"True Infinity" Overcomes

Connecting Nietzsche and Hegel, and distinguishing "good infinity" from "bad infinity" in terms of "over-coming."

Photo by Bilal O.

During “The Net (16),” preparing for the second Philosophy Portal on Nietzsche, we discussed the topic of “true infinity” and “spurious infinity,” as brought up by the brilliant Dimitri. For Hegel, a “spurious infinity” (or “bad infinity”) is an endless series, such as 1, 2, 3, 4, 5… or A, B, C, D, E…—it is basically a list that always grows (x + 1). Hegel doesn’t have much time for this and believes this “bad infinity” has thrown off a lot of our thinking in problematic ways; rather, Hegel would prefer to emphasize “true infinity” or “good infinity,” which is a “self-relating infinity.” But what does that mean?

Imagine a circle, which is basically a line that bends around and connects with its starting point. This line thus “relates to itself” and does so infinitely, for the circle always circles back around on itself. Furthermore, if we drew a straight line from one point of the circle to the other, we could keep (re)doing this an infinite number of times, suggesting another infinity. In this way, we see different manners in which a circle unveils a “self-relating infinity” and/or “true infinity.” By “true” here, Hegel means to suggest an infinity that actually exists in the world and our daily experience: though we tend to think of “infinite lists” as real and practical, Hegel makes the interesting point that this infinity is “bad’ and “false.” No one has experienced an “infinite list” in concretion, only abstraction, and an abstraction that cannot be made concrete is arguably not even an abstraction (it is hardly nothing). But I indeed experience the infinite ways that I can relate to the nearby air conditioner, my laptop, other people—I can constantly change myself, my hermeneutics, my ideas, and the like, thus changing how “I myself relate” to the thing (and myself through that thing). This is very real and occurs in everyday life constantly, and so it is a “true infinity,” meaning one that corresponds to actuality. The “bad infinity” is yet to be observed, and by definition couldn’t be, which is a reason Hegel is critical of it.

What does it mean to engage in “true infinity” as a subject to itself, though? As I can relate to my laptop in an infinity of ways, so I can “shrink the loop” until it “falls into me” relating to me, but here I run the risk of what is practically a “spurious infinity,” for I can just continually relate to myself the same way, over and over again. Yes, there is a “self-relating infinity,” but it’s practically no different than an endless list (the same can happen regarding a laptop, air conditioner, or “other” if my ideas never transform). For a “self-relating infinity” to not practically be a “bad infinity,” there must be a change in the nature of the relation with each rei-iteration, and that mans there must be a kind of transformation. What kind of transformation? Good question.

To allude to High Root’s excellent example, if I am going to move from being a rock-climber to being a rock-climber, I will have to climb more difficult mountains in more challenging ways. I can “be” a rock-climber and never challenge myself, but to “become” a rock-climber, I will have to overcome myself and excel at greater challenges. If I climb the same mountain of the same difficulty a hundred times, this will practically be a “bad infinity,” even though I am “self-relating” to the same mountain over and over again. Similarly, if I only climb mountains that are “like” one another, similar in difficulty and challenge, then this too will be a “bad infinity,” for I will basically be adding to an endless list (1, 2, 3, 4…), a repetition of “the same in kind.” In order for a repetition to be a negation, the repetition must be of “the act of rock-climbing” in a way that negates my previous notion of “rock-climbing” and sublates it into something higher and deeper that nevertheless maintains the same form; ergo, “rock-climbing” (with the italics). In this, my very relation to “rock-climbing” (and what it means to be a “rock-climber”) has profoundly transformed.

By “true infinity,” Hegel means this kind of “becoming,” which requires self-relation, for it is only a subject in relation to itself that “becoming” can be seen or judged to have occurred. If I have two different people, one who is a “rock-climber” and the other who is a “rock-climber,” there is no “becoming,” only “two different beings.” For “becoming” to occur, the same person who is a “rock-climber” must “become” (and come to relate) to his or her self as a “rock-climber”: the transformation must be in terms of “self-relation.” And it is this “infinity of becoming” which Hegel calls “true infinity”: all other notions of infinity are “false” and “spurious.”

On this point, we can note something important: “true infinity” requires (self) overcoming (“be-coming” is always “over-coming”). A previous self must be negated/sublated by another self, or otherwise we are only dealing with a spurious addition. If this is the case, then I believe we can see a way to connect Nietzsche and Hegel, for Nietzsche’s “Overman” is not a separate being, unique race or nationality, but rather the result of an internal (and dialectical) process within a person where he or she “overcomes” his or her own tendencies and desires to not be a “Last Man” (a process that must never end, for someone who is primarily an Overman today can be a Last Man tomorrow). As someone can be a Christian and not be a “perfect Christian,” so a person can identify with the “Overman” and not be entirely perfect or finished with his or her process of “becoming.” As I argue in my work on Nietzsche, “man” is the cave in Plato’s “Allegory of the Cave,” and the “Overman” is the one who leaves that cave; hence, each of us must leave “the cave of ourselves” to “overcome ourselves” and become “Overmen.” In this way, I see Nietzsche as proposing a “true infinity” in the Hegelian sense, for Hegel’s “true infinity” changes us to ourselves, and that requires us to realize that we are capable of more than we thought.

“Be-coming” requires “over-coming”—though we indeed “become” through time, and thus we all engage in a “self-relating infinity” that way, this “temporal becoming” might practically be no different than a “bad infinity” if we are not working to “overcome ourselves” through time. Yes, technically “temporal becoming” is not a “bad infinity,” so I don’t mind using the language of “becoming” to refer to a temporal procession, but if we want our “true infinity” to be most meaningful and deep, we will need to take Nietzsche seriously. At its deepest and most meaningful, “true infinity” overcomes.

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