October 04, 2023, 6-8 PM (note special time) in 234 Philosophy

Stephan Hartmann (LMU Munich)

Bayesian Coherentism

Coherence considerations guide our reasoning in science and in daily life. But what is coherence anyway? And why is it a useful concept? While mainstream epistemology struggled to answer these questions, formal epistemologists made some progress beginning in the mid-1990s. For various reasons, this debate more or less came to a halt after about ten years. In this talk, I survey earlier attempts and propose a fresh look at the issue. In doing so, I have three goals: (1) To provide an explication of the concept of coherence. (2) To derive and defend a new measure of coherence. (3) To explore the question under what conditions, if any, coherence is truth-conducive. For this purpose, the Bayesian framework proves to be particularly useful. I conclude with a new assessment of the role of coherence considerations in scientific and ordinary reasoning, and a defense of a position I call Bayesian Coherentism. The talk is based on joint work with Borut Trpin (MCMP).

February 07, 2024, 6-8 PM (note special time) in 234 Philosophy

Matt Mandelkern (NYU)

The Logic of Sequences

In the course of proving a tenability result about the probabilities of conditionals, van Fraassen (1976) introduced a semantics for conditionals based on sequences of worlds, representing a particularly simple special case of ordering semantics for conditionals. According to sequence semantics, ‘If p, then q’ is true at a sequence just in case q is true at the longest truncation of the sequence where p is true (if there is one). This approach has become increasingly popular in recent years. However, its logic has never been explored. We axiomatize the logic of sequence semantics, showing that it strengthens the Stalnakerian logic C2 in two ways: one which is prima facie attractive, and one which is surprisingly complex and difficult to assess. (Joint work with Cian Dorr.)

April 25, 2024, 2-4 PM (note special time) in 234 Philosophy

Sergei Artemov (CUNY Graduate Center)

Two Models of Provability

Gödel’s modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models. The first one is the modal logic GL, also known as the Provability Logic, which was shown in 1979 by Solovay to be the logic of the formal provability predicate. The second one is Gödel’s original modal logic of provability S4, together with its explicit counterpart, the Logic of Proofs LP, which was shown in 1995 by Artemov to provide an exact provability semantics for S4. These two models complement each other and cover a wide range of applications, from traditional proof theory to λ-calculi and formal epistemology.

Recommended reading: Artemov, S. (2007). On two models of provability. In Mathematical Problems from Applied Logic II: Logics for the XXIst Century (pp. 1-52). New York, NY: Springer New York. Download PDF