On the "spatialization" of time - Abstraction and mathematization

All these puzzles disappear when we realize that the mathematics just is an abstraction rather than anything concrete. In particular, it is abstracted from a concrete physical reality whose nature outruns anything captured by the mathematics, rather than being exhaustively constitutive of concrete physical reality. (Edward Feser, Aristotle's Revenge, p. 279)

The idea of space as a kind of receptable or container can be elucidated by noting what it rules out, such as the views of Descartes and Leibniz (Cf. Bittle 1941, p. 152). If space is what contains extended physical substance, then (contra Descartes) it cannot be identified with extended physical substance itself. Space qua container can either be filled or empty in a way a physical substance itself cannot be. (p. 199)

Is space and time merely mathematics? It would seem rather reductionistic to reduce things to mathematical formulae. But the problem is that this question is not actually important for whether time can be considered space-like with coordinates in space-time. For some reason, Edward Feser seems to think that the opposing view reduces everything to mathematics. Generally for most people with some version of a scientific worldview, that reductionistic approach is not taken. Rather, if the mathematics are true, then what we are saying is that the nature of space-time must reflect the mathematics we have found that describe reality.

It is this view of reality, rather than Feser's reductive picture, that informs scientific worldviews of reality. We do not spatialize time just because the math demands it, but rather because the math reflects the nature of reality. If reality does not spatialize time, then the math will not reflect it.

This is not to say that we must necessarily take 'time' to be just another spatial dimension, but rather that arguments against seeing 'time' as being different from 'space' cannot be argued from the fact that 'time' is 'space-like.' Whatever time is, it is space-like. It may have many dissimilarities to 'space,' but that is another argument altogether.

The reason why Feser thinks current understanding of space is insufficient is because he defines "space" in an Aristotelian manner. This is not however how "space" is defined scientifically, which is why there is nothing wrong with the spatialization of time.