Problems in probabilistic induction are of two general kinds. In the first, we have a linearly ordered sequence of symbols that must be extrapolated. In the second we want to extrapolate an unordered set of finite strings. A very general formal solution to the first kind of problem is well known and much work has been done in obtaining good approximations to it [LI 93, Ris 78, Ris 89, Sol 64a, ...

This research addressed how inductive reasoning and deductive reasoning are related. We directly compared the ideas that the same cognitive mechanisms are applied to both types of judgments and that different processes lead induction and deduction to use different information. In an experiment, subjects either judged inductive strength or deductive validity, for a common set of arguments. A fin...

The majority of historians agree that social and political reality significantly influences changes in historical thinking, and thereby the development of historical research. However, when we inquire after the mechanism or mechanisms regulating these influences, controversies appear. Differences in viewpoints result from the fact that the relationship between historiography and social life is ...

This is an elementary expository article regarding the application of Kleene’s Recursion Theorems in making definitions by recursion. Whereas the Second Recursion Theorem (SRT) is applicable in a first-order setting, the First Recursion Theorem (FRT) requires a higherorder setting. In some cases both theorems are applicable, but one is stronger than the other: the FRT always produces least fixe...

People sometimes think in terms of ‘we’ referring to a group they belong to. When making decisions, they frame the decision problem as: ‘What should we do?’ instead of ‘What should I do?’. We study one particular approach to such ‘we-reasoning’, economist Michael Bacharach’s theory of ‘team reasoning’, and relate it to philosopher Raimo Tuomela’s distinction between ‘I-mode’ reasoning and ‘we-m...