Paradoxes, Local Consequence and the Role and Future of Deductive LogicPeter, PeterSchroeder Heister

Paradoxes, Local Consequence and the Role and Future of Deductive Logic Abstract Starting from classical antinomies such as the liar paradox, I discuss several notions that have been central to logic since antiquity, in particular those of inference and consequence. Based on a prooftheoretic approach to these notions, I argue that single (‘local’) inference steps need to be justified individually, rather than devising a global concept (such as truth) first and defining consequence as the transmission of truth or provability. These considerations are embedded in some general remarks on which role logic may play in the foreseeable future. About Peter schroeder-Heister After studying philosophy, mathematics, musicology and theology at the universities of Bonn, Cologne and Aachen, Peter Schroeder-Heister received a Dr. phil. in Logic and Foundational Research from Universität Bonn in 1981 and a Habilitation in Philosophy from Universität Konstanz in 1988. He became Professor of Logic and Philosophy of Language at Universität Tübingen in 1989. Since 1991, he has held joint appointments at the Faculties of Philosophy and Computer Science. He spent his entire professorial career in Tübingen, declining offers from elsewhere in Germany and abroad. Visiting fellowships have led him to universities in Sweden, Serbia, the UK, China and France, and he was awarded an honorary doctorate from the University of Belgrade in 2015. Within his profession he has held the positions of programme chair, secretary general and treasurer of the Division of Logic, Methodology and Philosophy of Science and Technology. Schroeder-Heister’s main research topic is what he has called “proof-theoretic semantics”, which is based on the idea that the key notions of philosophical semantics should be those of argument and proof, rather than of denotation and truth. He has published a great number of scientific papers on this subject, both from a philosophical and from a computational perspective. Together with his Tübingen group, he has organised a number of influential conferences in the field and edited many collections on the topic. Further academic interests that have led to published work concern logic in computer science, the history of modern logic, and cognitive science, including issues of cognitive psychology. Schroeder-Heister will use his time at the Collegium to continue and intensify his work on a joint monograph on General Proof Theory with Professor Dag Prawitz (Stockholm University).