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
Comparative philosophy is gaining traction in professional academic philosophy, with specialist journals, organizations, books, and public campaigns. These inroads have been made in canonical areas of philosophy, including epistemology, metaphysics, logic, and value theory. Yet comparative philosophy still plays little role in practical applied ethics, an interdisciplinary research area in which work with practice and policy implications are dominated by the anglophone world. In this article, I explain why comparative work might be especially difficult in this type of applied ethics, and I suggest how comparative philosophers might overcome these challenges to connect their theoretical work with contemporary practical issues.
With responses from Wenqing Zhao (CUNY Baruch)
NOTE ON ENTRY FOR NON-COLUMBIA GUESTS: The door to Philosophy Hall will only open with a Columbia University ID card. If you do not have this card please arrive early where someone will be standing outside until the meeting begins. If you arrive late, you can ask someone walking nearby to let you in or contact Cole at cf2798@columbia.edu. Please only contact Cole as a final resource so as not to interrupt the talk.
RSVP IS REQUIRED FOR DINNER:. Dinner will take place at a nearby restaurant. Please contact Cole at cf2798@columbia.edu for further information. RSVPs are limited.
Comparative Philosophy Seminar:
- January 19 – Alex Watson (Ashoka University)
- February 2 – Davey Tomlinson (Villanova University)
- April 5 – Laura Specker (Fordham University)
- May 3 – Daniel Stephens (University at Buffalo)