On Understanding: Maxwell on the Methods of Illustration and Scientific Metaphor

In this paper I examine the notion and role of metaphors and illustrations in Maxwell's works in exact science as a pathway into a broader and richer philosophical conception of a scientist and scientific practice. While some of these notions and methods are still at work in current scientific research—from economics and biology to quantum computation and quantum field theory—, here I have chosen to attest to their entrenchment and complexity in actual science by attempting to make some conceptual sense of Maxwell's own usage; this endeavour includes situating Maxwell's conceptions and applications in his own culture of Victorian science and philosophy. I trace Maxwell's notions to the formulation of the problem of understanding, or interpreting, abstract representations such as potential functions and Lagrangian equations. I articulate the solution in terms of abstract-concrete relations, where the concrete, in tune with Victorian British psychology and engineering, includes the muscular as well as the pictorial. This sets the basis for a conception of understanding in terms of unification and concrete modelling, or representation. I examine the relation of illustration to analogies and metaphors on which this account rests. Lastly, I stress and explain the importance of context-dependence, its consequences for realism-instrumentalism debates, and Maxwell's own emphasis on method.     

Constructing dystopian experience: A Neurath-Cartwrightian approach to the philosophy of social technology

Social situations, the object of the social sciences, are complex and unique: they contain so many variable aspects that they cannot be reproduced, and it is even difficult to experience two situations that are alike in many respects. The social scientists' past experiences that serve as their background knowledge to intervene in an existent situation is poor compared to what a traditional epistemologist would consider ideal. A way of dealing with the variable and insufficient background of social scientists is by means of models. But, then, how should we characterize social scientific models? This paper examines Otto Neurath's scientific utopianism as an attempt to deal with this problem. Neurath proposes that social scientists work with utopias: broad imaginative plans that coordinate a multitude of features of a social situation. This notion can be used in current debates in philosophy of science because we notice that utopias, in Neurath's sense, are comparable to models and nomological machines in Nancy Cartwright's conception. A model-based view of science lays emphasis on the fact that scientists learn from the repeated operation of such abstract entities, just as they learn from the repetition of experiments in a laboratory. Hence this approach suggests an approximation between the natural and the social sciences, as well as between science and utopian literature. This is exemplified by analyzing the literary dystopia We, written by Yevgeny Zamyatin, to show that reasoning from and debating about utopian writings, even if fictional and pessimistic, creates phenomena of valuation, which are fundamental for constituting a background of experiences in the social sciences.     

The double nature of Maxwell's physical analogies

Building upon work by Mary Hesse (1974), this paper aims to show that a single method of investigation lies behind Maxwell's use of physical analogies in his major scientific works before the Treatise on Electricity and Magnetism. Key to understanding the operation of this method is to recognize that Maxwell's physical analogies are intended to possess an ‘inductive’ function in addition to an ‘illustrative’ one. That is to say, they not only serve to clarify the equations proposed for an unfamiliar domain with a working interpretation drawn from a more familiar science, but can also be sources of defeasible yet relatively strong arguments from features of the more familiar domain to features of the less. Compared with the reconstructions by Achinstein (1991), Siegel (1991), Harman (1998) and others, which postulate a discontinuity in Maxwell's approach to physical analogy, the account defended in this paper i) makes sense of the continuity in Maxwell's remarks on scientific methodology, ii) explains his quest for a “mathematical classification of physical quantities” and iii) offers a new and more plausible interpretation of the debated episode of the introduction of the displacement current in Maxwell's “On Physical Lines of Forces”.     

What's nu? A re-examination of Maxwell's ‘ratio-of-units’ argument,from the mechanical theory of the electromagnetic field to ‘On the elementary relations between electrical measurements’

