Litotes, often confused with meiosis and understatement, has long suffered neglect. By comparing synonymous key words in previous definitions, this essay defines litotes as “a trope in which an affirmative is expressed by the negation of its opposite,” and for the first time classifies litotes into three subtypes based upon Aristotle’s study of opposition: contradictory, contrary and relative. Focusing particularly on the strong contradictory type of litotes and its realization in The Analects of Confucius, with its nearly one hundred double negation litotes, we find they prominently serve the logical functions of achieving high probability, providing a sophisticated major premise, and elaborating strict definitions. Further, the essay argues that this strong argumentative function in logic leads to litotes’ epistemic power, a promising dimension for future research.
Scholarship on figures of speech in the past decades has contributed greatly to exploring the functions beyond the aesthetic ([13,27,29]); however, most research only investigates a few popular tropes (metaphor and metonymy in particular), leaving many important figures still unattended. Litotes, a powerful argumentative figure, is unduly and unfortunately neglected, in rhetorical scholarship as well as in argumentation studies, and, despite its correlation with morpholexical signatures of negation, it is virtually unknown in computational argument studies. This essay begins a systematic investigation of the argumentative functions of litotes, first by briefly tracing its scholarly history and then by closely examining the Chinese classic of Confucius’ Analects, a particularly rich text for the exploration of litotes, in part because of its argumentative style and in part because of the special resources of the Chinese language. This inquiry combines qualitative research methods with a quantitative approach, progressing logically with description illustrated by preliminary statistics and sample analyses. The theoretical support comes mainly from Aristotle’s Categories , Rhetoric , and Interpretation , and from Perelman & Olbrecht-Tyteca’s The New Rhetoric: A Treatise on Argumentation  with valuable reliance on Wang’s Ancient Chinese Language  and Gao’s On Chinese Grammar .
This research is through manual inspection. The complications of litotes types make automatic detection challenging at this stage; certainly, computational detection could not catch them all currently (unless tuned so broadly as also to generate many false positives), so I proceeded by manual inspection of The Analects: multiple careful readings, line-by-line, to ensure completeness and precision. The results not only justify this process, but they identify the features which can help automate such processes in the future. The inquiry, while confirming litotes familiar roles, discovers several new argumentative functions.
2.A universal figure with negligible research
Litotes – most generally known as an affirmative expressed by the negation of its opposite (as in “litotes is not an insignificant figure”) – is ubiquitous. Negation, of course, is universal. Horn in his renowned A Natural History of Negation claims, “All human systems of communication contain a representation of negation.” (:xiii), and later in The Expression of Negation he adds it “is a sine qua non of every human language, but is absent from otherwise complex systems of animal communication” (:1). Burke, indeed, defines man as “Inventor of the negative” (:498), and Royce calls “[t]he not-relation… one of the simplest and most fundamental relations known to the human mind” (:265). But it is important to note that the function of this relation is not always direct negation, and litotes is the most pervasive way that negation is deployed to a different purpose; in fact, to its inverse purpose, affirmation.
Litotes is universal in ordinary language and in texts of all domains and genres – literary and historical; philosophical and scientific; trivial and profound. Litotes by negation frequently appear in Homer’s Iliad and Odyssey, Thucydides’ History of the Peloponnesian War, Cicero’s Brutus and De Oratore, Kafkas’ Das Schloss, More’s Utopia and King Richard III, Confucius’ Analects, etc. (cf. [12,19,30,31,38]) However, in sharp contrast to its prevalence in language, its prevalence in research is meager – only a few dozen articles and two monographs.11
The most systematic of this existing research is perhaps Hoffmann’s dissertation-based monograph, Negatio Contrarii: A Study of Latin Litotes . She defines litotes as an evaluative expression expressed through the negation of its opposite (:42) – we will return to this definition – and plots out the syntactic features, semantic properties and pragmatic functions associated with this account. The functions she finds are mainly argumentative: periphrastic, evaluative, focusing. The first two can be regarded as ethotic, and the last as effecting salience. This is a good start, but there are other argumentative functions; for example, logical functions. This study aims to prove that litotes can help establish the enthymeme, “the substance of rhetorical persuasion” (:20), with higher probability and more resistance to refutation, and that it can serve as a sophisticated major premise. Further, while Hoffmann and other researchers (such as [14,24,25,43]) have offered their respective definitions and touched upon litotic types, they have not provided adequate justifications, leading to considerable confusion. We seek, in this paper, theoretical support for understanding the key concepts of litotes, chiefly negation and opposition (shown in the next section), so to establish a solid definition and classification for the figure as a foundation for the argumentative functions and corresponding forms.
