Paul D. Thorn

The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have postponed treatment of the problem associated with gerrymandered reference classes by appealing to an unexplicated notion of projectability . I address the lacuna in past theories by introducing criteria for being a relevant statistic . The prescription that only relevant statistics play a role in direct inference corresponds to the sort of projectability constraints envisioned by past theories.

Agents typically revise their beliefs when confronted with evidence that contradicts those beliefs, selecting from a number of possible revisions sufficient to reestablish consistency. In cases where an individual’s beliefs concern spatial relations, belief revision has been fruitfully treated as a decision about which features of an initially constructed spatial mental model to modify. A normative claim about belief revision maintains that agents should prefer minimal belief revisions. Yet recent studies have rebutted the preceding claim, where minimality is understood to consist in modifying the position of the fewest objects, showing instead that reasoners prefer revisions that modify the position of an object x while retaining the position of an object y, when the agent’s new evidence is a relational statement of the form ‘xRy’. We here present cases where the preceding effect is reduced, and show an effect of minimality as measured by the number of initial premises preserved.