Hempel's Paradox, Law-likeness and Causal Relations

It is widely thought that Bayesian confirmation theory has provided a solution to Hempel's Paradox (the Ravens Paradox). I discuss one well-known example of this approach, by John Mackie, and argue that it is unconvincing. I then suggest an alternative solution, which shows that the Bayesian approach is altogether mistaken. Nicod's Condition should be rejected because a generalisation is not confirmed by any of its instances if it is not law-like. And even law-like non-basic empirical generalisations, which are expressions of assumed underlying causal regularities, are not so confirmed if they are absurd in the light of our causal background knowledge or if their instances are not also possible instances of the relevant causal claim.     

Why Friedman's non-monotonic reasoning defies Hempel's covering law model

In this paper we will show that Hempel's covering law model can't deal very well with explanations that are based on incomplete knowledge. In particular the symmetry thesis, which is an important aspect of the covering law model, turns out to be problematic for these explanations. We will discuss an example of an electric circuit, which clearly indicates that the symmetry of explanation and prediction does not always hold. It will be argued that an alternative logic for causal explanation is needed. And we will investigate to what extent non-monotonic epistemic logic can provide such an alternative logical framework. Finally we will show that our non-monotonic logical analysis of explanation is not only suitable for simple cases such as the electric circuit, but that it also sheds new light on more controversial causal explanations such as Milton Friedman's explanation of the business cycle.We gratefully acknowledge the helpful suggestions and critical comments of Johan van Benthem, Bert Hamminga, Kevin Hoover, Theo Kuipers, and Rick Looyen.     

Comments on ‘Hempel's ambiguity’ by J. Alberto Coffa

Using Coffa's paper as a point of departure, this brief note is designed to show that Hempel's inductive-statistical model of explanation implicitly construes explanations of that type as defective deductive-nomological explanations, with the consequence that there is no such thing as genuine inductive-statistical explanation according to Hempel's account. This result suggests a possible implicit commitment to determinism behind Hempel's theory of scientific explanation.     

Fluctuating maximal God

International Journal for Philosophy of Religion - This paper explores a variety of perfect being theism that combines Yujin Nagasawa’s maximal God thesis with the view that God is not...     

A model-theoretic criterion of ontology

Conclusion My aim has been to adapt Quine's criterion of the ontological commitment of theories couched in standard quantificational idiom to a much broader class of theories by focusing on the set-theoretic structure of the models of those theories. For standard first-order theories, the two criteria coincide on simple entities. Divergences appear as they are applied to higher-order theories and as composite entities are taken into account. In support of the extended criterion, I appeal to its fruits in treating the various examples considered above and to the healthy intuitions of the non-noneists among us. Don't O(m) and E(m) comprise just the things we should have though existed according to a particular interpretation m of a language or a theory? Whatever the answer (and it will hardly be unanimous), I hope to have pointed the way towards a recognition of ontology as a worthwhile branch of modern theory.Earlier versions of parts of this paper were read at New York University, at the Australasian Association of Philosophy, and at the University of Sydney. I am very grateful to William Barrett, Keith Campbell, Gregory Currie, Kenneth Gemes, Toomas Karmo, and Stephen Read for comments and criticisms.     

A weighted procrustes criterion

The Procrustes criterion is a common measure for the distance between two matricesX andY, and can be interpreted as the sum of squares of the Euclidean distances between their respective column vectors. Often a weighted Procrustes criterion, using, for example, a weighted sum of the squared distances between the column vectors, is called for. This paper describes and analyzes the performance of an algorithm for rotating a matrixX such that the column-weighted Procrustes distance toY is minimized. The problem of rotatingX intoY such that an aggregate measure of Tucker's coefficient of congruence is maximized is also discussed.We wish to thank Richard A. Harshman and C. F. Jeff Wu for valuable discussions in the early stages of this work. We would also like to thank Jos ten Berge, John Gower, and the Editor, Associate Editor, and referees whose comments and suggestions greatly improved this paper.     

A multiscale Griffith criterion

In this letter, a compatibility-momentum tensor is proposed based on the strain compatibility condition of continuum mechanics. By rescaling the compatibility-momentum tensor, we construct a so-called multiscale energy-momentum tensor and the corresponding L-integral, which is path-independent if the interior region of the integration contour is dislocation-free. By applying the invariant L-integral to the field of a mode III elastoplastic crack under small-scale yielding condition, we derive a multiscale criterion for macroscopically brittle fractures.