3.Definition and classification
Litotes, a Greek word, like many rhetorical terms, means ‘plainness,’ ‘simplicity,’ or ‘smallness,’ with alternate spellings such as liptote, lyptote and leptotes (:258–9). It first shows up in the rhetorical tradition with the first century BCE rhetorician Dionysius of Halicarnassus, who uses it in a general way to characterize the muted, understated style of Isocrates , and begins to associate with a specific device in the fourth century CE. The Grammarian Servius, for instance, calls it a “kind of figure” which “indicates the contrary” (:353n4). But – like many other rhetorical terms, most notoriously the figures – litotes accrues various overlapping and sometimes conflicting definitions over the millennia. The common features can, however, be extracted as a first pass at a stable and fruitful definition. In the established dictionaries we find accounts such as these:
A figure of speech, in which an affirmative is expressed by the negative of the contrary. (The Oxford English Dictionary )
Understatement in which an affirmative is expressed by the negative of the contrary (Merriam-Webster’s International Dictionary of the English Language )
A figure of speech in which an affirmative is expressed by the negation of its opposite. (The American Heritage Dictionary of the English Language )
In more scholarly treatments we get somewhat richer and more useful accounts for argument analysis, most of them adumbrating both form and function:
The figure of speech by which a (nearly always) evaluative expression is periphrased by the negation of its opposite. (Hoffmann : 42)
Litotes occurs when a speaker avoids making an affirmative claim directly and instead denies its opposite. Often this amounts to a double negative. (Farnsworth :204)
A stylistic device which seeks to highlight an idea, an impression or a judgement. The negation of the contrary idea takes the place of the simple affirmative expression, in order to give it greater weight, hence [Servius’s use of the] superlative, strenuissima. (Pontier, paraphrasing Porphyrio and Servius :353–4)
The similarities among these accounts mainly lie in the kernel of each definition, referencing the paired formal characteristics of negative/negation with the semantic properties of contrary/opposite.
But similar as they are, identical they are not. Even for the seeming synonyms of negative and negation in this context, the latter seems to fit more. In comparing these two and other related synonymous terms, Hass concludes that negation is “originary” and “generative,” as “[t]he Latinate suffix ‘-ion’ denotes a verbal action made into a noun, or made, we might say, objective, perhaps even concrete… Negation then becomes the actual or actualized activity of negating” (:11), an insight that led him to entitle his book, Hegel and the Art of Negation. With regards to contrary and opposite, in the interests of precision, they are even harder to treat as equal. The former is categorized as one type of the latter by Aristotle (as elaborated below), an understanding adopted by later logicians. With these considerations, favouring opposite and negation, a blend of the definitions from The American Heritage Dictionary and Hoffmann (using both terms), provides us with the best working foundation.
As to the type of figure litotes belongs to, these definitions reveal it to be clearly an intermediate kind, with traits of both the tropes and the schemes, much like simile. Simile is universally categorized as a trope because of its conceptual character. Like a metaphor, the prototypical trope, it maps features across conceptual domains. But the one that distinguishes it from metaphor is the presence of a comparison marker, in English like or as; that is, similes require morpholexical-syntactic indexes, which give them some of the formal character of schemes. Litotes is the same. All the litotic types (double negation, most notably) require morpholexical-syntactic indexes. Litotes has the conceptual character of tropes (hinging on opposition) and the formal character of schemes (requiring the presence of negation markers).
