Nagel's analysis of reduction: Comments in defense as well as critique

Despite all the criticism showered on Nagel's classic account of reduction, it meets a fundamental desideratum in an analysis of reduction that is difficult to question, namely of providing for a proper identification of the reducing theory. This is not clearly accommodated in radically different accounts. However, the same feature leads me to question Nagel's claim that the reducing theory can be separated from the putative bridge laws, and thus to question his notion of heterogeneous reduction. A further corollary to the requirement that all the necessary conditions be incorporated in an adequate formulation of the putative reducing theory is that the standard example of gas temperature is not reducible to average molecular kinetic energy. As originally conceived, Nagel's conception of reduction takes no account of approximate reasoning and this failure has certainly restricted its applicability, perhaps to the point of making it unrealistic as a model of reduction in science. I suggest approximation can be accommodated by weakening the original requirement of deduction without jeopardizing the fundamental desideratum. Finally, I turn to briefly consider the idea sometimes raised of the ontological reducibility of chemistry.     

Taking up statistical thermodynamics: Equilibrium fluctuations and irreversibility

The microscopic explanation of the physical phenomena represented by a macroscopic theory is often cast in terms of the reduction of the latter to a more fundamental theory, which represents the same phenomena at the microscopic level, albeit in an idealized way. In particular, the reduction of thermodynamics to statistical mechanics is a much discussed case-study in philosophy of physics. Based on the Generalized Nagel–Schaffner model, the alleged reductive explanation would be accomplished if one finds a corrected version of classical thermodynamics that can be strictly derived from statistical mechanics. That is the sense in which, according to Callender (1999, 2001), one should not take thermodynamics too seriously. Arguably, the sought-after revision is given by statistical thermodynamics, intended as a macroscopic theory equipped with a probabilistic law of equilibrium fluctuations. The present paper aims to evaluate this proposal. The upshot is that, while statistical thermodynamics enables one to re-define equilibrium so as to agree with Boltzmann entropy, it does not provide a definitive solution to the problem of explaining macroscopic irreversibility from a microscopic point of view.     

Reduction redux

Putnam's criticisms of the identity theory attack a straw man. Fodor's criticisms of reduction attack a straw man. Properly interpreted, Nagel offered a conception of reduction that captures everything a physicalist could want. I update Nagel, introducing the idea of overlap, and show why multiple realization poses no challenge to reduction so construed.     

No understanding without explanation

Scientific understanding, this paper argues, can be analyzed entirely in terms of a mental act of “grasping” and a notion of explanation. To understand why a phenomenon occurs is to grasp a correct explanation of the phenomenon. To understand a scientific theory is to be able to construct, or at least to grasp, a range of potential explanations in which that theory accounts for other phenomena. There is no route to scientific understanding, then, that does not go by way of scientific explanation.     

In defence of story-telling

We argue that narratives are central to the success of historical reconstruction. Narrative explanation involves tracing causal trajectories across time. The construction of narrative, then, often involves postulating relatively speculative causal connections between comparatively well-established events. But speculation is not always idle or harmful: it also aids in overcoming local underdetermination by forming scaffolds from which new evidence becomes relevant. Moreover, as our understanding of the past's causal milieus become richer, the constraints on narrative plausibility become increasingly strict: a narrative's admissibility does not turn on mere logical consistency with background data. Finally, narrative explanation and explanation generated by simple, formal models complement one another. Where models often achieve isolation and precision at the cost of simplification and abstraction, narratives can track complex changes in a trajectory over time at the cost of simplicity and precision. In combination both allow us to understand and explain highly complex historical sequences.     

The curvature argument

Dasgupta (2015) has recently put forward a novel argument, which he calls the ‘curvature argument’, that aims to show that Galilean spacetime is not an ideal setting for our classical theory of motion. This paper examines the curvature argument and argues that it is not sound. The discussion yields a remark about the conditions under which a ‘symmetry argument’ demonstrates that a particular spacetime is a non-ideal setting for our theory of motion.     

