Rudolf Carnap: Scientific method as Bayesian reasoning
With the notable exception of Karl Popper, philosophers of science have accepted that the reasoning scientists use in order to establish their conclusions is, or is in part, inductive reasoning. There have been, and there continue to be, different views about what induction is, but there is considerable agreement that induction has some degree of cogency, even though it is incapable of the conclusiveness of deduction. Inductive conclusions drawn from given evidence are accepted, that is to say, with a certain degree of confidence. But if scientific reasoning is entitled to its customary reputation, then we need to justify these degrees of confidence as rational, and for this we must have a good way of understanding degrees of confidence. The traditional view, which, as we have seen, we can trace back to Leibniz in the seventeenth century, is that they are nothing other than probabilities. So the rationality of inductive conclusions depends on the rationality of probabilities. This dependence, though, will not enable us to clarify our understanding so long as we are confronted with alternative accounts of probability. The arguments of Keynes and Reichenbach plainly showed that different particular interpretations of probability yielded different specific accounts of what counts as sound inductive reasoning. They reflect the contrast, which began to emerge in the nineteenth century, between rationalist a priori and empiricist a posteriori accounts of scientific method.