It has not escaped our notice that morpholexical-syntactic signatures of litotes make the figure a more tractable trope than most for computational purposes. Computers do much better with formal patterns than with conceptual patterns. Finding a litotes is an easier proposition for a machine than finding a metaphor or a metonymy. And, to the extent that its form correlates with a range of argumentative functions, finding them offers important potentialities for such jobs as argument mining.
But categorially, we do have a decision to make, one that is licensed by tradition. Litotes is overwhelmingly, like simile, regarded as a trope in the rhetorical literature, a treatment we find very congenial. Firstly (and again like simile), its effect leverages semantics far more than syntax or lexis. Unlike, say rhyme or isocolon or antimetabole, the form contributes little to its salience as a device. Secondly, even its morpholexical-syntactic signature is semantically restricted (to markers of negation and opposition). Thirdly, it seems reasonable, when both formal and semantic characteristics are present, to give the nod to semantics; in categorical terms, tropes trump schemes. These considerations bring us to our definition of litotes: a trope in which an affirmative is expressed by the negation of its opposite.
The subclassification of litotes, with its attendant definitions, offers further challenges. A few subclassifications have been adumbrated in the literature (e.g. [19,24,43]), but none of them come with satisfactory criteria, which leaves litotes looking like a hodgepodge of subtypes. We propose a classifying criterion keyed to the central concept in our working definition: Aristotle’s interpretation of opposition in Categories can well serve as a criterion for classifying litotes. The Philosopher says
Things are said to be opposed to one another in four ways: as relatives or as contraries or as privation and possession or as affirmation and negation. Examples of things thus opposed (to give a rough idea) are: as relatives, the double and the half; as contraries, the good and the bad; as privation and possession, blindness and sight; as affirmation and negation, he is sitting – he is not sitting. :19
A. Contradictory litotes (negation + negation)
a) Thus I consent, sir, to this Constitution, because I expect no better, and because I am sure that it is not the best. ()
b) It was without satisfaction that I recognized my own handiwork in a great cut under his right eye and a considerable discolouration round the socket. (:341)
c) His wife was always out of humor, his home always uncomfortable; and in his breed of horses and dogs, and in sporting of every kind, he found inconsiderable degree of domestic felicity. (:297)
B. Contrary litotes (negation + antonym of a lexeme)
C. Relative litotes (negation + correlation/meronymy)
a) The class is in chaos, but it is the students’ fault.
b) I just made moderate suggestions, as my position was to lead.
c) all teachers of English are experienced.
d) This plant is to be found everywhere.
Comparatively speaking, the relative type is most neglected in litotes studies, due to lacking adequate dimensions in understanding “opposite,” but it offers a promising scope for future inquiry; the contrary type seems to be the most generative, as it can produce countless litotes with the sea of antonyms, but sometimes we may hesitate about their real identity – whether the negation plus antonym is uttered intentionally to replace the affirmative form; the contradictory type, with its schematic double negation, proves most uncontroversial and distinguishes itself markedly from other related figures, such as meiosis, irony, and oxymoron. So it serves as a natural prototype of litotes and we take up its usages in a most influential Chinese classic, The Analects of Confucius ([10,11]).
5.Litotes in The Analects
The Analects is a collection of 20 passages recording mainly the dialogues between Confucius and his disciples on all major aspects of life. Since its assembly after the Master’s death (479 BCE), the text has exerted tremendous influence both inside and outside of China. Of the various Chinese and English versions, we have chosen the authoritative Liu Baonan edition (Qing Dynasty ) and D.C. Lau’s highly recognized English translation  to extract the typical litotes data for analysis.
