The speech act of denying operates on words and on sentences.

1. Word negation

The lexical relation of opposition can connect morphologically different words, or pairs of words produced by prefixation.

The attachment of a prefix to a base word or to a root morpheme produces a new word, belonging to the same grammatical category. Negative prefixes produce derived negative terms. The base term and the derived terms are antonyms, that is opposites.

Frequently, the derived negative word serves to add a “not” to the whole semantic content of the positive word:

agree, agreement => don’t agree / dis-agree / dis-agreement.

Negative derived words do, however, tend to become independent:

they made, reached an agreement / they made, reached ^≠a disagreement

The specific nature of the opposition between base and derived words is idiosyncratic, that is, it is not possible to attach a semantic-lexical rule to the negative prefix in order to pinpoint the meaning of the derived word from the meaning of the base word.

Various negative prefixes can operate on the same basis:

social => unsocial, asocial, antisocial, nonsocial (after WCD)

Some dis- words do not have a positive counterpart, but are clearly negative, for example to discard: “to get rid of… useless, unwanted.” (MW, art. Discard).

Argumentation based on derived words is characterized by the fact that it leaves aside the variation of meaning between the base word and its derivative, in particular negative derivatives, S. Derived words.

2. Sentence negation

A negative statement E1 can be analyzed as not-E° (but cf. 2.3). Total negation rejects E° as globally untrue, incorrect, inadequate; it dismisses, turns down, refutes, rebuts, rectifies, … the primitive statement E°. Partial negation rectifies a segment or a feature of E°.

From the point of view of practical argumentation analysis, and following Ducrot (1972), there are three main types of sentence negation.

2.1 Dialogic negation

E° corresponds to an existing statement previously produced by another participant in the same linguistic action. This “confrontational metalinguistic negation” (Ducrot 1972, p. 38) is basic for refutation. Examples (after Ducrot, s. d).

— Rejection of a claim:

L0:   — The next presidential election will be held in two years.
L1:   — No, it will take place next year.

— Invalidation of a presupposition:

L0:   — Peter stopped smoking
L1:   — No, Peter never smoked.

— Rectification of the degree:

L0:   — Flood damages are substantial
L1:   — No, they are not substantial, they are indeed negligible / catastrophic.

— Correction of a linguistic rule:

L0:   — Look at the childsi
L1:   —No, Not the childs, the children.

— Correction of a contextual mismatch:

Student to teacher: — Wyhh, it’s 3.30! (end of class; in a whining and demanding tone)
Teacher to student: — No, it’s not 3.30! (said in the same tone), it is 3.30 (said in a factual and positive tone)

When working on a corpus of texts or argumentative interactions, the practical rule for the analysis of a negative statement E1 = “not E°” is to browse through the previous context for an addressed statement E° (or something close to the semantic content of E°). If there is one then, E1 rectifies E°, and the precise nature of the rectification can be specified, in the broad context of the argumentative question structuring the exchange.

E° may be in the “short” or “long” memory of the interaction. When dealing with a complex argumentative situation, that is to say with a question debated at different times, on various places according to several genres and formats, the discursive distance to retrieve E° may be rather long.

2.2 Polyphonic negation: E° is not recoverable in the context

There is no actual statement or semantic content corresponding to E°, for example when the speaker of E1 anticipates a foreseeable objection, S. Prolepsis. In that case, according to Ducrot’s original and robust version of the polyphonic nature of language, we can consider that the negative utterance articulates two voices, that of the rectifier and that of the rectified. As in the preceding case, the speaker adopts the position of the rectifier. Ducrot speaks in such cases of “conflictual polemical negation” (ibid.).

The two uses of negation, according to whether E° is or is not recoverable in context, are perfectly continuous. If the E° statement cannot be recovered in the immediate context, one will opt for a polyphonic analysis, referring the contents to voices, and not to actual participants, S. Interaction, Dialogue, Polyphony. There will however remain some doubt as to the precise scope of the rectification operated by the negation.

2.3 Descriptive negation

Ducrot mentions the case of a “descriptive negation”, which could not be split into two antagonistic voices:

Some uses of a syntactically negative sentence have neither conflictual nor opposing character. Negation is used without paying attention to its negative character, without, therefore, introducing into it any idea of dispute or doubt. Thus, to point out that today the weather is perfectly fine, I can use a negative sentence “not a cloud in the sky” as well as a positive sentence “the sky is perfectly blue and clear”. (Ibid.)

Such negative sentences have an autonomous meaning. This analysis is suitable for negative polarity statements, from which it is impossible to retrieve an underlying positive statement:

You can’t hold a candle to him.

It is also appropriate for negative prefix words without corresponding positive terms (see above).

3. Denying

The dialogic character of negation is systematically exploited in psychoanalysis, in which the negative utterance is considered to be the result of a negotiation between the conscious and the unconscious:

The manner in which our patients bring forward their associations during the work of analysis gives us an opportunity for making some interesting observations. “Now you’ll think I mean to say something insulting, but really I’ve no such intention.” We realize that this is repudiation, by projection, of an idea that has just come up. Or: “You ask who this person in the dream can be. It’s not my mother.” We amend this to: “So it is his mother.” In our interpretation we take the liberty of disregarding the negation and of picking out the subject matter alone of the association. It is as though the patient had said: “it’s true that my mother came into my mind as I thought of this person, but I don’t feel inclined to let the association work.”
Thus the content of a repressed image or idea can make its way into consciousness, on condition that it is negated. Negation is a way of taking cognizance of what is repressed; indeed it is already a lifting of the repression, though not, of course, an acceptance of what is repressed. We can see how in this the intellectual function is separated from the affective process. (Freud, [1925], p. 235)

4. Argumentative strategies using various forms of negation

The relation between discourse and counter-discourse is fundamental for the definition of an argumentative situation, negation and denial are therefore at the very foundation of argumentation studies.

S. Contradiction; Non contradiction principle
Figures of Opposition
Opposite words;— Opposites – A contrario —  Refutation by the opposite
Destruction of Speech; Objection; Refutation; Counter-argumentation.

To demonstrate comes from the Latin demonstrare “to show, to point out”. To demonstrate and to show verbs are synonymic in some contexts: “in what follows, I’ll show (= demonstrate) that…”.
In ordinary life, people engage in demonstrations of friendship, solidarity, affection… making an exhibition, a show of their sentiments, as they give proofs of love.The word demonstration, even in its most abstract uses, keeps a link with the visual and pictorial; if a proof involves touching with the finger, a demonstration shows. Argumentation has no such metaphorical backgrounds; it originates and deploys within language.

