It is demonstrated that the reduction of a physical theory S to another one, T, in the sense that S can be derived from T holds in general only for the mathematical framework. The interpretation of S and the associated central terms cannot all be derived from those of T because of the qualitative differences between the cognitive levels of S and T. Their cognitively autonomous status leads to an epistemic as well as an ontological pluralism. This pluralism is (...) consistent with the unity of nature in the sense of a substantive monism. (shrink)

The paper sets out a new strategy for theory reduction by means of functional sub-types. This strategy is intended to get around the multiple realization objection. We use Kim's argument for token identity (ontological reductionism) based on the causal exclusion problem as starting point. We then extend ontological reductionism to epistemological reductionism (theory reduction). We show how one can distinguish within any functional type between functional sub-types. Each of these sub-types is coextensive with one type of realizer. By (...) this means, a conservative theory reduction is in principle possible, despite multiple realization. We link this account with Nagelian reduction, as well as with Kim's functional reduction. (shrink)

Philosophers of science since Nagel have been interested in the links between intertheoretic reduction and explanation, understanding and other forms of epistemic progress. Although intertheoretic reduction is widely agreed to occur in pure mathematics as well as empirical science, the relationship between reduction and explanation in the mathematical setting has rarely been investigated in a similarly serious way. This paper examines an important particular case: the reduction of arithmetic to set theory. I claim that the reduction is (...) unexplanatory. In defense of this claim, I offer evidence from mathematical practice, and I respond to contrary suggestions due to Steinhart, Maddy, Kitcher and Quine. I then show how, even if set-theoretic reductions are generally not explanatory, set theory can nevertheless serve as a legitimate foundation for mathematics. Finally, some implications of my thesis for philosophy of mathematics and philosophy of science are discussed. In particular, I suggest that some reductions in mathematics are probably explanatory, and I propose that differing standards of theory acceptance might account for the apparent lack of unexplanatory reductions in the empirical sciences. (shrink)

The aim of this essay is a criticism of reductionism ? both in its ?static? interpretation (usually referred to as the layer model or level?picture of science) and in its ?dynamic? interpretation (as a theory of the growth of scientific knowledge), with emphasis on the latter ? from the point of view of Popperian fallibilism and Feyerabendian pluralism, but without being committed to the idiosyncrasies of these standpoints. In both aspects of criticism, the rejection is based on the (...) proposal of a global alternative. Hummell and Opp's research programme for the reduction of sociology to psychology is used as a starting?point and taken as the primary object of criticism. Following the introductory Section I, Section II analyses the three crucial notions of Hummell and Opp's research programme ? their explications of the notions of ?sociology?, ?psychology? and the concept of reduction itself ? and criticizes the authors? deficient ?logic of reduction?. Although the ?local? shortcomings of our authors? ?logic of reduction? do not affect reductionism as such, i.e. logically sound versions of reductionism as devised by Kemeny, Nagel, Oppenheim, Putnam, Woodger et al., it is argued that the logical soundness of sophisticated reductionism cannot compensate for its additional epistemological and methodological deficiencies. Section III analyses the ?dynamic? interpretation of reductionism as a particular developmental pattern of scientific growth. It is argued that even reductionism at its best can produce only cumulative progress, thus ?a priori? excluding scientific revolutions which are inevitably counter?inductive as well as counter?reductive. Section IV discusses the philosophical background of modern reductionism, and examines the effects both of reductionism and of anti?reductionistic pluralism on the autonomy of scientific fields. It is argued that pluralistic anti?reductionism undermines spurious claims for autonomy much more effectively than reductionism. As a ?local? improvement of the reductionistic research programme, the replacement of the predominant one?way reductionism by a less restrictive many?way reductionism is proposed. It is argued that the appropriate treatment for an allegedly backward science (say sociology) is not its reduction to an allegedly more advanced science (say psychology) but its non?reductive replacement by new theories (of the same or of another field) that do not incorporate the older ones. As a ?global? alternative to the reduction of sociology to psychology, the frontier?crossing direct application of psychological theories to sociological phenomena is proposed. A plea is made for a pluralistic science without reduction, based on intra? and interscientific criticism as the proper method for the advancement of knowledge. (shrink)

