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Konstanz, July 28-30, 2008

The background for the first Formal Epistemology Festival on Conditionals and Ranking Functions in Konstanz, Germany, was the 40th anniversary of Robert Stalnaker’s A Theory of Conditionals and the 20th anniversary of Wolfgang Spohn’s Ordinal Conditional Functions. A Dynamic Theory of Epistemic States. Besides the organizers Franz Huber, Eric Swanson, and Jonathan Weisberg, the other speakers were Igor Douven, David Etlin, Anthony Gillies, Alan Hájek, Hannes Leitgeb, Sarah Moss, Hans Rott, Wolfgang Spohn, Robert Stalnaker, Robert Williams, and Timothy Williamson. We exemplarily summarize four of the talks.

Robert Stalnaker opened the festival with his talk Nested Conditionals and Iterated Belief Revision. He drew a comparison between the iteration of modal operators and iterated belief revision. The former was accounted for by Kripke-style accessibility relations. To account for the latter, Stalnaker argued that we have to add structure to the belief model. This can partly be done by using conditionals to represent belief revision policies and thereby making belief dynamics explicit. We also have to understand the input as including meta-information. Stalnaker gave examples that showed that sometimes new information does not yield a change of our beliefs in atomic propositions, but a change of our belief revision behavior and thereby a change of our beliefs about conditionals.

Wolfgang Spohn’s talk Objectivizing Ranking Functions explained the extent to which ranking functions that describe subjective doxastic states, i.e. subjective grades of disbelief, can be objectively true or false. The basic idea is to uniquely associate propositions that can be true or false with how a given feature is realized in a ranking function and then to uniquely reconstruct the functions from these associated propositions. This works sometimes, and sometimes it does not. The most exciting positive example is direct causation that can be an objective notion even though its basic explication is a subjective one via ranking functions.

In his talk Conditionals and Actuality, Timothy Williamson explored the possibilities for adding a connective for indicative conditionals to a formal language containing an actuality operator. For this, he set up a number of plausible assumptions including an axiom for the actuality operator for an otherwise unspecified propositional language. He then showed that if reflexivity and distribution hold for the indicative conditional, a number of unintuitive consequences arise, since the indicative conditional must then behave like the material conditional in a wide range of cases.

Alan Hájek's talk Arrows and Haloes: Probabilities of Conditionals and Desire as Belief focused on the similarities between the debates about the thesis that probabilities of conditionals are conditional probabilities, and about the thesis that the extent to which we desire a proposition to be the case is equal to our degree of belief in the goodness of this proposition. Central to both debates are the triviality results of Lewis. But these results can be avoided in both cases by adopting indexical interpretations of the conditional and the goodness operator, respectively. Hájek discussed further objections and stressed the importance of an exchange between the debates.

The festival was the first of a series of small and thematically focused events in formal epistemology. The festivities of 2009 in Ann Arbor will feature Causal Decision Theory and Scoring Rules; the festivities of 2010 in Toronto will focus on Defeater/Default Logic and Perception.