Narrative, Rhetoric, and the Origins of Logic

Apostolos Doxiadis

StoryWorlds: A Journal of Narrative Studies, Volume 2, 2010, pp. 77-99(Article)

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Narrative, Rhetoric, and the Origins of Logic

Apostolos Doxiadis

In Vom Mythos zum Logos (1940), a book that became

emblematic of a now rather passé, idealized view of an-

cient Greek culture, Wilhelm Nestle proposed that the

greatest achievement of the Greeks was the abandon-

ment of the mythological interpretation of the world

in favor of a rationalist model, developed with the

tools of analytic thinking. Nestle’s account has since

been supplanted by newer approaches, which found a

lot more than myth in mythos and a lot less than pure

reason in logos. However, if we restrict the meaning of

his two terms and read mythos simply as “story” and

logos as “logic,” Nestle’s catchphrase takes us back to a

seminal event in cultural history, an event that has not

been examined with the attention it deserves.

More specifi cally, this essay argues that what we

call, for short, “the birth of logic” can best be under-

stood not as the abandonment of the narrative mode

storyworlds volume 2 201080

of thought (story) for the rational (logic), but as a transformation of as-pects of the former into the latter. This transformation occurred in the classical era (500-330 BCE) in certain Greek poleis, when the new demo-cratic institutions allowed multiple narrative representations of reality to come into confl ict, thus creating the need for choice among compet-ing versions. The medium for these verbal battles was the newly invent-ed prose genre of rhetoric.1

The idea that judicial practice, more particularly, was a context for the early development of logic is not new (Lloyd 1990; Asper 2004). However, most investigations have a blind spot where the relations of rhetoric—and thus of logic—to narrative are concerned. Focusing pre-cisely on this interface, I put forward a cognitively grounded account of classical forensic rhetoric as a tool for comparing narratives in con-test. My argument, in a nutshell, is that the tools and methods of logic were not invented ex nihilo but—as is common in cultural evolution—adapted from an earlier, existing practice: they were borrowings that sometimes involved what biologists call exaptations, which involve the assignment to new uses of features originally developed for another purpose, in this case the craft of poetic storytelling.

The following section lays groundwork for my argument, briefl y characterizing some of the cognitive properties of narrativity and the so-cially developed practice of storytelling. In the next I set the scene for Greek rhetoric, examining how narrativity is behind the generic format of the forensic speech, functioning as a macroscopic algorithm for creat-ing texts. In the fi nal section I turn to the microstructure of the forensic speech and the specifi c borrowings and exaptations of poetic storytelling patterns that are redeployed for purposes of demonstrative persuasion.

Ending in the early fourth century BCE, my account makes it pos-sible to speak of the shift transition from story to logical proof in Greek culture—a process we can think of as beginning with Homer (eighth century BCE) and ending with Euclid (c. 300 BCE)—as a much more

seamless transition than previous research would suggest.

On Narratives and Storytelling

For the purposes of my discussion, I distinguish between narrative and

storytelling, defi ning the fi rst as more general than the second. I make

Doxiadis: Origins of Logic 81

the distinction in order to separate narrativity, viewed as a basic hu-

man mental capacity, from the telling of stories, which is at least partly

shaped through cultural practice.

narrative

Narrative is a representation of action through a sequential symbolic

system—here I consider only human language. The action represented

need not be there in the real world: the events in Dostoyevsky’s Brothers

Karamazov did not actually happen, but it makes perfect sense to speak

of them, when referring to the novel, as if they did. Note that there are

two operative words here: action is at least as important in the study

of narrative as its representation. In fact, despite poststructuralist and

other theorists’ preference for “the signifi er over the signifi ed,” experi-

mental research of the past decades brings to the foreground the oft-

forgotten truth that “narratives are discourses that describe a set of ac-

tions” (Zacks, Tversky, and Iyer 2001: 5).

It is important to underscore the importance of action for narrative

understanding because “narrative is gappy; like a thin fabric. . . . If we

do start picking holes and looking at the gaps rather than at the smooth

surface, then indeed it does start to fall to pieces” (Gainsford 2001: 1).

What prevents a narrative from falling to pieces is, precisely, the un-

derlying, represented action. Mandler and DeForest (1979) showed that

when people hear a story, they model their recall on the represented ac-

tion, and not on the form in which it is told to them: the mental coding

of a narrative captures what narratologists call the fabula, the underly-

ing events in their chronological order, and not the sjuzet, the story as

constructed to suit a narrator’s choices.

