Some arguments against the assumption that ordinary people may share common knowledge are sound. The apparent cost of such arguments is the rejection of scientific theories that appeal to common knowledge. My proposal is to accept the arguments without rejecting the theories. On my proposal, common knowledge is shared by ideally rational people, who are not just mathematically simple versions of ordinary people. They are qualitatively different from us, and theorizing about them does not lead to predictions about our behavior. (...) Nevertheless, models of action that assume common knowledge have a role to play in our understanding of collective rationality. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

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 authors survey some debates about the nature and structure of physical theories and about the connections between our physical theories and naturalized metaphysics. The discussion is organized around an “ideal view” of physical theories and criticisms that can be raised against it. This view includes controversial commitments regarding the best analysis of physical modalities and intertheory relations. The authors consider the case in favor of taking laws as the primary modal notion, discussing objections related to alleged violations of the (...) laws, the apparent need to appeal to causality, and the status of probability. The “ideal view” includes a commitment that fundamental physical theories are explanatorily sufficient. The authors discuss several challenges to recovering the manifest image from fundamental physics, along with a distinct challenge to reductionism based on acknowledging the contributions of less fundamental theories in physical explanations. (shrink)

I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: linearization* property; I (...) then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable. (shrink)

This paper explores some connections between competing conceptions of scientific laws on the one hand, and a problem in the foundations of statistical mechanics on the other. I examine two proposals for understanding the time asymmetry of thermodynamic phenomenal: David Albert's recent proposal and a proposal that I outline based on Hans Reichenbach's “branch systems”. I sketch an argument against the former, and mount a defense of the latter by showing how to accommodate statistical mechanics to recent developments in the (...) philosophy of scientific laws. (shrink)

In his recent book, Time and Chance, David Albert claims that by positing that there is a uniform probability distribution defined, on the standard measure, over the space of microscopic states that are compatible with both the current macrocondition of the world, and with what he calls the “past hypothesis”, we can explain the time asymmetry of all of the thermodynamic behavior in the world. The principal purpose of this paper is to dispute this claim. I argue that Albert's proposal (...) fails in his stated goal—to show how to use the time‐reversible dynamics of Newtonian physics to “underwrite the actual content of our thermodynamic experience” (Albert 2000, 159). Albert's proposal can satisfactorily explain why the overall entropy of the universe as a whole is increasing, but it does not and cannot explain the increasing entropy of relatively small, relatively short‐lived systems in energetic isolation without making use of a principle that leads to reversibility objections. (shrink)

In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality (...) -- i.e. without making any assumptions about the system's dynamics or the nature of the interactions between its components -- that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another -- again fully general -- theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor, the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem. (shrink)

Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to the largest (...) macro-region. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. (shrink)

For many years—and with some energy since Laudan’s “Confutation of Convergent Realism” —the scientific realist has sought to accommodate examples of false-yet-successful theories in the history of science. One of the most prominent strategies is to identify ‘success fueling’ components of false theories that themselves are at least approximately true. In this article I develop both sides of the debate, introducing new challenges from the history of science as well as suggesting adjustments to the divide et impera realist strategy. A (...) new ‘recipe’ for the prospective identification of working/idle posits is considered. (shrink)

The paradox of phase transitions raises the problem of how to reconcile the fact that we see phase transitions happen in concrete, finite systems around us, with the fact that our best theories—i.e. statistical-mechanical theories of phase transitions—tell us that phase transitions occur only in infinite systems. In this paper we aim to clarify to which extent this paradox is relative to the mathematical framework which is used in these theories, i.e. classical mathematics. To this aim, we will explore the (...) philosophical consequences of adopting constructive instead of classical mathematics in a statistical-mechanical theory of phase transitions. It will be shown that constructive mathematics forces certain ‘de-idealizations’ of such theories: talk of actually infinite systems is meaningless, there are no discontinuous functions, and—in a sense which will be clarified—constructive real numbers reflect our imperfect methods of determining the values of physical quantities. As such, so it will be argued, constructive mathematics offers a means to gain insight in the idealizations introduced in classical theories and the philosophical issues surrounding them. (shrink)

The special composition question, which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, (...) the thermodynamic composition principle : Multiple systems in thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, might form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, “thermal contact” can be analyzed using the mereotopological predicate “self-connectedness”. Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected. (shrink)

I present a novel approach to the scholarly debate that has arisen with respect to the philosophical import one should infer from scientific accounts of phase transitions by appealing to a distinction between representation understood as denotation, and faithful representation understood as a type of guide to ontology. It is argued that the entire debate is misguided, for it stems from a pseudo-paradox that does not license the type of claims made by scholars and that what is really interesting about (...) phase transitions is the manner by which they force us to rethink issues regarding scientific representation, idealizations, and realism. (shrink)