In rhetoric, besides the meaning of “proof”, the word demonstration is used with two totally different meanings.
— A demonstration is a vivid representation of an event or a state of affairs as a picture, for an audience or a reader, put in the position of witness of the represented event. This figure is also called evidence or hypotyposis (Lausberg [1960], § 810).
—The demonstrative genre is another name for the epideictic or panegyric or laudatory genre, next to the deliberative and judicial genres (Lausberg [1960], § 239).

Demonstration is often opposed to argumentation as defining two different cultures without contact and communication, the world of science vs. the world of human affairs, the world of truth vs. that of opinion. This popular opposition is often considered a definitional characteristic of argumentation. Nonetheless, its substance and actual scope, the precise relations between argumentation and demonstration, should be considered as an essential issue for the development of argumentation studies.

1. The hypothetico-deductive demonstration, ideal of proof?

In logic, a demonstration is a discourse proceeding from axioms to theorem, according to specified deduction rules. The construction of a demonstrative sequence is guided by intentionality, since it aims at a stopping point, a remarkable, detachable result, the theorem.

A proof has been formalized if it can be presented as a mathematical demonstration. Formal proof is seen as characteristic of science as pure calculus, and is sometimes considered as the ideal of proof. This vision is contrasted with science as a description of reality (geography, zoology), or as a combination of calculation, observation and experimentation (physics, chemistry).

In the sciences, a demonstration is a discourse, bearing on true propositions: (true by hypothesis; or as a result of observations or experiments carried out according to a validated protocol; or as results obtained from previous demonstrations), and leading to a new, stable, true, proposition. Such a proposition marks a step forward in the field, and is likely to guide further developments in research.

Scientific practice presupposes many non-formal linguistic, cognitive or material operations, other than demonstration. Such operations might include grasping a situation, formulating the problem, conceiving a hypothesis, defining an experience, realizing an experimental setup, manipulating the objects and instruments, selecting, observing and describing the relevant data, making quantitative measurements and the relevant calculation, checking the results, imagining new experiences, drawing conclusions, editing the results for oral communication and publication, answering the colleagues’ objections, revising the claims, etc. We might add to this all the professional argumentative situations in which researchers must apply for new funding, write or evaluate a research project or to employ a new colleague. These argumentative operations require the coordinated management of technical, mathematical and natural languages, including a variety of semiotic media, figures, tables, schemes and diagrams. Argumentation in natural language plays a key role in all these mixed activities.

2. Two distinct fields: What we know, what we do

Argumentation deals with what is to be believed. Argumentation concerns the question of proof and demonstration, but goes beyond this. The exploratory function of argumentation extends beyond its epistemic role, to practical discussion (internal or external) of what, in view of one’s current interests, would be the most sensible next move. So for example, one might ask, “should I apply for this or that position, buy this or that car, ignore or accept offers of negotiation”. And human affairs extend still further, beyond the realm of practical decisions; generally speaking, argumentative situations emerge as soon as any kind of choice is possible. Argumentative situations can thus arise in regard to antagonistic feelings, what is really worthy of admiration or love, S. Emotions. In these areas the language of proof and demonstration does not makes sense, whereas the language of argument does.

One might think that in the case of certain issues concerning true beliefs and accurate scientific predictions, doubt is provisional, and that any doubt will be removed in view of scientific progress. When considering situations involving human agents, however, doubt is an essential component. In such situations, it is often impossible to completely dispel doubt, and one can legitimately ask what would have happened if …

We turn to argumentation when the data is incomplete or of poor quality and the assumptions and laws imperfectly defined; the deductions are, therefore, subject to a continuous principle of revision. As the last resort, we are referred to the question of time: an argued claim is a bet. Linked with urgency and occasion, argumentation is a time-limited process, different from the unlimited time afforded to the philosophical or scientific demonstration. There are essential differences in the modus operandi of argumentation and demonstration, their fields of application and the kind of problem they can apply to.

When operating in the field of knowledge, argumentation has an exploratory and creative function which goes beyond its demonstrative and critical function, S. Abduction. Argumentation produces hypotheses, opens up discussions and triggers the critical process of verification and revision.

Demonstration is by definition related to a domain; argumentation may combine heterogeneous evidence. Argumentation is the art of hierarchizing not only values^,, but also proofs and demonstrations. If one wants to explore the possibilities and economic interests of a major environmental management works, constructing a channel between the Green and the Yellow Oceans, for example, then the technical proofs, solutions and objections offered by geologists, economists and ecologists must be articulated and confronted with those of neighbors, citizens, investors and politicians. The negotiation will take place in view of calculations and technical proofs each as unique as the others, and argumentation in natural language will have to fully exert its synthetizing function.

3. Argumentation-proof and argumentation-demonstration:
The heritage

Several theories of otherwise very different orientations come together in order to oppose argumentation to demonstration. Historically, the notions of demonstration and argumentation inherited through Western tradition were developed in ancient Greece. Demonstration in science and mathematics (Archimedes, Euclid) was built without relation to argumentation in social affairs. According to Lloyd, Aristotle elucidated “the explicit concept of rigorous proof” ([1990], p. 77) in a scientific context where four types of argument were currently used:

The first of these is arguments in the legal and political domains, the second those in early Greek cosmology and medicine, the third mathematics in pre-Aristotelian period, and the fourth deductive arguments in philosophy. The first two relate primarily, to informal, the second pair to rigorous proof. (Ibid.)

The unity of the disciplines of proof can be shown by the examination of their vocabulary:

The same vocabulary, not only of evidence, examination, judgment, but also proof, appears also outside the specifically legal or political domain, notably in a variety of contexts in early Greek speculative thought. Both cosmology and medicine, and some extended passages from the Hippocratic Corpus merit particular attention. (Id., p. 78)

In Aristotle’s work, convincing rhetorical argumentation is characterized by its differences with valid logical demonstration (and probable dialectical deduction). Since then, argumentation has been conventionally referred to logical demonstration, to argumentation-demonstration, and not to argumentation-proof such as exemplified in the practices of scientists, practitioners, historians, police investigators, etc. Argumentation is most strongly linked to these practices, in virtue of its substantial nature and its relationship to practical action. For example, the essential concept of argumentative question does not derive from a logical concept, but from the medical descriptive concept of stasis, that is a state in which physiological fluids are blocked, and, metaphorically collaborative speech and actions are suspended.

