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In Toward a Directionalist Theory of Space: On Going Nowhere, H. Scott Hestevold formulates a new relationalist theory of space by appealing to the view that the universe is directioned and that there thereby exist spatial relations that Leibniz overlooked-directional relations such that specific directional relations would obtain between any two objects. This directionalist/relationalist theory would allow the reduction of space-implying claims to claims about objects and the directional relations they exhibit, and it would also preserve absolutist intuitions that motivate standard arguments for substantivalist space:intuitions involving, for example, absolute motion and the possibility that all objects are moving uniformly.

Extending the directionalist/relationalist theory of space to the Special Composition Question, Hestevold addresses the problem of when discrete objects compose a whole. He also uses the directionalist/relationalist theory to formulate reductivist theories of boundaries and holes-theories that may allow one to resist the view that boundaries and holes are ontologically parasitic entities. Finally, he explores directionalism/relationalism vis-a-vis spacetime, addressing questions such as whether the findings of modern physics provide adequate evidence that substantivalist spacetime exists; what problems underlie the dispute between spacetime substantivalists and relationalists; and in light of evidence for substantivalist spacetime, what ontological benefit follows from an endorsement of spacetime directional relations?