The standard theory of rationality

At the outset of this work I posed the question of what kind of support can be offered for the weak ordering and strong independence principles – the principles that form the cornerstone of the modern theory of expected utility and subjective probability. The various pieces of my answer are now in place, but the telling has required a series of explorations that have occupied many chapters. Let me try, now, to consider all of the pieces together and focus on what they imply with regard to the status of the two principles in question.

Recall, first of all, that although as a matter of logic the conjunction of PR, DC, and SEP entails both CF and CIND, that formal result does not provide much grounding for the principles in question. Those who find certain violations of CF or CIND plausible can argue from that conviction (via modus tollens) to the conclusion that not all of PR, DC, and SEP are acceptable. In particular, those who find SEP to be plausible can defend violations of either CF or CIND by accepting modifications of the underlying presupposition concerning what plans are feasible – adopting VSF – and, correspondingly, qualifying NEC and, hence, PR. As detailed in Section 8.7, the resulting weakened set of postulates does not suffice for the derivation of either CF or CIND.