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)

This article focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau’s laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations.explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear how to (...) unify abstract and causal explanations as instances of a single sort of thing. I conclude by examining the implications of the claim that explanations require objective dependence relations. If this claim is accepted, then there are several kinds of objective dependence relations. 1 Introduction2 A Case3 Abstract and Causal Explanations4 Recent Work on Mathematical Explanation5 Explanation and Dependence6 Conclusion. (shrink)

Scientific explanation is an important goal of scientific practise. Philosophers have proposed a striking diversity of seemingly incompatible accounts of explanation, from deductive-nomological to statistical relevance, unification, pragmatic, causal-mechanical, mechanistic, causal intervention, asymptotic, and model-based accounts. In this dissertation I apply two novel methods to reexamine our evidence about scientific explanation in practise and thereby address the fragmentation of philosophical accounts. I start by collecting a data set of 781 articles from one year of the journal (...) class='Hi'>Science. Using automated text mining techniques I measure the frequency and distribution of several groups of philosophically interesting words, such as "explain", "cause", "evidence", "theory", "law", "mechanism", and "model". I show that "explain" words are much more common in scientific writing than in other genres, occurring in roughly half of all articles, and that their use is very often qualified or negated. These results about the use of words complement traditional conceptual analysis. Next I use random samples from the data set to develop a large number of small case studies across a wide range of scientific disciplines. I use a sample of "explain" sentences to develop and defend a new general philosophical account of scientific explanation, and then test my account against a larger set of randomly sampled sentences and abstracts. Five coarse categories can classify the explanans and explananda of my cases: data, entities, kinds, models, and theories. The pair of the categories of the explanans and explanandum indicates the "form" of an explanation. The explain-relation supports counterfactual reasoning about the dependence of qualities of the explanandum on qualities of the explanans. But for each form there is a different "core relation" between explanans and explanandum that supports the explain-relation. Causation, modelling, and argument are the core relations for different forms of scientific explanation between different categories of explanans and explananda. This flexibility allows me to resolve some of the fragmentation in the philosophical literature. I provide empirical evidence to show that my general philosophical account successfully describes a wide range of scientific practise across a large number of scientific disciplines. (shrink)

This paper challenges the first Gettier counterexample to the tripartite account of knowledge. Noting that 'the man who will get the job' is a description and invoking Donnellan's distinction between their 'referential' and 'attributive' uses, I argue that Smith does not actually believe that the man who will get the job has ten coins in his pocket. Smith's ignorance about who will get the job shows that the belief cannot be understood referentially, his ignorance of the coins in his pocket (...) shows that it cannot be understood attributively. An explanation for why Smith appeared to have justified true belief is given by distinguishing between 'belief' and 'belief in truth'. Smith believes the sentence 'the man who will get the job has ten coins in his pocket' to be true (he mistakenly believes that Jones will get the job, of whom he knows that he has ten coins in his pocket) (hence his 'belief'), the sentence is true (hence 'truth'), and he has sufficient reason to assent to it (hence his 'justification'). But he does not believe the proposition expressed. Hence he does not know it either. (shrink)

Debates between contemporary platonist and nominalist conceptions of the metaphysical status of mathematical objects have recently included discussions of explanations of physical phenomena in which mathematics plays an indispensable role, termed mathematical explanations in science (MES). I will argue that MES requires an ontology that can (1) ground claims about mathematical necessity as distinct from physical necessity and (2) explain how that mathematical necessity applies to the physical world. I contend that nominalism fails to meet the first criterion and (...) platonism the second. I then articulate an alternative, Aristotelian approach to mathematical objects and defend such a view as meeting both criteria. (shrink)