Schaffner’s model of theory reduction has played an important role in philosophy of science and philosophy of biology. Here, the model is found to be problematic because of an internal tension. Indeed, standard antireductionist external criticisms concerning reduction functions and laws in biology do not provide a full picture of the limits of Schaffner’s model. However, despite the internal tension, his model usefully highlights the importance of regulative ideals associated with the search for derivational, and embedding, deductive relations (...) among mathematical structures in theoretical biology. A reconstructed Schaffnerian model could therefore shed light on mathematical theory development in the biological sciences and on the epistemology of mathematical practices more generally. *Received November 2006; revised March 2009. †To contact the author, please write to: Philosophy Department, University of California, Santa Cruz, 1156 High St., Santa Cruz, CA 95064; e‐mail: [email protected]. (shrink)

In 1973, Nickles identified two senses in which the term `reduction' is used to describe the relationship between physical theories: namely, the sense based on Nagel's seminal account of reduction in the sciences, and the sense that seeks to extract one physical theory as a mathematical limit of another. These two approaches have since been the focus of most literature on the subject, as evidenced by recent work of Batterman and Butterfield, among others. In this paper, I discuss a (...) third sense in which one physical theory may be said to reduce to another. This approach, which I call `dynamical systems reduction,' concerns the reduction of individual models of physical theories rather than the wholesale reduction of entire theories, and specifically reduction between models that can be formulated as dynamical systems. DS reduction is based on the requirement that there exist a function from the state space of the low-level model to that of the high-level model that satisfies certain general constraints and thereby serves to identify quantities in the low-level model that mimic the behavior of those in the high-level model - but typically only when restricted to a certain domain of parameters and states within the low-level model. I discuss the relationship of this account of reduction to the Nagelian and limit-based accounts, arguing that it is distinct from both but exhibits strong parallels with a particular version of Nagelian reduction, and that the domain restrictions employed by the DS approach may, but need not, be specified in a manner characteristic of the limit-based approach. Finally, I consider some limitations of the account of reduction that I propose and suggest ways in which it might be generalised. I offer a simple, idealised example to illustrate application of this approach; a series of more realistic case studies of DS reduction is presented in another paper. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

An examination of earlier views yields an account of theoretic change on which changes in theory which do involve changes in meanings of terms are classified as a special (and by no means exhaustive) case of theoretic change which, latter, is construed as a more general phenomenon. Only the general problem is given detailed consideration here. The account given considers the problem of how replacement of intensional theories by extensional ones may be treated within the general framework provided. Among (...) its results is the conclusion that rational changes in a scientific theory may be cogently construed as determined by warranted decisions that a new theory is more adequate (than the old one it replaces) with regard to purposes for which a theory is sought. (shrink)

The problem of idealization in empirical sciences is very rarely taken up in works concerned with the methodology of those sciences. It seems to be common knowledge that in advanced natural sciences references are made to concepts such as “perfectly rigid body,” “material point,” “perfect gas,” etc., but it remains a fact that the most important methodological concepts, concepts which have determined the present-day form of the philosophy of science, have been advanced without regard to the peculiarities of the (...) procedure mentioned above. And yet a moment's consideration suffices to raise doubts as to Carnap's physicalism and/or Popper's falsificationism if we just realize the trivial and commonly known truth that empirical sciences resort to idealizationism. For how are we to imagine a reduction of idealizational concepts to observation terms? And how are we to imagine that theorems which include idealizational concepts imply observation statements which refute, or at least are at variance with, those theorems? But it is a fact that such doubts have neither been raised by the authors of the conceptions mentioned above, nor have they been raised against them. (shrink)

Are the theoretical frameworks of phenomenology and of science compatible? And, if so, what would a reconciliation entail for science as it is practiced? Gallagher [2019] poses these two questions, answering the first in the affirmative and leaving the second unaddressed. I argue that treating the two as separate questions presupposes an inadequate distinction between theory and practice that Gallagher’s non-reductive framework motivates rejecting. Recognizing the intertwining of theory and practice allows us to answer Gallagher’s two (...) questions about phenomenology and science all at once, but it also motivates a less conciliatory conclusion than the one he offers. (shrink)

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, (...) using examples from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

Some people claim that evolution is "just a theory". Do you know what a scientific theory really is? Just a theory is an overview of the modern concepts of science. A clear understanding of the nature of science will enable you to distinguish science from pseudoscience (which illegitimately wraps itself in the mantle of science), and real social issues in science from the caricatures portrayed in postmodernist critiques. Prof. Ben-Ari's style is light (...) (even humorous) and easy to read, bringing the latest concepts of science to the general reader. Of particular interest is his analysis of the terminology of science (fact, law, proof, theory) in relation to the colloquial meaning of these terms. Between chapters are biographical vignettes of scientists — both familiar and unfamiliar — showing their common commitment to the enterprise of science, together with a diversity of backgrounds and personalities. This accessible, informative, and comprehensive work will give lay readers a good grasp of real science. (shrink)

