Science frequently gives us multiple, compatible ways of solving the same problem or formulating the same theory. These compatible formulations change our understanding of the world, despite providing the same explanations. According to what I call "conceptualism," reformulations change our understanding by clarifying the epistemic structure of theories. I illustrate conceptualism by analyzing a typical example of symmetry-based reformulation in chemical physics. This case study poses a problem for "explanationism," the rival thesis that differences in understanding require ontic explanatory differences. (...) To defend conceptualism, I consider how prominent accounts of explanation might accommodate this case study. I argue that either they do not succeed, or they generate a skeptical challenge. (shrink)

We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of a theory over another: ceteris paribus, a more general formulation is more fundamental. We illustrate this criterion through a novel interpretation of classical mechanics, based on three physical conditions. Two of these conditions suffice for recovering Hamiltonian mechanics. A third condition is necessary for Lagrangian mechanics. Hence, Lagrangian systems are a proper subset of Hamiltonian systems. Finally, we provide (...) a geometric interpretation of the principle of stationary action and rebut arguments for privileging Lagrangian mechanics. (shrink)

Reformulating a scientific theory often leads to a significantly different way of understanding the world. Nevertheless, accounts of both theoretical equivalence and scientific understanding have neglected this important aspect of scientific theorizing. This essay provides a positive account of how reformulation changes our understanding. My account simultaneously addresses a serious challenge facing existing accounts of scientific understanding. These accounts have failed to characterize understanding in a way that goes beyond the epistemology of scientific explanation. By focusing on cases in which (...) we have differences in understanding without differences in explanation, I show that understanding does not reduce to explanation. (shrink)

In this article I review attempts to define the term “ad hoc hypothesis,” focusing on the efforts of, among others, Karl Popper, Jarrett Leplin, and Gerald Holton. I conclude that the term is unhelpful; what is “ad hoc” seems to be a judgment made by particular scientists not on the basis of any well-established definition but rather on their individual aesthetic senses. Further, a hypothesis considered ad hoc can apparently be retroactively declared non–ad hoc on the basis of subsequent data, (...) rendering the term meaningless. (shrink)

Accounts of scientific explanation disagree about what’s required for a cause, law, or other fact to be a reason why an event occurs. In short, they disagree about the conditions for explanatory relevance. Nonetheless, most accounts presuppose that claims about explanatory relevance play a descriptive role in tracking reality. By rejecting the need for this descriptivist assumption, I develop an expressivist account of explanatory relevance and explanation: to judge that an answer is explanatory is to express an attitude ofbeing for (...) being satisfied by that answer. I show how expressivism vindicates ordinary scientific discourse about explanation, including claims about the objectivity and mind-independence of explanations. By avoiding commitment to ontic relevance relations, I rehabilitate an irrealist conception of explanation. (shrink)

This article examines a series of Schelling-like models of residential segregation, in which agents prefer to be in the minority. We demonstrate that as long as agents care about the characteristics of their wider community, they tend to end up in a segregated state. We then investigate the process that causes this and conclude that the result hinges on the similarity of informational states among agents of the same type. This is quite different from Schelling-like behavior and suggests that segregation (...) is an instance of macrobehavior that can arise from a wide variety of micromotives. (shrink)

The Wigner--Eckart theorem is central to the application of symmetry principles throughout atomic, molecular, and nuclear physics. Nevertheless, the theorem has a puzzling feature: it is dispensable for solving problems within these domains, since elementary methods suffice. To account for the significance of the theorem, I first contrast it with an elementary approach to calculating matrix elements. Next, I consider three broad strategies for interpreting the theorem: conventionalism, fundamentalism, and conceptualism. I argue that the conventionalist framework is unnecessarily pragmatic, while (...) the fundamentalist framework requires more ontological commitments than necessary. Conceptualism avoids both defects, accounting for the theorem's significance in terms of how it epistemically restructures the calculation of matrix elements. Specifically, the Wigner--Eckart theorem modularizes and unifies matrix element problems, thereby changing what we need to know to solve them. (shrink)

Alan Baker’s enhanced indispensability argument supports mathematical platonism through the explanatory role of mathematics in science. Busch and Morrison defend nominalism by denying that scientific realists use inference to the best explanation to directly establish ontological claims. In response to Busch and Morrison, I argue that nominalists can rebut the EIA while still accepting Baker’s form of IBE. Nominalists can plausibly require that defenders of the EIA establish the indispensability of a particular mathematical entity. Next, I argue that IBE cannot (...) establish that any particular mathematical entity is indispensable. Mathematical entities do not compete with each other in the way physical unobservables do. This lack of competition enables alternative formulations of scientific explanations that use different, but compatible, mathematical entities. The compatibility of these explanations prevents IBE from establishing platonism. (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