This non-operational opposition between demonstration and argumentation, which now functions as a commonplace, has been considerably restated and strengthened by the New Rhetoric, as well as by the non-referentialist positions of the theory of Argumentation within Language.

4. Demonstration against argumentation?

Demonstration and logical proof are classically opposed to argumentation on the basis of their premises and modes of inference. Things go much deeper than that, however. Natural language and discourse are inherently subjective, that is self- and we-related, focused on the “here” and “now”, S. Subjectivity. Words allow synonymy, homonymy and polysemy; their meaning is context-sensitive. Syntactic constructions must be interpreted. Discourse is figurative. Meaning and reference are negotiated and managed by relevance principles. These processes are stigmatized as being inherently “vague and elastic”; but the polymorphism of language should simultaneously be praised for its adaptability to new situations and its rule-changing capacity.

At a general level, it should be noted, firstly, that there is no reason to favor elementary logical demonstration over other scientific activities, of which it is, unquestionably a distinguished member. Secondly, oppositions make sense only if the opposed domains are comparable. Experimentation, mathematics, computerization, have taken the techno-sciences worlds apart, and it does not make much sense to compare a paper in a scientific journal publishing cutting edge research with a column in a newspaper.

4.1 The New Rhetoric

Perelman & Olbrechts-Tyteca’s Treatise has constructed a powerful, autonomous concept of argument by rejecting emotions out of the field of argument on the one hand, and by setting argumentation against demonstration on the other. The purpose of the Treatise is to circumscribe an autonomous discursive domain, where speech develops cut off from demonstration and emotion. In the very words of the Treatise, the couple argumentation / demonstration functions as an “antithetical pair” (Perelman & Olbrechts-Tyteca [1958], p. 422.), whose terms are the subject of a genuine “breaking of connecting links” or “dissociation” (id. p. 411 sq.). Systematically, the Treatise opposes argumentation to demonstration, as can be checked on every occurrence of the word demonstration mentioned in the index. This strategy, constitutes one of the building blocks of the Treatise.

The fundamental question of the difference of languages between argumentation and demonstration, is not addressed. In the Treatise, the form of demonstration opposed to argumentation is taken in a particular discipline, formal logic, which would be prototypical of demonstration as the inaccessible ideal of argumentation. This hardened and simplified image of demonstration promotes the antagonism argumentation / demonstration. This results in the exclusion of anything concerning sciences from the Treatise:

We seek here to construct such a theory [of argumentation] by analyzing the methods of proof used in the human sciences, law and philosophy. We shall examine arguments put forwards by advertisers in their newspapers, politicians in speeches, lawyers in pleadings, judges in decisions, and philosophers in treatises ([1958], p. 10)

No reference is made to any kind of scientific activity. Argumentation addresses human affairs only, and demonstration concerns mathematics and science. exclusively. The gap between “the two cultures” (Snow, 1961) is thus effective at the very foundation of argumentation as a discipline.

4.2 The Argumentation within Language theory

This theory considers that argumentative orientation is an essential characteristic of the semantic level of language, and concludes to the impossibility of developing argumentation as good reasons in discourse and interaction. Consider the following passage:

It has often been remarked that discourses concerning everyday life cannot achieve “demonstrations” in the logical sense of the word. Aristotle already noted that, by opposing to the necessary demonstration of the syllogism the incomplete and only probable argumentation of the enthymeme. Perelman, Grize, Eggs insisted on this idea. At first I thought I was merely following this tradition, my only originality being to refer to the nature of language the necessity of substituting argumentation for demonstration. I thought that the words of language were the cause or the sign of the fundamentally rhetorical, or, as we said, the “argumentative”, character of discourse. But I am now led to say much more. Not only do words not allow demonstration, but likewise they do not allow that degraded form of demonstration that would be argumentation. Argumentation is only a dream of discourse, and our theory should rather be called « the theory of non-argumentation” (Ducrot 1993, p. 234).

As Ducrot’s structuralist framework reduces the order of speech to that of language (Saussurian langue), it is quite coherent to deny any principle of intelligibility to argumentation in discourse.

5. Arguing the non-demonstrative character of argumentation

The refutation of the possibly demonstrative nature of ordinary discourse is threatened by skeptical paradoxes and exposed to self-refutation. It is difficult to argue about the argumentative or non-argumentative character of natural language discourse, whilst using natural language discourse.

Interaction studies have taught us a great deal about what everyday life discourses can achieve. Brief, local reasoning is accomplished in sequences in which language combines with action to achieve operational conclusions. We define, categorize, articulate causes and effects, and make analogies, which are all more or less insufficient, but which are all susceptible to criticism and rectification. Sometimes, these result in the satisfaction of all parties concerned.

By means of some conventions and adjustments, more sophisticated reasoning episodes can be developed in ordinary language. If the syllogism constitutes an example of a necessary demonstration, since the syllogism consists of a sequence of utterances in natural language, words allow at least syllogistic demonstration. All the same, figures and calculus are not entirely foreign to natural language, which also allows for some correct geometrical conclusions, so that the tenon exactly fits the mortise. Not only a logic, but also an everyday geometry, arithmetic, physics… underpin linguistic practices, and no metaphysical lack stops them from concluding properly, as shown by the following little calculation:

The Abbé du Chaila is one of the essential architects of the repression of the Protestants of the Cevennes, in Southern France. His murder is the origin of the Camisards’ war, in the 18th century.
The date of birth of the future abbot of Chaila remains a mystery, due to the disappearance of parish registers. It should be at the beginning of the year 1648. Indeed, François’s parents, Balthazar de Langlade and Francoise d’Apchier, were married on the 9th of April 1643 and had successively eight boys and two girls in ten years, at a rate of a child a year. François being the fifth child of the family was thus born in 1648, the four previous brothers being born in 1644, 1645, 1646 and 1647.
Robert Poujol, [The Abbé du Chaila (1648-1702)], 2001[1].

Any assertion about the demonstrative character of argumentation in general is hard to assess, regardless of the prestige of the authority supporting it. Arguments from natural signs, case-by-case arguments cannot be treated as an appeal to authority or arguments by analogy. Ordinary argumentative discourse might combine entirely heterogeneous types of arguments and fields of evidence, including rather technical and scientific episodes. One might argue correctly in natural language; sometimes, some truth emerges from judicial and historical debates when properly framed and managed; and argumentation plays a role in science acquisition.