Taking into account the three above-mentioned subtypes, it is no exaggeration to say that this classic is brimming with litotes. By concentrating on contradictory litotes – most identifiable for its highly schematic double negation (DN), and therefore also the most computationally amenable – we have detected throughout the entire collection (11750 Chinese characters), 97 DN pairs.55 They can be further divided into two: conditional double negations (CDNs) and non-conditional double negations (Non-CDNs); the conditional (66 pairs) mainly achieve logical function while the non-conditional (31 pairs) emphasize the affirmative.
The high frequency of DN litotes (near 100 pairs) may result from various factors, among which we attribute it first to the unusual richness of Chinese negators. According to Grammarian Wang (:260), there exist in ancient Chinese nine frequently used negators: “” (bù), “” (fú), “” (mú), “” (wù), “” (wèi), “” (fǒu), “” (fēi), “” (wú), “” (mò). In The Analects, all except “” (fú) and “” (fǒu) have appeared and we actually find one more adverb negator: “” (mò) collocated with “” (bù) for three times. Among all the negator collocations (about 20) in this analyzed text, the highest frequency goes to “” (bù)… “” (bù) (48 pairs), next “” (wú)… “” (bù) and “” (bù)… “” (wú) (11 for each). As stated by Lv  and Gao , “” (bù) (like not) is a dominating Chinese negator. Almost all the Chinese DN litotes are formed via two negators. As to the translated versions, the first negation is often formed by the negator of not, no, or never, in the order of frequency, the second negation either by a negator or a semantically richer negative word, such as unless or without. Comparatively speaking, DNs seem easier to formulate in Chinese (esp. ancient Chinese) because of its richer inventory of negators, and DN appears to achieve a stronger force with the prominently aligned negators than with one negator plus a negative lexeme (conjunction or preposition, etc.) or a negative-affix word.
As we will argue, however, litotes confers a distinctive style of argumentation. It condenses a subtle and resilient epistemic argument structure that both characterizes the ethos of The Analects and reflects the culture that has taken up and propagated its litotic formulations. On whether the preponderance of negators in ancient Chinese molded the argumentation of Confucius or whether Confucius harnessed that preponderance to his style, we have no position. It is a chicken or egg question. But The Analects presents us with a laboratory of litotes in which we can explore the argumentation of affirming by denying.
Typical examples follow, illustrating the two structures of litotic double negations. (Note: as you read through these examples you will see other instances of figuration – such as the epanaphora of 6 and the epistrophe of 8 – which exist in both the original text and in the English translation. We have not undertaken a study of these figures at this time. Litotes is a good day’s work on its own. But these examples should be enough to indicate how rich Confucius is, not to say how rich Chinese is, for further and broader research.)
5.1.Non-conditional double negations (non-CDNs)
Zǐ yuē: “Fù mǔ zhı¯ nián, bù kě bù zhı¯ yě.”
The Master said, “A man should be unaware of the age of his father and mother.” – Passage IV, Section 21
Zǐ yuē: “…shàng hào xìn, zé mín mò gǎn bú yòng qíng.”
The Master said, “…when they love trustworthiness, of the common people will dare not to show their true colours.” – Passage XIII, Section 4
Zǐ-gòng yuē: “…yán bù kě bú shèn yě.”
Tzu-kung (The Master’s disciple) said, “…That is why one really must be careful of what one says.” – Passage XIX, Section 25
5.2.Conditional double negations (CDNs)
Zǐ yuē: “Bú fèn bù qǐ, bù fěi bù fā.”
The Master said, “I never enlighten anyone who has been driven to distraction by trying to understand a difficulty or who has got into a frenzy trying to put his ideas into words.” – Passage VII, Section 8
Zǐ yuē: “Fēi lǐ wù shì, fēi lǐ wù tı¯ng, fēi lǐ wù yán, fēi lǐ wù dòng.”
The Master said, “Do not look it is in accordance with the rites; do not listen it is in accordance with the rites; do not speak it is in accordance with the rites; do not move it is in accordance with the rites.” – Passage XII, Section 1
Zǐ yuē: “Míng bú zhèng, zé yán bú shùn; yán bú shùn, zé shì bù
chéng; shì bù chéng, zé lǐ yuè bù xı¯ng; lǐ yuè bù xı¯ng, zé xíng fá
bù zhōng; xíng fá bù zhōng, zé mín wú suǒ cuò shǒu zú.”