Understanding terrestrial carbon metabolism is critical because terrestrial ecosystems play a major role in the global carbon cycle. Furthermore, humans have severely disrupted the carbon cycle in ways that will alter the climate system and directly affect terrestrial metabolism. Changes in terrestrial metabolism may well be as important an indicator of global change as the changing temperature signal. Improving our understanding of the carbon cycle at various spatial and temporal scales will require the integration of multiple, complementary and independent methods (...) that are used by different research communities. Tools such as air sampling networks, inverse numerical methods, and satellite data allow us to study the strength and location of the global- and continental-scale carbon sources and sinks. Bottom-up studies provide estimates of carbon fluxes at finer spatial scales and examine the mechanisms that control fluxes at the ecosystem, landscape, and regional scales. Bottom-up approaches include comparative and process studies that provide the necessary mechanistic information to develop and validate terrestrial biospheric models. An iteration and reiteration of top-down and bottom-up approaches will be necessary to help constrain measurements at various scales. We propose a major international effort to coordinate and lead research programs of global scope of the carbon cycle. (shrink)

Babylonian Poems of Righteous Sufferers: Ludlul Bël Nëmeqi and the Babylonian Theodicy. By Takayoshi Oshima. Orientalische Religionen in der Antike, vol. 14. Tübingen: Mohr Siebeck, 2014. Pp. xx + 572, 65 plts. €139.

‘Medically unexplained symptoms’, through the lens of the biopsychosocial model, are understood in mainstream psy disciplines and related literature as a primarily psychosocial phenomenon perpetuated by ‘dysfunctional’ psychology on the part of people labelled with such. Biopsychosocial discourse and practice in this field, underpinned by little empirical foundation and lacking theoretical coherency, are associated with harms sustained by people labelled with MUS. Yet, little attention is paid to the psychology of social actors and institutions whose practice and policy derives from (...) biopsychosocial theorising, or whose vested interests produce such theorising. This article contends that lack of reflexivity among psy practitioners and other social actors on individual, institutional and structural levels furthers biopsychosocial hegemony and contributes to harms. Non-reflexive behaviour on the part of practitioners within clinical and ‘therapeutic’ encounters and on the part of social actors within institutions and broader power structures is examined, and possible psychological underpinnings of non-reflexivity are explored. Notably, the concept of gain, drawn from dominant discourse around MUS, is applied broadly to explore what might be gained from eschewing reflexivity and from adhering to biopsychosocial narratives. Implications for practice, supervision, training and research are discussed, notably highlighting a need for critical reflexivity in all domains. (shrink)

To students and practitioners of anamorphic art, the name of Jean-François Niceron is more than preeminent; it has become iconic. La Perspective Curieuse was first published in 1638. An augmented version was then translated into Latin by Mersenne in 1646. A newly amended and augmented version was retranslated into French by Roberval in 1652. This book is an English translation of the 1652 text, with reference to the 1638 and 1646 versions. Considering the continued high reputation of the book, the (...) mathematics have been checked for correctness and consistency, and the authors have provided a full commentary, pointing out the most difficult turns of the 17th-century French, the respective contributions of Niceron, Mersenne and Roberval, and explaining Niceron's greatest insights and weaknesses. (shrink)

Physical pain has always been part of human experience, and throughout history it is recorded that doctors and wise men and women have sought to ease pain. The attitudes of those suffering pain, however, have varied from stoical acceptance to sullen endurance. Today, most people consciously seek to avoid pain or to have their pain eased, although they do not always expect what in fact appears to be possible. This study of 13 patients with protracted pain was carried out at (...) The London Hospital by a professional group to see how patients regarded their own pain and the efforts of doctors and nurses to relieve it. The attitudes of the doctors and nurses were also studied, and the results, despite the limitations of the survey, suggest that: [List: see text]. (shrink)

Eighteenth-century England saw the rise of a "peculiarly English" art form—landscape gardening—and a corresponding change in attitudes toward the antural world. While the French, who lived under tyranny, had a tightly organized, restrictive gardens, the "free" English enjoyed gardens where they were at liberty to wander. John Dixon Hunt examines eighteenth-century letters, literary and critical works, biographies, paintings, prints, and drawings to trace the gradual movement from formal regularity toward a carefully calculated naturalness.