An integrated bayesian vector auto regression and error correction model for forecasting electricity consumption and prices

The analysis and forecasting of electricity consumption and prices has received considerable attention over the past forty years. In the 1950s and 1960s most of these forecasts and analyses were generated by simultaneous equation econometric models. Beginning in the 1970s, there was a shift in the modeling of economic variables from the structural equations approach with strong identifying restrictions towards a joint time-series model with very few restrictions. One such model is the vector auto regression (VAR) model. It was soon discovered that the unrestricted VAR models do not forecast well. The Bayesian vector auto regression (BVAR) approach as well the error correction model (ECM) and models based on the theory of co integration have been offered as alternatives to the simple VAR model. This paper argues that the BVAF., ECM, and co integration models are simply VAR models with various restrictions placed on the coefficients. Based on this notion of a restricted VAR model, a four-step procedure for specifying VAR forecasting models is presented and then applied to monthly data on US electricity consumption and prices.     

Duality as a category-theoretic concept

In a paper published in 1939, Ernest Nagel described the role that projective duality had played in the reformulation of mathematical understanding through the turn of the nineteenth century, claiming that the discovery of the principle of duality had freed mathematicians from the belief that their task was to describe intuitive elements. While instances of duality in mathematics have increased enormously through the twentieth century, philosophers since Nagel have paid little attention to the phenomenon. In this paper I will argue that a reassessment is overdue. Something beyond doubt is that category theory has an enormous amount to say on the subject, for example, in terms of arrow reversal, dualising objects and adjunctions. These developments have coincided with changes in our understanding of identity and structure within mathematics. While it transpires that physicists have employed the term ‘duality’ in ways which do not always coincide with those of mathematicians, analysis of the latter should still prove very useful to philosophers of physics. Consequently, category theory presents itself as an extremely important language for the philosophy of physics.     

Essentially narrative explanations

This essay argues that narrative explanations prove uniquely suited to answering certain explanatory questions, and offers reasons why recognizing a type of statement that requires narrative explanations crucially informs on their assessment. My explication of narrative explanation begins by identifying two interrelated sources of philosophical unhappiness with them. The first I term the problem of logical formlessness and the second the problem of evaluative intractability. With regard to the first, narratives simply do not appear to instantiate any logical form recognized as inference licensing. But absent a means of identifying inferential links, what justifies connecting explanans and explanandum? Evaluative intractability, the second problem, thus seems a direct consequence. This essay shows exactly why these complaints prove unfounded by explicating narrative explanations in the process of answering three interrelated questions. First, what determines that an explanation has in some critical or essential respect a narrative form? Second, how does a narrative in such cases come to constitute a plausible explanation? Third, how do the first two considerations yield a basis for evaluating an explanation offered as a narrative? Answers to each of these questions include illustrations of actual narrative explanations and also function to underline attendant dimensions of evaluation.     

Local reduction in physics

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

The empirical basis of equilibrium: Mach, Vailati, and the lever

About a century ago, Ernst Mach argued that Archimedes’s deduction of the principle of the lever is invalid, since its premises contain the conclusion to be demonstrated. Subsequently, many scholars defended Archimedes, mostly on historical grounds, by raising objections to Mach’s reconstruction of Archimedes’s deduction. In the debate, the Italian philosopher and historian of science Giovanni Vailati stood out. Vailati responded to Mach with an analysis of Archimedes’s deduction which was later quoted and praised by Mach himself. In this paper, my objective is to show that the debate can be further advanced, as Mach indicated, by reframing it in terms of the empirical vs. the logical dimensions of mechanics. In this way, I will suggest, the debate about Archimedes’s deduction can be resolved in Mach’s favour.     

Defining disposition concepts: A brief history of the problem

The aim of this paper is twofold. Firstly, I give a brief account of the history of the debate on the problem of defining disposition concepts from its beginning in the late 1920s until today. This account is divided into four parts, corresponding with 2, 3, 4 and 5 of the paper, each of which deals with a major period of the debate. Section 2 reports up to the mid-1950s. Section 3 deals with important contributions to the discussion between 1955 and 1958. However, the progress made around that time was far ahead of the logical theory and techniques which were needed for foundational reasons and for a better understanding of the basic notions. Some logical techniques appropriate for that aim were developed in the late 1960s and early 1970s. Though not uncontroversial, those logical techniques resulted in improvements of the insights gained in the mid-1950s; I shall report on those logical techniques and their application to the problem of defining disposition concepts in Section 4. In the early 1990s, however, the whole tradition of defining disposition concepts in terms of conditionals has been challenged by some strong counter-examples which are treated in Section 5. Finally, the second of the aims of this paper is explored in Section 6, in which I sketch very briefly the current stage of the debate by discussing and evaluating the most recent approaches to the subject.     