The Master said, “When names are correct, what is said will not sound reasonable; when what is said does sound reasonable, affairs will not culminate in success; when affairs do culminate in success, rites and music will not flourish; when rites and music do flourish, punishments will not be exactly right; when punishments are exactly right, the common people will not know where to put hand and foot.” – Passage XIII, Section 3
Zǐ yuē: “Jǐ suǒ bú yù, wù shı¯ yú rén.”
The Master said, “Do not impose on others what you yourself do desire.” – Passage XV, Section 24
Kǒng Zǐ yuē: “Bù zhı¯ mìng, wú yǐ wéi jūn zi yě; bù zhı¯ lǐ, wú yǐ lì
yě; bù zhı¯ yán, wú yǐ zhı¯ rén yě.”
Confucius said, “A man has no way of becoming a gentleman he understands Destiny; he has no way of taking his stand he understands the rites; he has no way of judging men he understands words.” – Passage XX, Section 3, ending sentence of The Analects
These questions have compelling cultural implications as well. Many of The Analects’ most efficient expressions have entered Chinese culture with proverbial status, often as chengyu , and this includes its CDNs. Burke long ago suggested that proverbs, adages, and other condensed opinions or attitudes provide us with “equipment for living,” highly convenient and portable ways “of arming us to confront perplexities and risks” in everyday life (:61; see also 293–304). They provide a strategy for acting and they frequently imply the reasons for doing so. They are, in a very real sense, the taglines of arguments for culturally sanctioned conduct and belief (as illustrated in 5.3). We also know that proverbs, adages, and so on, are heavily figured in all languages: they frequently exhibit rhyme, assonance, isocolon, various strategies of repetition, and the like. Figuration is what makes them cognitively ‘sticky’; that is, salient upon first hearing, subsequently memorable, prone to cultural propagation. Fahnestock, picking up from a strain in Aristotle, tells us that figures
epitomize lines of argument that have great applicability and durability, and though these lines can be paraphrased in roundabout ways, they gain their greatest force in the stylistic concision of a recognizable figure. :xii
In answering the questions of what function CDN litotes serve and why that function is consonant with the argumentative style of The Analects, then, we are also answering questions that are suggestive about Chinese discourse and Chinese styles of argumentation as well. There are potentialities here for corpus research of a new sort: Are litotes more common in Chinese than in English? Is the presence of litotes proportionally significant among Chinese adages? In what contexts are they most prevalent? And the same questions can be asked for the entire panoply of rhetorical figures, with tremendous possibilities for charting universal, intra-cultural, inter-cultural, and cross-linguistic patterns of reasoning.
5.3.Logical function of CDN litotes
Logos in Aristotle’s Rhetoric comes in two basic flavours – by way of example (induction) or by way of enthymeme, which Aristotle glosses as rhetorical syllogism (deduction) – and Aristotle demonstrates his preference for the latter: “[s]peeches that rely on examples are as persuasive as the other kind, but those which rely on enthymemes excite the louder applause” (:26). The two modes are equal in persuasiveness, but deduction always feels somehow more powerful, certainly in Aristotle’s treatment. The Philosopher would have approved, then, of The Analects. All the above conditional double negation pairs function as, or contribute to, enthymemes, often characterized by two traits (:28): incompleteness (omission of one or more propositions) and probability (rather than certainty) of one or more premises. The CDN litotes of The Analects fulfill both of these requirements.
