This volume offers a broad, philosophical discussion on mechanical explanations. Coverage ranges from historical approaches and general questions to physics and higher-level sciences . The contributors also consider the topics of complexity, emergence, and reduction. Mechanistic explanations detail how certain properties of a whole stem from the causal activities of its parts. This kind of explanation is in particular employed in explanatory models of the behavior of complex systems. Often used in biology and neuroscience, mechanistic explanation models (...) have been often overlooked in the philosophy of physics. The authors correct this surprising neglect. They trace these models back to their origins in physics. The papers present a comprehensive historical, methodological, and problem-oriented investigation. The contributors also investigate the conditions for using models of mechanistic explanations in physics. The last papers make the bridge from physics to economics, the theory of complex systems and computer science . This book will appeal to graduate students and researchers with an interest in the philosophy of science, scientific explanation, complex systems, models of explanation in physics higher level sciences, and causal mechanisms in science. (shrink)

The idea at the core of the New Mechanical account of explanation can be summarized in the claim that explaining means showing ‘how things work’. This simple motto hints at three basic features of Mechanistic Explanation (ME): ME is an explanation-how, that implies the description of the processes underlying the phenomenon to be explained and of the entities that engage in such processes. These three elements trace a fundamental contrast with the view inherited from Hume and later (...) from strict logical empiricism (see Creath 2017), focused on epistemic and formal features of science and according to which issues concerning the kind of entities and processes that lie within a theory’s domain are extraneous to science and belong instead to ontology or metaphysics. Philosophers belonging to the new mechanical philosophy believe that the received view of scientific explanation (Hempel 2001), pivoting on the notion of law of nature, overshadows this insight. Since its origin in the 17th century, mechanical philosophy aimed to explain natural phenomena by reducing them to mechanisms. Traditional attempts to define the concept of mechanism involved the identification of a limited set of fundamental elements as, for instance, contact action, action at a distance, inertial motion (see e.g. Hesse 2005), and, more recently, transmission of a mark, or of a conserved quantity (see Frisch, this volume). The new mechanical philosophy rejects this austere characterization of mechanisms and mechanistic explanation and aim at providing a novel, philosophically rigorous explication of the concept of mechanism and of its role in scientific explanation and practice. ME has been adopted with profit in philosophy of special sciences (for instance in biomedical sciences, e.g. in the explanation of chemical transmission at synapses ((Machamer, Darden and Craver 2000), MDC henceforth); but also in social sciences, e.g. the three kinds of social mechanisms in Coleman’s analysis of Max Weber’s account of the role of the Protestant ethic in the growth of capitalism (Hedström and Swedberg 1998)), where exceptionless regularities are rarely ever found. In physics, it is generally possible to formulate explanations in law-based form, with the result that the plurality of explanatory forms might be overlooked. This should not come as a surprise, given that physics was the main inspiration for logical empiricists, and, in particular, Newtonian physics was a template for Hempel’s formulation of the covering law model. However, this situation is unfortunate, since, we will argue, knowing how things work is often part of the explanation of physical phenomena. In this chapter, we provide an introduction to the basic features of ME, with specific focus on its application to physics (section 1). The main part of the chapter is devoted to the defence of two theses: on the one hand, some domains of physics are not compatible with mechanistic reasoning and explanation (section 2); on the other hand, a comprehensive account of explanation in physics can’t dispense with ME (section 3). (shrink)

In pursuing philosophical enquiries in the foundations of physics, I have found myself operating with a concept of explanation which has a quite different logical syntax from the concept which Hempel has explicated. I suspect that the concept of explanation I operate with is not especially idiosyncratic, is not fully captured in the existing philosophical literature, and that it may be the more appropriate concept if we are to consider explanation as the goal of physics. (...) I therefore propose to give here a short account of the structure of this alternative concept of explanation. (shrink)

An account of physical explanation derived from the instance view of scientific explanation is outlined, and it is shown that this account does not cover explanations by theories which contain theoretical functions. An alternative account, also derived from the instance view, is proposed on the basis of Sneed's account of theories. It is shown that this account does cover theoretical explanations. Finally, it is shown that this account can accommodate explananda that record errors of measurement.