6. Argumentation in science education

Other connections have to be found between argumentation and scientific activities. The great rule followed by Quine to construct his formal logic shows the way:

This course is prompted by an inclination to work directly with ordinary language until there is a clear gain in departing from it. (1980, p. x).

Mutatis mutandis, we will say that the teaching and learning of scientific method are necessarily anchored in natural language and everyday argumentation, and that they depart from them only when they find a decisive gain in doing so. This leads to a focus on argumentation as an instrument for knowledge acquisition.

Demonstrative-scientific proof can be considered, on the one hand, as a finished product, impeccably exposed in published papers and textbooks; and, on the other hand, as a process, which can leave room for dialogue, arguments and rectification and progression. Argumentation being on the side of the process, its claims are in the making. It might therefore be an interesting option to orient the arguer’s capacity towards the exploration of scientific domains, monitored by competent advisers.

Finally, we must consider the question as to whether there is a break or a continuity between argumentation and demonstration. This is certainly a very important philosophical and epistemological issue, yet it is quite different from the empirical issue as to how best to construct scientific capacities. The teacher might consider that the gap is a fact (Duval 1992-1993, 1995) and choose to break with ordinary language and practices, as did teachers of “modern mathematics” in the seventies in France. They might otherwise try to use everyday capacities to build knowledge. Gap and continuity are pedagogical choices and constructs.

Science acquisition, scientific “enculturation” and education are key situations for the development of argumentation studies (Erduran & Jiménez-Aleixandre 2007). The humanities remain largely trapped in a conception of argumentation based on logocentric discourses, in which all and everything can be claimed. From this conception, a comfortable antagonism has been developed, with “logical demonstration” serving as a convenient antagonist. The repositioning of argumentation as a complex, combinatorial activity which seeks to manage heterogeneous evidence in possibly complex material contexts enables us to distance ourselves from this traditional logocentric vision. Discussions between two mechanics disagreeing on how to repair a failing engine, or two students disagreeing on the shape of the beams coming out of the lens are as prototypical of what is an argumentative situation as an ideological debate where the language is perpetually referred to itself.

The research program on argumentation in science education emerged in the late 1990s and early 2000s. It now represents a key field of development for argumentation in the near future (Baker 1996, De Vries, Lund, Baker 2002; Buty & Plantin 2009; Erduran & Jiménez-Aleixandre 2008).

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[1] Poujol R. L’ Abbé du Chaila (1648-1702). Montpellier: Les Presses du Languedoc, 2001. P. 31.

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Stevenson ([1938]) introduced the concept of persuasive definition in the following terms:

In any “persuasive definition” the term defined is a familiar one, whose meaning is both descriptive and strongly emotive. The purport of the definition is to alter the descriptive meaning of the term, usually by giving it greater precision within the boundaries of its customary vagueness; but the definition does not make any substantial change in the term’s emotive meaning. And the definition is used, consciously or unconsciously, in an effort to secure, by this interplay between emotive and descriptive meaning, a redirection of people’s attitudes. (Stevenson [1938], p. 210-211)

To make a definition persuasive, within Stevenson’s meaning, its descriptive content must be redefined, whilst its “emotional force” must be kept intact so as to be applied to the redefined content. Stevenson gives the following example; A and B are “discussing a mutual friend” (id, p. 211.)

— A points out a number of shortcomings of that person (education, conversation, literary references, subtlety of spirit) and concludes that “he is definitely lacking in culture.”

— B describes this friend under a number of favorable lines (imagination, sensibility, originality) and concludes that “he is a man of far deeper culture than many of us who have had superior advantages in education”.

First, both A and B value culture, and are willing to give the word culture and the judgment “X is a cultured person” a positive emotional orientation. Moreover, the word culture has a vague descriptive sense; B carves out of this descriptive sense a new definition, and shows that it fits their mutual friend. Stevenson analyses B‘s argumentative move as follows

His purpose was to redirect A‘s attitudes, feeling that A was insufficiently appreciative of their friend’s merits (id., p. 211).

The argumentative trick is located at point (b), that is:

(a) B wishes to value his friend.
(b) He redefines culture “within the boundaries of its customary vagueness” according to qualities possessed by his friend;
(c) and he concludes that his friend is cultured;
(d) and the friend benefits from the positive opinion associated with the idea of culture and cultured person.

Thus, a persuasive definition redefines the descriptive contents of a term not on the basis of context-free, objective general considerations, but with a view to applying this term to a pre-determined person, a singular case. This is what would make it deceptive. It should be noted however that Stevenson attributes a persuasive definition to B only. Yet it might be argued that A also carves his definition out of the vague meaning of “culture”, “within the boundaries of its customary vagueness”. A thus has a persuasive definition, in much the same way as B, of “culture” as literary references, etc., allowing him to exclude the common friend from the circle of the cultivated. A seeks to influence B just as much as B tries to influence A.

Point (d) implies that the argumentative orientation (called here “the emotive content”) is independent of the cognitive content, and not affected by the redefinition. Thus, this orientation has to be attached directly to the signifier.

As it operates a redistribution of meaning, persuasive definition exploits the processes of distinguo and dissociation.

A persuasive definition is a definition that does not meet the condition of separability between, on the one hand, the construction process of the definition, and, on the other hand, the use of the definitional features to include an individual or a special case in the category it determines and calls it by the category’s name. In other words, a persuasive definition is a definition which is conditioned by the intention of including a specific object, that is, an ad hoc definition, imagined or altered on the spot, for the purpose at hand, S. Orientation.

The criteria of what is “good school task” must be applied regardless of the categorization of such work in or out of that category. A skewed definition does not meet this criterion:

A good school task is a task in which student get involved and on which they worked hard. My son spent his weekend on his history course. Thus he handed in an excellent piece of work, and deserves a good grade.

The category “is a good school task” has been redefined so that it can apply to Mr. Doe’s son, leaving aside the contents of the work, traditionally regarded as the decisive factor. The target has been re-designed to fit the arrow, and the limited capacities of the archer.

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1. Definition in the categorization process

Categorization is the process through which an individual is identified as belonging to a category, and is given the name of this category, S. Categorization and Nomination. The definition is the reservoir of essential features allowing this identification.

2. Argumentation exploiting a definition

The definition (the definiens) of a word or an expression (boy, scotch bonnet, democracy, single parent, educated person, British citizen, natural disaster…) provides a stock of definitional features applicable to all the beings, individuals, institutions, events… designated by the definiendum (belonging to the category named by the word). Argumentation by definition applies the definition of the name to a being designated by that name. It operates as follows:

1. 1. An argument: a statement of the form “I is a D”: I is an individual (identified, categorized, perceived, named… as) “a D”.
   2. A license to infer, found in the definition of D considered as authoritative.
   3. A conclusion: everything said of the D or with them can be truly said of I.

