I show that Armstrong’s view of laws as second-order contingent relations of ‘necessitation’ among categorical properties faces a dilemma. The necessitation relation confers a relation of extensional inclusion (‘constant conjunction’) on its relata. It does so either necessarily or contingently. If necessarily, it is not a categorical relation (in the relevant sense). If contingently, then an explanation is required of how it confers extensional inclusion. That explanation will need to appeal to a third-order relation between necessitation and extensional inclusion. The (...) same dilemma reappears at this level. Either Armstrong must concede that some properties are not categorical but have essential powers – or he is faced with a regress. (shrink)

In this paper Beebee argues that the problem of induction, which she describes as a genuine sceptical problem, is the same for Humeans than for Necessitarians. Neither scientific essentialists nor Armstrong can solve the problem of induction by appealing to IBE, for both arguments take an illicit inductive step.

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)

In this paper I put forward what I think is a new approach to the problem of induction. I sketched the approach in brief sections of a book published in 1983. The same idea had occurred to the English philosopher John Foster and he presented it in a paper at about the same time.

This is a study of a crucial and controversial topic in metaphysics and the philosophy of science: the status of the laws of nature. D. M. Armstrong works out clearly and in comprehensive detail a largely original view that laws are relations between properties or universals. The theory is continuous with the views on universals and more generally with the scientific realism that Professor Armstrong has advanced in earlier publications. He begins here by mounting an attack on the orthodox and (...) sceptical view deriving from Hume that laws assert no more than a regularity of coincidence between instances of properties. In doing so he presents what may become the definitive statement of the case against this position. Professor Armstrong then goes on to establish his own theory in a systematic manner defending it against the most likely objections, and extending both it and the related theory of universals to cover functional and statistical laws. This treatment of the subject is refreshingly concise and vivid: it will both stimulate vigorous professional debate and make an excellent student text. (shrink)

Many necessitarians about cause and law (Armstrong 1983; Mumford 2004; Bird 2007) have argued that Humeans are unable to justify their inductive inferences, as Humean laws are nothing but the sum of their instances. In this paper I argue against these necessitarian claims. I show that Armstrong is committed to the explanatory value of Humean laws (in the form of universally quantified statements), and that contra Armstrong, brute regularities often do have genuine explanatory value. I finish with a Humean attempt (...) at a probabilistic justification of induction, but this fails due to its assumption that the proportionality syllogism is justified. Although this attempt fails, I nonetheless show that the Humean is at least as justified in reasoning inductively as Armstrong. (shrink)

How do we go about weighing evidence, testing hypotheses, and making inferences? The model of " inference to the best explanation " -- that we infer the hypothesis that would, if correct, provide the best explanation of the available evidence--offers a compelling account of inferences both in science and in ordinary life. Widely cited by epistemologists and philosophers of science, IBE has nonetheless remained little more than a slogan. Now this influential work has been thoroughly revised and updated, and features (...) a new introduction and two new chapters. Inference to the Best Explanation is an unrivaled exposition of a theory of particular interest in the fields both of epistemology and the philosophy of science. (shrink)

How do we go about weighing evidence, testing hypotheses, and making inferences? According to the model of _Inference to the Best Explanation_, we work out what to infer from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In _Inference to the Best Explanation_, Peter Lipton gives this important and influential idea the development and assessment it deserves. The (...) second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contrastive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of _Inference to the Best Explanation_ has also been updated throughout and includes a new bibliography. (shrink)

This is a study, in two volumes, of one of the longest-standing philosophical problems: the problem of universals. In volume I David Armstrong surveys and criticizes the main approaches and solutions to the problems that have been canvassed, rejecting the various forms of nominalism and 'Platonic' realism. In volume II he develops an important theory of his own, an objective theory of universals based not on linguistic conventions, but on the actual and potential findings of natural science. He thus reconciles (...) a realism about qualities and relations with an empiricist epistemology. The theory allows, too, for a convincing explanation of natural laws as relations between these universals. (shrink)

This book outlines a major new theory of natural laws. The book begins with the question of whether there are any genuinely law-like phenomena in nature. The discussion addresses questions currently being debated by metaphysicians such as whether the laws of nature are necessary or contingent and whether a property can be identified independently of its causal role.