PART II - PLAUSIBILITY, UNCERTAINTY AND PROBABILITY
Published online by Cambridge University Press: 22 September 2009
Summary
To acquire insight into a discipline one needs to comprehend how its practitioners reason plausibly. This is no less true for mathematics than it is for science. Understanding how mathematicians choose which problems to work on, how they formulate conjectures and the strategies they adopt to tackle them all require considerations of plausibility. Furthermore, it is also the case that the plausibility of a scientific theory may depend on the plausibility of mathematical results. This has always been so, but now we live in an era where for some physical theories the only testable predictions are mathematical ones it is coming to the fore. Thus, if we are to understand how physicists reckon on the plausibility of their theories, this must involve paying due consideration to the effect of verifying uncertain mathematical predictions.
Now, if one decides, as many have, to treat plausible and inductive reasoning in the sciences in Bayesian terms, it seems clear that one would want to do the same for mathematics. After all, it would appear a little extravagant to devise a second calculus. In any case, Bayesianism is usually presented by its proponents as capable of treating all forms of uncertain reasoning. If so, then we can say that Bayesianism in science requires Bayesianism in mathematics.
- Type
- Chapter
- Information
- Towards a Philosophy of Real Mathematics , pp. 101 - 102Publisher: Cambridge University PressPrint publication year: 2003