This re-examination of the earliest version of Maxwell's most important argument for the electromagnetic theory of light—the equality between the speed of wave propagation in the electromagnetic ether and the ratio of electrostatic to electromagnetic measures of electrical quantity—establishes unforeseen connections between Maxwell's theoretical electrical metrology and his mechanical theory of the electromagnetic field. Electrical metrology was not neutral with respect to field-theoretic versus action-at-a-distance conceptions of electro-magnetic interaction. Mutual accommodation between these conceptions was reached by Maxwell on the British Association for the Advancement of Science (BAAS) Committee on Electrical Standards by exploiting the measurement of the medium parameters—electric inductive capacity and magnetic permeability—on an arbitrary scale. While he always worked within this constraint in developing the ‘ratio-of-units’ argument mathematically, I maintain that Maxwell came to conceive of the ratio ‘as a velocity’ by treating the medium parameters as physical quantities that could be measured absolutely, which was only possible via the correspondences between electrical and mechanical quantities established in the mechanical theory. I thereby correct two closely-related misconceptions of the ratio-of-units argument—the counterintuitive but widespread notion that the ratio is naturally a speed, and the supposition that Maxwell either inferred or proved this from its dimensional formula.     

Whewell on the classification of the sciences

Despite deserving a place amongst the historic milestones of the philosophy of disciplines, the system of the sciences put forward by Whewell has so far received little interest. Yet his ideas had a significant impact on the researches subsequently carried out on the topic, exerting in particular a decisive influence on Peirce and Spencer. The present paper aims to display the innovatory nature of the philosophical foundations of the Whewellian classification of the sciences. In this respect, we will argue that the most striking feature of his disciplinary system lies in a heuristic categorization of the sciences according to their “methods of discovery”. This represents a double departure from both the Aristotelian and the Baconian disciplinary paradigms, which are instead underpinned by ontological and epistemological criteria, respectively. Next, we will explore the pivotal role of Whewell's classification of the sciences for his overall project of a philosophy of scientific discovery.     

Kant on anatomy and the status of the life sciences

This paper contributes to recent interest in Kant's engagement with the life sciences by focusing on one corner of those sciences that has received comparatively little attention: physical and comparative anatomy. By attending to remarks spread across Kant's writings, we gain some insight into Kant's understanding of the disciplinary limitations but also the methodological sophistication of the study of anatomy and physiology. Insofar as Kant highlights anatomy as a paradigmatic science guided by the principle of teleology in the Critique of the Power of Judgment, a more careful study of Kant's discussions of anatomy promises to illuminate some of the obscurities of that text and of his understanding of the life sciences more generally. In the end, it is argued, Kant's ambivalence with regard to anatomy gives way to a pessimistic conclusion about the possibility that anatomy, natural history, and, by extension, the life sciences more generally might one day become true natural sciences.     

Nagel on reduction

This paper attempts a critical reappraisal of Nagel's (1961, 1970) model of reduction taking into account both traditional criticisms and recent defenses. This model treats reduction as a type of explanation in which a reduced theory is explained by a reducing theory after their relevant representational items have been suitably connected. In accordance with the deductive-nomological model, the explanation is supposed to consist of a logical deduction. Nagel was a pluralist about both the logical form of the connections between the reduced and reducing theories (which could be conditionals or biconditionals) and their epistemological status (as analytic connections, conventions, or synthetic claims). This paper defends Nagel's pluralism on both counts and, in the process, argues that the multiple realizability objection to reductionism is misplaced. It also argues that the Nagel model correctly characterizes reduction as a type of explanation. However, it notes that logical deduction must be replaced by a broader class of inferential techniques that allow for different types of approximation. Whereas Nagel (1970), in contrast to his earlier position (1961), recognized the relevance of approximation, he did not realize its full import for the model. Throughout the paper two case studies are used to illustrate the arguments: the putative reduction of classical thermodynamics to the kinetic theory of matter and that of classical genetics to molecular biology.     

An overlooked autograph letter of Galileo on the thermometer

Scientism applies the ideas and methods of the natural sciences to the humanities and social sciences. Herbert Spencer applied the law of the conservation of energy to social questions and arrived at formula answers to the issues of the day. The kind of certitude that Spencer aimed for was possible only by ignoring a system of values. Much as he may have believed that he was above personal beliefs, there are values implicit in Spencer's theories and they are the values of the nineteenth-century British middle class. Reasoning by analogy is as valid in social theory as it is in the natural sciences. Spencer's error was in universally applying the idea of the conservation of energy to social systems by means of identity rather than by analogy. Scientists in Britain, where there was a self-assured scientific community, dismissed Spencer's theories as being unscientific, but he enjoyed a vogue in the United States.     