The corpus of physical theory is a paradigm of knowledge. The evolution of modern physical theory constitutes the clearest exemplar of the growth of knowledge. If the development of physical theory does not constitute an example of progress and growth in what we know about the Universe nothing does. So anyone interested in the theory of knowledge must be interested consequently in the evolution and content of physical theory. Crucial to the conception of physics as a paradigm of knowledge (...) is the way in which physical theory provides explanations of a vast diversity of natural phenomena on the basis of a very few fundamental principles. A central problem for the epistemologist is therefore what is theoretical explanation in physics? Here we can get good insight from what Redhead has said. Indeed one could agree with almost everything Redhead says and simply endorse much of his careful and extensive defence of the covering law account of explanation in the physical sciences at least as an ideal. However I shall, I fear, try the reader's patience by extending some of the considerations he introduced and raising those issues where we disagree, especially in the important area of statistical explanation. (shrink)

Despite the scientific revolutions of the twentieth century, mechanistic explanations show a striking methodological continuity from early modern science to current scientific practice. They are rooted in the traditional method of analysis and synthesis, which was the background of Galileo’s resolutive-compositive method and Newton’s method of deduction from the phenomena. In early modern science as well as in current scientific practice, analysis aims at tracking back from the phenomena to the principles, i.e., from wholes to parts, and from effects to (...) causes. Vice versa, synthesis aims at explaining the phenomena from the parts and their interactions. Today, mechanistic explanations are atomistic in a generalized sense. They have in common to explain higher-level phenomena in terms of lower-level components and their causal actions or activities. In quantum physics, the lower-level components are subatomic particles, and the causes are their quantum interactions. After the quantum revolution, the approach continues to work in terms of the sum rules which hold for conserved properties of the parts and the whole. My paper focuses on the successes and limitations of this approach, with a side glance at the recent generalization of mechanistic explanations in cognitive neuroscience. (shrink)

In what sense do the sciences explain? Or do they merely describe what is going on without answering why-questions at all. But cannot description at an appropriate ‘level’ provide all that we can reasonably ask of an explanation? Well, what do we mean by explanation anyway? What, if anything, gets left out when we provide a so-called scientific explanation? Are there limits of explanation in general, and scientific explanation, in particular? What are the criteria for (...) a good explanation? Is it possible to satisfy all the desiderata simultaneously? If not, which should we regard as paramount? What is the connection between explanation and prediction? What exactly is it that statistical explanations explain? These are some of the questions that have generated a very extensive literature in the philosophy of science. In attempting to answer them, definite views will have to be taken on related matters, such as physical laws, causality, reduction, and questions of evidence and confirmation, of theory and observation, realism versus antirealism, and the objectivity and rationality of science. I will state my own views on these matters, in the course of this essay. To argue for everything in detail and to do justice to all the alternative views, would fill a book, perhaps several books. I want to lead up fairly quickly to modern physics, and review the explanatory situation there in rather more detail. (shrink)

The statistical aspects of quantum explanation are intrinsic to quantum physics; individual quantum events are created in the interactions associated with observation and are not describable by predictive theory. The superposition principle shows the essential difference between quantum and non-quantum physics, and the principle is exemplified in the classic single-photon two-slit interference experiment. Recently Mandel and Pfleegor have done an experiment somewhat similar to the optical single-photon experiment but with two independently operated lasers; interference is obtained even (...) with beam intensity so small that only one photon is in the apparatus at a time. The result can be understood in terms of the superposition of states; or, in terms of the Uncertainty Principle, which is found to forbid the determination of which of the two lasers is the source of a given photon (if conditions for interference are to obtain). The Mandel-Pfleegor experiment gives a physical argument against the continuous localization of a photon that is assumed in the hidden variable theories and therefore gives further support for the generally accepted view that an observed entity (observed state) is created in the observation event. This aspect of quantum physics implies a subjectivism on the level of individual quantum-level occurrences, since there is in quantum theory no basis for asserting the existence of the event independently of observation of it. Extension of this subjectivism to large scale, non-quantum phenomena falls within the principles of quantum theory; counter considerations that argue against such an extension are noted. (shrink)

I offer an explanation of why inertial and gravitational mass are equal in Newtonian gravitation. I then argue that this is an example of a kind of explanation that is not captured by standard philosophical accounts of scientific explanation. Moreover, this form of explanation is particularly important, at least in physics, because demands for this kind of explanation are used to motivate and shape research into the next generation of physical theories. I suggest that (...) explanations of the sort I describe reveal something important about one way in which physical theories may be related diachronically. (shrink)