Narratives fl ow linearly in time, yet they mediate between worlds that

are largely nonlinear: both the world of action, with its manifold possi-

bilities, and our mental models of it are like complex, multidimensional

maps, representing not just objects but also relations, in webs of im-

mense connectivity. Narratives, by contrast, are like specifi c paths taken

through these worlds—partial, linear views of nonlinear environments.

The worlds of actions and mental representations are nonlinear in

two ways: for any event in them, we can speak of outgoing nonlinearity,

determined by the many possible events that can follow it (Bremond

storyworlds volume 2 201082

1980). Likewise, events have an incoming nonlinearity, mostly due to the

multifactorial nature of causality: more events or states of affairs than

one are usually necessary to cause an action (Pearl 2000). Arguably,

the ability to effect the translation from the nonlinear world of action

through the linear medium of narrative to the nonlinear world of men-

tal representations is a fundamental, at least partly innate, human cog-

nitive skill.

storytelling

To compose and understand interesting stories, however, our narrative

potential is not enough; a sophisticated cultural practice is also needed.

A “storytelling species” we may be, but not in the sense in which seagulls

are a “fl ying species.”

Like other higher cognitive functions, storytelling is instrumental in

ordering a complex and often chaotic environment. I am particularly

interested in two ways in which this is achieved. On the one hand, we

can conceive of stories as made up of discrete or modularized scenes,

which can be telescoped into shorter versions, or outlines. On the other

hand, as I begin to discuss in more detail in the next section, cultur-

al traditions forge patterns in storytelling, at both the macro- and the

microlevel. These patterns take the forms of structured story and scene

types, themes, and motifs, as well as low-level narrative formulas.

Rhetoric, Narrative, and Persuasion: Macrostructural Perspectives

In this section, I look at how narrative- and storytelling-related structures

are at the core of the generic pattern of the classical forensic speech.

At the center of any trial—then as now—is an action, something that

actually happened. But the narrative of it is never one. Many narratives

unfold during the process, including the partial accounts of the events

given by the witnesses, but all of the stories gravitate around the two

central narratives—those of the prosecution and the defense. Every trial

is like Akira Kurosawa’s Rashomon, a constellation of narrative views of

the same event. Yet unlike the fi lm, a trial has to end with a fi nal deci-

sion about what happened, that is, a conclusive narrative.

Doxiadis: Origins of Logic 83

Greek forensic rhetoric developed within the context of the classi-

cal trial process. In this process there were no lawyers, and though wit-

nesses gave statements, there was probably no—or very little—further

examination. The prosecution was conducted by a volunteer and the

defense by the defendant himself, though his speeches were written by

a professional rhetor, the logographos. The case was decided by a large

jury. The jurors did not discuss the process but voted directly after it.

They had to make two decisions: which of the two main narratives gave

a better fi t to the facts, and which law applied to the defendant’s actions.

Their thinking depended crucially on narrative probability, that is, the

degree to which it is plausible that a certain chain of events could have

occurred within the particular storyworld elaborated over the course of

the trial. They took into account written laws but were also affected by

various gnômai, proverb-like snippets of oral wisdom brought forward

by the speakers.

the forensic speech

Essentially designed to increase narrative probability, the forensic speech

is driven by the potentialities and constraints of narrative intelligence.

The generic form developed in the second half of the fi fth century and

has at its center the rhetor’s narrative of the events of the case being

tried: if the jurors believe that, the rhetor has won. The main aim of the

rest of the speech is to make this narrative even more persuasive.

To better understand the rhetorical genre, it is important to remem-

ber that the earliest extant forensic speeches, of Gorgias and Antiphon

(c. 430 BCE) are, together with the History of Herodotus, the fi rst prose

compositions in Greek. All extant Greek literature until then is in verse,

and so is all storytelling, in the epics of Homer and Hesiod (eighth and

seventh centuries), the narrative parts of so-called lyric poetry (seventh

and sixth centuries), and tragedy (fi fth century). The Homeric epics, es-

pecially, were an immense infl uence on all later Greek literature. Many

of their stylistic features survive not only in subsequent poetic forms

but also in the prose works of fi fth- and fourth-century historians and

philosophers. It is thus safe to assume that classical rhetoric was also in-

fl uenced by the mostly Homeric techniques of poetic storytelling.

Already by the end of the fi fth century a more or less standard tem-

storyworlds volume 2 201084

plate for the forensic speech is in place. Its very existence should be seen

as a lesson from poetry: poetic genres had developed on the infrastruc-

ture of clear, standardized patterns, and so too does rhetoric. The ge-

neric macrostructure of the forensic speech consists of four parts: intro-

duction, narration, proof, and epilogue.

