If we acknowledge along with dialectician Alain Badiou that mathematics is ontology, then what descriptive tasks are left for language? In other words, what is left in the phenomenal realm that mathematics cannot account for? In asking the question, we must grant that there is much about our human world that cannot be adequately described using numbers. Even if we abandon idealist metaphysics in favor of materialism, we need a theory which can occupy the position traditionally held by metaphysics.
We might think of mathematics as a grid which we project onto the existent. A grid made of points, making a dotted map which can then be laid over whatever we can make of the world through sensory input.
The map has been a wonder worker over the past few thousand years, but in the last 100 years or so we have had to acknowledge that the map does not fit the territory. However fine-grained we make the points, they will never fully account for the richness of the actual, never mind the richness of human behavior.
The non-identity of the existent with itself is fundamental. There are certainly unknown unknown reasons, for instance, why the standard model of macro-level physics will never fully account for quantum theory. But the physical sciences are not the province of dialectics, as much as Engel and even JBS Haldane tried to craft a dialectics of chemistry and physics. The physical sciences are very amenable to “digital” or quantitative models, whereas things like history and the individual subject are better represented using “analog” or qualitative models.
All you need is physics to describe the physical, but if you are trying to account for the immaterial agency of the human realm then what is needed is a metaphysics that will not contravene physics.