Stemming from the realization of the importance of the role of explanation in the science classroom, the Next Generation Science Standards call for appropriately supporting students to learn science, argue from evidence, and provide explanations. Despite the ongoing emphasis on explanations in the science classroom, there seems to be no well-articulated framework that supports students in constructing adequate scientific explanations, or that helps teachers assess student explanations. Our motivation for this article is twofold: First, we (...) think that the ways in which researchers in science education have studied scientific explanation are, at best, leaves much to be desired and, at worst, simply incomplete. Second, we believe that research about the teaching and learning of explanation in science classrooms must be guided by explicit models or frameworks that specify elements involved in constructing explanations particularly applicable to science. More importantly, we think that the development of such models or guidelines should be based on theoretical and philosophical foundations. In order to develop these frameworks or guidelines, we first outline and clarify models of scientific explanation developed by philosophers of science over the last few decades. In the second section of this article, we present a more recent philosophical work on scientific explanation, the pragmatic approach to studying scientific explanations. This approach suggests a toolbox for analyzing scientists’ scientific explanations, which provides a useful instrument to science education. In Section 3, we discuss the ways by which the previous two sections are useful in developing a K-12 scientific explanation schema. Implications for future research on students’ explanations are discussed. (shrink)

Not all scientific explanations work by describing causal connections between events or the world's overall causal structure. In addition, mathematicians regard some proofs as explaining why the theorems being proved do in fact hold. This book proposes new philosophical accounts of many kinds of non-causal explanations in science and mathematics.

In this chapter, it is described and assessed how political scientists use rational choice theories to offer causal explanations. We observe that the ways in which rational choice theories are considered to be successful in political science differs, depending on the explanandum in question. Political scientists use empirical variants of rational choice theories to explain the political behavior of individual agents and analytical variants to explain the behavior of collective actors. Both variants are used for distinct explananda, which ask (...) for different modes of explanation that raise in turn different explanatory demands toward rational choice theories. We argue that when political scientists discuss the explanatory usefulness of rational choice theories, they should assess them in light of the demands they are supposed to meet. This would enable a more nuanced and problem-oriented appraisal of rational choice theories in political science. (shrink)

Our lives, states of health, relationships, behavior, experiences of the natural world, and the technologies that shape our contemporary existence are subject to a superfluity of competing, multi-faceted and sometimes incompatible explanations. Widespread confusion about the nature of "explanation" and its scope and limits pervades popular exposition of the natural sciences, popular history and philosophy of science. This fascinating book explores the way explanations work, why they vary between disciplines, periods, and cultures, and whether they have any necessary (...) boundaries. In other words, Explanations aims to achieve a better understanding of explanation, both within the sciences and the humanities. It features contributions from expert writers from a wide range of disciplines, including science, philosophy, mathematics, and social anthropology. (shrink)

Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily (...) unified. I argue that it is possible for there to be such cases, and provide some toy examples to demonstrate this. I then identify a potential source of scientific case studies as a guide for future work. (shrink)

© The Authors [2018]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model...In his Moby Dick, Herman Melville writes that “to produce a mighty book you must choose a mighty theme”. Marc Lange’s Because Without Cause is definitely an impressive book that deals with a mighty theme, that of non-causal explanations in the empirical sciences and in mathematics. Blending a (...) variety of insights originating within the philosophy of science and the philosophy of mathematics, the book has an ambitious goal: capturing what features, in the many examples of putative explanations offered by mathematicians and scientists, make them genuinely explanatory.The architecture of Because Without Cause reflects its mighty character. The book is divided into four parts and eleven chapters, preceded by... (shrink)

We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the (...) CTE to mathematical explanations requires us to rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics. (shrink)

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)

Back cover: This book develops a philosophical account that reveals the major characteristics that make an explanation in the life sciences reductive and distinguish them from non-reductive explanations. Understanding what reductive explanations are enables one to assess the conditions under which reductive explanations are adequate and thus enhances debates about explanatory reductionism. The account of reductive explanation presented in this book has three major characteristics. First, it emerges from a critical reconstruction of the explanatory practice of the life (...) sciences itself. Second, the account is monistic since it specifies one set of criteria that apply to explanations in the life sciences in general. Finally, the account is ontic in that it traces the reductivity of an explanation back to certain relations that exist between objects in the world (such as part-whole relations and level relations), rather than to the logical relations between sentences. Beginning with a disclosure of the meta-philosophical assumptions that underlie the author’s analysis of reductive explanation, the book leads into the debate about reduction(ism) in the philosophy of biology and continues with a discussion on the two perspectives on explanatory reduction that have been proposed in the philosophy of biology so far. The author scrutinizes how the issue of reduction becomes entangled with explanation and analyzes two concepts, the concept of a biological part and the concept of a level of organization. The results of these five chapters constitute the ground on which the author bases her final chapter, developing her ontic account of reductive explanation. (shrink)