Introduction

In addition to fulfi lling requirements that stem from the circumstances

of the speech’s delivery, such as capturing the jurors’ attention, the in-

troduction must also focus on what is to be proven, both in terms of

narrative (what happened) and law (what law applies given what hap-

pened). Outlining a story’s plot inside the story itself is a storytelling

trick at least as old as Homer, probably developed to give order and uni-

ty, through anticipation and recapitulation, to the sprawling, digressive

oral style (Notopoulos 1951). Along the same lines, starting a storytelling

performance with an outline of the plot is standard epic practice. Its use

in the forensic speech’s introduction can thus be seen as a clear case of a

borrowing, a storyteller’s device being put to a new use by the rhetor.

Narration

Modern authors translating diêgêsis (Latin: narratio) as “statement of

facts” distort the original sense, defl ecting our attention from the close

affi nity between ancient legal thinking and narrativity. The speaker’s

purported aim in the narration is indeed merely to recount the “simple

facts.” The seemingly plain narrative, however, is in reality artfully—

though seemingly artlessly—constructed to increase narrative probabil-

ity (Gagarin 2003).

The one quality ancient theorists agree a narration should necessar-

ily possess is believability, whereby an action is represented, convincing-

ly, as true; on the same principle, the other side’s narration is contested

as being less believable. In a sense a narration is (a big part of) its own

proof. Quintilian (c. 35–c. 96 CE), in the strongest possible statement of

the narrative-as-proof view, writes: “What difference is there between

a proof and [a narration] save that the latter is a proof put forward in

continuous form, while the proof is a verifi cation of the facts as put

forward in the [narration]?” (1920: 93). In other words, what drives the

Doxiadis: Origins of Logic 85

change from mythos to logos is largely the new intention with which the

mythos is told: not to delight or instruct, but to convince.

Proof

The proof part of the speech is made necessary by the fact that the

speaker’s narration is contested by his opponent’s: additional argument

is needed, both to enhance the probability of the speaker’s own narra-

tion and to diminish that of the other side.

Some ancient authors further separate proof into division, the actual

proof, and refutation, the latter having the aim of anticipating some of

the opponent’s arguments. Division identifi es the contestable parts of

the narration, breaking them down into separate items that can be dealt

with more easily, each one in the form of a new narrative. These are

of two kinds: sub-narratives, parts of the narration expanded in greater

detail, and counternarratives, narratives alternative to the rhetor’s own.

Essential to the creation of both of these modes is the awareness that

narratives come from a much larger, nonlinear world of possibility,

from which new variations can be culled.

Subnarratives are usually created by closer examination of an event’s

incoming nonlinearity, through a more detailed look at the causes of

events. For example, in Gorgias’s Encomium of Helen, a display piece ex-

onerating the fabled beauty for her part in starting the Trojan War, the

rhetorical strategy is to show that Helen is free of blame whatever the

reason that made her follow Paris. In the brief division Gorgias lists all

four possible subnarratives to the main event: “Either she did what she

did by the wishes of fate and designs of the gods and decrees of ne-

cessity, or she was taken by force, or was persuaded by words, or con-

quered by Eros” (my translation; Greek text in Diels and Kranz 1966:

289). Gorgias does not opt here for any one subnarrative over another.

What is important is that that they exhaust all possibilities: if he man-

ages to deal successfully with each one in the proof proper, he will have

solved the whole problem.

Counternarratives are developed from looking at outgoing nonlinear-

ity, that is, identifying competing scenarios for the basic action. These

are then discredited, in favor of the speaker’s own narration.2 Here is

a part of the division from Antiphon’s On the Choreutes in which the

storyworlds volume 2 201086

chorêgos (sponsor) of a tragic performance is accused of having poi-

soned one of the chorus members: “In the fi rst place, then I will prove

to you that I did not tell the boy to drink the poison, compel him to

drink it, give it to him to drink, or even witness him drinking it” (Maid-

ment 1941: 259). But, the speaker will conclude, the boy drank the poi-

soned drink of his own accord.

The proof proper employs two kinds of arguments:

1. The inartistic proofs consist of witnesses’ statements, under oath

(free men) or torture (slaves), and contracts and laws, that is,

information that comes to the rhetor from outside. These are all

in the mode of action representation, either direct, in witnesses’

statements (“Eratosthenes was having an affair with the defen-

dant’s wife”), or conditional-generic, in laws and contracts (“If a

man is having an affair with a married woman . . . ”).