This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. Drawing on an analogy with the Aharonov–Bohm effect, it is suggested that the standard approach to the effects— the topological approach to fractional statistics—relies essentially on problematic idealizations that need to be revised in order for the theory to be explanatory. An alternative geometric approach is outlined and (...) endorsed. Roles for idealizations in science, as well as consequences for the debate revolving around so-called essential idealizations, are discussed. (shrink)

In this paper I show how certain requirements must be set on any tenable account of scientific representation, such as the requirement allowing for misrepresentation. I then continue to argue that two leading accounts of scientific representation— the inferential account and the interpretational account—are flawed for they do not satisfy such requirements. Through such criticism, and drawing on an analogy from non-scientific representation, I also sketch the outline of a superior account. In particular, I propose to take epistemic representations to (...) be intentional objects that come with reference, semantic contents and a representational code, and I identify faithful representations as representations that act as guides to ontology. (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)

Naturalized metaphysics remains a default presupposition of much contemporary philosophy of physics. As metaphysics is supposed to be about the general structure of reality, so a naturalized metaphysics draws upon our best physical theories: Assuming the truth of such a theory, it attempts to answer the “foundational question par excellence “, “how could the world possibly be the way this theory says it is?“ It is argued that attention to historical detail in the development and formulation of physical theories serves (...) as an ever-relevant hygienic corrective to the “sentiment of rationality“ underlying the naturalistic impulse to read ontology off of physics. (shrink)

A normal state on a von Neumann algebra defines a countably additive probability measure over its projection lattice. The von Neumann algebras familiar from ordinary QM are algebras of all the bounded operators on a Hilbert space H, aka Type I factor von Neumann algebras. Their normal states are density operator states, and can be pure or mixed. In QFT and the thermodynamic limit of QSM, von Neumann algebras of more exotic types abound. Type III von Neumann algebras, for instance, (...) have no pure normal states; the pure states they do have fail to be countably additive. I will catalog a number of temptations to accord physical significance to non-normal states, and then give some reasons to resist these temptations: pure though they may be, non-normal states on non-Type I factor von Neumann algebras can't do the interpretive work we've come to expect from pure states on Type I factors; our best accounts of state preparation don't work for the preparation of non-normal states; there is a sense in which non-normal states fail to instantiate the laws of quantum mechanics. (shrink)

Foundational puzzles surround gravitational thermal physics—a realm in which stars are treated as akin to molecules in a gas. Whether such an enterprise is successful and the domain of thermal physics extends beyond our terrestrial sphere is disputed. There are successes and paradoxical features. Callender :960–981, 2011) advocates reconciling the two sides of the dispute by taking a broader view of thermodynamics. Here I argue for an alternative position: if we are careful in distinguishing statistical mechanics and thermodynamics, then no (...) reconciliation is required. Both sides can live in harmony because whilst statistical mechanics applies, thermodynamics does not. This state of affairs—the applicability of statistical mechanics without the emergence of thermodynamic behaviour—can be explained in terms of an infamous infinite idealisation: the thermodynamic limit. (shrink)

The search for the statistical mechanical underpinning of thermodynamic irreversibility has so far focussed on the spontaneous approach to equilibrium. But this is the search for the underpinning of what Brown and Uffink have dubbed the ‘minus first law’ of thermodynamics. In contrast, the second law tells us that certain interventions on equilibrium states render the initial state ‘irrecoverable’. In this article, I discuss the unusual nature of processes in thermodynamics, and the type of irreversibility that the second law embodies. (...) I then search for the microscopic underpinning or statistical mechanical ‘reductive basis’ of the second law of thermodynamics by taking a functionalist strategy. First, I outline the functional role of the thermodynamic entropy: for a thermally isolated system, the thermodynamic entropy is constant in quasi-static processes, but increasing in non-quasi-static processes. I then search for the statistical mechanical quantity that plays this role—rather than the role of the traditional ‘holy grail’ as described by Callender. I argue that in statistical mechanics, the Gibbs entropy plays this role. (shrink)

In a previous article, I argued that some recent philosophical work on the use of fictions in science is, while illuminating about some aspects of current scientific practice, unduly limited to cases of well-established fictions. In other words, this earlier work contended, a philosophical account of scientific fictions can do more than merely describe scientific practices, but can aid in the resolution of disputes about the proper interpretation of scientific theories and the epistemic status of some scientific models. In the (...) present paper, I expand upon the variational account of fictions and idealizations... (shrink)

