Online research in philosophy

It has been the dominant view that probabilistic explanations of particular facts must be inductive in character. I argue here that this view is mistaken, and that the aim of probabilistic explanation is not to demonstrate that the explanandum fact was nomically expectable, but to give an account of the chance mechanism(s) responsible for it. To this end, a deductive-nomological model of probabilistic explanation is developed and defended. Such a model has application only when the probabilities occurring in covering laws can be interpreted as measures of objective chance, expressing the strength of physical propensities. Unlike inductive models of probabilistic explanation, this deductive model stands in no need of troublesome requirements of maximal specificity or epistemic relativization.

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.

1 Logical empiricism: Hempel 1.1 Earlier criteria of significance 1.2 Significance as dependent on constitutive terms 1.3 Partially interpreted systems 2 Explanation 2.1 Background: deductive nomological explanation 2.2 Causal explanation 2.3 The pragmatics of explanation 2.4 Theoretical explanation 3 Confirmation 3.1 Hypothetico deductive model 3.2 The new riddle of induction 4 Scientific change 4.1 Kuhn's revolutions 4.2 Darwin's contribution 5 Realism 5.1 Constructive empiricism 5.2 Structural realism 6 Laws 6.1 Laws and mere regularities 6.2 Systems 6.3 Universals 7 Assignments..

A serious problem for covering law explanation is raised and its consequences for the Hempelian theory of explanation are discussed. The problem concerns an intensional feature of explanations, involving the manner in which theoretical law statements are related to the events explained. The basic problem arises because explanations are not of events but of events under descriptions; moreover, in a sense, our linguistic descriptions outrun laws. One form of the problem, termed the problem of weak intensionality, is apparently solved by a simple logical move, but in fact the problem arises in a new, strong form. It is found that Hempel's model for deductive explanation (to which this discussion is confined) requires modification to handle the weak intensionality problem but then is faced with the problem of strong intensionality. In consequence, it is suggested that Hempel's important concept of explanation sketch is not as widely applicable as usually claimed, especially for explanations in the behavioral and social sciences and history. Reason is found to reject the covering law thesis that every scientific explanation must contain at least one law statement. An important feature of the discussion is that some of the main reasons given for altering the deductive model and for considering other forms of explanation are internal to the covering law theory.

A Hobbesian Model. If ever possible the modelling of the abstract pattern of the item of a philosophical theory belongs, alas!, to its interpretation. In the case of the Hobbesian theory of the natural right and the natural laws (Lev c. XIV, XV) the mathematics of the covenant-model and of its interpretation by an model of preferences and utilities is a neglect task till now. Its performance shows certain shortcomings of the Hobbesian theory.

Selection explanations explain some non-accidental generalizations in virtue of a selection process. Such explanations are not particulaizable - they do not transfer as explanations of the instances of such generalizations. This is unlike many explanations in the physical sciences, where the explanation of the general fact also provides an explanation of its instances (i.e. standard D-N explanations). Are selection explanations (e.g. in biology) therefore a different kind of explanation? I argue that to understand this issue, we need to see that a standard D-N explanation of some non-accidental generalization (al Fs are Gs) may also ipso facto explain its contrapositive (all non-Gs are non-Fs), but the explanation is particularizable with respect to the former but not to the latter. This can be seen by noting that the Raven Paradox counterexample to the H-D model of confirmation also generates a counterexample to the D-N model of explanation (all ravens are black does not explain why the non-black shoe is a non-raven). In such cases it is natural to take the generalization with the positive predicates to have a particularizable explanation. However, this need not be the case, and in selection explanations it is the generalization with the positive predicates whose explanation is no particularizable. Thus there is no need to suppose that selection explanations are fundamentally different.

Zusammenfassung Es gibt kein logisch gültiges Induktionsverfahren. Induktion ist Extrapolation von bisher erfahrenen Einzeltatsachen auf künftige. Die Zukunft ist aber selbst schon eine Extrapolation, keine Erfahrungstatsache, sondern Erwartung. Um sich nicht bloß auf historische Erkenntnis beschränken zu müssen, ist es unentbehrlich, die Voraussetzung zu machen, daß unter gleichen Bedingungen das Gleiche erfolgt. Auf Grund dieser Voraussetzung läßt sich deduktiv ableiten, was induktiv erwiesen werden sollte, aber nicht möglich ist. Logisch stichhaltige Begründung ist nur deduktiv möglich.

In this paper an attempt is made at developing the notion of a real and complete empirical explanation as excluding all forms of potential or incomplete explanations. This explanation is, however, no longer conceived as the proper aim of empirical science, for it can certainly be gleaned from recent epistemological publications that no comprehensive notion of a real and complete scientific explanation is likely to be constructed from within empirical science. Contrary to common understanding the empirical explanation, deductive-nomological as well as statistical explanation, is considered here only as motive of scientific activities, i.e., as common aim of a transcending cooperation of scientific and non-scientific social practice. Following from this the proper aim of empirical science now consists in the development of practically relevant explanatory theories.This redetermination of the aim of scientific activities of empirical science also means criticism of the unification of deductive-nomological and statistical explanations, as it has been proposed by Wolfgang Stegmüller in his pragmatisch-epistemische Wende. For both forms of empirical explanation must be referred to fundamentally different kinds of practical relevance, the former playing a more important role in the advancement of social practice. Stegmüller's development of a comprehensive probabilistic notion of empirical explanation, as tied up to pragmatic knowledge-situations, in a way already transcends a scientifically immanent determination of it, but he seems to have stopped halfway on the road to practically relevant empirical explanations. Several insufficiencies with his probabilistic notion of empirical explanation are shown up in this paper as a consequence of his abiding by pragmatic, and not penetrating to practical, knowledge-situations. The final result of it, however, consists in a clarification and a modification of the concept of deductive-nomological explanation, originally developed by Hempel and Oppenheim.

Die Frage, was eine wissenschaftliche Erklärung ist, stellt seit mehr als einem halben Jahrhundert ein zentrales Thema der Wissenschaftsphilosophie dar. Die heutige Diskussion begann mit einer richtungsweisenden Arbeit von Carl Hempel im Jahre 1942 über den Erklärungsbegriff in der Geschichtswissenschaft. In dieser Arbeit gab Hempel, frühere Überlegungen von John Stuart Mill, Karl Popper und anderen präzisierend, eine formale Definition der Erklärung eines singulären Faktums.1 Mit seiner dem zugrunde liegenden Auffassung, dass die Wissenschaften sehr wohl in der Lage sind, Erklärungen zu liefern, setzt sich Hempel ab von den zur damaligen Zeit vorherrschenden antimetaphysisch gestimmten Erklärungsskeptikern wie Pierre Duhem. Es ist jedoch wichtig zu betonen, dass Hempels Definition des Konzeptes der wissenschaftlichen Erklärung nicht wesentlich über das Deskriptive hinaus geht und damit auch und gerade von Empiristen akzeptiert werden kann. Bekanntlich versteht man unter einer Erklärung in Hempels Deduktiv-Nomologischen (D-N) Modell ein deduktiv gültiges Argument, zu dessen Prämisse (dem sog. Explanans) mindestens ein universelles Gesetz und eine Menge von singulären Sätzen gehört und dessen Konklusion das zu erklärende Faktum (das sog. Explanandum) ist.

Summary Directly concluded from a set of some well-known and some new conditions of adequacy, a definition of deductive-nomological explanation is given which is able to block all known anomalies, and is immune from the Eberle/Kaplan/Montague trivialization theorems. Among some other results it is further shown that law statements have to be logically equivalent to a conditional form.