What is the most appropriate form of structuralism about physics (for example, should structuralists accept that elementary bosons are genuine individuals)?
How can the widely accepted claims made by structural realists about continuity across theory change in science be made more precise?
Are structuralist views in metaphysics, for example, concerning properties and dispositions, justified?
Does a structuralist view of mathematics provide the best account of mathematical practice and the ontology and epistemology of mathematics?
How is structuralism best characterised?
In terms of incompleteness (objects lack certain kinds of properties)?
In terms of dependence (objects depend on each other or their structure for their existence and/or identity)?
In terms of contextual individuation (objects are individuated relationally rather than intrinsically)?
How are these characterizations related?
What are criteria of identity, and what adequacy conditions are appropriate for them? Should we be committed to some form of predicativity requirement and/or some form of identity of indiscernibles?
What is individuation? Do we need a substantive account of how objects are individuated?
How should the various metaphysical notions of dependence be analysed? What role will the notions of individuation and criteria of identity play in this analysis?
What are the relations between notions of entity, object, individual, and substance? What implications would structuralism have for these notions?
Assessment and applications
Which of the defences that have been given of structuralism are effective, and what kinds of structuralism do they support?
What metaphysical differences are there between abstract and concrete structures? Do the former require primitive contextual individuation, whereas in the latter contextual individuation is grounded in qualitative relations?
How does structuralism relate to ontological holism and to the thesis that there is no fundamental level to reality?
Is structuralism about the physical world compatible with Humean supervenience or some successor notion?