– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

The paper presents an analysis of the anumāna chapter of Jayarāśi’s Tattvôpaplava-siṁha and the nature of his criticism levelled against the anumāna model. The results of the analysis force us to revise our understanding of Jayarāśi Bhaṭṭa as a sceptic. Instead, he emerges as a highly critical philosopher. In addition, the nature of Jayarāśi’s criticism of the anumāna model allow us to conclude that anumāna should not be equated with inference, but rather is its limited subset, and may at best (...) be rendered as ‘disputational inference’, ‘debational inference’ or even ‘dialogical inference’. Jayarāśi applies a range of logical laws which clearly represent patterns of what can be classified as a priori reasoning and analytical justifications for knowledge, which were traditionally not reckoned sound. Against the backdrop of Jayarāśi’s criticism of anumāna, the paper also attempts to provide an explanation to why Indian philosophy and logic did not develop any concept of proper symbols and variables. (shrink)