A new theory of scientific explanation

Social Science Research Network, 2002

I shall endeavor to show that every physical theory since Newton explains without drawing attention to causes-that, in other words, physical theories as physical theories aspire to explain under an ideal quite distinct from that of causal explanation. If I am right, then even if sometimes the explanations achieved by a physical theory are not in violation of the standard of causal explanation, this is purely an accident. For physical theories, as I will show, do not, as such, aim at accommodating the goals or aspirations of causal explanation. This will serve as the founding insight for a new theory of explanation, which will itself serve as the cornerstone of a new theory of scientific method.

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 (also known as Kepler's 1-2-3 law) under theoretical principles provide a causal explanation for the planetary motions? My answer is a definitive no. As a matter of fact, on occasions subsumptions occur under differing theoretical principles that are incompatible with one another. I 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 physcis.

Philosophy of Science, 2011

I offer one possible 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 can be related diachronically.

The problems that exist in relating quantum mechanical phenomena to classical concepts like properties, causes, or entities like particles or waves are well-known and still open to question, so that there is not yet an agreement on what kind of metaphysics lies at the foundations of quantum mechanics. However, physicists constantly use the formal resources of quantum mechanics in order to explain quantum phenomena. The structural account of explanation, therefore, tries to account for this kind of mathematical explanation in physics, and hinges on the following claims: i) scientific models are central in scientific explanation; ii) in some cases the relevant information for the explanation/understanding of a phenomenon P consists in the sole structural properties of the (models displayed by the) theory; iii) in these cases, the interpretation of the formalism in terms of a categorial framework is unessential for the explanation of P and a mathematical model can be at the base of an objective and effective scientific explanation. The present paper will carry a reflection about some issues arising from R.I.G. Hughes and Robert Clifton's works in the attempt to outline some details of structural explanation. § 1 Introduction The pervasive role of mathematics in modern science has cross-fertilized the philosophy of science in many ways. Among them, a topic of growing interest is the epistemological status of mathematical explanations of natural phenomena. An extensive literature can be found on this subject, for instance in cognitive science – concerning the so-called computational explanations (McCulloch and Pitts 1943, Piccinini 2006), where the mental capacities of the brain are explained by its computations – and in more recent times a significant number of papers have investigated the role of mathematical explanations also in biology (Berger 1998). Since the role that mathematics plays in the explanation of natural phenomena can hardly be overrated, it seems remarkably odd that such a topic has been hitherto neglected in the philosophy of physics, the mathematised science par excellence. The current state of scientific knowledge and within it of the relationship between mathematics and explanation is well illustrated by Ruth Berger: " Today's science is often concerned with the behavior of extremely complicated physical systems and with huge data sets that can be organized in many different ways. To deal with this, scientists increasingly rely on mathematical models to process, organize, and generate explanatory information. Since much of the understanding produced by contemporary science is gathered during the process of mathematical modelling, it is incumbent upon philosophical accounts of explanation to accommodate modelling explanations. This is recognized by the semantic view of theories, which identifies mathematical modelling as one of the mains explanatory engines of science. " (Berger 1998, p.308) But the acknowledgement of the central role of models in science did not correspond to the recognition of a similar role in the more restricted field of scientific explanation: " Although many philosophers accept the basic features of the semantic view of theories, there have been surprisingly few attempts to reconcile it with our best philosophical accounts of scientific explanation. […] [C]ausal accounts cannot illuminate precisely those explanatory features of science which the semantic view deems most important. Specifically, causal accounts of explanation cannot accommodate, and often obscure, the crucial role which mathematical modelling

Foundations of Science, 1995

This paper describes the development of theories of scientific explanation since Hempel's earliest models in the 1940ies. It focuses on deductive and probabilistic whyexplanations and their main problems: lawlikeness, explanation-prediction asymmetries, causality, deductive and probabflistic relevance, maximal specifity and homogenity, tile height of the probability value. For all of these topic the paper explains the most important approaches as well as their criticism, including the author's own accounts. Three main theses of this paper are: (1) Both deductive and probabilistic explanations are important in science, not reducible to each other. (2) One must distinguish between (cause giving) explanations and (reason giving) justifications and predictions. (3) The adequacy of deductive as well as probabilistic explanations is relative to a pragmatically given background knowledge-which does not exclude, however, the possibility of purely semantic models.

This paper describes the development of theories of scientific explanation since Hempel's earliest models in the 1940ies. It focuses on deductive and probabilistic why-explanations and their main problems: lawlikeness, explanation-prediction asymmetries, causality, deductive and probabflistic relevance, maximal specifity and homogenity, tile height of the probability value. For all of these topic the paper explains the most important approaches as well as their criticism, including the author's own accounts. Three main theses of this paper are: (1) Both deductive and probabilistic explanations are important in science, not reducible to each other. (2) One must distinguish between (cause giving) explanations and (reason giving) justifications and predictions. (3) The adequacy of deductive as well as probabilistic explanations is relative to a pragmatically given background knowledge-which does not exclude, however, the possibility of purely semantic models.

International Studies in the Philosophy of Science, 2015

Many philosophers now regard causal approaches to explanation as highly promising, even in physics. This is due in large part to James Woodward's influential argument that a wide range of explanations (including explanations in physics) are causal, based on his interventionist approach to causation. This article focuses on explanations, widespread in physics, involving highly idealized models. These explanations are not causal, yet they do not fall under any of the types of non-causal explanation Woodward describes. I argue that causal explanation is simply not as widespread or important in physics as Woodward and others maintain.

THEORIA. An International Journal for Theory, History and Foundations of Science, 2012

Editors' introduction to the special issue on the Causality and Explanation in the Sciences conference, held at the University of Ghent in September 2011.

An interpretation of the formalism of quantum mechanics that can be regarded as uncontroversial is currently not available. Consequently, philosophers have often contrasted the poor explanatory power of quantum theory to its unparalleled predictive capacity. However, the admission that our best theory of the fundamental constituents of matter cannot explain the phenomena it describes represent a strong argument against the view that explanation is a legitimate aim of science, and this conclusion is regarded by the vast majority of philosophers as unacceptable.

2013