Wednesday, December 28, 2011

The vanishing mediator in ancient dialectic: Aristotle on middle term and topos

The term “vanishing mediator” was first coined by the literary critic and Marxist-Lacanian theoretician Frederick Jameson and then adopted and greatly expanded by Slavoj Žižek who also employed the term in a Marxist-Lacanian context. Thanks to the popularity of Žižek the term “vanishing mediator” then became salonfähig in postmodern and Lacanian circles. What is generally overlooked, therefore, is the fact that the concept (if not the term) of the vanishing mediator is much older, dating back to the beginnings of Western philosophy – to the logic of Aristotle, at least. The same holds, of course, for the philosophical (i.e. dialectical) problematic of mediation in general, which derives from the mediating role of the middle term in Aristotle’s syllogisms. The middle term (meson) is the mediator, first, between the two premises and, second, between the premises and the conclusion. Thus in the following syllogism:

“Every human is mortal
Socrates is a human
Therefore Socrates is mortal”

the term “human” is the middle term mediating between “Socrates” and “mortal” (each of which Aristotle calls an “extreme”,
akron). The middle term allowes the extremes to be linked in the conclusion. Note that the middle term itself does not appear in the conclusion. It is in fact common knowledge in Aristotelian syllogistics that middle terms never appear in the conclusions they make possible by mediating between the premises: middle terms disappear once they have fulfilled their mediating function. Hence the fact that the middle term is traditionally also known as the “silent term”. It is clear that this is the classic paradigm of what became known as the vanishing mediator. From Aristotle the thematic of the mediating middle term then found its way in Hegel’s and Marx’s dialectics of mediation. Thus in Hegel the vanishing role of the middle term returns in his notion of “mediated immediacy”, which is the synthesis of opposites between which the mediator has disappeared. There is no doubt that the Marxist thinker Jameson drew on this paradigm when he coined the term “vanishing mediator”, applying the dialectical notion of the middle term in a Lacanian context.

Middle terms and topoi as reminders of original sacrifice
Why is this important, apart from the need to correct a one-sideness in the current Žižekian use of the term “vanishing mediator”? It is important because it greatly enhances our insight into the intersubjective nature of the vanishing mediator. It reinforces the insight that the vanishing mediator should first and foremost be understood in the context of dialogical interaction, as the medium making such interaction possible. Why? Because Aristotelian syllogistics was originally developed in the context of Socratic and Platonic dialogue. The middle term was the conceptual medium that allowed the participants in dialogue to resolve their conflict. The middle term makes consensus possible and thereafter disappears from the agreed upon conclusion. This intersubjective nature of the vanishing mediator becomes especially clear in the thematic of Aristotle’s notion of topos (place), which points to an older, oral tradition of collective memory embodied in ‘common’ places. As I will argue below, Aristotle saw the topoi as sources of middle terms that resolve intersubjective dispute. The disappearance of the middle term in the course of the syllogism thus mirrors a more fundamental vanishing mediator, marked by the burial place of the original sacrificial victim (or victims) whose murder was the original foundation of the community (as elaborated by theorists like Freud and Girad – see below). These burial places were the original common places (topoi koinoi) on which collective memory – and hence the role of middle terms in public disputes – was based.

Middle terms in Aristotle’s logic
First, however, I will clarify the dialogical origin of the middle term by taking a closer look at the development of Aristotelian syllogistics. Aristotle’s work on logic consists of six books, collectively known as The Organon. Of these six books, three are about syllogistic logic proper:

(1) Topics, dealing with the dialectical syllogism, i.e. the syllogism as it is used in intersubjective discussion;
(2) Posterior Analytics, dealing with the apodictically certain syllogism, starting from self-evident premises;
(3) Prior Analytics, dealing with the syllogism in general and the different figures of the syllogism.

It is an established philological fact that chronologically the Topics came first. In the epilogue to the Topics Aristotle writes that this is the first book on logic instead of mere rhetoric (so not just his first book about logic, but the very first in Greek philosophy up till then). This is remarkable, since Aristotle starts the Topics by stating a much more practical, less theoretical aim, namely, to develop a rhetorical method for resolving disputes with a clear distinction between the roles of questioner and respondent. This was in fact the formal setting for Socratic dialogue, the use of intersubjective discussion as a privileged road to philosophic education and truth, as practiced in Plato’s Academy and later in the Lyceum of Aristotle himself. Aristotle speaks of “mental gymnastics” in this regard (101a 28). Somehow, then, this practical enterprise issued in the much more formal and theoretical result of syllogistic logic. It is clear then that Aristotle discovered syllogistic logic in the context of Socratic and Platonic dialogue (see Kapp 1965).

