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Two proof-systems P and P* are said to be complementary when one proves exactly the non-theorems of the other. Complementary systems come as a particular kind of refutation calculi whose patterns of inference always work by inferring unprovable conclusions form unprovable premises. In the first part of my talk, I will focus on LK*, the sequent system complementing Gentzen’s system LK for classical logic. I will show, then, how to enrich LK* with two admissible (unary) cut rules, which allow for a simple and efficient cut-elimination algorithm. In particular, two facts will be highlighted: 1) for any given provable sequent, complementary cut-elimination always returns one of its simplest proofs, and 2) provable LK* sequents turn out to be “deductively polarized” by the empty sequent. In the second part, I will observe how an alternative complementary sequent system can be obtained by slightly modifying the Gentzen-Schütte system G3. I will finally show how this move could pave the way for a novel approach to multi-valuedness and proof-theoretic semantics for classical logic.

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

Critique is an assertion of values pitted against a state of affairs. To say that things should not be the way they are–to respond to questions such as ‘Why do I think this political or economic arrangement is wrong (and why should I care?)?’ implies an ethical stance. Critique thus draws together fact and value, domains that a long tradition of moral thought has argued exist on distinct planes. For there are dimensions of political life that are incomprehensible without this conjunction between ethical motivations and social realities. But if they are to have political consequences, such questions cannot be confined to private introspection. Scale matters. This talk looks at the articulation between everyday interactions and social movements to show the interplay among the first, second, and third person stances that characterize ethical life. Drawing ethnographic examples from American feminism and Vietnamese Marxism, it considers some of the ways in which ethical intuitions emerge, consolidate, and change, and argues that objectifications and the reflexivity they facilitate help give ethical life a social history.

This essay tries to develop a “black radical Kantianism” – that is, a Kantianism informed by the black experience in modernity. After looking briefly at socialist and feminist appropriations of Kant, I argue that an analogous black radical appropriation should draw on the distinctive social ontology and view of the state associated with the black radical tradition. In ethics, this would mean working with a (color-conscious rather than colorblind) social ontology of white persons and black sub-persons and then asking what respect for oneself and others would require under those circumstances. In political philosophy, it would mean framing the state as a Rassenstaat (a racial state) and then asking what measures of corrective justice would be necessary to bring about the ideal Rechtsstaat.

Response by César Cabezas Gamarra.

Presented by the German Idealism Workshop

In 1804 Schelling diagnosed our impending “annihilation of nature” due to our conceptual detachment from and consequent economic exploitation of our natural world. His critique of Modernity’s Cartesian Idealisms, effected through his inversion of the Kantian categories, results in a philosophical project whose relevance to our ongoing climate crisis is difficult to overstate.

Bruce Matthews
Bard College/BHSEC, professor of philosophy, research in German Idealism and Romanticism, with a focus on life and thought of F.W.J. Schelling, whose recent work revolves around Schelling’s critique of modernity with its anticipation of, as he wrote in 1804, ‘the annihilation of nature,’ and its relevance to the Anthropocene.

“Schelling in the Anthropocene: A New Mythology of Nature,” (Symposium: Canadian Journal of Continental Philosophy, 2015), “Schelling: A Brief Biographical Sketch of the Odysseus of German Idealism,” in The Palgrave Handbook to German Idealism (2014), and “The New Mythology: Between Romanticism and Humanism,” in The Relevance of Romanticism (Cambridge University Press, 2014). Books include the forthcoming intellectual biography, Schelling: Heretic of Modernity (2018), Schelling’s Organic Form of Philosophy: Life as the Schema of Freedom (SUNY 2011).

Presented by the Philosophy Department at The New School for Social Research

There is a broad consensus that Aristotle introduced the concept of matter in order to develop a consistent account of substantial change. However, it is disputed which role matter fulfills in substantial change. According to the traditional interpretation, matter persists while taking on or losing a substantial form. According to a rival interpretation, matter does not persist in substantial change; instead, it is an entity from which a new substance can emerge and which ceases to exist in this process. In my view, both interpretations are problematic in the light of Aristotle’s broader ontological project and are at odds with the way Aristotle describes the substantial generation of living beings. On the basis of Aristotle’s biological theory, I will suggest that Aristotelian matter is a continuant in substantial generation, but does not satisfy the common criteria for persistence that apply to individual substances.

Anna Schriefl
Anna Schriefl is Wissenschaftliche Mitarbeiterin (assistant professor) at the University of Bonn, and currently a visiting scholar at the New School. She has published a book about Plato’s criticism of money and wealth, and most recently an introduction into Stoicism (both in German).