1. Approximations of arbitrarily large but finite systems are often mistaken for infinite idealizations in statistical and thermal physics. The problem is illustrated by thermodynamically reversible processes. They are approximations of processes requiring arbitrarily long, but finite times to complete, not processes requiring an actual infinity of time.2. The present debate over whether phase transitions comprise a failure of reduction is confounded by a confusion of two senses of “level”: the molecular versus the thermodynamic level and the few component versus (...) the many component level. (shrink)

It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

This article examines ontological/dynamical aspects of emergence, specifically the micro-macro relation in cases of universal behavior. I discuss superconductivity as an emergent phenomenon, showing why microphysical features such as Cooper pairing are not necessary for deriving characteristic properties such as infinite conductivity. I claim that the difficulties surrounding the thermodynamic limit in explaining phase transitions can be countered by showing how renormalization group techniques facilitate an understanding of the physics behind the mathematics, enabling us to clarify epistemic and ontological aspects (...) of emergence. I close with a discussion of the impact of these issues for questions concerning natural kinds. (shrink)

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests (...) interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics. (shrink)

I highlight that the aim of using statistical mechanics to underpin irreversible processes is, strictly speaking, ambiguous. Traditionally, however, the task of underpinning irreversible processes has been thought to be synonymous with underpinning the Second Law of thermodynamics. I claim that contributors to the foundational discussion are best interpreted as aiming to provide a microphysical justification of the Minus First Law, despite the ways their aims are often stated. I suggest that contributors should aim at accounting for both the Minus (...) First Law and Second Law. (shrink)

The paper discusses the recent literature on abstraction/idealization in connection with the “paradox of infinite idealization.” We use the case of taking thermodynamics limit in dealing with the phenomena of phase transition and critical phenomena to broach the subject. We then argue that the method of infinite idealization is widely used in the practice of science, and not all uses of the method are the same. We then confront the compatibility problem of infinite idealization with scientific realism. We propose and (...) defend a contextualist position for realism and argue that the cases for infinite idealization appear to be fully compatible with contextual realism. (shrink)

In this paper, a criticism of the traditional theories of approximation and idealization is given as a summary of previous works. After identifying the real purpose and measure of idealization in the practice of science, it is argued that the best way to characterize idealization is not to formulate a logical model – something analogous to Hempel's D-N model for explanation – but to study its different guises in the praxis of science. A case study of it is then made (...) in thermostatistical physics. After a brief sketch of the theories for phase transitions and critical phenomena, I examine the various idealizations that go into the making of models at three difference levels. The intended result is to induce a deeper appreciation of the complexity and fruitfulness of idealization in the praxis of model-building, not to give an abstract theory of it. (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)

In this survey, we discuss and analyze foundational issues of the problem of time and its asymmetry from a unified standpoint. Our aim is to discuss concisely the current theories and underlying notions, including interdisciplinary aspects, such as the role of time and temporality in quantum and statistical physics, biology, and cosmology. We compare some sophisticated ideas and approaches for the treatment of the problem of time and its asymmetry by thoroughly considering various aspects of the second law of thermodynamics, (...) nonequilibrium entropy, entropy production, and irreversibility. The concept of irreversibility is discussed carefully and reanalyzed in this connection to clarify the concept of entropy production, which is a marked characteristic of irreversibility. The role of boundary conditions in the distinction between past and future is discussed with attention in this context. The paper also includes a synthesis of past and present research and a survey of methodology. It also analyzes some open questions in the field from a critical perspective. (shrink)

Several modern accounts of explanation acknowledge the importance of abstraction and idealization for our explanatory practice. However, once we allow a role for abstraction, questions remain. I ask whether the relation between explanations at different theoretical levels should be thought of wholly in terms of abstraction, and argue that changes of the quantities in terms of which we describe a system can lead to novel explanations that are not merely abstractions of some more detailed picture. I use the example of (...) phase transitions as described by statistical mechanics and thermodynamics to illustrate this, and to demonstrate some details of the relationship between abstraction, idealization, and novel explanation. (shrink)

It has commonly been argued that certain types of mental descriptions, specifically those characterized in terms of propositional attitudes, are part of a folk psychological understanding of the mind. Recently, however, it has also been argued that this is the case even when such descriptions are employed as part of scientific theories in domains like social psychology and comparative psychology. In this paper, I argue that there is no plausible way to understand the distinction between folk and scientific psychology that (...) can support such claims. Moreover, these sorts of claims can have adverse consequences for the neuroscientific study of the brain by downplaying the value of many psychological theories that provide information neuroscientists need in order to build and test neurological models. (shrink)

