Philosophy of mathematics

The aim of this project is to develop a philosophy of mathematics. This will be done through closely interrelated studies addressing four fundamental issues. The first issue concerns the ontological aspect of mathematics. What kind of entities is mathematics dealing with? Answers to this question are illustrated through a historical sketch of contributions to the philosophy of mathematics. The second issue is of epistemological nature: How sure in mathematics? To what extent does a mathematical proof guarantee the truth of the mathematical statement it is assumed to prove? The third issue concerns the social nature of mathematics. How social is mathematics? This question addresses to what extent mathematics can be considered a social construction, reflecting linguistic norms and social rules. Fourth we consider what might be done through mathematics, and we address the question: How good is mathematics? This question brings us to consider to what extent social structures, technological constructs, management and decision making might be considered mathematics-based fabrication. And we consider if such fabrication acquires some particular quality by being mathematics-based.