Kant and the nature of matter: Mechanics,chemistry, and the life sciences

Kant believed that the ultimate processes that regulate the behavior of material bodies can be characterized exclusively in terms of mechanics. In 1790, turning his attention to the life sciences, he raised a potential problem for his mechanically-based account, namely that many of the operations described in the life sciences seemed to operate teleologically. He argued that the life sciences do indeed require us to think in teleological terms, but that this is a fact about us, not about the processes themselves. Nevertheless, even were we to concede his account of the life sciences, this would not secure the credentials of mechanics as a general theory of matter. Hardly any material properties studied in the second half of the eighteenth century were, or could have been, conceived in mechanical terms. Kant's concern with teleology is tangential to the problems facing a general matter theory grounded in mechanics, for the most pressing issues have nothing to do with teleology. They derive rather from a lack of any connection between mechanical forces and material properties. This is evident in chemistry, which Kant dismisses as being unscientific on the grounds that it cannot be formulated in mechanical terms.     

Maxwell's role in turning the concept of model into the methodology of modeling

This is a contribution towards a history and philosophy of modeling in its early stages in electromagnetism. In 1873, James Clerk Maxwell (1831–1879) hinted at the methodology of modeling at the end of his Treatise on Electricity and Magnetism. We focus on Maxwell's impact on physicists who immediately followed him, specifically Oliver Lodge (1851–1940) and George Francis FitzGerald (1851–1901). We begin with the role that the scientific concept of model played in the late nineteenth century, as assessed by Ludwig Boltzmann (1844–1906). We then discuss the role of hypothesis as a methodology, the appeal to (dynamical) illustration, and the way Maxwell applied model and working model in his studies of electromagnetism. We show that for Maxwell these key terms were kept distinct, but Lodge did not maintain these distinctions and, in this regard, FitzGerald followed Lodge. Notwithstanding Lodge's influence, Fitzgerald modified Maxwell's theory based on the mechanical model he designed, thereby implicitly taking the first step towards modeling. This methodology consists in drawing consequences from the (mechanical) model to the (electrodynamic) theory and modifying the latter in light of the functioning of the former. At the core of our argument is the thesis that it was a methodological novelty to move from the concept of model to the methodology of modeling. The introduction of modeling as a new methodology into physics in the late nineteenth century was a major event which deserves proper recognition.     

Chance,determinism and the classical theory of probability

This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning.     

Kant on science and normativity

The aim of this paper is to explore Kant’s account of normativity through the prism of the distinction between the natural and the human sciences. Although the pragmatic orientation of the human sciences is often defined in contrast with the theoretical orientation of the natural sciences, I show that they are in fact regulated by one and the same norm, namely reason’s demand for autonomy.     

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.     

From secondary causes to artificial instruments: Pierre-Sylvain Régis's rethinking of scholastic accounts of causation

Although several of Descartes's disciples established occasionalism as the natural outcome of Cartesianism, Pierre-Sylvain Régis forcefully resisted this conclusion by developing an account of secondary causes in which God does not immediately intervene in the natural world. In order to understand this view, it has been argued that Régis melds Aquinas's concurrentism with the new, mechanist natural philosophy defended in Cartesian physics. In this paper, I contend that such a reading of Régis's position is misleading for our understanding of both his account of secondary causality and the relationship between medieval debates and seventeenth century natural philosophy. I show that Régis's account of secondary causality denies two fundamental features at the core of the account proposed by Aquinas, namely that God acts immediately in nature and that secondary causes are per se causes. I contend that Régis's view more closely resembles a specific account of artificial instrumental causality developed by Duns Scotus. The comparison with Scotus shows that Régis is still dealing with conceptual tools that can be traced back to the scholastic tradition. Yet, Régis implements these tools to establish an account of causation that is fundamentally irreconcilable with scholastic natural philosophy.     

Rehabilitating the regulative use of reason: Kant on empirical and chemical laws

In his Kritik der reinen Vernunft, Kant asserts that laws of nature “carry with them an expression of necessity” (A159/B198). There is, however, widespread interpretive disagreement regarding the nature and source of the necessity of empirical laws of natural sciences in Kant's system. It is especially unclear how chemistry—a science without a clear, straightforward connection to the a priori principles of the understanding—could contain such genuine, empirical laws. Existing accounts of the necessity of causal laws unfortunately fail to illuminate the possibility of non-physical laws. In this paper, I develop an alternative, ‘ideational’ account of natural laws, according to which ideas of reason necessitate the laws of some non-physical sciences. Chemical laws, for instance, are grounded on ideas of the elements, and the chemist aims to reduce her phenomena to these elements via experimentation. Although such ideas are beyond the possibility of experience, their postulation is necessary for the achievement of reason's theoretical ends: the unification and explanation of the cognitions of science.     

