It may be thought odd that these two philosophers should have been selected for discussion together. They had no special connection with each other. They were not personally close. They did not teach or write in the same place. Nor were their personalities at all similar. None the less there are similarities of thought and perspective that make the conjunction illuminating.It may be thought even odder that these two philosophers should have been selected for discussion at all. After all, who (...) today reads them, or has even heard of them? Very few. If they ever were in fashion, they are not in fashion now. But this situation results from ignorance, which this series aims to dispel. Remember, it was meant to be a revelation to the ignorant as well as an inspiration. (shrink)

We mathematical animals should be grateful that mathematics is instrumentally useful. We should not, however, forget its other contributions to human happiness. Bertrand Russell and John Dewey offer timely reminders that provide insight into the role of non-mathematicians in the evaluation of mathematics.

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a (...) unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical. (shrink)