5.3.1.Achieving high probability
The conditional double negation sayings of The Analects are almost all of a probable nature, but they impress us as highly acceptable or extremely convincing. However – and this is the crucial point for the argumentative deployment of litotes – their affirmative counterparts often sound vulnerable. Take Example 4, (“I never enlighten anyone who has been driven to distraction…”), which is an adage frequently cited to justify kairotic education. Its affirmative sounds far from bright (“I always enlighten anyone who has been driven to distraction…”), and perhaps arrogant; we assume that even if the pupil has been driven to distraction, the Master may still not enlighten him if he does not show due respect, or if they are not at the right place or if some other required conditions are missing. Or, take 7, (“Do not impose on others what you yourself do desire.”) is irrefutable; but its direct affirmative, “Impose on others what you yourself desire” is highly problematic. The same with Example 8, (“A man has no way of becoming a gentleman he understands Destiny”) is unquestionably much more acceptable than its affirmative, (“A man becomes a gentleman if he understands Destiny”), for “understands Destiny” is just one necessary condition to be a gentleman who actually needs many other conditions to satisfy the qualifications.
To sum up, in each condition-result double negation pair, the condition is very often a necessary but not sufficient one. A non-sufficient condition cannot lead to a solid result. However, in the double negation, the Master wisely avoids the vulnerability of the corresponding affirmative proposition, by only stressing the indispensability of the necessary condition.88 Its probability, therefore, is increased high enough to resist almost all potential attacks. Or we may conclude that a proposition established by the conditional double negation proves much more acceptable with high probability in logic.
5.3.2.Making a sophisticated major premise
A typical rhetorical syllogism/enthymeme not only features probability, but truncation as well, often appearing with one or two propositions, leaving an implied reason or conclusion for the audience to infer, which not only achieves economy but also engages more interaction between the two parties . This is where conditional double negation expressions perform their outstanding role. The two brief dialogues below between Confucius and his son, Boyu, illustrate well the persuasive brevity of the CDNs.
(Have you studied Shi?)
(Whoever study Shi cannot speak well.)
These two dialogues took place in two days when Confucius inquired of his son about his study of the two classics. After receiving his frank replies, the Father each time instructed with just one non-imperative sentence; however, according to the context of that passage the son immediately studied the relevant text. That is, Boyu obeyed both instructions, though no instructions were in fact given; rather, he was given epitomized arguments framed by litotes. These two conversations present us with two forceful enthymemes with the major and minor premises, but leaving the conclusions for the interlocutor to deduce by himself:
|Whoever study Shi cannot speak well.||(Major premise)|
|[I have] Not [studied Shi] yet.||(Minor premise)|
|I cannot speak well unless I study Shi.||(Inferred conclusion)|
|Whoever study Li cannot establish himself.||(Major premise)|
|[I have]Not [studied Li] yet.||(Minor premise)|
|I cannot establish myself unless I study Li.||(Inferred conclusion)|
Almost all the conditional double negation expressions in The Analects serve as major premises to construct enthymemes either in combination with another proposition, or in certain contexts as one-proposition rhetorical syllogisms. For example, suppose one student, curious about the kitchen of the school canteen, is discussing with his classmate:
A: Let’s have a look at the kitchen.
B: Do not look unless it is in accordance with the rites/allowed or invited.
|Do not look unless allowed or invited.||(Major premise)|
|We are not allowed or invited.||(Implied minor premise)|
|We should not have a look [at the kitchen].||(Inferred conclusion)|
5.3.3.Elaborating a strict definition
In addition to achieving high probability and serving as nuanced major premises, the conditional double negations in The Analects sometimes are also used to aid in making a strict but elaborate definition, for example:
Yán Yuān wèn rén. Zǐ yuē: “kè jǐ fù lǐ wéi rén. …” Yán Yuān yuē:
“Qǐng wèn qí mù.” Zǐ yuē: “Fēi lǐ wù shì, fēi lǐ wù tı¯ng, fēi lǐ wù
yán, fēi lǐ wù dòng.” Yán Yuān yuē: “Huí suı¯ bù mǐn, qǐng shì sı¯ yǔ
Yen Yuan (the Master’s favorite disciple) asked about benevolence. The Master said, “To return to the observance of the rites through overcoming the self constitutes benevolence…” Yen Yuan said, “I should like you to list the items.” The Master said, “Do not look it is in accordance with the rites; do not listen it is in accordance with the rites; do not speak it is in accordance with the rites; do not move it is in accordance with the rites.” Yen Yuan said, “Though I am not quick, I shall direct my efforts towards what you have said.” – Passage XII, Section 1
6.CDN litotes as epistemic
Up to now, we have seen that conditional double negation litotes in The Analects performs a very strong logical function. These highly prized CDN adages, often as major premises, have been passed down, generation after generation, solidly establishing themselves as part of common sense, shared knowledge and guiding principles – the doxa – applied to various arguments in all domains, from daily activity to scholarly research; and they have extended gradually beyond Chinese culture to other cultures.
