Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

The detailed analysis of a particular quasi-historical numerical example is used to illustrate the way in which a Bayesian personalist approach to scientific inference resolves the Duhemian problem of which of a conjunction of hypotheses to reject when they jointly yield a prediction which is refuted. Numbers intended to be approximately historically accurate for my example show, in agreement with the views of Lakatos, that a refutation need have astonishingly little effect on a scientist's confidence in the ‘hard core’ of (...) a successful research programme even when a comparable confirmation would greatly enhance that confidence. Timeo Danaos et dona ferentis. (shrink)

Karl Popper defines an ad hoc hypothesis as one that is introduced to immunize a theory from some (or all) refutation but which cannot be tested independently. He has also attempted to explicate ad hocness in terms of certain other allegedly undesirable properties of hypotheses or of the explanations they would provide, but his account is confused and mistaken. The first such property is circularity, which is undesirable; the second such property is reduction in empirical content, which need not be. (...) In the former case, I argue that non-circularity is in any event preferable to non-ad hocness as a necessary condition for a satisfactory explanation or an explanans, as the case may be, and I try to sort out various persistent errors surrounding this comparison. In the latter case, I suggest that Popper is barking up the wrong tree, that important scientific progress sometimes does consist in just such reductions in empirical content as he proscribes. This provides a further reason for not taking ad hoc hypotheses as Popper conceives them to pose the danger for science he believes they do. (shrink)

Traditional analyses of the curve fitting problem maintain that the data do not indicate what form the fitted curve should take. Rather, this issue is said to be settled by prior probabilities, by simplicity, or by a background theory. In this paper, we describe a result due to Akaike [1973], which shows how the data can underwrite an inference concerning the curve's form based on an estimate of how predictively accurate it will be. We argue that this approach throws light (...) on the theoretical virtues of parsimoniousness, unification, and non ad hocness, on the dispute about Bayesianism, and on empiricism and scientific realism. * Both of us gratefully acknowledge support from the Graduate School at the University of Wisconsin-Madison, and NSF grant DIR-8822278 (M.F.) and NSF grant SBE-9212294 (E.S.). Special thanks go to A. W. F. Edwards.William Harper. Martin Leckey. Brian Skyrms, and especially Peter Turney for helpful comments on an earlier draft. (shrink)

One of the difficulties with which scientific endeavour is fraught is that of maintaining detachment. The scientist's interest in his work will lead him to formulate hypotheses and the hypotheses will lead him to expectations about future observations. Is disinterested investigation then possible? Surely the very formulation of a hypothesis engenders a paternal affection and a desire to preserve it. Knowing this, however, the scientist is able to guard against his expectations influencing his observations, defending thus both his objectivity and (...) his honour. But in cases where discriminations are exceptionally difficult to make, then here perhaps, in spite of fore-knowledge of the danger, and in spite of all precautions, an expectation may influence a judgement. (shrink)