Special sciences (such as biology, psychology, economics) describe various regularities holding at some high macroscopic level. One of the central questions concerning these macroscopic regularities is how they are related to the laws of physics governing the underlying microscopic physical reality. In this paper we show how a macroscopic regularity may emerge from an underlying micro- scopic structure, and how the appearance of multiple realizability of the special sciences by physics comes about in a reductionist-physicalist framework. On this basis we (...) explain how complexity at the high level can arise due to a sort of harmony between the microscopic dynamics and observer-dependent macroscopic properties. We show that observer-dependent properties, which underlie the emergence of macroscopic properties and of macroscopic complexity, are objective physical facts. We argue that such physical properties remove the mystery from the multiple realizability of special sciences’ kinds, since the latter are grounded in shared physical properties. Finally we explain how and in what sense in our reductive physicalist approach the special sciences are still autonomous after all. (shrink)

This paper proposes a classification of the intertheoretic relations in physics by bringing out the conditions for a relation of reduction which is eliminative, so that a theory reduced in terms of reductionism is superfluous in principle, and by distinguishing such a relation from another one based on comparison, which will be called neighbourhood of theories; the latter is a neighbouring relation between theories and is not able to support claims of eliminative reductionism. In the first part, it will be (...) argued that this differentiation between neighbourhood and eliminative reduction permits an adequate classification of the intertheoretic relations in physics. By means of this differentiation, the second part discusses reductionism and shows that there are indeed some historical examples of reduction in the aforementioned sense, but that modern physical theories are typically only neighbouring. (shrink)

I argue that there are two distinct approaches to understanding reduction: the ontology-first approach and the theory-first approach. They concern the relation between ontological reduction and inter-theoretic reduction. Further, I argue for the significance of this distinction by demonstrating that either one or the other approach has been taken as an implicit assumption in, and has in fact shaped, our understanding of what statistical mechanics is. More specifically, I argue that the Boltzmannian framework of statistical mechanics assumes and relies on (...) the ontology-first approach, whereas the Gibbsian framework should assume the theory-first approach. -/- . (shrink)

An important contemporary version of Boltzmannian statistical mechanics explains the approach to equilibrium in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognized as such and not clearly distinguished. This article identifies three different versions of typicality‐based explanations of thermodynamic‐like behavior and evaluates their respective successes. The conclusion is that the first two are unsuccessful because they fail to take the system's dynamics into account. The third, however, is promising. (...) I give a precise formulation of the proposal and present an argument in support of its central contention. †To contact the author, please write to: Department of Philosophy, Logic, and Scientific Method, London School of Economics, Houghton Street, London WC2A 2AE, England; e‐mail: [email protected]. (shrink)

Review of Laura Ruetsche's book "Interpreting Quantum Theories".

Gases reach equilibrium when left to themselves. Why do they behave in this way? The canonical answer to this question, originally proffered by Boltzmann, is that the systems have to be ergodic. This answer has been criticised on different grounds and is now widely regarded as flawed. In this paper we argue that some of the main arguments against Boltzmann's answer, in particular, arguments based on the KAM-theorem and the Markus-Meyer theorem, are beside the point. We then argue that something (...) close to Boltzmann's original proposal is true for gases: gases behave thermodynamic-like if they are epsilon-ergodic, i.e., ergodic on the entire accessible phase space except for a small region of measure epsilon. This answer is promising because there are good reasons to believe that relevant systems in statistical mechanics are epsilon-ergodic. (shrink)

Gibbsian statistical mechanics (GSM) is the most widely used version of statistical mechanics among working physicists. Yet a closer look at GSM reveals that it is unclear what the theory actually says and how it bears on experimental practice. The root cause of the difficulties is the status of the Averaging Principle, the proposition that what we observe in an experiment is the ensemble average of a phase function. We review different stances toward this principle, and eventually present a coherent (...) interpretation of GSM that provides an account of the status and scope of the principle. (shrink)

Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT—for example, the standard textbook formulation and the rigorous axiomatic formulation—that are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. New arguments are offered for basing the interpretation of QFT (...) on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case. *Received June 2009; revised August 2009. †To contact the author, please write to: Department of Philosophy, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada; e‐mail: [email protected]. (shrink)

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)

We offer a framework for organizing the literature regarding the debates revolving around infinite idealizations in science, and a short summary of the contributions to this special issue.

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)

ABSTRACT 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. 1Introduction 2Preliminaries 3Three Extremist Interpretations 3.1Algebraic imperialism 3.2Hilbert space conservatism 3.3Universalism 4Parochial (...) Observables 4.1Parochial observables for the imperialist 4.2Parochial observables for the universalist 5Conclusion. (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)