Hegel, in the preface of the phenomenology calls the concept of mathematics, magnitude; what would the concept of physics?

The Res Extensa of Descartes and Spinoza?

But Liebniz, in an *Essay on Dynamics says:

I have proclaimed elsewhere that there is more to the body than extension - indeed there is something in them that is prior

So, perhaps not; could it be Motion?

He goes to say:

It couldn't be the case that motion is the fundamental category in physics, because motion, when we analyse it, doesn't really exist.

And this by one of the modern founders of this science; thus under what concept or category do we capture this most successfully precise of the exact sciences? Surely not exactness...

2 Answers 2


Beware that the distinction you are assuming may not be there. Hegel writes in the Philosophy of Nature §202b that

The truly philosophical science of mathematics as theory of magnitude would be the science of measures, but this already presupposes the real particularity of things, which is only at hand in concrete nature.

Generally, Physics is a chapter of Nature (namely the second, while the first one is "Mechanics" about space, time and matter (and their unity...) which of course we would subsume with physics), and nature is the externalization of the Idea (here), and the Idea is that which is objective and true in the Notion (here) and the subjective part of the Notion is deductive logical thinking, where one would locate also the activity of mathematics.

Translated suitably, this should resonate well with common modern undertanding: fundamental modern physics is itself a mathematical theory (for amplification see the first few slides here), hence physics is in a sense that which is "objective" in mathematics, in that it is the part of mathematics that connects to, let me say, the real world.

So if we say that the concept of mathematics is magnitude, or measure, then there is an "objective" aspect of that, which is that which gives reality, that is nature, in particular physics.

In case you care, I am preparing notes with more details here, for a workshop next week.


Liebniz himself gives an answer shortly after your quote: extension and force. This can be interpreted in more modern language (and more formally). Extension and force can be identified with the canonical coordinates (operators) of classical (quantum) mechanics. I don't understand his argument against the reality of motion, but I do know that at the practical level, all of physics deals with change (or the absence thereof), which is the study of motion (sometimes of abstract features).

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