Workshop: The Limits of Incompleteness

The issue of incompleteness is paramount in logic. Since the discovery of Gödel’s (and Turing’s) limitative results for formal theories and computation, logicians, mathematicians and philosophers have addressed the issue, by, among other things, trying to reduce the impact and extent of incompleteness. For instance, in set theory, the discovery of the independence phenomenon has resulted in the search for new axioms potentially able to settle old (and new) problems, whilst logicians have progressively been able to draw more sharply the boundaries between the provable and the unprovable, complete and incomplete theories. The ‘incompleteness phenomenon’, however, is broader, as it touches on crucial issues such as, among others, the nature and limitations of the human mind, how machines learn and think, the status of mathematical objects, the limits of what we can observe and model physically. The purpose of this seminar is to address the limits of incompleteness as they arise in different research areas and themes, spanning logic, computation, philosophy and physics, by blending historical and more recent perspectives, in order to understand, in particular, how different disciplines react to the incompleteness phenomenon and attempt to overcome it with innovative and groundbreaking research programmes. The seminar will bring together both Romanian and international scholars who do top-class research in their respective areas. The seminar is part of the dissemination activities envisaged by Dr Claudio Ternullo’s MSCA-SOE-funded project: “Self-Similarity, Large Cardinals and Incompleteness” (PNRR-III-I9- Grant nr. 760146/31-10-2023).