Explanatory pluralism is the view that the best form and level of explanation depends on the kind of question one seeks to answer by the explanation, and that in order to answer all questions in the best way possible, we need more than one form and level of explanation. In the first part of this article, we argue that explanatory pluralism holds for the medical sciences, at least in theory. However, in the second part of the article we show (...) that medical research and practice is actually not fully and truly explanatory pluralist yet. Although the literature demonstrates a slowly growing interest in non-reductive explanations in medicine, the dominant approach in medicine is still methodologically reductionist. This implies that non-reductive explanations often do not get the attention they deserve. We argue that the field of medicine could benefit greatly by reconsidering its reductive tendencies and becoming fully and truly explanatory pluralist. Nonetheless, trying to achieve the right balance in the search for and application of reductive and non-reductive explanations will in any case be a difficult exercise. (shrink)

Science presents us with a variety of accounts of the world. While some of these accounts posit deep theoretical structure and fundamental entities, others do not. But which of these approaches is the right one? How should science conceptualize the world? And what is the relation between the various accounts? Opinions on these issues diverge wildly in philosophy of science. At one extreme are reductionists who argue that higher-level theories should, in principle, be incorporated in, or eliminated (...) by, the basic-level theory. According to this view, higher-level theories do not ultimately exhibit conceptual integrity or provide genuine explanations. At the other extreme are pluralists who take higher levels of description and explanation seriously and argue for their independence and indispensability. It was the aim of the first Sydney–Tilburg conference on “Reduction and the Special Sciences”, which took place at the Tilburg Center for Logic and Philosophy of Science (TiLPS) in Tilburg, The Netherlands, over the 10–12th April 2008, to bring researchers working on these questions together and provide a platform to discuss them in a focused way. The papers in this special issue were presented at this conference. We would like to thank the Royal Netherlands Academy of Art and Sciences (KNAW), the Sydney Centre for the Foundations of Science at the University of Sydney and TiLPS for financial and institutional support. We also thank the authors and referees of the papers for their work, and Hans Rott for his support of this project. (shrink)

The goals of reduction andreductionism in the natural sciences are mainly explanatoryin character, while those inmathematics are primarily foundational.In contrast to global reductionistprograms which aim to reduce all ofmathematics to one supposedly ``universal'' system or foundational scheme, reductive proof theory pursues local reductions of one formal system to another which is more justified in some sense. In this direction, two specific rationales have been proposed as aims for reductive proof theory, the constructive consistency-proof rationale and the foundational reduction (...) rationale. However, recent advances in proof theory force one to consider the viability of these rationales. Despite the genuine problems of foundational significance raised by that work, the paper concludes with a defense of reductive proof theory at a minimum as one of the principal means to lay out what rests on what in mathematics. In an extensive appendix to the paper,various reduction relations betweensystems are explained and compared, and arguments against proof-theoretic reduction as a ``good'' reducibilityrelation are taken up and rebutted. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and (...) in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

The reductive strategies, such as the deductive-nomological (DN) model of explanation, or the Nagel–Schaffner reduction, have been perceived negatively ever since their first applications in historical inquiry. However, the role of the analysis of inter-theory relations, such as the preservation of success and retrospective rationality, has hardly ever received much attention from historians of science. In this paper, I am exploring the applicability of the analysis of inter-theory relations for the rational reconstruction of the development of (...) class='Hi'>science. I demonstrate that the historiography of Anneliese Maier is a good example of a few reductive strategies at play in historical inquiry that do not submit to the same criticism that the synchronic reductive analysis of theories is submitted to. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search including proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences.

