 If any of this analysis of motion is taken literally then one arrives at a position regarding the ontology of spacetime rather like that of Newton’s regarding space: it is some kind of ‘substantial’ (or maybe pseudo-substantial) thing with the geometry of Galilean spacetime, just as absolute space possessed Euclidean geometry. This view regarding the ontology of spacetime is usually called ‘substantivalism’ (Sklar, 1974). The Galilean substantivalist usually sees themselves as adopting a more sophisticated geometry than Newton but sharing his substantivalism (though there is plenty of room for debate on Newton’s exact ontological views; see DiSalle, 2002, and Slowik 2016). The advantage of the more sophisticated geometry is that although it allows the absolute sense of acceleration apparently required by Newtonian mechanics to be defined, it does not allow one to define a similar absolute speed or velocity – x accelerates can be defined as a 1-place predicate in terms of the geometry of Galilean spacetime, but not x moves in general – and so the first of Leibniz’s problems is resolved. Of course we see that the solution depends on a crucial shift from speed and velocity to acceleration as the relevant senses of ‘motion’: from the rate of change of position to the rate of rate of change.