Within the philosophy of science, Bayesianism can be seen as positioned on the boundary between the logical empiricist legacy and a more practice-oriented, historical approach. Bayesianism in science points rather to the logical empiricist side, especially when it sees itself as an extension of logic. In mathematics, on the other hand, Bayesianism appears to point us away from logicism to the practice of mathematics. This we saw in the work of Pólya, someone very interested in what goes on behind the scenes. Now it was Pólya who suggested to his fellow Hungarian Imre Lakatos that he explore the early development of algebraic topology following on from the appearance of the Euler conjecture. Lakatos took him up on this advice, producing Proofs and Refutations – a dialectical account of the growth of mathematical knowledge.

Lakatos also came under the influence of Popper, whose negative attitude towards inductivism he shared. He could thus say of Pólya:

We have already encountered this hostile attitude towards inductivism in science in chapter 2.