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
A conference hosted by the Motherhood and Technology Working Group at the Center for the Study of Social Difference on the theme of “Conception and Its Discontents.”
Medical technologies have radically transformed the biological and social experience of motherhood. Advances in genomic and reproductive care, the circulation of novel kinship structures, the entrenchment of existing global networks of power and privilege, and the politics of contested bodily sites mark this emerging constellation.
Technological advancements have in particular impacted not just the understanding of conception, but the very process by which a human embryo is created, implanted, and matured. Egg freezing, embryo storage, IVF, and surrogacy afford women new freedoms in choosing when and how to become mothers, while also raising troubling questions about the pressures of capitalism and the extension of worklife, as well as the global inequalities present in the experience of motherhood. In addition, technologies have arisen allowing for unprecedented control over not just who becomes a mother, but what kind of embryo is allowed to be implanted and to grow. Technologies such as CRISPR and NIPT have re-introduced the question of eugenics, radically shifting the very epistemology of motherhood and what it means to be “expecting.” And contemporary abortion debates draw on technology in order to make arguments both for and against access, with imaging technologies being instrumentalized in the building of a sympathetic case for the unborn, and the very notion of a “heartbeat bill” reliant on the misreading of technologies for measuring fetal activity.
While these problems are urgent today, questions of conception and technology are by no means recent developments. The 18th century saw a flourishing of philosophical and scientific theories regarding the start of human life and its formation within the womb. Such theories relied on modern technologies, such as autopsy, to atomize and visualize the body. In the 19th and 20th centuries, eugenic medical science produced theories of reproductive difference between differing racial and social groups, leading to forced sterilization laws in both the US and in Germany. This long history of racializing the rhetoric of fertility and motherhood continues to influence political debates on immigration and demographic changes in the present.
Full conference details and schedule to come.
Please email disability@columbia.edu to request disability accommodations. Advance notice is necessary to arrange for some accessibility needs