According to Galileo the scientist is a philosopher of nature. But in the opinion of Galilei to study the nature the scientist must use mathematical truths and mathematical accuracy to know for certain, besides the scientist must verify theory by experiments. So scientific enterprise is in possession of two polarities: a theoretical constituent and an experimental constituent. Einstein thinks that scientific knowledge flows from the world of Lebenswelt thanks to new ideas by which we can construct a theory by a (...) deductive reasoning. The experiment gives us the possibility to control theory, but this verification is always questionable. So for Galilei and Einstein science have a conceptual dimension by which we can trace the outline of an objective world. (shrink)

Contribution to a review symposium on Marc Lange's Because without cause: Non-causal explanation in science and mathematics. Oxford: Oxford University Press, 2017.

In this paper I apply the mechanistic account of explanation to engineering science. I discuss two ways in which this extension offers further development of the mechanistic view. First, functional individuation of mechanisms in engineering science proceeds by means of two distinct sub types of role function, behavior function and effect function, rather than role function simpliciter. Second, it offers refined assessment of the explanatory power of mechanistic explanations. It is argued that in the context of malfunction (...) explanations of technical systems, two key desiderata for mechanistic explanations, ‘completeness and specificity’ and ‘abstraction’, pull in opposite directions. I elaborate a novel explanatory desideratum to accommodate this explanatory context, dubbed ‘local specificity and global abstraction’, and further argue that it also holds for mechanistic explanations of malfunctions in the biological domain. The overall result is empirically-informed understanding of mechanistic explanation in engineering science, thus contributing to the ongoing project of understanding mechanistic explanation in novel or relatively unexplored domains. I illustrate these claims in terms of reverse engineering and malfunction explanations in engineering science. (shrink)

In this paper, I outline two strands of evidence for the conclusion that the dynamical approach to cognitive science both seeks and provides covering law explanations. Two of the most successful dynamical models—Kelso’s model of rhythmic finger movement and Thelen et al.’s model of infant perseverative reaching—can be seen to provide explanations which conform to the famous explanatory scheme first put forward by Hempel and Oppenheim. In addition, many prominent advocates of the dynamical approach also express the provision of (...) this kind of explanation as a goal of dynamical cognitive science. I conclude by briefly outlining two consequences. First, dynamical cognitive science’s explanatory style may strengthen its links to the so-called “situated” approach to cognition, but, secondly, it may also undermine the widespread intuition that dynamics is related to emergentism in the philosophy of mind. (shrink)

The dispute between the empiricist and interpretivist conceptions of the social sciences is properly conceived not as a matter of reduction or covering laws. Features specific to the social sciences include the following. Explanations of human behavior make reference to intentional causation; social phenomena are permeated with mental components and are self-referential; social science explanations have not been as successful as those in natural science because of their concern with intentional causation, because their explanations must be identical with (...) the propositional content of the mind of the actor, and because a social phenomenon exists only if people believe it exists. Elements of an apparatus necessary to analyze this problematic social ontology are given and include selfreferentiality, constitutive rules, collective intentionality, linguistic permeation of the facts, systematic interrelationships among social facts, and primacy of acts over objects. (shrink)

This book provides a comprehensive overview of the nature of explanations as given in both natural and social sciences. It discusses models of explanation adopted in natural and social sciences. The author also elaborates upon naturalistic and anti-naturalistic views and other types of explanations such as functional, purposive, etc in social science. The volume elaborates upon themes like bridge principle; functional explanation; purposive explanation; teleological explanation; prediction; methodological individualism; methodological collectivism; illocutionary redescription; principle of action; (...) and dispositional explanations, to understand whether the explanations given in the realm of social sciences are the same or different from the explanations that are given in the field of natural sciences. This introductory book is a must read for students and scholars of philosophy of science, logic, science and technology studies, social sciences, and philosophy in general. (shrink)

