PART III - THE GROWTH OF MATHEMATICS
Published online by Cambridge University Press: 22 September 2009
Summary
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 owe this revival of mathematical heuristic in this century to Pólya. His stress on the similarities between scientific and mathematical heuristic is one of the main features of his admirable work. What may be considered his only weakness is connected with this strength: he never questioned that science is inductive, and because of his correct vision of deep analogy between scientific and mathematical heuristic he was led to think that mathematics is also inductive.
(Lakatos 1976: 74n.)We have already encountered this hostile attitude towards inductivism in science in chapter 2.
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- Information
- Towards a Philosophy of Real Mathematics , pp. 149 - 150Publisher: Cambridge University PressPrint publication year: 2003