A New‐Keynesian DSGE model for forecasting the South African economy

This paper develops a New‐Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model for forecasting the growth rate of output, inflation, and the nominal short‐term interest rate (91 days Treasury Bill rate) for the South African economy. The model is estimated via maximum likelihood technique for quarterly data over the period of 1970:1–2000:4. Based on a recursive estimation using the Kalman filter algorithm, out‐of‐sample forecasts from the NKDSGE model are compared with forecasts generated from the classical and Bayesian variants of vector autoregression (VAR) models for the period 2001:1–2006:4. The results indicate that in terms of out‐of‐sample forecasting, the NKDSGE model outperforms both the classical and Bayesian VARs for inflation, but not for output growth and nominal short‐term interest rate. However, differences in RMSEs are not significant across the models. Copyright © 2008 John Wiley & Sons, Ltd.     

Understanding,explanation, and unification

In this article I argue that there are two different types of understanding: the understanding we get from explanations, and the understanding we get from unification. This claim is defended by first showing that explanation and unification are not as closely related as has sometimes been thought. A critical appraisal of recent proposals for understanding without explanation leads us to discuss the example of a purely classificatory biology: it turns out that such a science can give us understanding of the world through unification of the phenomena, even though it does not give us any explanations. The two types of understanding identified in this paper, while strictly separate, do have in common that both consist in seeing how the individual phenomena of the universe hang together. Explanations give us connections between the phenomena through the asymmetric, ‘vertical’ relation of determination; unifications give us connections through the symmetric, ‘horizontal’ relation of kinship. We then arrive at a general definition of understanding as knowledge of connections between the phenomena, and indicate that there might be more than two types of understanding.     

Was Feyerabend an anarchist? The structure(s) of ‘anything goes’

The near consensus in the secondary literature on Feyerabend is that his epistemological anarchism, characterized by the slogan ‘anything goes’, was not a positive proposal but the conclusion of a reductio argument against his opponents (Lloyd 1997; Staley 1999; Munévar 2000; Farrell 2003; Tsou 2003; Oberheim 2006; Roe 2009). This makes anarchism a mere criticism rather than a substantive position in its own right. In this paper, I argue that Feyerabend held anarchism as a positive thesis. Specifically, I present two possible interpretations of anarchism: one where anarchism is entailed by Feyerabend's radical view of pluralism and another where scientists must be ‘methodological opportunists’, which Feyerabend held simultaneously from at least 1970. I then consider how these positions fare against the more influential criticisms of anarchism (Nagel 1977; Worrall 1978; Godfrey-Smith 2003). I conclude by suggesting two avenues to constraining a literal interpretation of ‘anything goes’ on Feyerabendian grounds.     

Kant's universal conception of natural history

Scholars often draw attention to the remarkably individual and progressive character of Kant's Universal Natural History and Theory of the Heavens (1755). What is less often noted, however, is that Kant's project builds on several transformations that occurred in natural science during the seventeenth and eighteenth centuries. Without contextualising Kant's argument within these transformations, the full sense of Kant's achievement remains unseen. This paper situates Kant's essay within the analogical form of Newtonianism developed by a diverse range of naturalists including Georges Buffon, Albrecht von Haller and Thomas Wright. It argues that Kant's universal conception of natural history can be viewed within the free-thinking and anti-clerical movement associated with Buffon. This does not mean, however, that it breaks from the methodological rules of Newtonianism. The claim of this paper is that Kant's essay contributes to the transformation of natural history from a logical system of classification to an explanation for the physical diversity of natural products according to laws.     

The ontic conception of scientific explanation

Wesley Salmon's version of the ontic conception of explanation is a main historical root of contemporary work on mechanistic explanation. This paper examines and critiques the philosophical merits of Salmon's version, and argues that his conception's most fundamental construct is either fundamentally obscure, or else reduces to a non-ontic conception of explanation. Either way, the ontic conception is a misconception.     

Interpretation neutrality in the classical domain of quantum theory

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

Spacetime Visualisation and the Intelligibility of Physical Theories

This paper argues that spacetime visualisability is not a necessary condition for the intelligibility of theories in physics. Visualisation can be an important tool for rendering a theory intelligible, but it is by no means a sine qua non. The paper examines the historical transition from classical to quantum physics, and analyses the role of visualisability (Anschaulichkeit) and its relation to intelligibility. On the basis of this historical analysis, an alternative conception of the intelligibility of scientific theories is proposed, based on Heisenberg's reinterpretation of the notion of Anschaulichkeit.