Kapp: “Wir wissen aus gewissen Abschnitten in den späteren Schriften Platons, dass in Wirklichkeit Platon der Erfinder des Begriffs der geistigen Gymnastik war, und dass er deren Praxis in seine Schule, die ursprüngliche “Akademie”, einführte, als Pflichtfach zur Vorbereitung zukünftigen Philosophen. Was Aristoteles zum Besten seiner eigenen Schule dieser erzieherischen Praxis hinzufügte, war eine systematische Einführung: die Topik. So kam es, [...] dass der usprüngliche Gegenstand der Logik der “dialektische Syllogismus” war, der Syllogismus, der sich im Gespräch entwickelt.” (1965: 23)

A detail from Raphael's School of Athens
As the vanishing mediator making resolution of intersubjective dispute possible, the middle term must – more than the other terms involved in the dispute – express or symbolize shared knowledge or belief, since it forms the conceptual bridge between the different (terms used by the) disputants. In Aristotle, however, this privileged social nature of the middle term is not so obvious. This is due to the fact that Aristotle (like Plato before him) thought and worked in the transition from oral to literary culture in ancient Greece. With Socrates, who didn’t write books, philosophy was still a basically oral and social affair, taking place in dialogue. This focus on dialogue was obviously crucial to Plato as well, the only and crucial difference being that Plato also wrote dialogues. In contrast to oral culture, which is basically intersubjective, the writing and reading of books promotes a more individualistic mode of thought, the self-sufficient engagement of a thinker with his own private thoughts as these are reflected or stimulated by words on a page. Thus Plato could define thinking as “the silent conversation of the soul with itself (Theaetetus 189e4-190a7). Aristotle took this transition from oral to literary culture a step further, dropping even the literary form of dialogue in favour of scientific discourse. As as result, the privileged intersubjective nature of the middle term gradually disappeared from sight in Aristotelian thought. This is especially clear in the Topics, which – as we have seen – starts out as a practical guide for dialogical dispute but which concludes by presenting syllogistics as a more or less formal logic of which the validity is independent from the intersubjective context of dialogue. This loss of the intersubjective context also becomes clear in Aristotle’s treatment of the topoi as sources of middle terms.

Topoi as collective meta-beliefs
It is of course to the topoi that the Topics owes its title. Yet precisely what Aristotle meant by a topos (place, location) is not so clear and has been a matter of dispute for centuries. Although he lists around a hundred of topoi in the Topics, he nowhere provides something approaching a definition (he is a bit – but not much – clearer in the Rhetoric). What is clear is that most Aristotelian topoi are general rules or instructions saying that a conclusion of a certain form can be derived from premises of a certain form (which is in line with the original practical intention of the Topics as a guide for dialogical dispute). As such the topoi are means for finding the proper middle term that will decide a given dispute (see Slomkowski 1997). For example, if a speaker aims to convince his audience of the proposition that “monkeys cannot laugh”, a typical Aristotelian topos would be the advice to determine whether the contrary (i.e. the ability to cry) can be said of monkeys. Aristotle: “For having shown that the thing in question will not admit of the contrary of the accident asserted, we shall have shown that the accident neither belongs nor can possibly belong”. (Topics, book II, chapter 7) This topos would then enable the following syllogism:

Monkeys cannot cry.
If something cannot cry, it cannot laugh either.
Hence, monkeys cannot laugh.

The above topos thus leads to the middle term “cannot cry” as the conceptual bridge between “monkeys” and “cannot laugh”. If succesful, the notion of crying appeals to beliefs common to the speaker and his opponent and audience, beliefs to the effect that monkeys do not cry and hence do not laugh either (although it may look as if they do). It is this commonality of the beliefs connected to the middle term that makes the latter succesful in enabling a syllogism that will convince all the disputants. Thus the topoi are sources of common beliefs that can be used to bring dialogical disputes to a satisfying conclusion. As such, the topoi could be defined as collective meta-beliefs or abstract schemes of common knowledge, pointing to the appropriate collective first-order beliefs and corresponding middle terms.

The spatiality of topoi
Undoubtedly, this analysis of the topoi as collective meta-beliefs will make them even more mysterious. What is the psychological and epistemological nature of these meta-beliefs? How do they differ from the first-order beliefs to which they point? Aristotle does not answer these questions. He merely lists the topoi without explaining what a topos is. But we can achieve some clarity here by focusing on a related problem, namely:  Why does Aristotle call these meta-beliefs “topoi” (places, locations)? What is the spatial nature – in any – of the collective meta-beliefs? This question has deluded scholars for a long time. It is now generally accepted, however, that Aristotle’s use of “topos” is derived from an older tradition, the ancient art of memory known as the method of loci (also called “the memory palace” and “the mental walk”). This link to an older tradition is in line with the fact that “topos” is not defined in the Topics. Apparently Aristotle assumed familiarity with the term among his readers. As Robin Smith – one of the first to sysematically develop this view – writes in the commentary to his authoritative translation of the Topics: “Now, there is good evidence that Aristotle’s dialectical method drew on mnemonic systems in use during his time. These systems appear to have been based on the memorization of a series of images of actual locations (e.g. houses along a street) in a fixed order; items to be memorized were then superimposed on these images, making it possible to recall them”. (Smith in Aristotle 1997: xxvii)