In this light, the CDN litotes, when employed to state things generally, prove to be knowledge generative or technically speaking, epistemic. Perelman and Olbrechts-Tyteca in the manifesto-like “Conclusion” of The New Rhetoric: A Treatise on Argumentation, note that “[w]e combat uncompromising and irreducible philosophical oppositions presented by all kinds of absolutism: dualisms of reason and imagination, of knowledge and opinion” (:510). This is an ethical statement, of course, enforcing the Belgians’ commitment to an argumentation that fully accommodates, respects, and advances values. But it is an epistemic statement as well, a key part of their credo for an ethics of reason and the warrants of knowledge. Their argumentation justifies that opinions to which the strong “adherence of minds” (:45) is forged should be no other than securely founded knowledge. CDN expressions with high probability as we see above (Examples 4, 7, 8, etc.) are undoubtedly well justified opinions which can be catalogued as one type of knowledge, and litotes, we therefore also see, is a figure that effectively epitomizes and successfully propagates such knowledge.
Masse, in his research on the epistemic dimensions of litotes in early modern scientific discourse, summarizes the conflicting features of oppositional knowledge: “In the one case, oppositional knowledge leads to algorithmic succinctness; on the other, it provides stumbling and building blocks, and thus loquacity” (:121). The first case is epitomized by CDN litotes.
Not all litotes are epistemic, however, from what we have seen; judging the three subtypes identified above – contradictory, contrary, relative – we note that the last two usually offer situational responses which do not generalize or are not serious enough to propagate as knowledge. At least, their epistemic power requires more evidence than we could find, or than The Analects appears to offer. Rather, it is the contradictory type, conditional double negation in particular, that generates views rational enough to be treated as knowledge. As to the features of the litotes-generating knowledge, besides the algorithmic succinctness Masse identifies, we conclude that what CDN knowledge features most, is its high probability which can well justify its objectivity and acceptability.
The rich variety of negators in ancient Chinese may partially account for the pervasiveness of DN litotes in The Analects; however, we argue that what is important about them lies in the various argumentative functions they successfully perform. With regard to the function of litotes, previous studies have mainly revealed its highlighting (), evaluative (), understating () roles, which are primarily vehicles of ethos (especially the last two in combination). While some litotes in The Analects certainly exhibit the highlighting function and the ethotic features of being euphemistic, modest, or cautious, we show that the most prominent function of the most prominent litotes, conditional double negation, is to achieve the strong logical function, the irresistible high probability in particular, and hence correspondingly realize the epistemic power of knowledge producing, accumulating and disseminating.
This epistemic logical function of litotes contributes to the project of shedding a new light on figure studies, of freeing them from the aesthetic cave, to reveal the cognitive dimensions and the argumentative contributions they make to discourse. More particularly, our exploration of this litotic function, like the other contributions to this special issue, contributes to the enterprise of computational rhetoric, the enterprise of plumbing such functions with the powerful machines and perceptive algorithms of our age. Because litotes is a trope, it implicates directly the semantics of discourse, making it especially valuable for such meaning-probing tasks as text summarization and argument mining. But because of its schemic elements – its morpholexical-syntactic signatures of negation – litotes is also more tractable computationally than most semantic figures.
