A quick fact check. Again, I claim no mathematical expertise, but in [Martin Taylor 2016.09.15.13.41], it appears to me that Martin’s objection is that (1) is with respect to a particular trajectory while (2) is an abstraction over an infinite set of possible trajectories. Specifically, he says that the V in one equation (velocity during a particular trajectory) is not necessarily the same as the V in the other (velocities during possible trajectories), and velocity refers to both time and space in both instances. Yes, (1) refers to V and R during a particular time interval while (2) is timeless, but time vs. space is not the issue that he stated.
The conversion of [Martin Taylor 2016.09.15.13.41] to a Discourse post is difficult to read and omits some data, so I have created a PDF from my csgnet/gmail copy. The ‘Bruce’ that Martin mentions is Bruce Abbott.
That was in 2016, eight years ago. Is there someplace else that Martin abandons this objection and replaces it with an objection that the derivatives of one equation are in respect to time and the derivatives of the other are in respect to space?