Joel David Hamkins: Lectures on the Philosophy of Mathematics

Lectures by Joel Kamnitzer

One can define an action of sl2 on a category to be a sequence of categories with functors between them satisfying certain relations. Such actions were studied by Chuang-Rouquier in the context of representations of the symmetric group in positive characteristic. They used this action to build an equivalence of categories which settled a case of Broue’s conjecture. Later, Cautis, Licata, and th...

Lectures on the Foundations of Mathematics

THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world— explicating such facts presents philosophy with some of its subtlest problems. Let me begin by reminding you of some c...

Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education

Philosophy of Mathematics for the Masses – Extending the Scope of the Philosophy of Mathematics Philosophy of Mathematics for the Masses

reality, so that should count against classifying their position as platonist. They are certainly not constructivists, yet some versions of formalism (term formalists) do consider mathematics to be about symbols, and so are not obviously nominalist either (there is quantification over abstract objects, and if these symbols are to count as being mathematical, that would preclude viewing the posi...

The Philosophy of Mathematics

THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world—explicating such facts presents philosophy with some of its subtlest problems. We shall discuss some of the attempts ma...