There has been a growing trend to include non-causal models in accounts of scientific explanation. A worry addressed in this paper is that without a higher threshold for explanation there are no tools for distinguishing between models that provide genuine explanations and those that provide merely potential explanations. To remedy this, a condition is introduced that extends a veridicality requirement to models that are empirically underdetermined, highly-idealised, or otherwise non-causal. This condition is applied to models of electroweak symmetry (...) breaking beyond the Standard Model. (shrink)

The focus in the literature on scientific explanation has shifted in recent years towards modelbased approaches. The idea that there are simple and true laws of nature has met with objections from philosophers such as Nancy Cartwright (1983) and Paul Teller (2001), and this has made a strictly Hempelian D-N style explanation largely irrelevant to the explanatory practices of science (Hempel & Oppenheim, 1948). Much of science does not involve subsuming particular events under laws of nature. It is (...) increasingly recognized that science across the disciplines is to some degree a patchwork of scientific models, with different methods, strategies, and with varying degrees of successful prediction and explanation. And so accounts of scientific explanation have reflected this change of perspective and model-based approaches have flourished in the explanation literature (Batterman, 2002b; Bokulich, 2008; Craver, 2006; Woodward, 2003). (shrink)

This article claims the validity of abductive reasoning, or inference to the best explanation, as a practice of discovery of explanatory scientific hypotheses. Along the way to achieve this objective I present here a series of arguments that question the feasibility of Bayesianism as a theory of scientific confirmation. Having solved this issue, I resort to an episode of contemporary astrocosmology that I interpret as an eloquent example of the effectiveness of abductive methodology in contemporary theoretical physics.

The principle of least action (PLA) has often been cited as a counterexample to the dominant mode of causal explanation in physics. In particular, PLA seems to involve an appeal to final causes or some other teleological ideology. However, Ben-Menahem (Causation in science, Princeton University Press, Princeton, 2018) argues that such implications no longer apply given that PLA can be recovered as limiting case from quantum theory. In this paper, I argue that the metaphysical implications of PLA-based explanations (...) are not undermined by its status as derivative. However, I contend that PLA functions as a diachronic constraint that licenses explanations by constraint (Lange, Because without cause: non-casual explanations in science and mathematics. Oxford University Press, Oxford, 2016). PLA-based explanations, on this account, are non-causal but also differ from familiar cases of teleological explanations in several respects. (shrink)

In this book Philip Clayton defends the rationality of religious explanations by exploring the parallels between explanatory effects in the sciences and the explanations offered by religious believers, students of religion, and theologians. Clayton begins by surveying the types of religious explanation, offering a synopsis of the most significant competing positions. He then critically examines recent important developments in the philosophy of science regarding the nature of scientific explanations—including the work of Popper, Hempel, Kuhn, and Lakatos in the natural (...) sciences and Habermas, Weber, and Schütz in the social sciences. Clayton outlines the process of rational evaluation in these disciplines, defining the explanatory quest as the attempt to make sense of or bring coherence into subjective and intersubjective worlds. He briefly discusses explanations in philosophy and then turns to the explanatory role of individual religious experience, drawing on a coherence theory of meaning and on the conclusions from his discussion of science. Based on his defense of the doubting or “secular” believer, he concludes by advocating a model of theology in which questions about the truth of a religious tradition are intrinsic to its theology. “A valuable exposition of the thesis that the explanatory work of theology possesses formal similarities with that of the physical sciences, the social sciences, and philosophy. Clayton exhibits an impressive command of a broad area of scholarship, and his reflections are balanced and carefully argued.” –Michael J. Buckley, S.J., professor of religion at the Jesuit Theological Seminary and author of _At the Origins of Modern Atheism_ “I know of no philosopher writing today who has dealt in as informed and thoughtful a way with the broad subject of this book. Clayton guides the reader through important discussions with ease, illuminating the path all along the way.” –Josiah B. Gould, professor of philosophy at the State University of New York, Albany. (shrink)

