Context: Newton personally believed in the concept of absolute space since it reinforced the idea of an absolute God, but the entire premise was proven false by what we know as ‘relativity of motion’ which makes use of Newton’s laws of motion.
Excerpts from ‘A Brief History of Time’ by Stephen Hawking:
“… Aristotle believed in a preferred state of rest, which any body would take up if it were not driven by some force or impulse. In particular, he thought that the earth was at rest. But it follows from Newton’s laws that there is no unique standard of rest.”
“Newton was very worried by this lack of absolute position, or absolute space, as it was called, because it did not accord with his idea of an absolute God. In fact, he refused to accept lack of absolute space, even though it was implied by his laws.”
We use Leibniz’s calculus anyway, and both were developed at the same time, prompted by the same paper. Newton just happened to publish first (I think) and was more well known at the time.