The seminar is held in hybrid format, in person (Múzeum krt. 4/i Room 224) and online. To join online click the following Zoom link: https://us02web.zoom.us/j/889933315?pwd=Q3U3V3VQdXpXckhJYWRrcWRiMUhhQT09 ________________________________________________________

4 November (Friday) 4:15 PM  Room 224 + ONLINE

Jan Faye

Department of Communication, Section for Philosophy University of Copenhagen

The implication of natural selection on scientific knowledge

Today naturalism in the philosophy of science is associated with the position that our best scientific theories should inform philosophy. Most people believe that naturalism indicates that philosophy should abandon a priori arguments and use the same methods and considerations as the natural sciences use. However, very few philosophers have realized that if one really wants to be more than a naturalist by name one should also take into consideration what evolutionary biology and cognitive science may have to offer with respect to human epistemology and its possible limits. It is among the most respected facts within the natural sciences that human beings have evolved by natural election from common ancestors whom we share with monkeys and the great apes. This means that our cognitive capacity is not much different from that of the great apes. Our cognitive capacity is adapted to processing sensory information from the environment in which hominins lived for millions of years after our lineage to Homo sapiens and that to the chimpanzees separated. The main difference between us and them is the evolution of spoken and written language in humans, which allows us to develop science and technology. However, human language evolved to express our sensory and behavioral experiences but it also allows us to formulate new ideas and to develop abstract thinking. As I see it, the man problem in epistemology and philosophy of science is that human beings too often reify their abstract thoughts by believing that such thoughts express knowledge about abstract objects. In my presentation, I will discuss these issues and explain how an evolutionary naturalist, like myself, views the realist-antirealist debate in philosophy of science.

11 November (Friday) 4:15 PM  Room 224 + ONLINE

Miklós Hoffmann

Institute of Mathematics and Computer Science Eszterházy Károly University, Eger Department of Computer Graphics and Image Processing University of Debrecen

Who proves a mathematical proof?

In this talk we study the impact of the rapid development of automatic theorem proving and artificial intelligence based mathematical discovery on mathematics and, in general, on human invention and science as a profession. The title of this talk intentionally refers to an early paper of Imre Lakatos, entitled „What does a mathematical proof prove?”. We examine his concept of mathematical proof, and we explore the question of what long-term effects this concept have had and still have on the ever-changing role and notion of mathematical proof. We also consider the position of Max Weber, who sees the essence of scientific activity and being a scientist, on the one hand, in specialization and, on the other hand, in passion. The view of mathematical discovery as a never-ending dialectical, performative process is of central importance in understanding what kind of proof we consider forward-looking and useful from the point of view of mathematics.