(In)determinacy in Mathematics

The topic of this conference is a cluster of related and hotly debated issues in the philosophy of mathematics involving determinacy and pluralism. Questions of determinacy and indeterminacy concern, roughly, how sharp or precise our mathematical words and concepts are, and whether there is an objective ‘fact of the matter' corresponding to every mathematical claim. Questions of pluralism concern the issue of whether there are multiple, equally good, legitimate theories of certain mathematical subject-matters, such as arithmetic, geometry, or set theory.

This conference will bring together researchers in these fields to present their recent work and discuss new options for development. Possible questions for discussion include:

• How should we understand determinacy and indeterminacy in mathematics? Is determinacy fundamentally best understood as linguistic, or conceptual, or metaphysical? How (if at all) is it best formalized?

• Are there different kinds of (in)determinacy in mathematics? What are the relations between different putative kinds of (in)determinacy in mathematics, e.g. indeterminacy of reference vs indeterminacy of truth value?

• Do different mathematical subfields (e.g. geometry, arithmetic, set theory) exhibit different kinds of (in)determinacy?

• How should pluralism about some mathematical domain be best understood?

• Is pluralism the right response to indeterminacy?

• What is the bearing of second-order or higher-order logic on all these debates?