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
We are excited to announce a public talk featuring Elie During as part of French philosopher Gaston Bachelard’s 60th death anniversary. On the face of it, The Dialectic of Duration, Gaston Bachelard’s 1936 essay, is a pungent—if often unfair—criticism of the Bergsonian doctrine of time and creative evolution. The constructive side of this Anti-Bergson has received less attention: it implies a genuine poetics of time based on the intuition of the sporadic and oscillatory nature of becoming. Bachelard’s rhythmic theme is consistent with the idea of “surrationalism” introduced that same year as a formal counterpart to the surrealist experiments carried out on the fringes of conscious experience. Inspired by the explosive potential of scientific revolutions already celebrated in Le Nouvel Esprit Scientifique, the surrationalist project can be interpreted as that of a poetics of reason. André Breton believed it would “act simultaneously as a stimulant and restraining influence” (“Crisis of the Object”). Insights from the scientific investigation of time as well as poetic and musical experience will help us see how this double action is in keeping with the eruptive dynamics of imagination and reason, as much as with Bachelard’s ideal of “self-surveillance”.
Elie During is an Associate Professor of Philosophy at the University of Paris Ouest. His research focuses on the philosophical implications of relativity theory. His publications include an introduction to Poincaré’s philosophy of science (La Science et l’Hypothèse, 2001), an essay on the nature of time (The Future does not Exist, 2014), two critical editions of Bergson, a coedited volume on contemporary metaphysics of realism (Choses en soi, 2018, English translation forthcoming from Edinburgh University Press), and most recently a critical edition of Bachelard’s Dialectique de la durée (2021).
Organized by
Julie Beauté, Aix-Marseille Université, ADES (France)
Alexander Campolo, Durham University (UK)
Jeanne Etelain, New York University (USA)
Sam Kellogg, New York University (USA)
Alexander Miller, Ghent University (Belgium)
Pierre Schwarzer, New York University (USA)
Meg Wiessner, New York University (USA)