The Three Papers comprising this series, together with my earlier [34] also published in this journal, constitute an attempt to set out the major issues in the theoretical domain of reduction and to develop a general theory of theory reduction. The fourth paper, [34], though published separately from this trio, is integral to the presentation and should be read in conjunction with these papers. Even so, the presentation is limited in scope – roughly, to intertheoretic reduction among empirical (...) theories – and informal in presentation – not least because a satisfying formal account of theories has yet to be offered. And despite the length, the treatment is still condensed; often corroborating and/or intuitively helpful detail has had to be consigned to footnotes or omitted. I approach the problem from within my own naturalistic realist philosophy of science and formal analysis of abstract hierarchy in theory. The sources for the former are [25], [29], [31], and [32] and those for the latter essentially [27] and [30]. Hierarchical notions played a significant role in the already published [34]. (shrink)

One of the hallmarks of Kantian philosophy, especially in connection with its characterization of scientific knowledge, is the importance of unity, a theme that is also the driving force behind a good deal of contemporary high energy physics. There are a variety of ways that unity figures in modern science—there is unity of method where the same kinds of mathematical techniques are used in different sciences, like physics and biology; the search for unified theories like the unification of electromagnetism (...) and optics by Maxwell; and, more recently, the project of grand unification or the quest for a theory of everything which involves a reduction of the four fundamental forces under the umbrella of a single theory. In this latter case it is thought that when energies are high enough, the forces , while very different in strength, range and the types of particles on which they act, become one and the same force. The fact that these interactions are known to have many underlying mathematical features in common suggests that they can all be described by a unified field theory. Such a theory describes elementary particles in terms of force fields which further unifies all the interactions by treating particles and interactions in a technically and conceptually similar way. It is this theoretical framework that allows for the prediction that measurements made at a certain energy level will supposedly indicate that there is only one type of force. In other words, not only is there an ontological reduction of the forces themselves but the mathematical framework used to describe the fields associated with these forces facilitates their description in a unified theory. Specific types of symmetries serve an important function in establishing these kinds of unity, not only in the construction of quantum field theories but also in the classification of particles; classifications that can lead to new predictions and new ways of understanding properties like quantum numbers. Hence, in order to address issues about unification and reduction in contemporary physics we must also address the way that symmetries facilitate these processes. (shrink)

Theories in the usual sense, as characterized by a language and a set of theorems in that language ("statement view"), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models ("non-statement view", J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called "representations" of theories in the statement sense and vice versa, where representations (...) are understood as functions that map sentences of one theory into another theory. It is argued that commensurability between theories should be based on functions on open formulas and open terms so that reducibility does not necessarily imply commensurability. This is in accordance with a central claim by Stegmüller on the compatibility of reducibility and incommensurability that has recently been challenged by D. Pearce. (shrink)

The inapplicability of variations on theory reduction in the context of genetics and their irrelevance to ongoing research has led to an anti-reductionist consensus in philosophy of biology. One response to this situation is to focus on forms of reductive explanation that better correspond to actual scientific reasoning (e.g. part–whole relations). Working from this perspective, we explore three different aspects (intrinsicality, fundamentality, and temporality) that arise from distinct facets of reductive explanation: composition and causation. Concentrating on these aspects generates (...) new forms of reductive explanation and conditions for their success or failure in biology and other sciences. This analysis is illustrated using the case of protein folding in molecular biology, which demonstrates its applicability and relevance, as well as illuminating the complexity of reductive reasoning in a specific biological context. (shrink)

Recent debates about the metaphysics of mind have tended to assume that inter-theoretic reductions are the norm in the natural sciences. With this assumption in place, the apparent explanatory gaps surrounding consciousness and intentionality seem unique, fascinating, and perhaps metaphysically significant. Over the past several decades, however, philosophers of science have largely rejected the notions that inter-theoretic reduction is either widespread in the natural sciences or a litmus for the legitimacy of the special sciences. If we adopt a post-reductionist (...) philosophy of science, with a commitment to theory pluralism, the epistemic statuses of the standard positions in philosophy of mind (reductionism, non-reductive physicalism, dualism) are all significantly changed. Moreover, central problems of recent philosophy of mind – reducibility and the explanatory gap – seem themselves to be in need of rethinking if reductions are rare and the sciences have “explanatory gaps all the way down.” This article examines the prospects of the standard metaphysical positions, plus two types of pluralism, in light of post-reductionist philosophy of science. (shrink)

The numerous and diverse roles of theory reduction in science have been insufficiently explored in the philosophy literature on reduction. Part of the reason for this has been a lack of attention paid to reduction2 (successional reduction)---although I here argue that this sense of reduction is closer to reduction1 (explanatory reduction) than is commonly recognised, and I use an account of reduction that is neutral between the two. This paper draws attention to the utility---and incredible versatility---of theory (...) reduction. A non-exhaustive list of various applications of reduction in science is presented, some of which are drawn from a particular case-study, being the current search for a new theory of fundamental physics. This case-study is especially interesting because it employs both senses of reduction at once, and because of the huge weight being put on reduction by the different research groups involved; additionally, it presents some unique uses for reduction---revealing, I argue, the fact that reduction can be of specialised and unexpected service in particular scientific cases. The paper makes two other general findings: that the functions of reduction that are typically assumed to characterise the different forms of the relation may instead be understood as secondary consequences of some other roles; and that most of the roles that reduction plays in science can actually also be fulfilled by a weaker relation than (the typical understanding of) reduction. (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.

