This is one of two papers about emergence, reduction and supervenience. It expounds these notions and analyses the general relations between them. The companion paper analyses the situation in physics, especially limiting relations between physical theories. I shall take emergence as behaviour that is novel and robust relative to some comparison class. I shall take reduction as deduction using appropriate auxiliary definitions. And I shall take supervenience as a weakening of reduction, viz. to allow infinitely long definitions. The overall claim (...) of this paper will be that emergence is logically independent both of reduction and of supervenience. In particular, one can have emergence with reduction, as well as without it; and emergence without supervenience, as well as with it. Of the subsidiary claims, the four main ones are: : I defend the traditional Nagelian conception of reduction ; : I deny that the multiple realizability argument causes trouble for reductions, or ``reductionism'' ; : I stress the collapse of supervenience into deduction via Beth's theorem ; : I adapt some examples already in the literature to show supervenience without emergence and vice versa. (shrink)

In this paper I critically review the long history of attempts to formulate and derive the geodesic principle, which claims that massive bodies follow geodesic paths in general relativity theory. I argue that if the principle is interpreted as a dynamical law of motion describing the actual evolution of gravitating bodies as endorsed by Einstein, then it is impossible to apply the law to massive bodies in a way that is coherent with his own field equations. Rejecting this canonical interpretation, (...) I propose an alternative interpretation of the geodesic principle as a type of universality thesis analogous to the universality behavior exhibited in thermal systems during phase transitions. (shrink)

According to the standard realistic interpretation of classical electrodynamics, the electromagnetic field is conceived as a real physical entity existing in space and time. The problem we address in this paper is how to understand this spatiotemporal existence, that is, how to describe the persistence of a field-like physical entity like electromagnetic field. First, we provide a formal description of the notion of persistence: we derive an “equation of persistence” constituting a necessary condition that the spatiotemporal distributions of the fundamental (...) attributes of a persisting physical entity must satisfy. We then prove a theorem according to which the vast majority of the solutions of Maxwell’s equations, describing possible spatiotemporal distributions of the fundamental attributes of the electromagnetic field, violate the equation of persistence. Finally, we discuss the consequences of this result for the ontology of the electromagnetic field. (shrink)

In this essay, I provide an overview of the debate on infinite and essential idealizations in physics. I will first present two ostensible examples: phase transitions and the Aharonov– Bohm effect. Then, I will describe the literature on the topic as a debate between two positions: Essentialists claim that idealizations are essential or indispensable for scientific accounts of certain physical phenomena, while dispensabilists maintain that idealizations are dispensable from mature scientific theory. I will also identify some attempts at finding a (...) middle ground between the essentialists and dispensabilists camps. Finally, I will raise questions for future research on essential and infinite idealizations via the notion of exploration. (shrink)

By the 1960s many, perhaps most, philosophers had adopted 'physicalism' – the view that physical causes fully account for mental activities. However, controversy persists about what counts as 'physical causes'. 'Reductive' physicalists recognize only microphysical (elementary-particle-level) causality. Many, perhaps most, physicalists are 'non-reductive' – they hold that entities considered by other 'special' sciences have causal powers. Philosophy of chemistry can help resolve main issues in philosophy of mind in three ways: developing an extended mereology applicable to chemical combination; testing whether (...) 'singularities' prevent reduction of chemistry to microphysics; and demonstrating 'downward causation' in complex networks of chemical reactions. (shrink)

This paper discusses a conception of physics as a collection of theories that, from a logical point of view, is inconsistent. It is argued that this logical conception of the relations between physical theories is too crude. Mathematical subtleties allow for a much more nuanced and sophisticated understanding of the relations between different physical theories.

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) of them a model or a framework for modelling, from well-established mathematics or physics.I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit N→∞ of a parameter N.But on the other hand, this does not show that the N=∞ limit is “physically real”, as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real.My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics). (shrink)

In this paper I critically review the long history of attempts to formulate and derive the geodesic principle, which claims that massive bodies follow geodesic paths in general relativity theory. I argue that if the principle is interpreted as a dynamical law of motion describing the actual evolution of gravitating bodies as endorsed by Einstein, then it is impossible to apply the law to massive bodies in a way that is coherent with his own field equations. Rejecting this canonical interpretation, (...) I propose an alternative interpretation of the geodesic principle as a type of universality thesis analogous to the universality behavior exhibited in thermal systems during phase transitions. (shrink)

We examine arguments for distinguishing between ontological and epistemological concepts of fundamentality, focusing in particular on the role that scale plays in these concepts. Using the fractional quantum Hall effect as a case study, we show that we can draw a distinction between ontologically fundamental and non-fundamental theories without insisting that it is only the fundamental theories that get the ontology right: there are cases where non-fundamental theories involve distinct ontologies that better characterize real systems than fundamental ones do. In (...) order to reconcile these distinct ontologies between fundamental and non-fundamental theories, we suggest that ontology must be understood as scale-dependent. (shrink)