In his discussion of the problematic of Kantian synthetic judgment and the “paradox of pedagogy” found in Plato’s doctrine of anamnesis, as put forward in the Meno, Kojin Karatani makes the following intriguing remarks:

In many courts of law, both opponents must obey a common rule that technically allows the prosecutor and the defense attorney to exchange roles at any time. Those who do not acknowledge and adhere to the legal language game are either ordered out of court or ruled incompetent by the court. In this sort of game, no matter how forcefully or enthusiastically they might oppose one another, neither opponent occupies the position of “the other.” As Rescher notes, this dialogue always has the potential to become a monologue. Indeed, in the works of Aristotle and Hegel, dialectics did become a monologue. And though Plato’s dialogues were written in the form of conversation, finally they, too, must be considered dramatic monologues—as Bahktin pointed out in Problems of Dostoevsky’s Poetics. Western philosophy thus began as an introspective—that is, monologic—dialogue, or, alternatively, dialogic monologue.

Karatani then goes on to assert that mathematics is privileged because its knowledge goes beyond that of the subjective I of dialogic monologue, a characteristic that finds its expression Plato’s and Euclid’s notion that “only that which survives the process of legal argumentation can be deemed mathematics.”

In this manner, mathematical proof is presumed to be produced by intersubjectivity, that is, by that which lies beyond individual cognition. The true Socratic/Platonic invention is not the idea that reason inheres in the world or the self, as is often claimed, but rather that only that which goes through the dialogic process is rational. Those who refuse dialogue, no matter how deep the truth they may grasp, are irrational. Whether or not the world or the self contains reason in and of itself ultimately counts for nothing; only those who are subjected to dialogue are rational.

This leads Karatani to defend Kant’s use of mathematics in the Critique of Pure Reason against the logical positivist critiques, arguing that Kant’s position radicalizes the notion of mathematics as rational, intersubjective dialogue by inscribing deep within mathematics the problem of alterity in communication. Kant achieves this, according to Karatani, through an introduction of what Karatani calls the “transcendental other,” a secular other who is “everywhere and everytime in front of us,” or in other words, the thing-in-itself.

All of this is very interesting, to my mind, but I think Karatani’s identification of Hegel as a practitioner of “dialogue as monologue” proceeds a bit too smoothly. A particularly revealing quote on this matter comes at the end of Hegel’s Phänomenologie des Geistes, in the section on “Kraft und Verstand, Erscheinung und übersinnliche Welt,” in which he writes:

In dem Erklären ist eben darum so viele Selbstbefriedigung, weil das Bewußtsein dabei, um es so auszudrücken, in unmittelbarem Selbstgespräche mit sich, nur sich selbst genießt, dabei zwar etwas anderes zu treiben scheint, aber in der Tat sich nur mit sich selbst herumtreibt.

In the above passage, Hegel identifies the problem of communication as a reliance on positing a false alterity vis-a-vis the process of dialogue as monologue. In other words, although consciousness appears to be in “communication” (or, alternatively, “pedagogy,” if we are to translate things back into the terminology of Platonic dialogues) with some Other outside of consciousness, consciousness is in actuality communicating only with itself, and it is interesting to note that Hegel uses the language of enjoyment (“Selbstbefriedigung,” which can be rendered more formally as “self-enjoyment,” or more crudely as masturbation, as well as the verb “geniessen,” to enjoy) to describe this activity, as well as that of busyness and the drive, both of which I think ought to be seen in light of Freud.

This, I think, opens up a new set of questions regarding both the particular status of the transcendental other, of mathematics and language as systems of mediation and/or alterity, as well as the more Hegelian trope of the necessity of error in the dialectic. Moreover, we might ask ourselves, when we engage in communication with “the other,” to what extent this other is in fact a genuine marker or placeholder of alterity, or instead only the mere appearance of alterity as posited by a certain “drive” towards dialogue as monologue, in order to realize the subject’s jouissance through this very self-activity.