Formal Epistemology Seminar

Upcoming Talks

Doherty Hall 4303

February 26, 2018, 12–1:20

Adam Marushak

Probability Modals and Infinite Domains

Abstract: Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural

language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving words such as “likely” and “probable”—intuitions that Kratzer (1991; 2012) fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, Holliday & Icard (2013) has been widely thought to undercut this motivation: they present a new method of lifting an ordering on worlds to an ordering on propositions that promises to explain the intuitions just as well. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. I show that Holliday & Icard’s (2013) semantics fails to validate one intuitively valid inference pattern when the domain of epistemic possibilities is infinitely large. In contrast, probabilistic semantics validates the inference nonetheless. I consider several ways of patching Holliday & Icard’s (2013) semantics to validate the desired inference. But I argue that each has considerable costs that have no analogue for probabilistic semantics. As a result, probabilistic semantics remains the better explanation of the data.

Past Talks

February 12, 2018, 12–1:20

Adam Bjorndahl

Topological Subset Space Models for Public Announcements

Abstract: I introduce topological semantics for public announcements in subset spaces. Standard models treat the precondition for a public announcement of φ to be the truth of φ; in the present context, this is strengthened to the knowability of φ, semantically rendered via the interior operator. I argue that this approach improves on previous models and offer several motivating examples to this effect, with emphasis on the crucial role of topological structure in this setting. I also provide a simple sound and complete axiomatization of the resulting logic.

February 14, 2018, 12–1:20

Teddy Seidenfeld

When Large also is Small: conflicts between Measure Theoretic and Topological senses of a negligible set

(joint work with Jessi Cisewski, Joseph B. Kadane, Mark J. Schervish, and Rafael Stern)

Abstract: In this presentation I review some old and some new results about the conflicts between measure-theoretic and topological senses of being a “negligible” (or “small”) set.  These results help to explain why familiar probability strong-laws cannot be reconciled with a topological perspective where P-null sets (where the strong laws fail) also are meager sets.

February 19, 2018, 12–1:20

Dmitri Gallow

Updating for Externalists

Abstract: Externalists believe that it is possible to have the total evidence E without having the evidence that E is your total evidence. Externalism is inconsistent with the conjunction of the principle of conditionalization and the principle of reflection. So externalists must reject at least one of these principles. Adam Elga affords an argument that the externalist should reject reflection. However, Bernhard Salow has recently argued persuasively that this leads to indefensible consequences: the externalist conditionalizer must condone deliberately designing experiments which you can recognize in advance will make you arbitrarily confident of a falsehood. Deliberate self-delusion like this is not rational. So the externalist must reject conditionalization. There are two extant proposals for which update rule externalists should adopt in its stead: one defended by Matthias Hild and Miriam Schoenfield; and one which I have defended for the special case of experiments whose outcomes are theory-dependent. Pace Hild and Schoenfield, the first proposal is inconsistent with externalism. And the second proposal is insufficiently general to rescue the externalist from all cases of deliberate self-delusion. I therefore show how to generalize the second update rule to a wider class of externalist experiments, and show that, so generalized, the update will always satisfy the principle of reflection (and, therefore, will never permit deliberate self-delusion).


Seminar on Formal Epistemology (80-521/80-821)

  1. Syllabus [updated Feb. 22]

Modal Logic (80-315/80-615)

  1. Canvas

  2. Syllabus

Choice, Decisions, and Games (80-305/80-605)

  1. Syllabus

Formal Methods Seminar (80-603)

Game Theory (80-405/80-705)

  1. Syllabus

Philosophy of Logic and Language (80-387/80-687)

  1. Syllabus

Other Resources

Epistemic Logic and Topology (slides)

Proofs Practice (worksheet)