The memory palace

In this technique the subject memorizes the layout of for example a building (or village or landscape), associating different items of information to the different locations in the building, such that the items of information can be easily retrieved from memory by making a ‘mental walk’ through the building. The building, which can be either reall or imaginary, is then the topos (place) utilized in memory retrieval. This technique is still in use and its efficiency has been confirmed by psychologistst and neuroscientists. Many winners of memory contests claim to use this technique in order to recall historical facts, faces, names, numbers etc. A famous example is provided by the Greek poet Simonides (c. 556 BC-468 BC) who was lucky enough to walk out of a banquet just before the building collapsed: the ravaged bodies of the dead were unrecognizable, but Simonides could remember all the faces by remembering the seating arrangements at the banquet. Thus he put to use the mnemonic technique he normally used when reciting long poems.

In the Topics Aristotle clearly alludes to this technique: “For just as in the art of remembering, the mere mention of the places instantly makes us recall the things, so these will make us more apt at deductions (Topics 163b28–32; Aristotle also alludes to this technique in On the soul 427b18–20, On Memory 452a12–16, and On Dreams 458b20–22). However, although his term “topos” derived from this older mnemonic technique, it is clear that the spatial aspects of this technique were all but gone in Aristotle’s treatment of the topoi. In the Topics he merely lists many more or less abstract logical suggestions (such as the one cited above) listed under general headings like “from contraries”, “from similarities”, “from more and less” etc. This loss of the spatial aspect of the topoi in Aristotle is most probably due to the fact, mentioned above, that his thought toke place in the transtion from oral to literary culture. The method of loci is typical of oral culture, where the absence of writing forced people to commit huge amounts of information to memory. Instead of reading a book to retrieve information, they ‘read’ a real or imagined spatial structure like a landscape as a code for the information they needed (and this notion of reading a landscape for example is reminiscent of Derrida’s notion of archi-writing). For Aristotle, then, who wrote and read books, the spatial aspects of memorization became less and less relevant.

Topoi as ‘burial places’: Girard and Freud on original sacrifice
For a proper understanding of the vanishing mediator, it is nevertheless important to keep the originally spatial and social nature of the topoi in mind. Above I defined the Aristotelian topos as a source of shared beliefs connected to middle terms capable of functioning as vanishing mediators in syllogisms, bringing dialogical disputes to a close. I referred to the topoi as collective meta-beliefs or schemes of common knowledge. Taking the originally spatial nature of the topoi in account, it becomes clear that the original topoi – as these functioned in oral culture in general and intersubjective discussion in particular – must have been real historical places with special (and possibly mythical) significance for the community in question. In short: the first commonplaces must have been real common places (topoi koinoi). The mere mention of such a common place triggered in the audience a host of shared beliefs capable of bridging the conceptual gap between the disputants.

Why do some places function as such common places, associated with the collective meta- beliefs of a community? This is something I want to investigate further, but for now I want to suggest that this is where the broader psychoanalytical meaning of the notion of vanishing mediator comes to the fore. The original common places where the ‘burial places’ of the sacrificed vanishing mediator. Following thinkers like Freud and René Girard, we can see communities as founded on sacrifice. To begin with Girard: according to his theory, the beginnings of human society are based on the religious transformation of mimetic violence into the collective sacrifice of a scapegoat. Before the beginning of humanity, according to Girard, hominids copied one another’s violence in a frenzy of mimetic retaliation that can best be described as the violence of all against all. At some point, instead of being directed at everyone in general and no one in particular, this violence became focused on a specific victim, who was marked out by some kind of distinctiveness or weakness. In the collective murder of this victim, or scapegoat, the violence of all against all was brought to a halt as the first community was united by its murder of the victim. In Girard's theory, this distinction between the victim and the community stands at the origin community.

A similar theory has been proposed by Freud. In Totem and Taboo (1913), he proposed that human societies were initially organized much like those of great apes, with one dominant male (the primal father) monopolizing the females. Freud suggested that eventually the displaced sons of the primal father banded together and killed their oppressive patriarch – however, this act proved deeply traumatic. According to Freud, remorse over the deed produced the first sensation of guilt, and the primal father became internalized as the prohibiting super-ego. The guilty males, united by their murder of the patriarch, formed the first community. The primal father is later manifested in the omnipotent figure of “God the father”, in the deified kings of ancient civilizations, and in the charismatic patriarchal leaders of more recent history.

    Etruscan mural of human sacrifice

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