Fifty years ago, Carl Gustav Hempel published his famous book Aspects of Scientific Explanation. Since then the number of publications on this subject has grown exponentially. An occasion like this deserves to be commemorated. In this article I offer a modest tribute to this great methodologist of science. This paper tackles the uses of explanation in theoretical sciences. In particular it is concerned with the possibility of causal explanations in physics. What I intend to do is to (...) focus on the issue of whether the explanation of Kepler’s empirical laws of the planetary motions can be a causal explanation. More specifically my point is: can the deductive subsumption of Kepler’s 3rd Law under theoretical principles provide a causal explanation for the planetary motions? My answer is a definitive no. As a matter of fact, on occasion subsumptions occur under differing theoretical principles that are incompatible with one another. In such cases we would have incompatible scientific explanations. This is precisely the situation facing the scientific explanation of Kepler’s laws, in particular the third law. Since there exist incompatible gravitational theories, it is impossible for the scientific account of Kepler’s law to be a causal explanation of the planetary motions. This is just one example of the difficulties faced by causal explanations in sciences such as theoretical physics. (shrink)

(1988). Historical explanations in modern physics? The lesson of quantum mechanics. International Studies in the Philosophy of Science: Vol. 3, No. 1, pp. 68-79.

(1988). Historical explanations in modern physics? The lesson of quantum mechanics. International Studies in the Philosophy of Science: Vol. 3, No. 1, pp. 68-79.

Certain features of psycho-Analytic explanations are contrasted with those found in physics. I conclude that some of the objections against them are based on a methodology that is taken from newtonian mechanics or, Rather, The misinterpretation of it current in the past century. (edited).

Hodgkin and Huxley’s model of the action potential is an apparent dream case of covering‐law explanation in biology. The model includes laws of physics and chemistry that, coupled with details about antecedent and background conditions, can be used to derive features of the action potential. Hodgkin and Huxley insist that their model is not an explanation. This suggests either that subsuming a phenomenon under physical laws is insufficient to explain it or that Hodgkin and Huxley were wrong. (...) I defend Hodgkin and Huxley against Weber’s heteronomy thesis and argue that explanations are descriptions of mechanisms. †To contact the author, please write to: Department of Philosophy, Philosophy‐Neuroscience‐Psychology Program, Washington University in St. Louis, One Brookings Drive, Wilson Hall, St. Louis, MO 63130; e‐mail: [email protected]. (shrink)

The paper tries to provide an alternative to Hempel’s approach to scientific laws and scientific explanation as given in his D-N model. It starts with a brief exposition of the main characteristics of Hempel’s approach to deductive explanations based on universal scientific laws and analyzes the problems and paradoxes inherent in this approach. By way of solution, it analyzes the scientific laws and explanations in classical mechanics and then reconstructs the corresponding models of explanation, as well as the (...) types of scientific laws appearing in it. Finally, it compares this reconstruction with the approaches of J. Woodward and C. Hitchcock, C. Liu and with the views of M. Thalos on analytic mechanics. (shrink)

I discuss Aristotle's anomalous terminology in Physics A.1 (involving "universals" and "particulars") and its coherence with Aristotle's notion of scientific demonstration.

This feels like a time of environmental and moral crisis without parallel.... Not only do human beings seem not to believe in anything but, despite exponential advances in information production, we do not appear to know much either. This book is a guide for everyone who feels understandably perplexed. The book considers issues as diverse as: the lure of alternative religions and belief systems; the use of the rhetoric of economics to justify amoral decisionmaking; green politics and genetically-modified crops; new (...) technology's power to preserve the status quo; and the true impetus behind the Human Genome Project. Presenting an explanation of recent findings in science and their relationship with society and politics, the book seeks to give guidance towards responsible political action. Starting from themes developed in the companion volume The Search for Mind, the author attempts to provide intellectual roots for the 'anti-capitalist' or 'anti-globalization' movement and, in particular, treats social protest as a form of knowledge-seeking. The author brings to very topical and controversial concerns some much-needed clarity. Complete with reader-friendly summaries of current thought in the biological, physical, and social sciences, this book is designed primarily for the popular market but will also appeal to those working or studying in these fields. (shrink)

Many biologists and philosophers have worried that importing models of reasoning from the physical sciences obscures our understanding of reasoning in the life sciences. In this paper we discuss one example that partially validates this concern: part-whole reductive explanations. Biology and physics tend to incorporate different models of temporality in part-whole reductive explanations. This results from differential emphases on compositional and causal facets of reductive explanations, which have not been distinguished reliably in prior philosophical analyses. Keeping these two facets (...) distinct facilitates the identifi cation of two further aspects of reductive explanation: intrinsicality and fundamentality. Our account provides resources for discriminating between different types of reductive explanation and suggests a new approach to comprehending similarities and differences in the explanatory reasoning found in biology and physics. (shrink)

The scope and nature of reductionist explanation in quantum physics is analyzed, with special attention being paid to the situation in quantum physics.