A definition (a definiens) is a rich set of proposals about “what that kind of being is”. It includes doxical assertions based on common knowledge about these beings, to be found in the examples illustrating the definiens as well as in the definiens properly said. To call a being “a D” is to allocate to this being all the properties defining the name “D”, as well as scripts, duties and obligations attached “to Ds”. In other words, the definition (the definiens) of “what is a D” is a stock of inference licenses applicable to all the persons and objects called D.

Using the definition allows inferences of the following type, S. Common Place.

— “Harry is a British citizen”: this claim expresses a categorization of the person Harry, derived from the information that he was born in Bermuda, S. Layout. The categorization (“— is a British Citizen”) corresponds to a local modeling of the person “as-a-British-citizen”, which makes it accessible to the inferential definitional machine. Armed with this information, we can draw from the knowledge stock that defines “what it is to be an Englishman”, and conclude, according to the needs of the moment, that:

He takes tea at five
He will need a drop of milk
We can certainly address him in English
If he has committed a crime abroad, his judicial treatment will be led according the relevant international convention

— “My dear, you’re a little girl!” Traditional wisdom says that girls are like this, should do this and that, etc. So, my daughter, you’re like that, and you must behave accordingly:
— “This is a Scotch bonnet” so, it is “very aromatic, it is delicious prepared in an omelet”; better yet, you can “dry it out, and use it as an aromatic”[1], S. Categorization.
— “Now you are undoubtedly one of the great democracies” so we can re-establish diplomatic relations and encourage our citizens to spend their vacation on your beaches.
— “Mrs. Doe is a mother who lives alone” so, on the basis of such and such administrative and financial provisions, she is entitled to a single parent allowance of a certain amount.
— “Mrs. Smith is a PhD student” so she enjoys certain rights and must fulfill certain duties defined by the PhD Charter in force at the university where she is enrolled.
— “He is a bastard” so I do not trust him.

Argumentation by definition ascribes to a definite being a feature actually found in the definition of its name, as found in a dictionary or an encyclopedia. More broadly, it attaches to a being any feature borrowed from the stereotyped notion of the kind of beings bearing that name.
Argumentation by definition is the epitome of what Billig calls “bureaucratic thinking”, which is fundamental in everyday life (Billig [1987], p. 124).

If the criteria used for categorization are defined within a rigorous scientific framework, then argument by definition will be an essential scientific tool. Similarly, in the legal domain, the criteria qualifying an act make it possible to apply the legal syllogism, which delivers routine legal decisions.

3. Lexical definitions as inferential resources for categorization and argumentation from the definition

Some basic argumentative inferences embedded in a word are made explicit in its lexical definition and are suggested in the examples of its usage. Language dictionaries are stocks of accepted ideas and accepted connections between ideas; as such, they provide legitimate inferences from and to a word in the language and culture to which they belong (Raccah 2014) S. Orientation. These inferences are considered rational and convincing insofar as they are the expression of a shared semantic heritage, the treasure trove of discursive rationality. Let us consider the word rich. By merging the definitions of some current dictionaries, we are able to gain some insight into the elementary “licenses to infer”, diversions, or “drifts” from and to this word, that is, the semantic inferences which characterize a basic understanding of the word “rich”. The following information comes from definitions from MW, tfd; CD).

(i) … so he is rich. This claim is justified:

— On an analytical basis: … (he has) a lot of money; of valuable assets, SO he is rich
— On the basis of signs: … (he owns) expensive materials, workmanship (such as mahogany furniture), SO, he is rich
— On the basis of his or her moral character and motives:
he is determined to get rich quickly,  SO, he will probably become rich

 (ii) He is rich, so… On the same analytical basis, or from signs, one can deduce:

… (he has) a lot of money; of valuable assets
… (he owns) expensive materials, workmanship (such as mahogany furniture)
… he does not have to work
… he has forgotten his humble background —

This last conclusion admits of exceptions: He is rich, but…

… Even when he became rich and famous, he never forgot his humble background.

(iii) An implicit principle, “everybody can get rich” eliminates two rebuttals:

Having a humble background:
Even when he became rich and famous, he never forgot her humble background:

Lacking of formal education:
A lack of formal education is no bar to becoming rich.

(iv) A main opposition: the rich vs. the poor, allows the application of the topic from opposites:

There’s one law for the rich and another for the poor.

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[1] Entry Mousseron in J. and J. Manuel Montegut (1975). Atlas des Champignons [Atlas of Mushrooms] Paris: Globus, 1975.

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1. Method for constructing a sound definition

When a definition is at issue, one technique of definition can be played against another. Typically, definitions based on common usage, on true meaning of the word, on the scientific meaning of the word can be opposed to each other.

Just as there are rules for arguments establishing a correct causal relationship, there are rules for establishing a correct definition, and therefore, critical rules for evaluating, definitions, S. Arguments establishing vs. exploiting a relationship.
These rules depend on the social or scientific fields to which the defined beings belong, and adapt to the various definition types. The more general ones are as follows.

(i) Does the definition correctly disambiguate the term according to its meanings (homonymy) and acceptances (polysemy)? S. Ambiguity.

(ii) Does the definition avoid circularity? If not, it enters a vicious circle. Words being defined with words, the whole dictionary is actually circular. As explanations or arguments in general, definitions should try to defer circularity as far as possible; that is, the definition (definiens) cannot use the word it is supposed to define (definiendum), nor a (near) synonym of the word. Nonetheless, definition through synonyms or the simple negation of an antonym does help if one of these defining words is better known than the definiendum.

(iii) Does the definition cover all the uses of the word? Does the meaning of a passage remain the same when the definiens is replaced by the definiendum? If not, the definition should be amended.

(iv) Does the definition make it possible to sort out the beings that are called by that name from those that are not? A definition might be criticized because it is too broad (it applies to heterogeneous objects or beings) or because it is too narrow (it excludes objects or beings it would be desirable to integrate). S. Definition and Argument, § 2, for the role of ostension and exemplification.

(v) Does it help? That is, does it provide sufficient information to clarify the meaning of the word, and, if need be, does it give some functional indications, or point to the scientific or specialized uses of the word?

(vi) Is the definition brief, clear, and simple? Does it use unknown, obscure or ambiguous words?

