Topics in Philosophy of Mathematics - B

Abstraction and abstract objects. The language of mathematics abounds with apparent reference to abstract objects. Are there really such objects? If so, what are these objects, and how are they related to operations of abstraction? The course considers some of the most important recent approaches to mathematical objects: numbers as magnitudes, nominalism, Fregean and neo-Fregean abstraction, as well as structuralism and structural abstraction. Some central topics include: Do we need abstract objects over and above equivalence relations that are congruent with respect to various properties? What is the relation between abstract objects and abstract properties? What is the status of uninstantiated properties or abstract objects? What is the relation between (neo-)Fregean and structuralist abstraction?

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