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
Thursday, September 29th, 2022
Christina Van Dyke (Barnard College)
Title “I feel it in my fingers, I feel it in my toes: Imaginative Meditation and Experience of Love in Medieval Contemplative Philosophy”
4:10-6:00 PM
716 Philosophy Hall
The COVID-19 pandemic is said to be a once-in-a-century incident, and it brought to us a sense of crisis at various levels. What is a crisis, though? Can any unnerving moment or period be called a crisis, or are there different dimensions of a crisis to which we need to be attentive? Is solidarity possible after experiencing a crisis like Covid-19? Can Buddhism make any contribution to facilitating solidarity? This presentation explores the meaning and nature of a crisis and our responses to it by drawing on modern Korean political thinker Pak Ch’iu’s (1909–1949) analysis of crisis and feminist-Buddhist thinker Kim Iryŏp’s (1896–1971) Buddhist philosophy. By doing so, this presentation considers what social, political, existential, and even religious meaning we can draw from our experience of crises, and what questions these insights present to us.
With responses from Karsten Struhl (John Jay College of Criminal Justice, CUNY)
Presented by THE COLUMBIA SOCIETY FOR COMPARATIVE PHILOSOPHY
RSVP is required for dinner. If you would like to participate in our dinner, a $30 fee is required. Please contact Lucilla at lm3335@columbia.edu for further information.
When someone is in a conscious state, must they be aware of that state? The Buddhist philosopher Dignāga offers a brilliant route to answering this question by leveraging the role awareness might play as a constraint on memory. I begin by clarifying his strategy and what conclusions it might be used to establish. Here I examine different candidate directions of explanation between consciousness and inner awareness. I interpret the metaphor of consciousness as a lamp that lights itself, and use the metaphor to distinguish between his view and contemporary higher-order theories of consciousness. I then turn to explain why the memory argument fails. The first main problem is that, contrary to Dignāga’s contemporary defenders, there is no good way to use the argument to reach a conclusion about all conscious states. The second main problem is that the proposed awareness constraint on memory is highly problematic, in tension both with ancient objections as well as current psychology.
With responses from Lu Teng (NYU Shanghai)