Proof Theory: Logical and Philosophical Aspects

This is an intensive class on logical bilateralism, taught by Sara Ayhan and me at esslli 2026. Logical bilateralism is an approach to meaning and consequence that foregrounds a symmetry between certain notions, like assertion and denial, proof and refutation or truth and falsity. Bilateralist approaches to such dual distinctions take both sides as primitive rather than—as in conventional ‘unilateralist’ approaches—taking one notion to be fundamental and defining the other in its terms. In recent years different bilateralist logical systems have been developed, displaying a wide variety in their specific orientation. What is missing so far is a systematic framework putting these very different approaches on a map and thereby highlighting similarities, distinctions and connections between them. Though giving a complete picture will also not be possible within the scope of the intended course, our aim is to familiarize the attendants with many different forms of logical bilateralism and…