Revisiting the Foundations of Probability

Abstract

We show that the dominant definitions of probability are seriously flawed. While finite frequentism fails to define, infinite frequentism is not operational. Similarly, the Dutch Book arguments used to establish the existence of subjective probability fail to do so. An alternative definition of probability as a metaphor is offered. It is shown that this definition resolves several puzzles regarding the interpretation of common frequentist procedures. In particular, there are no “true” values for parameters, and no way to formulate a “sharp” null hypothesis. If one model offers a good match to the data, all nearby models will also be good models, and hence equally “true”. Viewing models as metaphors also resolves some puzzles in the philosophy of science generated by Popper’s falsification and Kuhn’s paradigm shifts. Falsification is the discovery of a limitation in the scope, and a paradigm shift is the discovery of an alternative metaphor; neither invalidates or “falsifies” previous scientific knowledge. This also explains the progress of science.