasant ways in the infinite-dimensional case, and are even difficult to work with on their own. Even in cases where an appropriate family of spacetimes (...) is finite-dimensional, and so admits a measure of the relevant sort, however, it is always the case that the family is not a compact topological space, and so does not admit a physically significant, well behaved probability measure. Problems of a different but still deeply troubling sort plague arguments about likelihood in that context, which I also discuss. I conclude that most standard forms of argument used in cosmology to estimate the likelihood of the occurrence of various properties or behaviors of spacetimes have serious mathematical, physical and conceptual problems. (shrink)

In this paper, I analyze the extent to which classical phase transitions, especially continuous phase transitions, impose a challenge for reduction- ism. My main contention is that classical phase transitions are compatible with reduction, at least with the notion of limiting reduction, which re- lates the behavior of physical quantities in different theories under certain limiting conditions. I argue that this conclusion follows even after rec- ognizing the existence of two infinite limits involved in the treatment of continuous phase transitions.