A. Questions for Discussion
9.1 Substantivalism vs Relationism
Leibniz writes:
"if space was an absolute being, there would something happen for which it would be impossible there should be a sufficient reason. ... 'tis impossible there should be a reason, why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner, and not otherwise; why every thing was not placed the quite contrary way, for instance, by changing East into West."
- Imagine that the entire universe were viewed through a mirror, flipping East and West. Would it be possible to tell the difference between this and the actual world?
- What about if the entire universe were shifted in a rigid way by two meters in some direction?
- Leibniz takes this to be a reductio ad absurdum of the statement that "space is an absolute being". Which metaphysical principle does he need to assume for this to be true? Is it a reasonable assumption?
- What other reasons are there to accept or reject substantivalism? What reasons are there to accept or reject relationism?
9.2 The Hole Argument
- What is a manifold of spacetime events? How is it different than a manifold with a metric and matter?
- "Leibniz Equivalence" is the statement that, If two distributions of fields are related by a smooth transformation, then they represent the same physical systems. How is this related to Leibniz's "shift" argument above?
- Describe the hole argument. What are the two problems that this creates for substantivalism about the manifold of spacetime events?
B. Further Discussion (Optional)
- Is being a substantivalist about the manifold of events the only way to be a substanvialist in general relativity? What alternatives (if any) can you imagine?
- Can the hole argument be applied in any other contexts besides general relativity? What happens when you apply it to the case of the map projection?
- What is the status of substantivalism according to general relativity, in your view?