(vii) Is the definition objective? Does it exclude the judgments of value and ideological preferences towards the beings or properties defined? S. Orientation; Persuasive definitions.

Methods and rules such as those mentioned above serve as a guide for the establishment of definitions and, consequently, for their criticism.
— The following set of available arguments in their positive form argue that the definition is sound, and in their negative form they argue that the definition is unsound.

(i) it correctly disambiguates the definiens
(ii) It avoids circularity
(iii) It covers all the uses of the word
(iv) It is neither too broad nor too narrow
(v) It is helpful
(vi) It is brief, clear, and simple
(vii) It is objective.

— These arguments are mobilized in debates on definitions or involving definitions (Schiappa 1993; 2000), that is, when there is a stasis of definition (see infra); S. True meaning of a word
— They are fundamental to the criticism of argumentations that use a definition, showing for example that the underlying definitions are poorly constructed and do not comply with such and such a rule.

3. Questions of definition

A stasis of definition, or question of definition, occurs when it appears that discourse and counter-discourse are based on incompatible definitions of the same object:

S1: — The rights of free speech and demonstration are fundamental to democracy.
S2: — What is fundamental in a democracy, is the right to have an iPhone and something to eat.

A definitional question ensues: which features are essential (central) features and which ones are accidental (peripheral) to characterize a democratic state?

Incompatible categorizations result in a question of definition:

S1:      — A Syldavian Diplomat killed in an accident
S2:      — Murder of a Syldavian Diplomat

Confidential information was disclosed:
S1:      — A new manifestation of the malfunctioning of Syldavian Services
S2:      — There are traitors in our services.

The investigator, in the role of the third party, transforms the two conflicting discourses into an argumentative question, and initiates an investigation to clarify what happened, on the basis of legal definitions:

What is murder? What is an accident?
What are the crucial differences between carelessness and betrayal?

The stasis of definition can develop as follows:

S1₁: — Syldavia is now a true democracy!
S2₁: — How dare you talk about democracy in a country that does not recognize the rights of minorities?
S1₂: — According to the dictionary, democracy is …; nothing in this definition mentions the rights of minorities; so, Syldavia is for sure a true democracy
S2₂: — This definition is poor and ideologically biased.

— The confrontation of the positions S1₁ and S2₁ produces a question of categorization.
— S1₂ rejects the objection of S2₁ by referring to the dictionary; he or she might as well have quoted the recognized conventions, international law, consensus, etc.
— S2₂ ratifies the stasis of definition

According to Humpty Dumpty, the best way to resolve of a stasis of definition is to appeal to power:

[Humpty Dumpty] […] — and that shows that there are three hundred and sixty-four days when you might get un-birthday presents—”
“Certainly,” said Alice.
“And only one for birthday presents, you know. There’s glory for you!”
“I don’t know what you mean by ‘glory’”, Alice said.
Humpty Dumpty smiled contemptuously. “Of course, you don’t—till I tell you. I meant ‘there’s a nice knock-down argument for you!”’
“But ‘glory’ doesn’t mean ‘a nice knock-down argument,’” Alice objected.
“When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”
“The question is,” said Alice, “whether you can make words mean so many different things.”
“The question is,” said Humpty Dumpty, “which is to be master—that’s all.”
Alice was too much puzzled to say anything, so after a minute Humpty Dumpty began again. […]
Lewis Carroll, Through the Looking Glass, 1872 [1]

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[1] Quoted after Lewis Carroll, Through the Looking Glass. Chapter 6, Humpty-Dumpty. 2016. No pag. http://www.gutenberg.org/files/12/12-h/12-h.htm#link2HCH0006. (11-08-2017)

All typologies of argumentation have one or several entries “Definition”, frequently the first on the list. Issues focusing on definition of terms, S. Stasis arise in highly productive forms of argumentation.

1. Defining definition

The definition of a word is a description of its meaning(s) in relation with its use(s).

Not only words but also phrases need to be defined. Fixed or semi-fixed phrases, that is idiomatic expressions, such as beat around the bush, have also to be defined, since their global meaning does not result from the mechanic combination of the meanings of their components.
Moreover, social life produces conventional expressions used with a specific meaning that requires a definition:

What is a single parent?
What constitutes an emergency situation? An urgent case?

Depending on the nature of the word and the circumstances of the questioning, these questions ask about the meaning of the word, or about information about the kind of object to which the word refers, or about the circumstances in which it is possible to use the word.
In argumentative situations, even the meaning of current words can be disputed: What is an educated person?

The meaning of a word in ordinary language is not a “backstage spirit” animating the word, but a discourse “equivalent”; “having the same meaning”:

uncle                      =      “brother of the mother or the father”
[definiendum]       =      [definiens]

The definition establishes a semantic equivalence between a term, the definiendum, “what is to define”, the dictionary entry, and a discourse, the definiens “what defines” (sometimes called “definition” by metonymy).
The definiens is a discourse answering questions like “what does the word X mean?” “What is X?”.

From a logical perspective, the equivalence definiendum / definiens meets two requirements, one semantic and one formal.
— In semantic terms (intension) definiens and definiendum must have the same meaning.
— In formal terms (extension), the definiens and definiendum must be intersubstitutable in all contexts, the global meaning of the passage remaining the same.
The definition is substituted to the word defined, when the discourse containing this word has to be clarified; the word is substituted for its definition when the discourse has to be abridged.

The definition of “fish” as a species of animal draws on the field of natural sciences. The definition of “democracy”, “citizen” and “citizenship”, combines political sciences and political and ideological ideals. The definition of “single parent” refers to laws and ordinances. The vague concept of a “cultivated person” will combine a little of all the arts and letters. Advances in knowledge, history, and usages will change the meaning of the words and the kind of beings and objects they refer to.

Argumentative situations de-stabilize the meaning of words, and the definition of commonly used words may require revision and further clarification.

2. Kinds of definition

Different methods can be used to build a sound definition of a word, S. Arguments Establishing vs Exploiting a relationship. They propose criteria that come to the fore when the meaning of a word is at stake, when one wants to de-stabilize an unsatisfactory definition, or justify a challenged one.

2.1 Giving cues to the meaning of a word or a phrase: Ostension

Ostension is a gesture, the act of showing to somebody a concrete object. Defining a concrete noun by ostension is to show a sample of the objects or beings referred to:

Want to know what a duck is? Well, look at that one just flying by!

Ostension underlies the famous argument:

I cannot explain how, but I do recognize a boletus badius when I see one!

