The Creativity of Mathematics and Philosophy, Composing, 03/03/2015

My friend B studies Hegel. This is something that I’m very glad he does, because I simply can’t bring myself to it. Hegel and I have such different sensibilities and approaches to philosophy and by implication pretty much everything else, for me to become a genuine scholar of his work, a route B has taken, at least for part of his professional life as a university worker.

Periodically, he’ll post quotations from Hegel on his Facebook wall, because that sort of thing is actually pretty cool. It’s verbose and difficult language, but it’s philosophically rich, at least through the act of interpretation. Mind you, I don’t always find it philosophically rich in the creative sense, which is why Hegel scholarship and myself don’t always get along.

No, I can't say I've been a fan.
B quotes Hegel from The Science of Logic:
“Not only does arithmetic not contain the concept and the intellectual task of conceptualization that goes with it: it is the very opposite of the concept. Here, because of the indifference of the combined to the combining - a combining that lacks necessity - thought finds itself engaged in an activity which is at the same time the utter externalization of itself, a tour de force in which it moves in an element void of thought, drawing relations where there is no capacity for necessary relations. The subject matter is the abstract thought of externality itself.”
And another quote from the Logic, later in the comments, in response to my question about what specific kind of mathematics Hegel implied:
“Essentially, however, the perversity of enlisting mathematical categories for injecting some determination into the method and content of philosophical science shows in the fact that, inasmuch as mathematical formulas signify thoughts and conceptual distinctions, this meaning must rather first be indicated, determined and justified in philosophy. In its concrete science, philosophy must take its logical element from logic, not from mathematics.”
I wondered if Hegel really did intend to treat all mathematics as if it were simple arithmetic, and B confirmed that arithmetic was really what he was referring to in the first quote. B clarified for me that Hegel was opposed to the notion that a philosopher should develop concepts based on mathematical ideas because they were entirely abstract, with no concrete meaning. 

His critique of Gottfried Leibniz was essentially on these grounds, that the framework of a philosophy can only begin from the concretely meaningful foundation of logic. This would make Leibniz’s inspiration for so much of his philosophy from his innovations developing differential calculus a dead end.

Having learned a few ideas from the
philosophy of physics scene about John
Clerk Maxwell and field dynamics, I'd
think that this was a form of mathematics
that Hegel would have found interesting,
had he lived long enough. But
apparently not.
Hegel’s concept of the concrete is one of the central notions of his philosophical approach, and it’s exactly why I’m not really a fan of his. I consider philosophy, above all else, a creative enterprise. It’s a tradition of creating concepts, new ways to understand the universe, our place in it, and ourselves. We shouldn’t build a restriction into that creativity in philosophical practice itself.

There should be checks on philosophical creativity in the moment, for many reasons. As a discipline of progressing human thought, it has to speak to human concerns of some kind. Most obviously, you should prevent your philosophical exploration from completely going off the rails and taking you to a land so divorced from reality that you could only use it in heavily experimental sci-fi or fantasy. 

But you should also let developments in related fields of human activity guide your philosophical work. It could be the sciences, mathematics, art, medicine, politics. We should root our concepts in some worldly endeavour to keep them relevant to human life. That’s what I did with Ecology, Ethics, and the Future of Humanity, grounding a philosophical exploration in ecological and biological sciences, giving these relatively abstract concepts a mission statement through environmentalist politics. 

In a way, I have a similar rule as Hegel about what makes good philosophy. The only difference is that I understand philosophy as working best when it’s in a dialogue with other disciplines and knowledge traditions of humanity. Hegel always struck me as understanding philosophy to stand separate and superior from all human endeavours. I don’t really know if I’m built to do philosophy like that.

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