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)

It is argued in this paper that the valid argument forms coming under the general heading of Demonstrative Induction have played a highly significant role in the history of theoretical physics. This situation was thoroughly appreciated by several earlier philosophers of science and deserves to be more widely known and understood.

I argue that Newtonian-style deduction-from-the-phenomena arguments should only carry conviction when they yield unexpectedly simple conclusions. That in that case they do establish higher rational probabilities for the theories they lead to than for any known or easily constructible rival theories. However I deny that such deductive justifications yield high absolute rational probabilities, and argue that the history of physics suggests that there are always other not-yet-known simpler theories with higher rational probabilities on all the original evidence, and that these (...) later turn out closer to the truth. My analyses rely on the modern Solomonoff-Levin solution to the problem of constructing a mathematically and philosophically acceptable inductive logic. (shrink)