The seminar is held in hybrid format, in person (Múzeum krt. 4/i Room 224) and online.


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.

18 November (Friday) 4:15 PM  Room 224 + ONLINE
Sebastian Horvat* and Iulian Toader**
*Faculty of Physics, University of Vienna
**Institute Vienna Circle, Vienna
On Williamson on quantum logic and classical mathematics
Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the adoption, in non-mathematical domains, of a wide range of non-classical logics, including quantum logics (QL). In this talk, we first reconstruct the argument and present its restriction to the case of QL. Then we show that there is no inconsistency whatsoever between applying classical mathematics to quantum phenomena and adopting QL in reasoning about them. Furthermore, after identifying the premise in Williamson's argument that turns out to be false when restricted to QL, we argue that the same premise fails for a wider variety of non-classical logics. Finally, we explain how all this relates to the problem of mathematical representation.