Theory Reduction

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model extends (...) the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

This expository paper presents a general framework for representing levels and inter-level relations. The framework is intended to capture both epistemic and ontological notions of levels and to clarify the sense in which levels of explanation might or might not be related to a levelled ontology. The framework also allows us to study and compare different kinds of inter-level relations, especially supervenience and reduction but also grounding and mereological constitution. This, in turn, enables us to explore questions such as whether (...) supervenience implies explanatory reducibility and whether there can be irreducible higher-level explanations or even “emergent” higher-level properties. The paper finally discusses some further philosophical applications: to the free-will debate, the determinism-indeterminism distinction, indexicality and consciousness, and the relationship between positive and normative facts. (shrink)

There is a widely shared belief that the higher-level sciences can provide better explanations than lower-level sciences. But there is little agreement about exactly why this is so. It is often suggested that higher-level explanations are better because they omit details. I will argue instead that the preference for higher-level explanations is just a special case of our general preference for informative, logically strong, beliefs. I argue that our preference for informative beliefs entirely accounts for why higher-level explanations are sometimes (...) better—and sometimes worse—than lower-level explanations. The result is a step in the direction of the unity of science hypothesis. 1Introduction2Background: Is Omitting Details an Explanatory Virtue? 2.1Anti-reductionist arguments2.2Reductionist argument2.3Logical strength3Bases, Links and Logical Strength4Functionalism and Fodor’s Argument5Two Generalizations6Should the Base Really Be Maximally Strong?7Anti-reductionist Arguments Regarding the Base8Should the Antecedent of the Link Really Be Maximally Weak? (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)

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)

Principles are central to physical reasoning, particularly in the search for a theory of quantum gravity (QG), where novel empirical data is lacking. One principle widely adopted in the search for QG is UV completion: the idea that a theory should (formally) hold up to all possible high energies. We argue---/contra/ standard scientific practice---that UV-completion is poorly-motivated as a guiding principle in theory-construction, and cannot be used as a criterion of theory-justification in the search for QG. For this, we explore (...) the reasons for expecting, or desiring, a UV-complete theory, as well as analyse how UV completion is used, and how it should be used, in various specific approaches to QG. (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)

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)

The mind-brain identity theory, the thesis that sensations are identical with properties or processes of the brain, was introduced into contemporary discussion by U.T. Place, Herbert Feigl, and J.J.C Smart in the 1950s. Despite its widespread rejection in the following decades, the identity theory has received several carefully articulated defenses in recent years. Aside from developing novel responses to well-known arguments against the identity theory, contemporary identity theorists have argued that the epistemological resources available to support the adoption of identities (...) are more plentiful than has often been supposed; further, they have argued that mind-brain identities allow for the resolution of otherwise intractable explanatory puzzles about the phenomenal properties of experience. From an epistemological perspective, identity theorists have thus argued that a central reason for believing theoretical identities—both mind-brain identities as well as more mundane identities such as water = H2O—stems from the explanatory power that they confer. Yet from an explanatory perspective, identity theorists have maintained that identities cannot themselves be explained; indeed, they have maintained that it is hardly intelligible to request an explanation for an identity. This paper considers these ideas draws out an important tension between them. The central claim is that insofar as identity theorists insist on the explanatorily efficacy of identities, they should concede that there is a good sense in which theoretical identities can be explained. However, it is moreover argued that this concession is not especially problematic and, indeed, ought to be welcomed by identity theorists. (shrink)

Philosophers of science have offered different accounts of what it means for one scientific theory to reduce to another. I propose a more or less friendly amendment to Kenneth Schaffner’s “General Reduction-Replacement” model of scientific unification. Schaffner interprets scientific unification broadly in terms of a continuum from theory reduction to theory replacement. As such, his account leaves no place on its continuum for type irreducible and irreplaceable theories. The same is true for other accounts that incorporate Schaffner's continuum, for example, (...) those developed by Paul Churchland, Clifford Hooker, and John Bickle. Yet I believe a more general account of scientific unification should include type irreducible and irreplaceable theories in an account of their partial reduction, specifically, when there is a reduction of their tokens. Thus I propose a “Reduction-Reception-Replacement” model wherein type irreducible and irreplaceable theories are accepted or received for the purpose of unifying domains of particulars. I also suggest a link between this kind of token reduction and mechanistic explanation. (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)