This paper aims to understand how recent discussion of novel and robust behaviour in physics might be applied in biology and other special sciences. In particular, it looks at the prospects for extending an account of novel explanation to biological examples. Despite the differences in the disciplines, the prospects look good, at least when we look at a biological example in which a certain kind of reduction is possible.

Explanation in biology has long been characterized as being very different from explanation in other scientific disciplines, very much so from explanation in physics. One of the reasons was the existence in biology of explanation types that were unheard of in the physical sciences: teleological explanations (e.g. Hull 1974), evolutionary explanations (e.g. Mayr 1988), or even functional explanations (e.g. Neander 1991). More recently, and owing much to the rise of molecular biology, biological explanations have been (...) depicted as mechanisms (e.g; Machamer, Darden and Craver 2000). The aim of this volume is to shed some new light on the diversity of explanation types in biology. What are the different types of explanation that occur in biology? Are these types of explanation specific to particular sub-disciplines of biology, or to particular types of problems across biology? How do they relate to each another? Do they compete with one another for answering the same questions? Or do they complement each other, providing insights to different questions? What are the reasons for such diversity? Can this diversity be overcome by a broader unifying model of explanation or is it more profound and irreducible? Why? This volume aims at making sense of this diversity of types of explanations that are found in biology, of their relationship with one another. After all, explanation in biology may prove not only different from explanation in the physical sciences, but also much more diverse than originally anticipated. (shrink)

The Scientific Revolution is often associated with a transition to a ``mechanistic'' world view. However, ``mechanization'' is not the term that best captures the distinctive nature of modern physics: ``mathematization'' would be a better characterization. Modern physics attempts to find mathematical relations between quantities, and does not require that these relations be interpreted in terms of mechanisms. Moreover, in modern physics there are cases in which it is unnatural to give the mathematical formalism a mechanistic interpretation, even (...) if ``mechanistic'' is broadly construed. Both on the level of ontology and that of explanation physics turns out to be more general and liberal than what is suggested by the catchphrase that physics explains by identifying mechanisms. Although mechanistic explanation remains an important conceptual tool, in particular for achieving understanding, it is not the only one available and cannot lay claim to fundamentality. (shrink)

For an ‘explanation' of physical facts by laws of nature, we have to establish a relation between physical facts and laws of nature. It is an open question, whether the laws of nature govern the facts with necessity or whether the laws are related to the facts merely by supervenience. In addition, it is not quite clear, whether the known laws of physics describe only artificially simplified cases, e.g. isolated situations, or whether the laws of physics actually (...) grasp real facts. Known solutions of these problems refer to situations where laws of classical physics are applied to phenomena of classical physics. However, if the same laws were applied to matter of facts of the domain of modern physics, then in many cases there would be no ‘explanation' in the sense mentioned. These new problems can be treated either by additional ‘interpretations' of the theories in question, or by a radical change of the ontological preconditions of classical physics. (shrink)

This article examines three candidate cases of non-causal explanation in computational neuroscience. I argue that there are instances of efficient coding explanation that are strongly analogous to examples of non-causal explanation in physics and biology, as presented by Batterman, Woodward, and Lange. By integrating Lange’s and Woodward’s accounts, I offer a new way to elucidate the distinction between causal and non-causal explanation, and to address concerns about the explanatory sufficiency of non-mechanistic models in neuroscience. I (...) also use this framework to shed light on the dispute over the interpretation of dynamical models of the brain. _1_ Introduction _1.1_ Efficient coding explanation in computational neuroscience _1.2_ Defining non-causal explanation _2_ Case I: Hybrid Computation _3_ Case II: The Gabor Model Revisited _4_ Case III: A Dynamical Model of Prefrontal Cortex _4.1_ A new explanation of context-dependent computation _4.2_ Causal or non-causal? _5_ Causal and Non-causal: Does the Difference Matter? (shrink)

There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their (...) metaphysical nonfundamentality. I conclude by sketching how Du Châtelet’s conception of mathematical indispensability differs interestingly from many contemporary approaches. (shrink)

In this paper I defend an intermediate position between the ‘bare mathematical results’ view and the ‘transmission’ view of mathematical explanations of physical phenomena (MEPPs). I argue that, in MEPPs, it is not enough to deduce the explanandum from the generalizations cited in the explanans. Rather, we must add information regarding why those generalizations obtain. However, I also argue that it is not necessary to provide explanatory proofs of the mathematical theorems that represent those generalizations. I illustrate this with the (...) bridges of Königsberg case. -/- . (shrink)

This chapter contains sections titled: Introduction: No Need for Special Biological Laws? The Reductionist Principle Strong Emergence Complex Relations in Biology A Misinformed Slogan and Its Contributions Genes Causation Systems Biology Metaphysical Coda Postscript: Counterpoint Acknowledgments Notes References.

