The explanatory and heuristic power of mathematics

Mathematics is, and has been for a very long time, one of the most successful autonomous fields of research. However, the last five centuries have seen it become so deeply interwoven in virtually every area of scientific inquiry to convince Kant that “in any special doctrine of nature there can be only as much proper science as there is mathematics therein” (Kant 1786/2004, 6; emphases in original). While the distinction between pure and applied mathematics remains somewhat elusive, philosophers have been interested in understanding the nature of each. Moreover, the idea that there are actually two uses of mathematics, an explanatory and a heuristic one, has begun to feature more and more prominently in recent philosophical debates

Human-Effective Computability

We analyse Kreisel's notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church's thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman

Naturalising Mathematics: A Critical Look at the Quine-Maddy Debate

This paper considers Maddy’s strategy for naturalising mathematics in the context of Quine’s scientific naturalism. The aim of this proposal is to account for the acceptability of mathematics on scientific grounds without committing to revisionism about mathematical practice entailed by the Quine-Putnam indispensability argument. It has been argued that Maddy’s mathematical naturalism makes inconsistent assumptions on the role of mathematics in scientific explanations to the effect that it cannot distinguish mathematics from pseudo-science. I shall clarify Maddy’s arguments and show that the objection can be overcome. I shall then reformulate a novel version of the objection and consider a possible answer, and I shall conclude that mathematical naturalism does not ultimately provide a viable strategy for accommodating an anti-revisionary stance on mathematics within a Quinean naturalist framework

Epistemic Church's Thesis and Absolute Undecidability

publishe

Epistemic Church's Thesis and absolute undecidability

publishe