"Relationism and the Rigid Body: Counting Possibilities in Mechanics"
I will argue for the philosophical
significance of two related topics within classical mechanics. Both topics
have a long history, but are so deep as to still be active research areas,
even for systems described by just a handful of real numbers. The first topic
is the relations between continuous symmetries and conserved quantities,
which go under the title of Noether's ``first theorem''. This theorem unifies
the ways in which mechanical problems can be simplified by appealing to a
symmetry of the system considered. The second topic is the modern theory
of symplectic reduction, which builds on the ideas in Noether's theorem.
It has countless scientific applications, for example to understanding the
rigid body. But I will stress how it helps one to formulate precisely the
positions in the debate between substantival and relational views of space.
This help consists principally in making precise haecceitist and non-haecceitist
ways of counting possibilities.