This paper explores how data serve as evidence for phenomena. In contrast to standard philosophical models which invite us to think of evidential relationships as logical relationships, I argue that evidential relationships in the context of data-to-phenomena reasoning are empirical relationships that depend on holding the right sort of pattern of counterfactual dependence between the data and the conclusions investigators reach on the phenomena themselves.

A toast is due to one who slays Misguided followers of Bayes, And in their heart strikes fear and terror With probabilities of error! (E.L. Lehmann).

In seeking general accounts of evidence, confirmation, or inference, philosophers have looked to logical relationships between evidence and hypotheses. Such logics of evidential relationship, whether hypothetico-deductive, Bayesian, or instantiationist fail to capture or be relevant to scientific practice. They require information that scientists do not generally have (e.g., an exhaustive set of hypotheses), while lacking slots within which to include considerations to which scientists regularly appeal (e.g., error probabilities). Building on my co-symposiasts contributions, I suggest some directions in which a (...) new and more adequate philosophy of evidence can move. (shrink)

1. Introduction. The papers by Hellman and Mayo offer up a rich menu of problems and proposed solutions, so there is much here for a friendly critic to fasten on. In order to bring a modicum of focus to my commentary, I shall limit my remarks to the Duhem problem and its radiations in epistemology and methodology. Both Mayo and Hellman claim to have solutions to that hoary old problem and they tout these solutions as key indicators of the explanatory (...) power of their respective technical epistemologies, whether Bayesian or Neyman/Pearsonian. Like Mayo, I shall be arguing that the Bayesian treatment of Duhem's problem is no solution at all; that, indeed, it fails to grapple with the core challenges posed by the purported ambiguities of falsification. My response to Mayo's more detailed, and I think more right-headed, treatment of the Duhem problem will be more complex. While I believe that she is moving in the right direction in many respects, I think that she fails to see one key dimension of the Duhemian conundrum. Indeed, she risks solving not Duhem's problem but quite a different one. I shall gently try to encourage her to steer her way back towards the central task. (shrink)

This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

The Bayesian theory is outlined and its status as a logic defended. In this it is contrasted with the development and extension of Neyman-Pearson methodology by Mayo in her recently published book (1996). It is shown by means of a simple counterexample that the rule of inference advocated by Mayo is actually unsound. An explanation of why error-probablities lead us to believe that they supply a sound rule is offered, followed by a discussion of two apparently powerful objections to the (...) Bayesian theory, one concerning old evidence and the other optional stopping. (shrink)

In this paper, I present a simple and straightforward logic of induction: a consequence relation characterized by a proof theory and a semantics. This system will be called LI. The premises will be restricted to, on the one hand, a set of empirical data and, on the other hand, a set of background generalizations. Among the consequences will be generalizations as well as singular statements, some of which may serve as predictions and explanations.

This short paper serves as an introduction to a debate between representatives of two fundamentally different points of view regarding the nature of scientific inference. Colin Howson and Peter Urbach represent a Bayesian point of view and Deborah Mayo represents a version of classical statistics called error statistics. The paper begins by reviewing earlier versions of the same two points of view due to Rudolf Carnap and Hans Reichenbach, respectively. After a few remarks about philosophical approaches to understanding scientific reasoning (...) between 1960 and 1980, I turn to substantive differences between the two approaches. (shrink)

What is required for something to be evidence for a hypothesis? In this fascinating, elegantly written work, distinguished philosopher of science Peter Achinstein explores this question, rejecting typical philosophical and statistical theories of evidence. He claims these theories are much too weak to give scientists what they want--a good reason to believe--and, in some cases, they furnish concepts that mistakenly make all evidential claims a priori. Achinstein introduces four concepts of evidence, defines three of them by reference to "potential" evidence, (...) and characterizes the latter using a novel epistemic interpretation of probability. The resulting theory is then applied to philosophical and historical issues. Solutions are provided to the "grue," "ravens," "lottery," and "old-evidence" paradoxes, and to a series of questions. These include whether explanations or predictions furnish more evidential weight, whether individual hypotheses or entire theoretical systems can receive evidential support, what counts as a scientific discovery, and what sort of evidence is required for it. The historical questions include whether Jean Perrin had non-circular evidence for the existence of molecules, what type of evidence J. J. Thomson offered for the existence of the electron, and whether, as is usually supposed, he really discovered the electron. Achinstein proposes answers in terms of the concepts of evidence introduced. As the premier book in the fabulous new series Oxford Studies in Philosophy of Science, this volume is essential for philosophers of science and historians of science, as well as for statisticians, scientists with philosophical interests, and anyone curious about scientific reasoning. (shrink)