Online research in philosophy

The intuitive notion of a statistical explanation has been explicated in different ways; recently it has even been claimed that there are no statistical explanations at all. In an attempt to clarify the disputed issue, the approaches adopted by Hempel, by Jeffrey, Salmon and Greeno, and by Stegmuller are analyzed critically, as far as they are concerned with the explanation of particular events. A solution of the controversy is proposed on the basis of a concept of explanation which refers essentially to a causal analysis of the explanandum. The possibility of statistical explanations, then, becomes contingent upon the existence of indeterministic causation. In conclusion, therefore, a conception of causality is sketched which shows that indeterminism and causal connection are compatible, at least from an epistemological point of view, so that statistical explanation can be seen to represent a specific and possibly irreducible scientific activity.

Issues concerning scientific explanation have been a focus of philosophical attention from Pre- Socratic times through the modern period. However, recent discussion really begins with the development of the Deductive-Nomological (DN) model. This model has had many advocates (including Popper 1935, 1959, Braithwaite 1953, Gardiner, 1959, Nagel 1961) but unquestionably the most detailed and influential statement is due to Carl Hempel (Hempel 1942, 1965, and Hempel & Oppenheim 1948). These papers and the reaction to them have structured subsequent discussion concerning scientific explanation to an extraordinary degree. After some general remarks by way of background and orientation (Section 1), this entry describes the DN model and its extensions, and then turns to some well-known objections (Section 2). It next describes a variety of subsequent attempts to develop alternative models of explanation, including Wesley Salmon's Statistical Relevance (Section 3) and Causal Mechanical (Section 4) models and the Unificationist models due to Michael Friedman and Philip Kitcher (Section 5). Section 6 provides a summary and discusses directions for future work.

Reminiscences of Peter, by P. Oppenheim.--Natural kinds, by W. V. Quine.--Inductive independence and the paradoxes of confirmation, by J. Hintikka.--Partial entailment as a basis for inductive logic, by W. C. Salmon.--Are there non-deductive logics?, by W. Sellars.--Statistical explanation vs. statistical inference, by R. C. Jeffre--Newcomb's problem and two principles of choice, by R. Nozick.--The meaning of time, by A. Grünbaum.--Lawfulness as mind-dependent, by N. Rescher.--Events and their descriptions: some considerations, by J. Kim.--The individuation of events, by D. Davidson.--On properties, by H. Putnam.--A method for avoiding the Curry paradox, by F. B. Fitch.--Publications (1934-1969) by Carl G. Hempel (p. [266]-270).

An argument has been recently proposed by Watkins, whose objective is to show the impossibility of a statistical explanation of single events. This present paper is an attempt to show that Watkins's argument is unsuccessful, and goes on to argue for an account of statistical explanation which has much in common with Hempel's classic treatment.

The purpose of this paper is to provide a systematic appraisal of the covering law and statistical relevance theories of statistical explanation advanced by Carl G. Hempel and by Wesley C. Salmon, respectively. The analysis is intended to show that the difference between these accounts is inprinciple analogous to the distinction between truth and confirmation, where Hempel's analysis applies to what is taken to be the case and Salmon's analysis applies to what is the case. Specifically, it is argued (a) that statistical explanations exhibit the nomic expectability of their explanandum events, which in some cases may be strong but in other cases will not be; (b) that the statistical relevance criterion is more fundamental than the requirement of maximal specificity and should therefore displace it; and, (c) that if statistical explanations are to be envisioned as inductive arguments at all, then only in a qualified sense since, in particular, the requirement of high inductive probability between explanans and explanandum must be abandoned.

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.

Hempel's high probability requirement asserts that any rationally acceptable answer to the question 'Why did event X occur?' must offer information which shows that X was to be expected at least with reasonable probability. Salmon rejected this requirement in his S-R model. This led to a series of paradoxical consequences, such as the assertion that an explanation of an event can both lower its probability and make it arbitrarily low, and the assertion that the explanation of an outcome would have qualified as an explanation of its non-occurrence as well. We argue that if inductive explanations are to be seen as generalizations of the causal-deterministic model, or if they are to be seen as satisfying the requirement--fulfilled by the D-N model--that explanations ought to identify certain features of the universe that are nomically responsible for the explanadum event, then the high probability requirement seems to be unacceptable. If this is so, a realistically inspired theory of inductive explanation will be committed to the paradoxes that follow from Salmon's model.

Carl G. Hempel has often stated that inductive-statistical explanations, as he conceives them, are inductive arguments. This discussion note raises the question of whether such arguments are to be understood as (1) arguments of the traditional sort, containing premises and conclusions, governed by some sort of inductive "acceptance rules," or (2) something more closely akin to Carnap's degree of confirmation statements which occur in an inductive logic which entirely eschews inductive "acceptance rules." Hempel's writings do not seem unequivocal on this issue. It is suggested that adoption of construal (2) would remove the need for Hempel's high probability requirement on I-S explanations.