2 Interpreting Probability 5 2 . 1 Interpreting Probability Theory

This paper aims to examine the theoretical context of the synchronic and diachronic versions of the Dutch Book argument. The paper begins with a brief characterization of the significance of making an interpretation of the theory of probability after Kolmogorov’s contribution. Following this, the core of an intended model – i.e., subjective probability or degrees of belief – will be described as part of the Bayesian doctrine. The second part of this paper includes the details of the Synchronic and Diachronic Dutch Book theorems and arguments. Finally, a criticism of each of these arguments is presented. On the one hand, Hajék’s parody of the argument by a symmetric Good Book argument will show a fundamental flaw in the traditional argument. On the other hand, a paradox presented by van Fraassen concerning the Diachronic argument will emphasize that even if it follows from Bayesianism that we should update our beliefs by conditionalization on evidence, the strict endorsement of the principle of conditionalization commits us to accept a seemingly irrational principle. With these two criticisms in mind, it is hoped that our susceptibility to being Dutch Booked by Dutch Book arguments will be to some extent diminished.