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
The speaker will be Prof. Lewis Gordon of the University of Connecticut, on “From Harlem to the World: Philosophy from a Center of the Black World with Questions for the 21st Century.” Gordon will talk about worldliness and public aspects of philosophy, placing them in the context of Harlem both at City College and the public world of Africana philosophy from Du Bois to Malcolm X to contemporaries such as Nathalie Etoke. He will conclude with a set of questions for 21st century philosophy to consider.
Lewis R. Gordon is Professor and Head of the Department of Philosophy at UCONN-Storrs; Honorary President of the Global Center for Advanced Studies; Honorary Professor in the Unit for the Humanities at Rhodes University, South Africa; and Distinguished Scholar at The Most Honourable PJ Patterson Centre for Africa-Caribbean Advocacy at The University of the West Indies, Mona. He co-edits the journal Philosophy and Global Affairs, the Rowman & Littlefield book series Global Critical Caribbean Thought, and the Routledge-India book series Academics, Politics and Society in the Post-Covid World. He is the author of many books, including, most recently, Freedom, Justice, and Decolonization (Routledge, 2021) and Fear of Black Consciousness (hardcover, NY: Farrar, Straus and Giroux, 2022; in the UK, London: Penguin Books, 2022), Picador paperback 2023. He is the 2022 recipient of the Eminent Scholar Award from the Global Development Studies division of the International Studies Association.