At present, the science of consciousness is structured around the search for the neural correlates of consciousness. One of the alleged advantages of the NCCs framework is its metaphysical neutrality—the fact that it begs no contested questions with respect to debates about the fundamental nature of consciousness. Here, we argue that even if the NCC framework is metaphysically neutral, it is structurally committed, for it presupposes a certain model—what we call the Lite-Brite model—of consciousness. This, we argue, represents a (...) serious liability for the NCC framework for the plausibility of the Lite-Brite model is very much an open question, and the science of consciousness would be better served by a framework that does not presuppose it. Drawing on interventionist ideas in the philosophy of science, we suggest that the Difference-Maker framework can provide just such an alternative. Instead of searching for the neural correlates of consciousness, we ought to be searching for the difference makers of consciousness. We detail how a shift to searching DMCs will change both the practice of consciousness science and the interpretation of existing results. (shrink)

underpinning of the cognitive sciences. I argue, however, that it often fails to provide adequate explanations, in particular in conjunction with competence theories. This failure originates in the idealizations in competence descriptions, which either ?block? the cascade, or produce a successful cascade which fails to explain cognition.

This paper considers the question of whether the influential distinction between levels of explanation introduced by David Marr can be used as a general framework for contemplating levels of explanation in cognitive sciences. Marr introduced three levels at which we can explain cognitive processes: the computational, algorithmic, and implementational levels. Some argue that Marr’s levels of explanation can only be applied to modular cognitive systems. However, since many psychological processes are non-modular, it seems that Marr’s levels of (...) explanation cannot explain such psychological processes. To show that the latter claim is not convincing, the paper draws upon an influential paradigm from cognitive sciences that is based on the principle of free energy. Based on this paradigm, the paper argues that even non-modular psychological processes can be computationally analyzed and algorithmically implemented. The conclusion of the paper is that, at least under the assumption that the func- tion of the mind is to minimize free energy, Marr’s levels of explanation can be successfully used as a general framework for understanding psychological processes at different levels of description. (shrink)

Biology and history are often viewed as closely related disciplines, with biology informed by history, especially in its task of charting our evolutionary past. Maximizing the opportunities for cross-fertilization in these two fields requires an accurate reckoning of their commonalities and differences-precisely what this volume sets out to achieve. Specially commissioned essays by a team of recognized international researchers cover the full panoply of topics in these fields and include notable contributions on the correlativity of evolutionary and historical explanations, applying (...) to history the latest causal-mechanical approach in the philosophy of biology, and the question of generalized laws that might pertain across the two subjects. The collection opens with a vital interrogation of general issues on explanation that apart from potentially fruitful areas of interaction (could the etiology of the causal-mechanical perspective in biology account for the historical trajectory of the Roman Empire?) this volume also seeks to chart relative certainties distinguishing explanations in biology and history. It also assesses techniques such as the use of probabilities in biological reconstruction, deployed to overcome the inevitable gaps in physical evidence on early evolution. Methodologies such as causal graphs and semantic explanation receive in-depth analysis. Contributions from a host of prominent and widely read philosophers ensure that this new volume has the stature of a major addition to the literature. (shrink)

Emile Meyerson's writings on the philosophy of science are a rich source of ideas and information concerning many philosophical and historical aspects of the development of modem science. Meyerson's works are not widely read or cited today by philosophers or even philosophers of science, in part because they have long been out of print and are often not available even in research libraries. There are additional chevaux de!rise for all but the hardiest scholars: Meyerson's books are written (...) in French (and do not all exist in English versions) and deal with the subject matter of science - ideas or concepts, laws or principles, theories - and epis temological questions rather than today's more fashionable topics of the social matrix and external influences on science with the concomitant neglect of the intellectual content of science. Born in Lublin, Poland, in 1859, Meyerson received most of his education in Germany, where he studied from the age of 12 to 23, preparing himself for a career in chemistry.! He moved to Paris in 1882, where he began a career as an industrial chemist. Changing his profession, he then worked for a time as the foreign news editor of the HAVAS News Agency in Paris. In 1898 he joined the agency established by Edmond Rothschild that had as its purpose the settling of Jews in Palestine and became the Director of the Jewish Colonization Association for Europe and Asia Minor. These activities represent Meyerson's formal career. (shrink)