One of the hallmarks of Kantian philosophy, especially in connection with its characterization of scientific knowledge, is the importance of unity, a theme that is also the driving force behind a good deal of contemporary high energy physics. There are a variety of ways that unity figures in modern science—there is unity of method where the same kinds of mathematical techniques are used in different sciences, like physics and biology; the search for unified theories like the unification of electromagnetism (...) and optics by Maxwell; and, more recently, the project of grand unification or the quest for a theory of everything which involves a reduction of the four fundamental forces under the umbrella of a single theory. In this latter case it is thought that when energies are high enough, the forces, while very different in strength, range and the types of particles on which they act, become one and the same force. The fact that these interactions are known to have many underlying mathematical features in common suggests that they can all be described by a unified field theory. Such a theory describes elementary particles in terms of force fields which further unifies all the interactions by treating particles and interactions in a technically and conceptually similar way. It is this theoretical framework that allows for the prediction that measurements made at a certain energy level will supposedly indicate that there is only one type of force. In other words, not only is there an ontological reduction of the forces themselves but the mathematical framework used to describe the fields associated with these forces facilitates their description in a unified theory. Specific types of symmetries serve an important function in establishing these kinds of unity, not only in the construction of quantum field theories but also in the classification of particles; classifications that can lead to new predictions and new ways of understanding properties like quantum numbers. Hence, in order to address issues about unification and reduction in contemporary physics we must also address the way that symmetries facilitate these processes. (shrink)

I analyse Rueger’s application of Kim’s model of functional reduction to the relation between the thermal conductivities of metal bars at macroscopic and atomic scales. 1) I show that it is a misunderstanding to accuse the functional reduction model of not accounting for the fact that there are causal powers at the micro-level which have no equivalent at the macro-level. The model not only allows but requires that the causal powers by virtue of which a functional predicate is defined, are (...) only a subset of the causal powers of the properties filling the functional specification. 2) The fact that the micro-equation does not converge to the macro-equation in general but only under the constraint of a “solvability condition” does not show that reduction is impossible, as Rueger claims, but only that reduction requires inter-level constraints. 3) Rueger tries to analyse inter-level reduction with the conceptual means of intra-level reduction. This threatens the coherence of his analysis, given that it makes no sense to ascribe macroproperties such as thermal conductivity to entities at the atomic level. Ignoring the distinction between theses two senses of “reduction” is especially confusing because they have opposite directions: in intra-level reduction, the more detailed account reduces to the less detailed one, whereas in inter-level reduction, the less detailed theory is reduced to the more detailed one. 4) Finally I criticize Rueger’s way of using Wimsatt’s criteria for emergence in terms of non-aggregativity, to construct a concept of synchronic emergence. It is wrong to require, over and above non-aggregativity, irreducibility as a criterion for emergence. (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)

Ontology should be conceived as supervenient on scientific theories. They tell us what categories of things there really are. Thus, we would have a unique system of ontology if we would attain the unity of science through a reductionist program. For this, it should be clear how a relation of intertheoretical reduction (with ontological implications) is to be conceived. A formal proposal is laid out in this paper. This allows us also to define the notion of a fundamental (...) class='Hi'>theory. Now, it appears that, considering the state of really existing science, the idea of reductionism as based on this explication is highly implausible. However, even if this is the case, the question whether it is possible to build up a unique ontological system remains open. Its resolution depends on the notion of compatibility between fundamental theories, and its application to existing theories and their empirical bases. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and (...) in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (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)

It is often claimed (1) that levels of nature are related by supervenience, and (2) that processes occurring at particular levels of nature should be studied using dynamical systems theory. However, there has been little consideration of how these claims are related. To address the issue, I show how supervenience relations give rise to ‘supervenience functions’, and use these functions to show how dynamical systems at different levels are related to one another. I then use this analysis to describe (...) a graded approach to non-reductive physicalism, and to critically assess Davidson’s arguments for psychological anomaly. I also show how this approach can inform empirical research in cognitive science. (shrink)

