Periodic Reporting for period 1 - INFINITY (Infinity in Mathematics: A Philosophical analysis of Critical Views of Infinity)
Período documentado: 2019-07-01 hasta 2021-06-30
The project has proved that critical views of infinity offer a wealth of powerful new philosophical and mathematical ideas that can be applied beyond the scope of the original foundational debate and, in this way, have the potential to reshape the philosophical discussion on infinity in mathematics. The five milestones indicated in the proposal have been fully achieved during the project. The project has successfully clarified the most fundamental aspects of critical views of infinity from a philosophical and from a logical perspectives. By presenting her work at major conferences in logic and in the philosophy of mathematics, by writing research papers on the topics of the grant, by organising two specialist workshops and carrying out outreach activities, the ER has succeeded in stimulating a renewed debate on the infinite in mathematics from a variety of perspectives, bringing together mathematicians and philosophers from various backgrounds.
The benefit of the project’s research for society resides primarily in its having promoted a rich exchange of ideas between philosophers and mathematicians, which can, in principle, pave the way for new mathematical and philosophical ideas. Historically, such exchanges have resulted in new powerful mathematical ideas, as witnessed, for example, by Hilbert’s programme and Brouwer’s intuitionism. New mathematical ideas have, in turn, often given rise to fundamental new applications to the physical sciences and, more recently, to technology, with a clear benefit for society. The case of the infinite is paradigmatic in this respect, as the critical views of infinity that have been the focus of this project have given rise to forms of mathematics that are increasingly important for their applications to computer-aided mathematics and computer programming.
A characteristic of this project has been its innovative methodology, as the ER has made essential use of the history of mathematics for renewing the contemporary debate on the infinite, both within philosophy and mathematics. To this purpose, she has made extensive use of her detailed knowledge of mathematical logic. The project has thus drawn new ties between the historical and the contemporary debate, connecting apparently unrelated ideas. It has also prompted new cooperation between mathematicians and philosophers across the EU and beyond.
The project has greatly enhanced the ER’s interdisciplinary profile by substantially improving her philosophical skills. Under the guidance of the supervisor, Prof. Øystein Linnebo, the ER has refined and expanded her philosophical knowledge and gained crucial new skills towards publishing in philosophy. The project has furthermore highly increased her international visibility, as witnessed by prominent Keynote invitations at major conferences in mathematical logic and philosophy of mathematics. The ER is currently Researcher at IFIKK (Oslo) within a grant awarded by the Research Council of Norway (developed together with Prof. Øystein Linnebo). Consequently, her collaboration with the University of Oslo is ongoing, clearly demonstrating the success of the EU’s mobility strategy.