After Perception, Hegel discusses what is basically the attitude of mathematical physics. Harris in his commentary notes that Hegel is much more sympathetic to natural science than some of his supporters have seemed to recognize. Hegel accepts mathematical physics as an authoritative account of the physical world, and is impressed by the concept of mathematical natural law.

More generally, this is where Hegel introduces what he calls Understanding, which seeks to give a fully univocal (thus also formalizable) account of things. Understanding will have permanent value in securing definiteness and discipline of thought. Hegel often makes sharp remarks about its limitations, so it is important to recognize that he also respected its strengths.

Perception already took a relational approach to the properties of things, but still held fast to the idea that its objects were independent things. Newton’s concept of force as characterized by mathematical law effectively takes a relational approach to determination in the physical world as a whole. Mechanics treats force subject to mathematical laws as the objective reality underlying the world of Perception and “things”, which it treats as Appearance rather than an immanent truth.

Force for Hegel is a supersensible rational construct. For the Newtonian physicist, it is a supersensible reality. Hegel approves of the physicist’s recognition that sensible reality is not all there is, and applauds what he sees as the physicist’s thoroughgoing relational approach. His main caveat is just that what the physicist sees as an independent physical necessity that is only described by mathematics, Hegel see entirely in terms of the formal necessity of the mathematics and logic used in the physicist’s theory.

This concludes the “Consciousness” section of the Phenomenology, where “consciousness” for Hegel is the attitude that treats objects and objectivity in a “pre-Kantian” way, as just being out there. The physicist’s thoroughly relational approach to the external world takes this to its highest sophistication. What remains is to examine the ways in which there is actually continuity and reciprocity between “us” and the world we inhabit, and the role that we play in its development.