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Propositional dynamic logic (PDL) is a framework for reasoning about nondeterministic program executions (or, more generally, nondeterministic actions). In this setting, nondeterminism is taken as a primitive: a program is nondeterministic iff it has multiple possible outcomes. But what is the sense of “possibility” at play here? This talk explores an epistemic interpretation: working in an enriched logical setting, we represent nondeterminism as a relationship between a program and an agent deriving from the agent’s (in)ability to adequately measure the dynamics of the program execution. More precisely, using topology to capture the observational powers of an agent, we define the nondeterministic outcomes of a given program execution to be those outcomes that the agent is unable to rule out in advance. In this framework, determinism coincides exactly with continuity: that is, determinism is continuity in the observation topology. This allows us to embed PDL into (dynamic) topological (subset space) logic, laying the groundwork for a deeper investigation into the epistemology (and topology) of nondeterminism.

The seminar is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning, decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy (logic and epistemology), statistics, economics, and computer science. The seminar is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the seminar and distinguished guest speakers.

details tba

02/08/2019 Faculty House, Columbia University
4:00 PM

03/29/2019 Faculty House, Columbia University
4:00 PM

04/19/2018 Faculty House, Columbia University
4:00 PM

Convergence to the truth is viewed with some ambivalence in philosophy of science. On the one hand, methods of inquiry that lead to the truth in the limit are prized as marks of scientific rationality. But an agent who, by using some method, expects to always converge to the truth seems to fail a minimum standard of epistemic modesty. This point was recently brought home by Gordon Belot in his critique of Bayesian epistemology. In this paper I will study convergence to the truth theorems within the framework of Edward Nelson’s radically elementary probability theory. This theory provides an enriched conceptual framework for investigating convergence and gives rise to an appropriately modest from of Bayesianism.

The seminar is concerned with applying formal methods to fundamental issues, with an emphasis on probabilistic reasoning, decision theory and games. In this context “logic” is broadly interpreted as covering applications that involve formal representations. The topics of interest have been researched within a very broad spectrum of different disciplines, including philosophy (logic and epistemology), statistics, economics, and computer science. The seminar is intended to bring together scholars from different fields of research so as to illuminate problems of common interest from different perspectives. Throughout each academic year, meetings are regularly presented by the members of the seminar and distinguished guest speakers.

details tba

02/08/2019 Faculty House, Columbia University
4:00 PM

03/22/2019 Faculty House, Columbia University
4:00 PM

04/19/2018 Faculty House, Columbia University
4:00 PM

Jacob Soll, in conversation with Pierre Force, John Shovlin, Carl Wennerlind, and Emmanuelle Saada

After two government bailouts of the U.S. economy in less than twenty years, free market ideology is due for serious reappraisal. In Free Market: the History of an Idea, Jacob Soll details how we got to this current crisis, and how we can find our way out by looking to earlier iterations of free market thought. Contrary to popular narratives, early market theorists believed that states had an important role in building and maintaining free markets. But in the eighteenth century, thinkers insisted on free markets without state intervention, leading to a tradition of ideological brittleness. That tradition only calcified in the centuries that followed. Tracing the intellectual evolution of the free market from Cicero to Milton Friedman, Soll argues that we need to go back to the origins of free market ideology in order to truly understand it—and to develop new economic concepts to face today’s challenges.

Jacob Soll is professor of history and accounting at the University of Southern California. He has been awarded numerous prestigious prizes including two NEH Fellowships, the Jacques Barzun Prize, a Guggenheim Fellowship, and, in 2011, the MacArthur Fellowship. He also advises political and financial leaders across the globe to promote accounting standards and financial transparency.

Joining Jacob Soll to discuss his book will be: Pierre Force, Professor of French and History at Columbia; John Shovlin, Professor of History at NYU; and Carl Wennerlind, Professor of History at Barnard College. Emmanuelle Saada, Professor of History and French at Columbia, will moderate the discussion.

This event is co-sponsored by the Maison Française and the Department of History.