As Aristotle stated, scientific explanation is based on deductive argument--yet, Wesley C. Salmon points out, not all deductive arguments are qualified explanations. The validity of the explanation must itself be examined. _Four Decades of Scientific Explanation_ provides a comprehensive account of the developments in scientific explanation that transpired in the last four decades of the twentieth century. It continues to stand as the most comprehensive treatment of the writings on the subject during these years. Building on the historic 1948 essay (...) by Carl G. Hempel and Paul Oppenheim, "Studies in the Logic of Explanation,” which introduced the deductive-nomological model on which most work on scientific explanation was based for the following four decades, Salmon goes beyond this model's inherent basis of describing empirical knowledge to tells us “not only _what,_ but also _why_.” Salmon examines the predominant models in chronological order and describes their development, refinement, and criticism or rejection. _Four Decades of Scientific Explanation_ underscores the need for a consensus of approach and ongoing evaluations of methodology in scientific explanation, with the goal of providing a better understanding of natural phenomena. (shrink)

It is a pleasure for me to give this opening address to the Royal Institute of Philosophy Conference on ‘Explanation’ for two reasons. The first is that it is succeeded by exciting symposia and other papers concerned with various special aspects of the topic of explanation. The second is that the conference is being held in my old alma mater, the University of Glasgow, where I did my first degree. Especially due to C. A. Campbell and George Brown there was (...) in the Logic Department a big emphasis on absolute idealism, especially F. H. Bradley. My inclinations were to oppose this line of thought and to espouse the empiricism and realism of Russell, Broad and the like. Empiricism was represented in the department by D. R. Cousin, a modest man who published relatively little, but who was of quite extraordinary philosophical acumen and lucidity, and by Miss M. J. Levett, whose translation of Plato's Theaetetus formed an important part of the philosophy syllabus. (shrink)

Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be ‘coincidental’, ‘accidental’, or ‘fortuitous’. The notion of a ‘ mathematical coincidence’ has so far failed to receive sufficient attention from philosophers. I argue that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. I argue that although the components of a mathematical coincidence (...) may possess a common explainer, they have no common explanation ; that two mathematical facts have a unified explanation makes their truth non-coincidental. I suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. I also argue that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence. (shrink)

The Nature of Selection is a straightforward, self-contained introduction to philosophical and biological problems in evolutionary theory. It presents a powerful analysis of the evolutionary concepts of natural selection, fitness, and adaptation and clarifies controversial issues concerning altruism, group selection, and the idea that organisms are survival machines built for the good of the genes that inhabit them. "Sober's is the answering philosophical voice, the voice of a first-rate philosopher and a knowledgeable student of contemporary evolutionary theory. His book merits (...) broad attention among both communities. It should also inspire others to continue the conversation."-Philip Kitcher, Nature "Elliott Sober has made extraordinarily important contributions to our understanding of biological problems in evolutionary biology and causality. The Nature of Selection is a major contribution to understanding epistemological problems in evolutionary theory. I predict that it will have a long lasting place in the literature."-Richard C. Lewontin. (shrink)

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

Reprint of the original, first published in 1869.

What is the nature of causation? How is causation linked with explanation? And can there be an adequate theory of explanation? These questions and many others are addressed in this unified and rigorous examination of the philosophical problems surrounding causation, laws and explanation. Part 1 of this book explores Hume's views on causation, theories of singular causation, and counterfactual and mechanistic approaches. Part 2 considers the regularity view of laws and laws as relations among universals, as well as recent alternative (...) approaches to laws. Part 3 examines the issues arising from deductive-nomological explanation, statistical explanation, the explanation of laws and the metaphysics of explanation. Accessible to readers of all levels, this book provides an excellent introduction to one of the most enduring problems of philosophy. (shrink)

I examine the question why in Proclus' view genetic processes provide demonstrative explanations, in light of the interpretation of Aristotle's theory of demonstration in late antiquity. I show that in this interpretation mathematics is not an explanatory science in the strict sense because its objects, being immaterial, do not admit causal explanation. Placing Proclus' account of demonstrative explanation in this context, I argue that this account is aimed at answering the question whether mathematical proofs provide causal explanation as opposed to (...) grounds. I show further that Proclus can answer this question in the affirmative due to his realist view of mathematical objects and the priority he ascribes to causal relations over logical relations. (shrink)

Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...) issues in the philosophy of mathematics; in particular it may help platonists respond to a recent challenge by Joseph Melia concerning the force of the Indispensability Argument. (shrink)

Certain scientific explanations of physical facts have recently been characterized as distinctively mathematical –that is, as mathematical in a different way from ordinary explanations that employ mathematics. This article identifies what it is that makes some scientific explanations distinctively mathematical and how such explanations work. These explanations are non-causal, but this does not mean that they fail to cite the explanandum’s causes, that they abstract away from detailed causal histories, or that they cite no natural laws. Rather, in these explanations, (...) the facts doing the explaining are modally stronger than ordinary causal laws or are understood in the why question’s context to be constitutive of the physical arrangement at issue. A distinctively mathematical explanation works by showing the explanandum to be more necessary than ordinary causal laws could render it. Distinctively mathematical explanations thus supply a kind of understanding that causal explanations cannot. 1 Introduction2 Some Distinctively Mathematical Scientific Explanations3 Are Distinctively Mathematical Explanations Set Apart by their Failure to Cite Causes? 4 Distinctively Mathematical Explanations do not Exploit Causal Powers5 How these Distinctively Mathematical Explanations Work6 Conclusion. (shrink)

Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...) by Philip Kitcher and Michael Friedman of explanation or understanding as involving the unification of theories that had antecedently appeared heterogeneous. For the second narrowing, I’ll take up one specific feature (among many) of theories and their basic concepts that is sometimes taken to make the theories and concepts preferred: in some fields, for some problems, what is counted as understanding a problem may involve finding a way to represent the problem so that it (or some aspect of it) can be visualized. The final section develops a case study which exemplifies the way that this consideration – the potential for visualizability – can rationally inform decisions as to what the proper framework and axioms should be. The discussion of unification (in sections 3 and 4) leads to a mathematical analogue of Goodman’s problem of identifying a principled basis for distinguishing grue and green. Just as there is a philosophical issue about how we arrive at the predicates we should use when making empirical predictions, so too there is an issue about what properties best support many kinds of mathematical reasoning that are especially valuable to us. The issue becomes pressing via an examination of some physical and mathematical cases that make it seem unlikely that treatments of unification can be as straightforward as the philosophical literature has hoped. Though unification accounts have a grain of truth (since a phenomenon (or cluster of phenomena) called “unification” is in fact important in many cases) we are far from an analysis of what “unification” is.. (shrink)

Kant seems to have been the first to notice that there is something peculiar about the difference between right and left, but he failed to say exactly what the peculiarity is. His clearest account of the matter is in his inaugural lecture (see Bibliography at the end of the paper): We cannot describe [in general terms] the distinction in a given space between things which lie towards one quarter, and things which are turned towards the opposite quarter. Thus if we (...) take solids which are completely equal and similar but incongruent, such as the right and left hands . . . . although in every respect which admits of being stated in terms intelligible to the mind through a verbal description they can be substituted for one another, there is yet a diversity which makes it impossible for their boundaries to coincide. (shrink)