Leibnizian metaphysics underpins the near universally held view that spacetime must be inextendible – that it must be “as large as it can be” in a sense. But here we demonstrate a surprising fact within the context of general relativity: the property of inextendibility turns out to be “unstable” when attention is restricted to certain collections of “physically reasonable” spacetimes.

Shifts are a well-known feature of the literature on spacetime symmetries. Recently, discussions have focused on so-called dynamic shifts, which by analogy with static and kinematic shifts enact arbitrary linear accelerations of all matter (as well as a change in the gravitational potential). But in mathematical formulations of these shifts, the analogy breaks down: while static and kinematic shift act on the matter field, the dynamic shift acts on spacetime structure instead. I formulate a different, `active' version of the dynamic shift which does act on matter.

It is widely accepted by physicists and philosophers of physics alike that there are certain contexts in which general relativity will "break down". In such cases, one expects to need some as-yet undiscovered successor theory. This paper will discuss certain pathologies of general relativity that might be taken to signal that the theory is breaking down, and consider how one might expect a successor theory to do better. The upshot will be an unconventional interpretation of the "Strong Cosmic Censorship Hypothesis".

I explain that a target of Newton's example is the inadequacy of Descartes’s definition of motion. But I also a raise a serious problem for the current reading which comes from the attribution of “absolute and true circular motion” to the water revolving inside the bucket. The solution resides in an examination of Newton’s meticulous experimental setup as a self-contained, realistic description of how the quantity of true motion of a body of water changes I argue that the example should be read as real experiment and that it exemplifies a double methodological aspect.