Cognitive Structuralism: How do we know mathematical structures?

Jan Westerhoff

Abstract

Many contemporary epistemologies of mathematics suggest that we know mathematical structures by abstracting from our knowledge of physically instantiated structures we find in the world. Unfortunately such accounts do not harmonize with most theories which explain how human beings actually acquire mathematical knowledge.

This talk will discuss these difficulties and will then suggest an alternative foundation for mathematical knowledge. The underlying idea is that mathematical knowledge should be explained as derived from basic cognitive capacities all human beings have (such as the ability to iterate, to permute, to form recursive structures). Such abilities are a fundamental part of our linguistic knowledge, but also occur in many other parts of our cognitive lives. I will try to argue that an epistemology based on such cognitive abilities can solve many familiar problems within the philosophy of mathematics.

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