The Point Well Missed: Kant's Punctual I and Schopenhauer's Optics of Philosophical Writing

Unser sämtliches Wahrnehmungsvermögen gleicht dem Auge. Die Objekte müssen durch entgegengesetzte Media durch, um richtig auf der Pupille zu erscheinen

(Novalis)¹

When we speak of human beings as "individuals" we usually have discrete and countable entities in mind, each of them someone different from the others. This usage seems unremarkable, but it is actually at odds with the literal meaning of the term "individual." For the term in question was originally coined after the model of the Greek word atomos designating the smallest indivisible part of matter; yet the frequent use we make of fractions of one should remind us that an indivisible being must be less than one and hence cannot be "someone." This consideration suggests that the number one cannot be regarded as the mathematical equivalent of individuality in the strict sense. A more appropriate schema can be found in the point, defined by Euclid as that which has no parts. It follows from this standard definition that the point cannot serve as a unit of counting. However small the object whose magnitude we want to put a count on, we will need to use a unit of measurement consisting of more than one point.

Contrary to the everyday, numerical, meaning of the term "individual," there is a long-standing philosophical tradition in which the human mind is taken to be individual in the rigorous sense just delineated. This view is paradigmatically expressed in comparisons of the subject to the mathematical point. What Charles Taylor calls the "punctual self" rose to ascendancy when the modern aspiration for disengaged mastery over the world was extended to the human being itself.² If we can remake ourselves without reliance on contingently given contents of experience, then the "real" self is not one of these contents but the formally defined, extensionless point of view from which all such contents are worked upon and judged. The punctual analogy is thus intimately tied to what Taylor terms the ideal of "radical reflexivity," which stipulates that we think of the human being not as a thing in the world but as a self whose true being is accessible only from the first-personal standpoint of active self-consciousness.

How compelling the view summarized by Taylor proved to be can be estimated by recalling such disparate figures it has informed as the Romantic ironist envisioned by Friedrich Schlegel and the protagonist of Robert Musil's The Man Without Qualities. Equally relevant are disputes in philosophy of mind about the systematic elusiveness of the I. Indeed, Taylor could hardly discern the contours of this emergent conception so clearly in the writings of Locke if his vantage point were not thoroughly informed by subsequent developments. For the definitive articulation of the punctual notion of the subject, it is not to Descartes or Locke that we must turn but to the later lineage of transcendental-philosophical thought that was inaugurated by Kant, in no small measure against the Cartesian tradition. By conjoining a theory of the subject with a theory of space implying a very specific understanding of the mathematical point, Kantian philosophy makes possible a particularly incisive formulation of the punctual analogy.

To establish the specificity of this formulation, contrasts drawn to cognate views are necessary. By way of beginning, therefore, I shall compare the Kantian variant of the punctual analogy to alternative formulations of the analogy proposed by Cantor, Leibniz, Jean Paul and Hegel. My main concern in this essay is, however, not with the inherent plausibility of Kant's notion of the subject but with its implications for philosophical authorship. These implications are less clearly evident in the works of Kant himself, whose systematic mode of exposition deliberately brackets the movements of thought involved in the genesis of philosophical insight, than in the writings of one of his most brilliant and idiosyncratic readers, Arthur Schopenhauer. In asking what sort of work the punctual analogy inherited from Kant does in articulating Schopenhauer's vision, my aim is to highlight the ways in which this analogy complicates...