A conventional wisdom about the progress of physics holds that successive theories wholly encompass the domains of their predecessors through a process that is often called reduction. While certain influential accounts of inter-theory reduction in physics take reduction to require a single "global" derivation of one theory's laws from those of another, I show that global reductions are not available in all cases where the conventional wisdom requires reduction to hold. However, I argue that a weaker "local" form of reduction, (...) which defines reduction between theories in terms of a more fundamental notion of reduction between models of a single fixed system, is available in such cases and moreover suffices to uphold the conventional wisdom. To illustrate the sort of fixed-system, inter-model reduction that grounds inter-theoretic reduction on this picture, I specialize to a particular class of cases in which both models are dynamical systems. I show that reduction in these cases is underwritten by a mathematical relationship that follows the broad prescriptions of Nagel/Schaffner reduction, and support this claim with several examples. Moreover, I show that this broadly Nagelian analysis of inter-model reduction encompasses several cases that are sometimes cited as instances of the "physicist's" limit-based notion of reduction. (shrink)

Models represent their target systems in one way or another. But what does it mean for a model to represent something beyond itself? This paper details different aspects of this problem and argues that the semantic view of theories does not provide us with an adequate response to any of these.

We introduce a new model of reduction inspired by Kemeny and Oppenheim’s model [Kemeny & Oppenheim 1956] and argue that this model is operative in a “ruthlessly reductive” part of current neuroscience. Kemeny and Oppenheim’s model was quickly rejected in mid-20th-century philosophy of science and replaced by models developed by Ernest Nagel and Kenneth Schaffner [Nagel 1961], [Schaffner 1967]. We think that Kemeny and Oppenheim’s model was correctly rejected, given what a “theory of reduction” was supposed to account for at (...) that time. But their guiding insights about what constitutes scientific reduction—increases in explanatory scope and systematization—reflect actual practices of current reductionistic neuroscience. The key rehabilitative step to make their insights fit current scientific details is to restate them using resources from recent work on causal-mechanistic explanation. We begin with a scientific case study, drawn from the relatively new field of “molecular and cellular cognition”. It provides an explanation of the well-known Ebbinghaus spacing effect on learning and memory in terms of interactions between a transcriptional enhancer protein and its inhibiting phosphatase in neurons recruited into the memory trace. Next we briefly describe some popular models of reduction from mid-20th-century philosophy of science. We point out how these models fail to illuminate key features of our scientific case study. Finally we present our causal-mechanistically updated Kemeny and Oppenheim-inspired model and argue that it nicely accounts for the details of our scientific case study. We close with a remark that will hopefully undercut the surprise many may feel to learn that a long-rejected philosophical account of reduction actually is at work in one of the most prominent reductionistic endeavors in current science. (shrink)

Reductionism is often understood to include two theses: (1) every singular occurrence that the special sciences can explain also can be explained by physics; (2) every law in a higher-level science can be explained by physics. These claims are widely supposed to have been refuted by the multiple realizability argument, formulated by Putnam (1967, 1975) and Fodor (1968, 1975). The present paper criticizes the argument and identifies a reductionistic thesis that follows from one of the argument's premises.

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general (...) view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified and often ambiguous picture that treats reduction simply as a matter of taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. (shrink)

I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of (...) physical reality that both serve to describe. Focusing on the relationship between classical and quantum mechanics, I argue that while certain formal results concerning singular \ limits have been taken to preclude the possibility of reduction between these theories, such results at most provide support for the claim that singular limits block reduction in the formal sense; little if any reason has been given for thinking that they block reduction in the empirical sense. I then briefly outline a strategy for empirical reduction that is suggested by work on decoherence theory, arguing that this sort of account remains a fully viable route to the empirical reduction of classical to quantum mechanics and is unaffected by such singular limits. (shrink)

Any theory of reduction that goes only so far as carried in Parts I and II does only half the job. Prima facie at least, there are cases of would-be reduction which seem torn between two conflicting intuitions. On the one side there is a strong intuition that reduction is involved, and a strongly retentive reduction at that. On the other side it seems that the concepts at one level cross-classify those at the other level, so that there is no (...) way to identify properties at one level with those at the other. There is evidence to suggest that there will be no unique mental state/neural state association that can be set up, because, e.g., many different parts of the nervous system are all capable of taking over ‘control’ of the one mental function. And it is alleged that infinitely many, worse: indefinitely many, different bio-chemo-physical states could correspond to the economic property ‘has a monetary system of economic exchange’; and similarly for the property ‘has just won a game of tennis’. Yet one doesn't want an economic system or a game of tennis to be some ghostly addition to the actual bio-chemo-physical processes and events involved. Similarly one hopes that neurophysiology allied with the rest of natural science will render human experience and behaviour explicable. (shrink)

Halvorson argues that the semantic view of theories leads to absurdities. Glymour shows how to inoculate the semantic view against Halvorson's criticisms, namely by making it into a syntactic view of theories. I argue that this modified semantic-syntactic view cannot do the philosophical work that the original "language-free" semantic view was supposed to do.

With this manifesto, John Dupré systematically attacks the ideal of scientific unity by showing how its underlying assumptions are at odds with the central conclusions of science itself.

We reconsider the Nagelian theory of reduction and argue that, contrary to a widely held view, it is the right analysis of intertheoretic reduction. The alleged difficulties of the theory either vanish upon closer inspection or turn out to be substantive philosophical questions rather than knock-down arguments.

The Dappled World: A Study of the Boundaries of Science. nancy cartwright. Plato's Reception of Parmenides. john a. palmer.

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)

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

It is often supposed that the spectacular successes of our modern mathematical sciences support a lofty vision of a world completely ordered by one single elegant theory. In this book Nancy Cartwright argues to the contrary. When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in (...) their own diverse ways. This patchwork makes sense when we realise that laws are very special productions of nature, requiring very special arrangements for their generation. Combining classic and newly written essays on physics and economics, The Dappled World carries important philosophical consequences and offers serious lessons for both the natural and the social sciences. (shrink)

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.

It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view (...) of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought. (shrink)

Interference phenomena are a well-known and crucial feature of quantum mechanics, the two-slit experiment providing a standard example. There are situations, however, in which interference effects are (artificially or spontaneously) suppressed. We shall need to make precise what this means, but the theory of decoherence is the study of (spontaneous) interactions between a system and its environment that lead to such suppression of interference. This study includes detailed modelling of system-environment interactions, derivation of equations (‘master equations’) for the (reduced) state (...) of the system, discussion of time-scales etc. A discussion of the concept of suppression of interference and a simplified survey of the theory is given in Section 2, emphasising features that will be relevant to the following discussion (and restricted to standard non-relativistic particle quantum mechanics.[1] A partially overlapping field is that of decoherent histories, which proceeds from an abstract definition of loss of interference, but which we shall not be considering in any detail. (shrink)

This paper addresses the recent resurgence of Nagel style reduction in the philosophical literature. In particular, it considers the so-called multiple realizability objection to reductionism presented most forcefully by Sober in 1999. It is argued that this objection misses the point of multiple realizability and that there remain serious problems for reductionist methodologies in science.

I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level model to that of the high-level model that approximately (...) commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application to a number of particular inter-theory reductions in physics involving quantum theory. I consider three reductions: first, connecting classical mechanics and non-relativistic quantum mechanics; second,connecting classical electrodynamics and quantum electrodynamics; and third, connecting non-relativistic quantum mechanics and quantum electrodynamics. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity. (shrink)