I critically evaluate Bickle’s version of scientific theory reduction. I press three main points. First, a small point, Bickle modifies the new wave account of reduction developed by Paul Churchland and Clifford Hooker by treating theories as set-theoretic structures. But that structuralist gloss seems to lose what was distinctive about the Churchland-Hooker account, namely, that a corrected theory must be specified entirely by terms and concepts drawn from the basic reducing theory. Set-theoretic structures are not terms or concepts but the (...) structures that they describe. Second, and more serious, a familiar problem for classical positivist account of reduction resurfaces within this newest wave of thinking, namely, commitment to property identities and inter-theoretic bridge laws (a problem I discussed at more length in "Collapse of the New Wave"). Indeed, this problem is exacerbated by Bickle’s conciliatory treatment of property plasticity, since he is willing to grant that a large number of special science terms denote multiply realized properties, at least if realistically construed. Still, in the end, Bickle sidesteps the reduction of properties by appealing to Hooker’s "function-to-structure token reduction." This is an interesting move with an intriguing concept of reduction. But problems remain. For, third, Bickle and Hooker's function-to-structure token reduction is actually a guised form of eliminative materialism. But that should be unacceptable since the position extends well beyond any modest revisionism for suspect items from a folk theory, say, in folk psychology or folk biology. Instead, it applies to functional terms and concepts employed throughout well-developed and explanatorily successful sciences. (shrink)

"New wave" reductionism aims at advancing a kind of reduction that is stronger than unilateral dependency of the mental on the physical. It revolves around the idea that reduction between theoretical levels is a matter of degree, and can be laid out on a continuum between a "smooth" pole (theoretical identity) and a "bumpy" pole (extremely revisionary). It also entails that both higher and lower levels of the reductive relationship sustain some degree of explanatory autonomy. The new wave predicts that (...) reductions of folk psychology to neuroscience will be located in the middle of this continuum; as neuroscientific evidence about mental states checks in, theoretical folk psychology will therefore be moderately revised. However, the model has conceptual problems which preclude its success in reviving reductionism, and its commitment to a syntactic approach wrecks its attempt to rescue folk psychology. Moreover, the architecture of the continuum operates on a category mistake that sneaks in an eliminativist conclusion. I argue that new wave reductionism therefore tends to be eliminativism in disguise. (shrink)

I critically evaluate the influential new wave account of theory reduction in science developed by Paul Churchland and Clifford Hooker. First, I cast doubt on claims that the new wave account enjoys a number of theoretical virtues over its competitors, such as the ability to represent how false theories are reduced by true theories. Second, I argue that the genuinely novel claim that a corrected theory must be specified entirely by terms from the basic reducing theory is in fact too (...) restrictive for scientific practice and should be rejected. Basic theories co-evolve with nonbasic theories in a mutually interactive way, and thus the basic theories incorporate the concepts and concerns of nonbasic theories. Third, I show that once its ontological consequences are duly noted, the reductive part the new wave account collapses into the classical theory developed within the logical empiricist tradition. As such, it still falls prey to standard anti-reductionist argument based upon multiple realizability and the cross-classification of special science and physical science terms. (shrink)

In light of the phenomenon of multiple realizability, many philosophers wanted to preserve the mind-brain identity theory by resorting to a “narrow reductive strategy” whereby one (a) finds mental properties which are (b) sufficiently narrow to avoid the phenomenon of multiple realization, while being (c) explanatorily adequate to the demands of psychological theorizing. That is, one replaces the conception of a mental property as more general feature of cognitive systems with many less general properties, for example, replacing the conception of (...) pain as a general property across different species with a number of species-specific kinds of pain. Many critics focused on (c), arguing that species-specific properties are not explanatorily adequate because they do not capture what is common in pain across species. In this paper I focused on (b). I argued that if one carries the narrow reductive strategy out in such a way to avoid all multiple realizability that occurs within a species, for example, accommodating individual differences by postulating a more narrow pain-relative-to-an-individual-at-a-time, then the result is for all intents and purposes a claim about tokens and not types or properties at all (the position is now about individuals having properties at times, a structured token event). I also added an important point about explanation, viz., that properties-relative-to-individuals-at-times would not serve the explanatory goals of science by failing to generalize to other individuals. (shrink)