2. The artistic proofs are already to be found in the earliest extant

speeches, interwoven with the inartistic. These are created by the

rhetor and come in three varieties: ethos (relating to character),

pathos (appealing to the jurors’ emotions), and logos, with argu-

ments addressed to reason (dianoia). The latter, Aristotle tells

us, “lie in the speech itself, demonstrating (deiknunai) or seem-

ing to demonstrate” (my translation; Greek text in Aristotle 1926:

16). The logos part of the proof deals piecemeal with the sub- or

counternarratives set out in the division, making the ones that

are favorable to the speaker even more probable, and disfavorable

ones more improbable.

Epilogue

Modern writers often translate this as peroration, and mostly it is that, a

rounding up and emotional appeal to the jurors to support the rhetor’s

story, possibly with an addition of a gnômê, as for example at the end of

Antiphon’s Prosecution of the Stepmother for Poisoning: “I have stated my

case; I have championed the dead man and the law. It is upon you that

the rest depends; it is for you to weigh the matter and give a just deci-

sion. The gods of the world below are themselves, I think, mindful of

those who have been wronged” (Maidment 1941: 31).

Doxiadis: Origins of Logic 87

Putting It Together: The Microstructure of Persuasive AccountsRhetoric had its origin to a considerable extent in the attempt to give to prose the

same qualities of beauty which its elder sister, poetry, already possessed.

—Samuel E. Bassett, “YΣTEPON ΠPOTEPON OMHPIKΩΣ”

I now turn to the microstructure of the Greek forensic speech to see how

it too, like the macrostructure, was crucially affected by earlier story-

telling practices.

The fi rst instances of the patterned reasoning we call logic appear in

the artistic proofs of the logos of the forensic speech. Bassett’s astute ob-

servation gives us the strongest key to understanding how these patterns

suddenly begin to materialize in mid-fi fth century. Though seemingly

coming out of nowhere, in reality the patterns for reasoning come from

poetic storytelling. I argue, more specifi cally, that to construct their

persuasive arguments Greek rhetors made extensive use of two related

techniques of archaic poetic storytelling, chiasmus and ring composition.

The logical microstructures later theorized by Aristotle as syllogisms

were purifi ed versions of these two techniques of poetic composition, in

their elementary form.

Narrative is made up of strings of words, representations that de-

scribe either actions (“The king killed a stag”) or states (“The queen was

fat”).3 “Jack eats a sandwich and Jill is doing homework” can be broken

down in two bits of action joined with an “and”; but these smaller bits

cannot be broken down further, and are thus atomic. Narrative phras-

es are put together in quotidian narrative through links that are either

temporal (as in “and then”), spatial (“elsewhere”), causal (“and so”), as-

sociative (“which brings to mind”), or elucidatory (“who was the son of

. . . ”). The aim of this joining up is, always, the representation of action

in a storyworld.

In archaic Greek storytelling, gnômai are added to action and state

phrases, as basic stock. The early poet-storytellers compose their poems

in a syntax of nonsubordination, phrases put together one after the oth-

er in what was called lexis eiromenê, or “strung-along style” (Notopou-

los 1951). Its major forms are parataxis, where action phrases are con-

catenated, with or without the conjunction and, and apposition, where

storyworlds volume 2 201088

each phrase incrementally adds to the image of the previous, as in the

beginning of the Iliad:

Sing muse

the terrible wrath of Peleus’ son Achilles

which caused Achaeans myriads of troubles

and sent many mighty souls of heroes to Hades

and made their bodies carrion, to dogs and birds

of all kinds. (My translation)

In poetic storytelling, the basic narrative reasons for linking phrases

(temporal, causal, etc.) are supplemented with those demanded by the

fi gures and patterns molded by tradition. Chief among these in Homer

is the simile, which is a form of analogical composition (“this looks like

this”). But other patterns are common, among them chiasmus and ring

composition. Though these structures could have come to Greece from

earlier literary traditions, like Sumero-Akkadian and Ugaritic, where

they are also prevalent, it is quite possible that they are cognitive univer-

sals (Douglas 2007).

Chiasmus (X) and ring composition (RC)—some scholars use the

terms interchangeably—are symmetrical structures of phrases of the

form ABB*A* (X) and ABCB*A* (RC) where B* and A* mirror ele-

ments of B and A, respectively, either in word or subject. Note that

X/RCs can be of arbitrary length, that is, A1 A

2 A

3 . . . A

N A*

N ... A*

3 A*

2

A*1 (X), and A

1 A

2 A

3 . . . A

N . . . A*

3 A*

2 A*

1 (RC). RCs can also be many

tiered, with an element of Ai in an RC breaking down into further RCs,

as Ai1 A

i2 A

i3 . . . A

iN . . . A*

i3 A*

i2 A*

i1, and so on, like a tree’s branches.

