A Note on Infinity

I don't think I've completely grasped the Kant/Schiller discourse and De Man's evaluation but I would like to make a small note about the notion of the infinite with regard to defining the sublime. Kant (whose writing is easily mappable in a kind of definition/theorem/proof/example way) says of the sublime, “We call sublime what is absolutely large” (521). Of the infinite, “The infinite is absolutely large” (521). Hence the sublime is infinite. Then, “To be able even to think the infinite as a whole indicates a mental power that surpasses any standard of sense” (524). This infinite aspect of the sublime to Kant is the notion of infinite progression, of an “object” increasing linearly, exponentially, or etc. in magnitude to infinity so that our minds necessarily cannot grasp it. Kant further says, “This basic measure...is a self-contradictory concept (because an absolute totality of an endless progression is impossible)” (524). However, I think that the “absolute totality” of the infinite is what Schiller particularly gets at. “Absolute totality” and “endless progression” in fact, are not contradictory (in my view). We just need to stop thinking in terms of “lines”. But first here's Schiller's first definition of the sublime in the reading, “The feeling of the sublime is a mixed feeling. It is a combination of woefulness, which expresses itself in its highest degree as a shudder, and of joyfulness” (3). Interestingly enough, Kant's first (in our reading) definition of the sublime centers on a notion of the absolute, namely the absolutely large, while later he highlights the impossibility of quantifying or concretely conceiving this “absolute”. Schiller's initial definition is decidedly not absolute, but a feeling which is itself unstable, mixed with contradictory emotions. Schiller characterizers the attempt to conceptualize the sublime: “We refer [the sublime object] either to our power of comprehension, and succumb in the attempt to form for ourselves an image or a concept of it; or we refer it to our vital power, and consider it as a power before which those of ours vanish into nothing” (3). Thus Schiller throws Kant into a new light. To comprehend the sublime, as Kant also agrees, would denote a certain demise; again it is impossible to comprehend the infinite in the way Kant conceptualizes it. However Schiller opens another door, a kind of abandonment to the “power” of the sublime in which we can “delight in the sensuous infinite, because we can think what the senses no longer grasp and the understanding no longer comprehends” (3). It is possible to be attracted to the sublime precisely for its ability to expose the limits of human understanding, which to Kant is an incredibly real terror and for Schiller, an incredibly alluring terror. I think it is Schiller's embrace of the “terror” that allows us to re conceptualize the infinite; yes, it is still incomprehensible but at the same time it can be a kind of absolute. 

De Man compares Kant's mathematical sublime to Schiller's practical sublime: “In Kantian terms we say that the mathematical sublime is the inability to grasp magnitude by means of models of extension, by means of spatial models. For Kant, the mathematical sublime is characterized by the failure of representation” and “what Schiller calls the practical sublime is characterized by the physical inferiority of the body when it is in danger.” (139). Thus Schiller's sublime concretizes the incomprehensible idea of Kant's magnitude through its relation of the physical body. As De Man says, “This notion of physical danger, of a threatening physical Nature, in an empirical sense, we are threatened concretely by fire” (139). My point is this, Schiller shifts Kant's idea of the inconceivable infinite into an infinite that can be an absolute. Consider: an example of Kant's sense of the infinite would be a string of numbers infinitely magnified. Our brains most likely cannot process beyond ~10^6 orders of magnitude let alone infinity. However, imagine summing the area under a curve with rectangular bars. As the number of bars increases to infinity, you are left with an absolute.