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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.

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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

The rich philosophical and mathematical disputes that took place between Isaac Newton and Gottfried Leibniz at the start of the eighteenth century have received more historical attention than any other exchange in the history of philosophy. Nevertheless, in this talk, Robert Iliffe discusses a prominent but neglected aspect of their disagreement, namely the mutual claim that their opponents’ conceptual foundations were fictional, and were the product both of diseased thinking and of illegitimately organized intellectual structures. Newton assailed Leibniz’s allegedly debased metaphysics in various prominent places, and mobilized allies such as Roger Cotes and John Keill to do the same. Nevertheless, by far the most sophisticated critique of illicit philosophical assumptions was launched against Newton by Leibniz in his correspondence with Samuel Clarke. In the Fifth letter to Clarke, Leibniz identified core Newtonian positions as infantile, vulgar, and profoundly irreligious, asserting that they were dangerous fictions that were less plausible and much less edifying than the rational romances of writers in the previous century. Although Leibniz saved his most potent intellectual weapons for his final letter to Clarke, Robert Iliffe suggests that his attack on the fictional status of Newton’s work was no mere codicil to his general critique of Newton’s philosophy, but instead lay at the heart of it. This famous debate, while of course somewhat sui generis, is indicative of more general and dynamic features of intellectual debate.

Event Speaker

Robert Iliffe, Professor of the History of Science at the University of Oxford

Event Information

This event is free and open to the public; Registration required. Please contact scienceandsociety@columbia.edu with any questions.

This event is part of the New York History of Science Lecture Series.

With responses from Mark Siderits (Illinois State University)

ABSTRACT: Buddhist philosophers often draw a distinction between two different kinds of truth: conventional truth (saṃvṭi-satya) and ultimate truth (paramārtha-satya). Abhidharma Buddhists philosophers typically understand this distinction in terms of an ontological distinction between two different kinds of entities: ultimately real entities (paramārtha-sat) and conventionally real entities (saṃvṛti-sat). Similar to contemporary philosophical discussions about ordinary objects, Buddhist philosophers debate the ontological status of conventional entities and the semantics of discourse concerning them. Mark Siderits (2015, 2021, 2022) has influentially argued for an eliminitivist position he calls “Buddhist reductionism” that interprets the Abhidharma position as one that denies conventional entities exist but that retains discourse involving apparent reference to them. However, in a recent article Kris McDaniel (2019), a prominent defender of ontological pluralism, challenges that view by proposing that the Abhidharma Buddhist distinction between conventional truth and ultimate truth be “defined up” from a more basic distinction between two different ways an entity can exist: conventionally or ultimately. In this paper I argue that Saṃghabhadra’s account of conventional reality and truth does lends itself well to McDaniel’s proposal but I will also argue that the account of conventional and ultimate truth that results differs in important ways from the models he offers. I will end by offering a modification of McDaniel’s account of conventional truth that is derived from Saṃghabhadra’s pluralist ontology. That view will, unlike the views suggested by both Siderits and McDaniel, allow for there to be ultimate truths about what is conventionally true.

Dinner will be kindly offered by the Columbia University Seminars. 

RSVP is required for dinner. Please email Lucilla with eating requirements at lm3335@columbia.edu. 

In Sanskrit epistemology, philosophers are preoccupied with the notion of pramā. A pramā, roughly, is a mental event of learning or knowledge-acquisition. Call any such mental event a knowledge-event. In A Confection of Refutation (Khaṇḍanakhaṇḍakhādya), the 12th century philosopher and poet Śrīharṣa argued that knowledge-events are indefinable. Any satisfactory (and therefore non-circular) definition of knowledge-events will have to include an anti-luck condition that doesn’t appeal back to the notion of learning or knowledge-acquisition itself. But there is no such anti-luck condition. What is novel about Śrīharṣa’s argument is that it is motivated by his commitment to a certain “knowledge first” approach to epistemology: the view that knowledge-events are epistemically prior to other non-factive mental states and events. On this view, when we are trying to determine whether an agent has undergone a knowledge-event, we don’t initially ascribe to them some other non-factive mental event, and then check if that event meets some further conditions (like truth or reliability) necessary for it to count as a knowledge-event; rather, we treat certain mental events by default as knowledge-events until a defeater comes along.  Surprisingly, Śrīharṣa argues that this kind of “knowledge first” epistemology should give us reason to doubt whether our ordinary attributions of knowledge-events are reliably tracking any sui generis psychological kind. In this talk, I reconstruct Śrīharṣa’s position.

With responses from Rosanna Picascia (Swarthmore College)

RSVP is required for dinner. Dinner will take place at a nearby restaurant. Please contact Lucilla at lm3335@columbia.edu for further information.

Verity Harte is a specialist in ancient philosophy, with particular research interests in ancient metaphysics, epistemology and psychology, especially of Plato and Aristotle. She is the author of Plato on Parts and Wholes: The Metaphysics of Structure, and is the editor of several important books on ancient philosophy.