A famous modern example of simple X is John F. Kennedy’s “Ask not

what your country can do for you, but what you can do for your country.”

For elementary versions of RC, we can look at those limericks where the

fi rst line is repeated at the end.

X/RC is prevalent in the Homeric epics (van Groningen 1958), at

least partly because of its power as a mnemonic device. As memory is

often structured on an inner, underlying spatial form, the existence of a

going-there-and-back model could be at the root of X/RC. This would

account for, among other things, the epics’ use of a series of questions

and answers that are answered in exact reverse order, as in Odysseus’s

Doxiadis: Origins of Logic 89

questions to his mother, Anticleia, in Hades (Od. 11.171–203, summa-

rized in Reece 1995: 213):

A—What killed you? (171)

B—A long sickness? (172)

C—or Artemis with her arrows? (172–73)

D—How is my father? (174)

E—How is my son? (174)

F—Are my possessions safe? (175–76)

G—Has my wife been faithful? (177–79)

G*—Your wife has been faithful. (181–83)

F*—Your possessions are safe. (184)

E*—Your son is thriving. (184–87)

D*—Your father is alive but in poor condition. (187–96)

C*—Artemis did not kill me with her arrows. (197–99)

B*—Nor did a sickness kill me. (200–201)

A*—But my longing for you killed me. (202–3)

RC is not just mnemotechnics, however. Reece calls it “perhaps the most

important structuring device of oral narrative, building bridges between

the many components of the larger poem . . . weaving the digressionary

material into the larger fabric of the narrative.” Though it may have be-

gun as an unconscious mechanism and “survived for its mnemonic and

tectonic value,” it soon became “an aesthetic principle as well, becoming

a desirable and expected pattern of oral narrative” (220).

chiasmus and ring composition: from old form to new function

I focus here on the use of X/RC as a vehicle for the emerging process of

proof, in the microstructure of rhetorical speeches.4

Bassett was the fi rst to see in X/RC more than aesthetic value: “We . . .

may ask how far the chiastic order was determined by . . . [the] arrange-

ment of ideas . . . [along with] poetic economy and possibly the element

of surprise which sharpens the attention of the listener . . . [Potentially rel-

evant, too, is] the psychological factor, the advantage of using one idea to

suggest another, and thus to make the thought continuous” (1920: 59; my

italics). The importance of surprise cannot be exaggerated, especially

storyworlds volume 2 201090

when coupled with the seemingly antithetical notion of continuity. Real

understanding—by human beings, not machines—often depends on

sudden leaps of the imagination, surprisingly bridging, through insight,

what was previously a discontinuity—a concept at least as old as Plato’s

exaiphnês, the “suddenly” in which the Forms are revealed to the soul.

Paul Friedrich, proposing X as one of the elements of lyric epiphany,

writes of it creating “an illusion . . . of a synchronic, monocular vision of

an absolute aesthetic truth—usually with a radical closure” (2001: 218).

Like a joke, an X’s effect is not reducible to the sum of its parts: when

you try to explain it, you gain in clarity only what you lose in impact. It

is precisely this operation of X/RC that could be at the heart of the ex-

aptation process at work here. What was possibly invented and survived

initially for mnemotechnic use or its pleasing, symmetrical rhythm was

later used for its capacity to give continuity and unity to phrases that

could not be directly connected via the rationale of action representa-

tion—in other words, via the rationale for putting sentences together

that had been dominant until the fl owering of rhetoric.

In what follows I present a brief typology of X/RC in early classi-

cal speeches in an attempt to identify the point of transformation, the

historical moment when poetic storytelling practices are fi rst employed,

not to tell stories, but to show that one story is more convincing than

another. We cannot know to what extent this transformation was con-

sciously effected. But Socrates’ view of the rhetors and the sophists as

confi dence-tricksters could well be motivated by his belief that they

were merely playing with words, that they were, so to speak, “putting

the signifi er over the signifi ed”—which, in a very literal sense, is exactly

what they were doing.

Ring Composition as Cognitive Tool

The most basic tricks of rhetoric verbal prestidigitation were two, the

paradeigma, described by Aristotle as “rhetorical induction,” and the en-

thymeme, the “rhetorical syllogism.” I propose that these methods of ar-

gumentation are intimately related to RC and X.

