Of Kant’s Straight Lines

Rhetoric 240, Professor J Butler

U.C. Berkeley, Fall 2009

A figure populates Kant’s Critique of Pure Reason—it is the figure of the straight line. If the principle task of the Critique of Pure Reason is to explain the a priori conditions of experience as given in space and time, Kant privileges the figure of the straight line to illustrate certain axiomatic claims about such conditions of human cognition and experience. The straight line, for instance, is used to illustrate the proof that all geometric judgments contain in them a priori synthetic knowledge, as in “A straight line between two points is the shortest” or “Two straight lines cannot enclose a space.” But Kant also uses the figure of the straight line to illustrate a more metaphysical conundrum, a certain enigma, of time: we cannot represent time without drawing a straight line.[1]

In the Critique of Pure Reason, time cannot assume any other geometric shape nor can it be extended beyond one-dimension. Time cannot have the form of a circle, triangle, parallelogram or the depth of a three-dimensional shape. This is so because Kant argues that when we think of time, we necessarily think of a line, because the passage/passing of time from past, present, and future phases is one of succession. Because time can go only forward, our experience of time is bound by this serial consecution. For Kant, temporality can only be linear and progressive, and the drawing of the straight line becomes analogous to, indeed a graphic figuration of, how we experience time. And insofar as the straight line gives representational shape to time, the graphic inscription marks a certain spatialization of time. The straight line becomes an inscription of the possible in this sense, for it solves the problem of representing time to ourselves, by making it something external, empirical and perceptible. Because the straight line is conceived as a solution to a problem, of overcoming the impossibility of representing time to ourselves, the figure reveals how Kant understood the relationship between (the aporias of) time and (the limits of) human cognition. Kant thereby dramatizes the problematic relationship between temporality and human finitude in a scene of writing. The straight line, after all, is not merely abstract or conceptual; it is also something made graphic and material by a subject who inscribes the figure. And because we are to imagine this drawing as happening in time and taking time, the spatial inscription at once bears the subject’s signature as it archives its being in time. Why did Kant think the line, in particular its formal qualities of straightness and unidimensionality, as the only possible means of representing time to ourselves?

The first question, then, what is time and why must it be inscribed as a straight line? Kant does not proceed in the Aristotelian manner, he does not begin merely with a notion of time as a series of “nows” that may be configured in terms of a number of changes with respect to a before and an after. For to think of time as composed of “nows” is already to give it external shape. Before affirming the empirical reality of time as a divisible moment, as a “now,” Kant first distinguishes time as a transcendental idea, as a pure form of subjective intuition that is the condition of all possible experience. For Kant, time is first and foremost something internal, it is our immediate sense of interiority, what he calls “inner sense,” and as such, time determines the relations of representations in intuition. Time is thus not an entity or a property that subsists in itself outside the subject. Time is something in us, and Kant is quite literal on this point. Time is what we sense internally, and as an a priori pure form of intuition, time is the universal condition of all appearances, for all objects of the senses, all possible experience, stand in relations of time. If time has a reality, it is “real” only with regard to how objects are given to our senses. Time is what is presupposed in order for appearance to be possible, time in-itself is something that cannot be cognized. Kant thereby defines time as a “subjective condition of our (human) intuition (which is always sensible, i.e., insofar as we are affected by objects), and in itself, outside the subject, is nothing” (B51, p. 181).

If time is understood as a form of inner sense, and if interiority marks the proper boundary of the temporal, then to extend time beyond what is internal is to commit a breach. Time has no reality outside sense experience because once taken outside the subject, time becomes nothing. Kant demarcates time in this manner in order to distinguish time from space. Just as time is the intuition of our self and our inner state, space is the ground of all representation that appear as something outside the subject. Time and space are mutual conditions of possible experience in that (1) for something to appear, it must be posited as an object that is outside the subject, whose form is space; (2) but at the moment this object is cognized, its spatial form is internalized, or mediated through relations of time by virtue of the representation becoming, in this instance, a determination of the mind. Kant thus restricts all human knowledge within the boundaries of space and time, and these boundaries constitute the parameters of human finitude. Yet the nature of human finitude is such that the boundaries between space and time do not always hold, they confound each other when brought into relation. To make possible a connective relationship between time and space, Kant suggests that a breach must be made, namely, time must be inscribed spatially as a straight line. Kant writes,

