What Do Mathematicians Want? Probabilistic Proofs and the Epistemic Goals of Mathematicians
Several philosophers have used the framework of means/ends reasoning to explain the methodological choices made by scientists and mathematicians (see, e.g., Goldman 1999, Levi 1962, Maddy 1997). In particular, they have tried to identify the epistemic objectives of scientists and mathematicians that will explain these choices. In this paper, the framework of means/ends reasoning is used to study an important methodological choice made by mathematicians. Namely, mathematicians will only use deductive proofs to establish the truth of mathematical claims. In this paper, I argue that none of the epistemic objectives of mathematicians that are currently on the table provide a satisfactory explanation of this rejection of probabilistic proofs.
Summary Government action during food crises in southern Africa frequently exacerbates the problems, driving food staple prices well beyond import parity. We argue that an inability to make credible commitments, due largely to a lack of trust between public and private sectors, contributes to this dynamic. Empirical policy analysis can facilitate resolution only within a consultative process involving a broad range of stakeholders. The policies emerging from such a process are not likely to approximate first best recommendations. Yet the precise policies may be less important than the fact that they exist and that main stakeholders find them credible.