This book provides a post-positivist theory of deterministic and probabilistic causality that supports both quantitative and qualitative explanations. Features of particular interest include the ability to provide true explanations in contexts where our knowledge is incomplete, a systematic interpretation of causal modeling techniques in the social sciences, and a direct realist view of causal relations that is compatible with a liberal empiricism. The book should be of wide interest to both philosophers and scientists. Originally published in 1989. The Princeton Legacy (...) Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

This thesis looks at explanation in the natural sciences, the social sciences, and in religious reflection. Although these fields differ radically in the objects studied and the methods employed, they do evidence certain formal commonalities when one inquires into the nature of the explanatory endeavor as it is manifested in each. By exploring the links between explanations and the various contexts or disciplines in which they occur, I attempt to provide a general framework for speaking of rational explanations in (...) these diverse areas. ;In an opening chapter I consider several alternatives regarding the epistemic status of religious explanations, focusing finally on the model of "intersubjective explanation." Contemporary defenses of intersubjective religious explanation are placed within the context of the broader faith/reason debate, and a quick survey is made of recent advocates of this position. I then turn to the methodology dispute in the philosophy of the natural sciences . My aim is to mediate between purely formal analyses of explanatory structure and the more recent emphasis on contextual and pragmatic factors. ;In the social sciences, many have argued, explanation is subordinate to intuitive understanding. After tracing the explanation versus understanding debate from Dilthey to the present, I present the recent work of Jurgen Habermas as a case study in the problems of social scientific rationality. Explanations in the social sciences are rational reconstructions of human meaning contexts, and "Verstehen" is required as a precondition for material adequacy. Such explanations are linked to the individual or communal effort to "make sense" of, or bring coherence into, subjective and intersubjective "worlds." ;After an excursus on philosophical explanations and the problem of philosophical rationality, I attempt a brief phenomenology of religious beliefs as explanations. As in the social sphere, religious explanations represent the believer's attempt to "make sense" of her experience in light of a given religious tradition. Although the comprehensive nature of religious explanations makes comparisons difficult--in the limit case they verge on ineffability--the concepts of meaning and coherence allow us to speak of the rationality of religious belief without total equivocation. ;The final chapter turns to the study and evaluation of religious explanations as they occur in the discipline of theology. Under the rubric "theology as a science," I defend theology's dual status as an academic discipline and as believing reflection in the service of the religious community. Through vitally concerned with the truth of its assertions, theology also shares the goals of coherence and intersubjective criticizability with its scientific counterparts. (shrink)

Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.

ABSTRACT Can there be mathematical explanations of physical phenomena? In this paper, I suggest an affirmative answer to this question. I outline a strategy to reconstruct several typical examples of such explanations, and I show that they fit a common model. The model reveals that the role of mathematics is explicatory. Isolating this role may help to re-focus the current debate on the more specific question as to whether this explicatory role is, as proposed here, also an explanatory one.

Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I (...) discuss potential future directions of research for each side in the debate over the existence of abstract mathematical objects. (shrink)

The existence of causal explanations in science has been an issue of interest in Western philosophy from its very beginnings. That is the reason this work, following an idea of Mario Bunge, makes a historical review of this matter. The modern treatment of this subject takes place since the postulation by Popper and Hempel of the D-N model of scientific explanation, whose viability is scrutinized here from different points of view in the current philosophy of science. The main object (...) of this paper is to present two arguments against the possibility of causal explanations in theoretical physics. The first one concerns the existence, in certain cases, of inter-theoretical incompatibilities, and the second refers to the need to resort, in other cases, to concatenations of laws of different theories and disciplines. The final conclusion will be the defence of a form of theoretical explanation, which follows the Popper-Hempel model, but devoid of any ontological and metaphysical connotations. (shrink)