The numerous and diverse roles of theory reduction in science have been insufficiently explored in the philosophy literature on reduction. Part of the reason for this has been a lack of attention paid to reduction2 (successional reduction)—although I here argue that this sense of reduction is closer to reduction1 (explanatory reduction) than is commonly recognised, and I use an account of reduction that is neutral between the two. This paper draws attention to the utility—and incredible versatility—of theory (...) reduction. A non-exhaustive list of various applications of reduction in science is presented, some of which are drawn from a particular case-study, being the current search for a new theory of fundamental physics. This case-study is especially interesting because it employs both senses of reduction at once, and because of the huge weight being put on reduction by the different research groups involved; additionally, it presents some unique uses for reduction—revealing, I argue, the fact that reduction can be of specialised and unexpected service in particular scientific cases. The paper makes two other general findings: that the functions of reduction that are typically assumed to characterise the different forms of the relation may instead be understood as secondary consequences of some other roles; and that most of the roles that reduction plays in science can actually also be fulfilled by a weaker relation than (the typical understanding of) reduction. (shrink)

Discussions of unified science frequently suppose that the various scientific theories should be combined into one unified theory, and it is usually supposed that this should be done by successive reductions of the various theories to some fundamental theory. Yet, there has been little systematic study of the characteristics of unified theories, and little foundational support for the use of reductions as a unifying procedure. In this paper I: (a) briefly review some of my previous work on (...) microreductions, (b) state some conditions which are necessary in order for a theory to be unified, (c) argue that when certain identities exist between the elements in the domains of two theories, then the only satisfactory way to combine these two theories into one unified theory is by a micro-reduction, and (d) indicate briefly some further applications and consequences of this work. (shrink)

In this book, Roy Bhaskar sets out to revindicate ontology, critiquing the reduction of being in favor of knowledge, which he calls the "epistemic fallacy".

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O (...) comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type. (shrink)

Science presents us with a variety of accounts of the world. While some of these accounts posit deep theoretical structure and fundamental entities, others do not. But which of these approaches is the right one? How should science conceptualize the world? And what is the relation between the various accounts? Opinions on these issues diverge wildly in philosophy of science. At one extreme are reductionists who argue that higher-level theories should, in principle, be incorporated in, or eliminated (...) by, the basic-level theory. According to this view, higher-level theories do not ultimately exhibit conceptual integrity or provide genuine explanations. At the other extreme are pluralists who take higher levels of description and explanation seriously and argue for their independence and indispensability. It was the aim of the first Sydney–Tilburg conference on “Reduction and the Special Sciences”, which took place at the Tilburg Center for Logic and Philosophy of Science (TiLPS) in Tilburg, The Netherlands, over the 10–12th April 2008, to bring researchers working on these questions together and provide a platform to discuss them in a focused way. The papers in this special issue were presented at this conference. We would like to thank the Royal Netherlands Academy of Art and Sciences (KNAW), the Sydney Centre for the Foundations of Science at the University of Sydney and TiLPS for financial and institutional support. We also thank the authors and referees of the papers for their work, and Hans Rott for his support of this project. (shrink)

In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions (...) of a reducing theory T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (shrink)

The propositions, that what we see around us is real and that reality should be represented by the statevector, conflict with quantum theory. In quantum theory, the statevector can readily become a sum of states of comparable norm, each state representing a different reality. In this paper we present the Continuous Spontaneous Localization (CSL) theory, in which a modified Schrodinger equation, while scarcely affecting the dynamics of a microscopic system, rapidly "reduces" the statevector of a macroscopic system (...) to a state appropriate for representing individual reality. (shrink)

Nagel’s official model of theory-reduction and the way it is represented in the literature are shown to be incompatible with the careful remarks on the notion of reduction Nagel gave while developing his model. Based on these remarks, an alternative model is outlined which does not face some of the problems the official model faces. Taking the context in which Nagel developed his model into account, it is shown that the way Nagel shaped his model and, thus, its well-known (...) deficiencies, are best conceived of as a mere by-product of his philosophical background. (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)

To model the organization of levels' of cortical dynamics, at least some general scheme for hierarchy, functional diversity, and proper intrinsic control must be provided. Rhythmic control forces the system to iterate its state by short trajectories, which makes it much more stable and predictable without discarding the desirable ability of chaotic systems to make rapid phase transitions. Rhythmic control provides a fundamentally different systems dynamics, one not provided by models that allow the emergence of continuous trajectories in the systems (...) state space. (shrink)