Applying the concepts of dynamical systems theory to explain cognitive phenomena is still a fairly recent trend in cognitive science and its potential and consequences are not nearly mapped out. A decade ago, dynamical approaches were introduced as a paradigm shift in cognitive science and in this paper I concentrate on how to substantiate this claim. After having considered and rejected the possibility that continuous time is the crucial factor, I present Kelso's model of a near-cognitive phenomenon which (...) invokes self-organization as the guiding principle. Then, the explanatory strategy implicit in this approach is explicated and its underlying assumption presented. Finally, I discuss how we should characterize this explanatory framework using the notion of emergence. (shrink)

Here the author explains the different ways in which explanation is made. He start saying how we explain things that we don't understand in everyday life, were sometimes simple relates or ideas are enough (to explain complex things to a kid, for example), and for us, when we don't understand something, we organise our thinking in order to find a explanation which has to be intelligible, adequate and correct. In science, they are not always like that, and (...) they start trying to explain the unfamiliar things of the familiar, trying always to develop a theory of the most general kind, which will enable him to explain and predict. They are not looking for adequate, but for correct explanation, which in their case takes the form of a hipotesis. In history they behave just like in everyday life explanations, with little place for generalisations (just middle range), in intelligibility, adequacy, and correctness, because they can not venture in general theory. In conclusion, there is little to say about historical explanation which doesn't fit into everyday life explanation. (shrink)

The debate between the defenders of explanatory unification and explanatory pluralism has been ongoing from the beginning of cognitive science and is one of the central themes of its philosophy. Does cognitive science need a grand unifying theory? Should explanatory pluralism be embraced instead? Or maybe local integrative efforts are needed? What are the advantages of explanatory unification as compared to the benefits of explanatory pluralism? These questions, among others, are addressed in this Synthese’s special issue. In the (...) introductory paper, we discuss the background of the questions, distinguishing integrative theorizing from building unified theories. On the one hand, integrative efforts involve collaboration between various disciplines, fields, approaches, or theories. These efforts could even be quite temporary, without establishing any long-term institutionalized fields or disciplines, but could also contribute to developing new interfield theories. On the other hand, unification can rely on developing complete theories of mechanisms and representations underlying all cognition, as Newell’s “unified theories of cognition”, or may appeal to grand principles, as predictive coding. Here, we also show that unification in contemporary cognitive science goes beyond reductive unity, and may involve various forms of joint efforts and division of explanatory labor. This conclusion is one of the themes present in the content of contributions constituting the special issue. (shrink)

Are explanations in the social sciences fundamentally different from explanations in the natural sciences? Many philosophers think that they are, and I call such philosophers ‘difference theorists’. Many difference theorists locate that difference in the alleged fact that only in the natural sciences does explanation essentially include laws.

Are explanations in the social sciences fundamentally different from explanations in the natural sciences? Many philosophers think that they are, and I call such philosophers ‘difference theorists’. Many difference theorists locate that difference in the alleged fact that only in the natural sciences does explanation essentially include laws.

Explanations in cognitive science and computational neuroscience rely predominantly on computational modeling. Although the scientific practice is systematic, and there is little doubt about the empirical value of numerous models, the methodological account of computational explanation is not up-to-date. The current chapter offers a systematic account of computational explanation in cognitive science and computational neuroscience within a mechanistic framework. The account is illustrated with a short case study of modeling of the mirror neuron system in terms (...) of predictive coding. (shrink)

Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 714-719, November 2019.