Ostensive definitions can only be applied to concrete beings materially present in the context of speech. Ostension is fundamentally ambiguous: the same gesture shows the chestnut horse and its chestnut color, but it is disambiguated by the context.
Ostension bypasses meaning; it lacks the discursive element considered essential for a proper definition.
Ostension is a key auxiliary for the definition of concrete things. The more closely the concrete object or being resembles the prototype of its category, the more effective ostension will be.

2.2 Focusing on the referential capacities of the word

The consideration of a variety of cases is crucial for the criticism of definition: Does the definition under scrutiny permit to correctly refer to all the beings or cases currently referred to by the corresponding name? S. Arguments justifying a definition.

2.2.1 Definition by exemplification

Definition by exemplification approaches the meaning of a word by giving an example of its use:

What is a hoax? Well, that is, for example, remember when reputable media announced that blondes and blonds would disappear by 2202? [1]

The example given, if prototypical, provides a good basis to capture the meaning of the word.

2.2.2 Definition by enumeration (in extension)

Definitions in extension proceed through the enumeration of all the individuals the word or expression refers to. Thus, the expression “conventional binary logic connector” is defined in extension as a member of the set {~, &, V, W}, S. Connective
A democracy is a state mentioned in the list of democracies established in the Democracy Dictionary:

Syldavia is a democracy since it is on the “Democracy List”.

Definition by extension provides the basis for case-by-case arguments. If “honestly acquired money” is defined as acquired “either through work, inheritance, financial investment, or winning the lottery”, then it can be indirectly proved that a sum of money was ill-gotten by showing that it has been acquired neither by work, nor by inheritance, nor is the legitimate product of a financial investment, etc.

2.3 Definition as instructions for use

2.3.1 Operational definition

Operational definition associates a term X with a set of operations permitting to determine whether or not that individual is an X. An operational definition do not say what an X essentially is; it simply indicates how to find all the individuals X refers to.

The expression “prime number” is defined as “a number that is only divisible by itself and by the unit”. This definition unambiguously determines whether or not a given number is a prime number.

2.3.3 Functional definitions

As operational definitions, functional definitions do not consider the essence, or the technical design of the instrument named. The referent is characterized in terms of its functions, goals, objectives. To know what a compass is, is to know that, it points north (magnetic), and is used accordingly.

2.4 Describing the meaning of the word

2.4.1 Essentialist definition (definition in intension)

Essentialist definitions require that the definition “focus on the essence (and not the accident), and proceed by next genus and specific difference” (Chenique 1975, p. 117).  An individual receives the name of its category, identified through a series of generic features common to its superordinate genre and differentiating features specifying its species. S. Classification.

Essentialist definitions work well for natural species. In general vocabulary, the contrast is between central and peripheral features. A dictionary of Syldavian institutions would include an entry “President of the Syldavian Republic (SR)”, defined through the modes of election, the constitutional role etc. These core elements can be complemented by anecdotal characteristics, such as “lives in the Parnassus Palace”; “her spouse is called ‘the first lady or man of Syldavia’”, etc. The latter information refers unambiguously to the President (they apply to him or her and only to him or her, the substitutability condition is fulfilled), but doesn’t contribute to clarifying the meaning of “President of the SR”. In Aristotelian terms, free accommodation at the Parnassus Palace is not an essential property attached to the office of President of the SR.

Essentialist definitions seek to express the true sense of the word, corresponding to the very nature of the things it designates, that is, their permanent essence. They go beyond the linguistic knowledge of the word (lexical definition), and even beyond the knowledge of the things defined (encyclopedic definition), always reflecting an imperfect state of knowledge.
In Platonic terms, an essentialist definition claims to retain the idea of ​​the thing: “what is virtue?”. In theory, the essentialist definition is ruled by a methodology, based on an “intuition of the essence of the thing”, S. Classification. Ancient dialectic was the instrument used to build correct essentialist definitions.

While a pragmatic definition of the word democracy is based on the many socio-historical uses of the word, an essentialist definition tries to establish the ideal, essential characteristics of democracy, sometimes to condemn the current uses of the word on behalf of “true democracy”, S. True meaning. It may be that no real democracy corresponds to the essence of democracy. The essentialist definition is used as an important critical tool in idealist or conservative argumentation (Weaver 1953). 

2.4.2 Lexicographical definition

Lexicographical definitions are found in language dictionaries, as opposed to encyclopedic dictionaries. Language dictionaries must meet multiple conditions:

— Collect all the words and idioms of a language (or the vocabulary used at a particular period).
— Provide a description of their various meanings, their uses in speech, and their stereotypical figurative uses.
— Give the typical contexts of use associated with these meanings.
— Specify the syntactic constructions corresponding to these meanings.
— Locate them in the various semantic fields to which they belong, that is, specify their relationships with their (quasi-) synonyms and antonyms, and their position in their derivational families.

The dictionary is a highly legitimized and legitimizing institution. From the perspective of argumentation studies, lexical meaning being inferential, the dictionary should be seen first of all, as a huge stock of “inferring principles”, S. Argumentation based on a definition (3).

Linguistic definitions simultaneously draw on different kinds of definition. Knowledge of words (lexical definitions) and knowledge of things (encyclopedic scientific definitions) are theoretically clearly separated. They are, however, inextricably linked for current terms having an encyclopedic definition. “When the barometer falls, the weather turns bad”: is the deduction backed by a meteorological physical law expressing knowledge about the variations in atmospheric pressure? Or is it included in the linguistic meaning of the word? Knowing the functional meaning of the word “barometer” is to know that “when it falls, the weather turns bad.”

All words are worthy of a lexical definition, but only those having “plenty of being” are worthy of scientific knowledge, and are registered in the encyclopedia. The border between the two categories is unstable and dependent on the state of research; conversation, once considered a futile and elusive thing, was conceptualized fruitfully by conversation analysis and ethnomethodology. These sciences have given “more being” to their object.

 2.4.3 Scientific definition of concepts and lexicographic definitions of words

Encyclopedias collect only conceptual terms. Encyclopedic definitions summarize the state of knowledge about things and concepts referred to by the term. A good definition of a thing stabilizes a well-constructed knowledge.
Scientific definitions can use a re-defined common term, (see infra stipulative definitions). The mass of the physicist is not the mass of the language dictionary:

In physics, mass is a property of a physical body. It is the measure of an object’s resistance to acceleration (a change in its state of motion) when a force is applied. It also determines the strength of its mutual gravitational attraction to other bodies. In the theory of relativity, a related concept is the mass-energy content of a system. The SI unit of mass is the kilogram (kg). (Wikipedia, Mass).