A major example of the refi tting of storytelling practices, from po-

etic to logical uses, can be found in the rhetorical adaptation of the Ho-

meric use of paradeigma (Latin: exemplum). This is typically an appeal

Doxiadis: Origins of Logic 91

to a mini story, usually mythological, to justify a certain behavior. What is of particular interest is that the standard framing device for paradeig-ma in Homer is RC. Figure 1 presents an example, in abridged form: Achilles, addressing Priam, proposes that they set aside their mourning for Patroclus and Hector, respectively, and have dinner. This arrange-ment reinforces the injunction through analogy with the old story, in a way that is both continuous and, because of its symmetry, aesthetically pleasing—and thus more convincing.5

Fifth-century rhetoric borrows this structural model almost exactly, though the aim of the patterning changes, occasionally, from injunc-tion to demonstration. This change happens when an action phrase (“a did so”) becomes a state phrase (“a is so”), the verb morphing into the copula “is.” The central element of the RC can still be a mini story, but it is often a gnômê, as in the case of a speech by Lysias (c. 400 BCE) rep-resented in fi gure 2. A husband is defending himself for having mur-dered a man surprised in fl agrante delicto with his wife. Here he is ap-pealing to the fact that the punishment for adultery by Athenian law is death, arguing that he has done nothing more than apply the law him-self (Lamb 1930/2006: 21; bracketed phrases are mine, added for clarity).

To our more developed logical sense, the sequence 1 2 3 contains most of the defendant’s reasoning, with link 1–2 being a fortiori and 2–3 analogical. In terms of information given, 2* is mere repetition. But it is this that completes the RC, creating a continuous link from the defen-dant’s action to the court’s decision. Thus, it is not just the undeniable truth of 3 that makes the appeal (1*) much stronger than a mere “please

acquit me.” It is also the connectivity of the pattern.

1. Let us eat (601)

2. For even Niobe ate (602)

3. This was her story (603–612)

2*. She ate (613)

1*. So let us also eat (618)

Fig. 1. Abridged from the Odyssey 24.601–618 (Willcock 1964: 141). My numbering and formatting follow the standard notation for RC.

storyworlds volume 2 201092

One might argue that in this case the RC argument is more rhetori-

cal than logical. But that is exactly the point: at this historical stage there

is no clear demarcation of the two; and it is only through an examina-

tion of this intermediate stage that the roots of logic in poetic narration

are laid bare.

Chiasmus as Cognitive Tool

G. E. R. Lloyd (1966) has identifi ed analogy and polarity as two major

conceptual categories of archaic thought, both having roots in mythol-

ogy. The RC pattern we just described is obviously based on analogy,

whereas the two basic X-type arguments that follow—there could be

others—depend on polarities.

For an example of the fi rst X-type argument, let us look at how Gor-

gias, in the Encomium, disposes of the fi rst item in his division, that

Helen’s abduction was decided by the gods. A passage that seems pon-

derous and repetitious to the modern mind—these are standard accu-

sations against Gorgianic style—becomes razor sharp if we see it as the

extended X that it is. Thus, as shown in fi gure 3, the contrasting ele-

ments in 1 and 1* and the identical elements in 2 and 2* drive the outer

parallelism, while the central pair 33* is a gnômê that the audience can

naturally accept as true, in pure ABB*A* form.

It may be suggested that this passage too is an example of pure argu-

ment, without any narrative elements. However, there are three reasons

1. Wherefore I, sirs, not only stand acquitted of wrongdoing by the laws,

2. but am also directed by them [the laws] to obtain this satisfaction: it is for you

to decide whether they are to be valid or of no account.

3. For to my thinking every city makes its laws in order that on any matter

which perplexes us we may resort to them and inquire what we have to

do.

2*. And so it is they [the laws] who, in cases like the present, exort the wronged

parties to obtain this satisfaction.

1*. I call upon you to support their opinion.

Fig. 2. On the murder of Eratosthenes (Lamb 1930/2006: 21).

Doxiadis: Origins of Logic 93

why it is, again, something of a cultural centaur, half-argument and half-narrative. First, the outer elements 1 and 1* contain injunctions; in other words, the X leads from action to action (from “hold the right person responsible” to “acquit Helen”). Second, it is true that 2 and 3 begin with “for,” thus indicating a logical type of connection with the previous phrases, 1 and 2, respectively. But 2* and 1* are without such direct links, from 3 and 2*. Their existence and position is therefore pat-tern-dictated. The importance of form over content is seen especially in 2*, which is logically redundant—but completes the pattern. And third, it is too early in intellectual history to speak of pure argument; there is as yet no theory and no practice to support a formal syllogism. All there is, is a traditional way of weaving verbal patterns—here put to new use. Clearly, we have here another case of the form being stronger than the content: the poetic effect of X adds persuasive power to the construc-tion, a cognitive reinforcement of meaning that it would be misleading to call merely “logic,” in our modern understanding of the world.