For time cannot be a determination of outer appearances; it belongs neither to a shape or a position … And just because this inner intuition yields no shape we also attempt to remedy this lack through analogies, and represent the temporal sequence through a line progressing to infinity, in which the manifold constitutes a series that is of only one dimension, and infer from the properties of this line to all the properties of time. (B50, p. 180)

We return, then, to the second part of our initial question, why must time be inscribed as a straight line? Some preliminary answers. Because time can only be the form of inner sense, if taken beyond the relations of interiority, time risks becoming nothing, hence in order to maintain its actuality it must be represented in the form of space. In Kant, this representation of time is necessary because the straight line renders a measure of duration against which the passage of time, and hence all alterations that happens in time, can be apprehended. According to Kant, without this representation of time as a straight line, no knowledge is possible, for there would be no measure against which one thing can be related to another or, in other words, no synthesis is possible. Moreover, the straight line supplies a representation of time as duration (i.e., a composition of “nows”) moving forward, which is necessary if we are to affirm the existence of a thing as a substance that endures over and in spite of the passing of time. What of the fact that Kant invites us to imagine the straight line as being drawn by a subject? For instance, Kant writes, “in order to cognize something in space, e.g. a line, I must draw it, and thus synthetically bring about a determinate combination of the given manifold, so that the unity of this action is at the same time the unity of consciousness (in the concept of a line), and thereby is an object (a determined space) first cognized.” (B138, p. 249). According to Kant, one draws a straight line in order to make sense of time by spatializing it, and that this inscription is “the action of the synthesis of the manifold,” which itself reveals the “synthetic unity of consciousness” (B154, p. 258).

For Kant, the straight line becomes what we suggested earlier as the inscription of the possible as it relates to the subject in at least two ways. First, the drawing of the straight line can be interpreted as a way of making cognizable the manifold of intuition for the subject in the form of temporal succession. The drawing of the straight line—the spatial inscription of time as moving forward—is a figuration of how one submits the manifold (simultaneity) into an object of possible experience (succession). Because Kant insists that we cannot cognize the multiple simultaneity that inheres in the manifold, the line, in particular its formal quality of straightness, illustrates how one economizes—synthesizes—the simultaneity of the manifold by reducing it to a serial succession, a unidimensional line. Second, the drawing of the straight line secures the “synthetic unity of consciousness” because the act of inscription is one that not only belongs to the subject, but is an act that confirms that part of the subject which is unconditioned by space and time and therefore endowed with the power of spontaneity. This unconditioned dimension of the subject that is distinct from the empirical self is what Kant calls the transcendental apperception, the “I think” that is the ground of synthesis. The “I think” that accompanies all representations is thematized in Kant as the subject that spontaneously draws a straight line, a line, which, as it is drawn forward, spatializes or brings into material presence that which was previously unrepresentable at the edge of the trace. The straight line therefore operates as a privileged trope for the principle of identity that binds the continuity between the object of sensible experience and the subject understood as a self-identical consciousness. Kant insists that we must have in mind and draw a straight line when we think of time and synthesize the manifold, for the inscription of the straight line enables the subject to overcome the relentless division of time. The writing of the self in Kant thus seems to be reduced merely to a logical form of self-movement, as though the shape of consciousness can materialize itself only as a straight line in the Kantian scene. We ask, however, what happens when, at the very edge of the trace, the drawing subject slips, steps out of the strict path of rational necessity, and curls the line into a script? What happens to our understanding of time when time becomes narrative, when the inscription of the line becomes something else, transforms into exposition, into writing? Beyond the merely linear and the chronological, what other shapes or forms of time become possible?