Among the diverse goals we seek in this essay, we would be most pleased to find it has sparked more and deeper studies into litotes, to begin redressing the great disparity between the scanty research and universality of litotes. Viva litotes!
1 Most closely related articles have been included in Sections 2 and 3; the two monographs are Hoffmann’s Negatio Contrarii , illustrated in the next paragraph, and Mathias Mayer’s Franz Kafkas Litotes: Logik und Rhetorik der doppelten Verneinung . Other significant work on litotes in this narrow group includes articles by van der Wouden , Horn , Neuhaus , and the very recent work by Horn .
2 This integration might be controversial (or needs further illustration), as noted by one reviewer who observes that privation has not been discussed in connection with litotes. But nothing much hinges on our absorption of privation (rather than the strategy of ignoring privation that others adopt). In any case, the neglect of privation by other thinkers on litotes certainly supports our three subcategories of litotes.
3 In Horn’s “Duplex, negation, affirmat, … the economy of double negation,” the happy/unhappy pair is treated as “contrary opposition,” white/non-white as “contradictory opposition” . This is confusing, for the semantics of all negating affixes mean not, which is definitely regarded as contradictory by Aristotle. So we treat them equally as contradictory.
4 As Hoffmann  summarized that adjectives should be most active in forming this type of English litotes, here are more examples: “John is a man of no common ability.”; “This is no rare occurrence.”; “It gave me no small pleasure to receive a letter from you.”
5 We exclude, of course, non-affirmative double negations, especially parallel negations. For example:
(Tzu-Kung [Master’s disciple] said, “Poor without being obsequious, wealthy without being arrogant. What do you think of this saying?”) – Passage I, Section 15.
6 A meticulous reviewer suggests offering interlinear translation/glossing, but that is extremely hard for ancient Chinese; so we choose to provide phonetic transliteration between each Chinese and English version, as usually done.
7 Quite a few books on figures of speech have touched upon this type (not… + without/unless), but not yet used the name of conditional double negation, e.g. Xu (:283): “We can’t learn English well without watching out for idiomatic ways of saying things.”; and “You will not succeed unless you work harder.” In Farnsworth (:210), when discussing litotes’ function of definition, he actually cites a CDN created by Melville in Moby-Dick: “Had these Leviathans been but a flock of simple sheep, pursued over the pasture by three fierce wolves, they could not possibly have evinced such excessive dismay” (:362) (The italics in the last example are made by the author to be consistent with the other two.) So we have a reason to treat CDN as a subtype of contradictory litotes though a CDN is not entirely the same as its corresponding affirmative.
8 Even if the condition is sufficient, it is still often seen in DN, for example in Laotse’s adage:
It is because he does contend that he is without reproach. 
Here, “ (contend)” is a sufficient condition of “ (reproach)”.
9 These translations are partially done by the author, as Lau’s version is not desirable enough. Shi and Li are two classics, the former is a collection of poems reflecting life in Zhou Dynasty (11–6BC), the latter, a compilation of rituals observed in preQin periods.
I would like to thank very gratefully, Randy Allen Harris, for his tremendous contribution to this article – from the early stage of enlightening discussions to the later period of very substantial revision and meticulous edits in all aspects. I regard this work as definitely coauthored, which is one of the reasons I opt for the academic we throughout, to indicate the plurality of this research. But Prof Harris resolutely left out his name. [Editor’s note: I have been firm on this point not because of any wish to dissociate myself with this paper, nor with the superb research of Ying Yuan, but because I regard it as bad form for an editor to include work of his/her own in a volume he/she has edited. I have also, of course, as all editors do, put in an oar with other contributions to this volume, and even taken the rudder for short times – RAH]. I also wish to thank sincerely Jeanne Fahnestock, Yameng Liu, Mingan Luo, Chrysanne Di Marco, Jelena Mitrović, and two anonymous reviewers who have greatly encouraged and benefited this exploration in various ways. Further, this research has been supported by Chinese National Social Science Fund Project: “On Argumentative Textual Functions of Major Tropes and Schemes” (15BYY178).
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