The second type-X argument prevalent in rhetoric is guided by a spe-cifi c form of polarity, contradiction, already an accepted principle at the time.6 The central ABBA structure starts with two phrases that, together, form a hypothesis: “If a happens (A),” “then b happens (B).” The third element (B*) is a denial of B, either from the narration (“b did not hap-

pen”) or based on narrative possibility (“b couldn’t have happened”).

The fourth element, A*, completes the X pattern symmetrically.

1. Now if through the fi rst [will of the gods or decree of fate], it is right for the responsible

one to be held responsible;

2. for the gods’ predetermination cannot be hindered by human

premeditation.

3. For it is the nature of things, not for the strong to be hindered by the

weak,

3*. but for the weaker to be ruled and drawn by the stronger,

2*. God is a stronger force than man in might and in wit and in other ways.

1*. If then one must place blame on fate and on a god, one must free Helen [who is not

responsible] from disgrace.

Fig. 3. Encomium of Helen (my translation; Greek text in Diels and Kranz 1966: 289–90).

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The following is a simple example of this type, from Antiphon’s First Tetralogy, a “textbook” speech on a fi ctitious case, in which the prosecu-tor is accusing the defendant of having murdered a man and his slave in a secluded spot, motivated by personal enmity. In this passage, Antiphon

is trying to rule out one of the counternarratives (Maidment 1941: 55):

Malefactors are not likely to have murdered him, as nobody who was

exposing his life to a very grave risk would forgo the prize when it was

securely within his grasp; and the victims were found still wearing their

cloaks.

There is something strange about this simple X-pattern: the 1* has been moved to the top. In proper X form, as shown in fi gure 4, the argument would have read:

This arrangement totally conforms to Aristotle’s conception of a syl-logism as ex anangês (from necessity): if we accept 1, 2, and 2* as true, then 1* is a necessary conclusion. But it also exhibits the characteristic effect of the X that it is; specifi cally, it “tightens and closes; there is an element of inevitability as exit replays introitus” (Friedrich 2001: 241).

Figure 5 presents this type of argument in generic form, the arrows

marking the links from one phrase to the next:

Notice that links i and ii make linear sense, the fi rst logically (2 com-

pletes 1), and the second formally (2* is an anadiplosis of 2, a repetition

1. Nobody who was exposing his life to a grave risk [the malefactors]

2. Would forgo the prize (i.e. the cloak) when it was within his grasp.

2*. And the victims were found wearing their cloaks.

[1*. Malefactors are not likely to have murdered him.]

1. Counter-story A 2. Contains action B2*. Action Bdid not occur

1*. Counter-story A did not happen.

i ii iii

Fig. 4. Antiphon’s First Tetralogy argument, in proper logical form.

Fig. 5. The second X-type argument.

Doxiadis: Origins of Logic 95

of the last word of a sentence at the start of the next). But link iii is not justifi ed from the content of the previous phrase: there is no linear rule taking us from 2* to 1*. This linking can be explained only if we map the implicational connections (represented with dotted arrows in fi g-

ure 6) in two dimensions:

Thus, for the implication to hold we need links iv and v operating together. Now we can see the full power of X structure: though the text only states the four phrases in linear order, the X form encodes their re-lationships in a way that implies the latent connections. In other words, X linearly encodes a nonlinear pattern.

Figure 7 presents a longer example, from Gorgias’s Defense of Pala-medes, another mythological case. Here Gorgias builds a subnarrative with details from real-world knowledge:

1*. I did not commit treason. {INSTEAD OF: If I committed treason.}

2. Treasonable action must begin with discussion

3. [If] a discussion [occurs]

4. [It] implies [there is a] meeting,

4*. Which [meeting] was impossible [for]

5. no one could come to me and I could

6. not go to anyone, nor

7. could a written message be sent.

[3*. So there was no discussion.]

[2*. So there was no treasonable action.]

[1*. I did not commit treason.]

Fig. 7. Gorgias, Defense of Palamedes (my translation; Greek text Diels and Kranz 1966: 295–96).

1. Counter-story A 2. Contains action B2*. Action Bdid not occur.

1*. Counter-story A did not happen

i

iv

ii

iiiv

Fig. 6. The nonlinear expansion of the second X-type argument.

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Similar to the previous example, the X here starts with 1* (the nega-

tion of 1: “If I committed treason”). The form of the X in the speech

is 1*2344*, with 1 as well as 3*2*1* omitted, while 5–7 are outside the X

structure, offering additional evidence for 4*.

