PhD defense by Mikkel Willum Johansen – Niels Bohr Institute - University of Copenhagen

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PhD defense by Mikkel Willum Johansen

Naturalism in the philosophy of mathematics

Time: Wednesday, January 12, 2011 at 10:00 am
Place: Niels Bohr Institute, Blegdamsvej 17, København, auditorium A.

Abstract:

In modern philosophy of mathematics a number of different naturalistic explanations of mathematical knowledge have been given. In my dissertation I present and discuss the strengths and weaknesses of three such approaches. These are 1) evolutionary biology, 2) cognitive science, and 3) sociology of science. Each of these approaches claim that mathematical knowledge can be explained by a particular type of facts about human nature. The type of facts varies with the approach; the evolutionary biology approach states facts from evolutionary theory, the cognitive science approach states cognitive facts etc.

My aim in the dissertation is double. On the one hand, I want to evaluate the different approaches, but on the other I want to give a new and more adequate naturalistic explanation of mathematics. As I see it, mathematics is much too rich to be understood on a single level of explanation. Explanations solely operating within a single theoretical framework, such as cognitive semantics or evolutionary biology are valuable in many ways, but in my view they inevitably lead to an unproductive reductionism. As I see it, mathematics cannot be reduced to a single type of phenomena or facts. For this reason, the main aim of the dissertation is to show how explanation from both the biological, the cognitive and the social level of explanation can be pieced together to form consistent and non-reductive understanding of mathematics.

The thesis can be downloaded from: http://www.nbi.dk/natphil/prs/mwj/Dissertation-mwj2010.pdf

Assessment committee:

Professor Carl Winsløv, Department of Science Education, University of Copenhagen (chairman); Professor Paolo Mancosu, Department of Philosophy, University of California Berkeley; Professor Stig Andur Pedersen, Deparment of Philosophy and Science Studies, Roskilde University.

Co-chairman [ordstyrer]:

Kjeld Bagger Laursen, Department of Mathematical Sciences and Department of Science Education, University of Copenhagen

Supervisors:

Professor Jesper Lützen, Department of Mathematical Sciences, University of Copenhagen, Associate professor Claus Emmeche, Center for the Philosophy of Nature and Science Studies, University of Copenhagen.