Edward Gresham’s Astrostereon,or A Discourse of the Falling of the Planet (1603), the Copernican paradox,and the construction of early modern proto-scientific discourse

This paper investigates the functioning of the ‘Copernican paradox’ (stating that the Sun stands still and the Earth revolves around the Sun) in the late sixteenth- and early seventeenth-century England, with particular attention to Edward Gresham's (1565–1613) little-known and hitherto understudied astronomical treatise – Astrostereon, or A Discourse of the Falling of the Planet (1603). The text, which is fully appreciative of the heliocentric system, is analysed within a broader context of the ongoing struggles with the Copernican theory at the turn of the seventeenth century. The article finds that apart from having a purely rhetorical function, the ‘Copernican paradox’ featured in the epistemological debates on how early modern scientific knowledge should be constructed and popularised. The introduction of new scientific claims to sceptical audiences had to be done both through mathematical demonstrations and by referring to the familiar concepts and tools drawn from the inventory of humanist education. As this article shows, Gresham's rhetorical techniques used for the rejection of paradoxicality of heliocentrism are similar to some of the practices which Thomas Digges and William Gilbert employed in order to defend their own findings and assertions.     

Where explanation ends: Understanding as the place the spade turns in the social sciences

Explanations implicitly end with something that makes sense, and begin with something that does not make sense. A statistical relationship, for example, a numerical fact, does not make sense; an explanation of this relationship adds something, such as causal information, which does make sense, and provides an endpoint for the sense-making process. Does social science differ from natural science in this respect? One difference is that in the natural sciences, models are what need “understanding.” In the social sciences, matters are more complex. There are models, such as causal models, which need to be understood, but also depend on background knowledge that goes beyond the model and the correlations that make it up, which produces a regress. The background knowledge is knowledge of in-filling mechanisms, which are normally made up of elements that involve the direct understanding of the acting and believing subjects themselves. These models, and social science explanations generally, are satisfactory only when they end the regress in this kind of understanding or use direct understanding evidence to decide between alternative mechanism explanations.     

Evaluation of correlation forecasting models for risk management

Reliable correlation forecasts are of paramount importance in modern risk management systems. A plethora of correlation forecasting models have been proposed in the open literature, yet their impact on the accuracy of value‐at‐risk calculations has not been explicitly investigated. In this paper, traditional and modern correlation forecasting techniques are compared using standard statistical and risk management loss functions. Three portfolios consisting of stocks, bonds and currencies are considered. We find that GARCH models can better account for the correlation's dynamic structure in the stock and bond portfolios. On the other hand, simpler specifications such as the historical mean model or simple moving average models are better suited for the currency portfolio. Copyright © 2007 John Wiley & Sons, Ltd.     

Technoscientific approaches to deep time

In this paper, I argue that in order to understand the process behind the knowledge production in the historical sciences, we should change our theoretical focus slightly to consider the historical sciences as technoscientific disciplines. If we investigate the intertwinement of technology and theory, we can provide new insights into historical scientific knowledge production, preconditions, and aims. I will provide evidence for my claim by showing the central features of paleontological and paleobiological data practices of the nineteenth and twentieth centuries. In order to work with something that is imperfect and incomplete (the fossil record), paleontologists used different technological devices. These devices process, extract, correct, simulate, and eventually present paleontological explananda. Therefore, the appearance of anatomical features of non-manipulable fossilized organisms, phenomena such as mass-extinctions, or the life-like display of extinct specimens in a museum's hall, depend both on the correct use of technological devices and on the interplay between these devices and theories. Consequently, in order to capture its underlying epistemology, historical sciences should be analyzed and investigated against other technoscientific disciplines such as chemistry, synthetic biology, and nanotechnology, and not necessarily only against classical experimental sciences. This approach will help us understand how historical scientists can obtain their epistemic access to deep time.