A mind trained in X/RC—as the classical mind undoubtedly was—

can naturally supply 3*–1*, and effect closure, as 1–4 is a cascading pat-

tern of questions and answers, the one leading to the other. We have

here a chase of the demonstrandum through a series of implied ques-

tions in Homeric form: (1) How would I have committed the crime of

treason? (2) To commit it, shouldn’t I have had a discussion with some-

one? (3) Wouldn’t this imply a meeting?

So, the second X-type argument has the generic form 1*23 . . . NN*,

where 1 as well as the rest of the sequence . . . 3*2*1* is omitted.7 The rea-

son why this is an X, despite the lacunae in its form, has to do with the

particular nature of rhetorical proofs, which are almost always gappy in

this exact way: the more obvious things are left unsaid. To be rhetorically

persuasive, a concatenation of phrases need only be complete enough to

lead a listener over its inevitably many gaps. In fact, Aristotle calls the en-

thymeme syllogismos ellipês (truncated syllogism), stressing that in rheto-

ric “the conclusion must neither be drawn from too far back nor should

it include all the steps of the argument”; the fi rst situation “causes obscu-

rity,” while the second “is simply a waste of words because it states much

that is obvious” (my translation; Greek text in Aristotle 1926: 288).

Conclusion

In a justly famous study, emblematic of the “narrative turn” in the hu-

man sciences, Jerome Bruner states: “There are two modes of cognitive

functioning, two modes of thought, each providing distinctive ways of

ordering experience, of constructing reality.” These are the logico-scien-

tifi c, which Bruner rather confusingly calls paradigmatic, and the narra-

tive. The two are “irreducible to one another,” and “efforts to reduce one

mode to the other or to ignore one at the expense of the other inevita-

bly fail to capture the rich diversity of thought” (1985:11).

That the two modes are irreducible to one another, however, does not

mean that they don’t interact. After all, narrative came fi rst: for many

Doxiadis: Origins of Logic 97

millennia it was the main language-related higher-cognitive activity in

existence. This cognitive ability supported the design and delivery of

particular stories, intricate artifacts, molded by the skills of their tellers

through centuries of practice. Archaic Greece had a strong storytelling

tradition, a tradition rich in patterns. When political and social change

created new demands on speech, in the fi fth century, older forms were

gradually adapted to new uses. My examination of the ways in which

narrativity and storytelling practices shaped both the generic form and

the microstructure of demonstrative speeches provides insight into the

intertwined genealogies of Bruner’s two modes of thought, suggesting

that though the logico-scientifi c mode is not reducible to the narrative,

it is at least partly derived from it.

Notes

I am most grateful to David Herman for his invaluable editorial suggestions.

My thanks also go to Pavlos Calligas, for setting me right on a couple of philo-

sophical points.

1. We consider here only the fi rst of the three subgenres of Greek rhetoric, foren-

sic, deliberative, and epideictic.

2. The way counternarratives are proposed in division, only to be discredited,

adopts the form of priamel, in another possible case of cultural exaptation.

This fi gure, whose fi rst extant uses are in Homer, takes the form of a series of

foils, proposed but then rejected in favor of the main subject of the poem. Here

is a typical priamel from Sappho (my translation; Greek text in Lobel and Page

1963: fr. 16).

Some say that cavalry, some infantry,

some a fl eet is the most beautiful [thing] on the dark earth,

but I say one’s lover.

3. The narrative mode also includes characters’ speech, in dialogue or thought

(monologue). These don’t appear in rhetoric, however, which makes use only

of indirect speech.

4. The only examination of the use of RC in rhetoric, to my knowledge, is

Worthington’s mostly macrostructural analysis of Aeschines and Deinarchus.

Worthington sees RC as a stylistic device, mostly employed by rhetors for the

post-trial rewriting of speeches, for “publication.” Interestingly, he correlates

presence of RC with historical fabrication, as “it is hard to reconcile the sophis-

tication of complex ring structures in some parts of a speech with historical

accuracy” (1994: 19).

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5. Interestingly, Nestle describes this common Homeric pattern as thesis-reason-

narrative-reason-thesis (quoted in Willcock 1964: 142).

6. The fact that Odysseus says enantiotata (“totally opposed things”) about the

defender, in Defense of Palamedes, is considered by the speaker tantamount to a

proof that he is lying.

7. One of the fi rst mathematical proofs of whose original form we have a more

or less clear picture, and which was contemporaneous with the fi rst extant

speeches of Antiphon and Gorgias, follows precisely the same type-X pattern

(Doxiadis forthcoming a, b).

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