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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.

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).

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.