Whereas, in current language, the word mass is defined and illustrated as follows,

1
a: a quantity or aggregate of matter usually of considerable size
b (1): expanse, bulk — (2): massive quality or effect — (3): the main part or body <the great mass of the continent is buried under an ice cap (…) (4): aggregate, whole <men in the mass>
c: the property of a body that is a measure of its inertia and that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field
2
: a large quantity, amount, or number <a mass of material>
3
a: a large body of persons in a group <a mass of spectators>
b: the great body of the people as contrasted with the elite —often used in plural <the underprivileged and disadvantaged masses (…) (MW, Mass)

Arguments establishing a scientific definition of things are domain-dependent. An astronomy conference was necessary to redefine the term planet, and end the controversy over the status of Pluto.

The usual definition can be hardly recognizable under the technical definition. The following definition correspond to an everyday experience:

1. A blocking of the alpha activity preceded by a transitional element that is expressed in the cortex region (a temporal tip-cortex)
2. A more or less pronounced muscle jerk (a start);
3. Neuro-vegetative events, such as tachycardia and decreased skin resistance.
So, I was referring to the “classical” reaction of surprise that you all know.
Henri Gastaud, [Discussion], 1974[1]

This is a scientific definition of surprise, “in the sense of ‘surprise reaction’ that is to say the set of phenomena observed by the neurophysiologist, when a sudden unexpected stimulus occurs.” (Ibid.)

2.5 Giving a phenomenon its scientific name:
Stipulative definition, neology and baptism

Stipulative definitions are also called “definition of name”:

The only definitions recognized in geometry are what the logicians calls definitions of name, that is, the arbitrary application of names to things which are clearly designated by terms perfectly known. (Pascal Geom., p. 525)

They play a key role in the scientific creation of words. When a new class of phenomena or beings has been identified and characterized, they must be given a name. While in the general case, the defining process begins with a given term and looks to clarify its pre-established definition, stipulative definitions start with a clear and well-established meaning (the definiens), and seek a word to refer to this content; it is a baptism. To this end, one might choose a usual word emptied of its ordinary meaning. By convention, physicists use the word charm to speak of a particular particle, the charm quark. The equivalence condition between the technical use of the word and its definition is fully satisfied.

In other cases, the word chosen to name the new phenomenon retains something of its ordinary meaning, and it is arguable that “my word fits better than yours the nature of the phenomenon”. As each and every person has a preferred terminology, the relatively arbitrary nature of the stipulative neologism can lead to terminological inflation and a “war of words”, which can be overcome by invoking the primacy of the reality of things. Should we call such argumentative patterns:

serial reasoning or subordinate argumentation?
linked reasoning or coordinate argumentation?
convergent reasoning or multiple argumentation?

If no agreement can be reached, the issue can be radically settled, “You may even call it ‘Ivan Ivanovich’ as long as we all know what you mean.” (Jakobson 1971, p. 557).

3. Argumentation and definition

3.1 Argumentation constructing or evaluating a definition

Definitions are argumentatively constructed in reference to a set of rules, S. Argumentations establishing a definition.
These rules generate a set of specific argumentative lines that are exploited when a conflict of definitions occurs, such as:

What do you precisely call a terrorist, a democracy, a spin doctor?

Persuasive definitions are definitions restructured in order to include or exclude an individual from their scope. They can be criticized as violating the non-circularity principle.

3.2 Argumentation based on a pre-existing definition

In this second case, the definition of a word is used as a stock of arguments.

3.1.1 Definition used to categorize and name an individual

The argumentation naming an individual attaches this individual to a category name W, in reference to the definition of this category, S. Categorization and nomination.

This is a mushroom

3.1.2 Definition used to enrich the description of an individual

In this form of argumentation, the speaker allocates to an individual any feature mentioned in the definition of its name.
If Syldavia is a democracy (category), and that “having fixed elections dates” is a defining essential feature of democracy, then one might infer that there will be elections in Syldavia in a not too distant future, S. Argumentation based on a definition.

3.1.3 A Discursive ploy: Demanding a definition

The request for a definition might be made with the intention of blocking the development of the opponent’s argumentative line, S. Destruction of speech. The following exchange takes place in a discussion about various personalities competing for a scientific distinction:

S1:      — Doe has a lot of prestige.
S2:      — What do you call prestige?

This inevitably leads to a stasis of definition, in which many participants are not eager to participate.
The internal magazine of a research institution objects to a traditional claim from laboratories:

“[Lack of technical staff] would lead to a lack of “optimum efficiency” in laboratories. First, how do we define the optimal efficiency of a laboratory?

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[1] After Wikipedia, Disappearing blond gene (10-09-21)
[1] Gastaud H. (1974) “Discussion”. In Morin E. & Piattelli-Palmarini M. (eds). (1974). L’Unité humaine. Paris: Le Seuil. P. 183.

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Researchers in artificial intelligence have developed the formal study of argumentation as defeasible reasoning in a logical, computational, and epistemological perspective.

1. Default reasoning

From the logical point of view, defeasible reasoning is studied within non-monotonic logic. Unlike conventional (“monotonic”) logic, non-monotonic logic admits the possibility that a conclusion can be deductible from a set of premises {P1} and not from {P1} plus new premises. In terms of belief, the challenge is to formalize the basic idea that the provision of new information may lead to revision of the belief derived from a formerly limited set of data.

From an epistemological perspective, the theory of defeasible reasoning (Koons 2005) concerns beliefs that permit exceptions: in general, birds fly; but penguins (Sphenisciformes, Spheniscidae) are birds and do not fly. As a consequence, if the only thing one knows about Tweety is that Tweety is a bird, it is not possible, strictly speaking, to infer that Tweety can or cannot fly. Nonetheless, in the absence of any information suggesting that Tweety is a penguin (or some other flightless bird), the theory of revisable reasoning admits the conclusion “Tweety flies”. It validates exception-conditioned inferences:

Since A (Tweety is a bird), normally B (Tweety flies).

The premise does support the conclusion, but it may nonetheless be true and the conclusion false. A conclusion considered to be correct on the basis of the knowledge which has now become available, may later turn out to be false if further knowledge is gained.

The theory of defeasible reasoning also addresses more complex issues such as the following. We know that:

(1) Birds fly
(2) Tweety is a bird
(3) Tweety does not fly
(4) Birds have highly developed wings muscles

In these conditions, can we deduce (5) from (1) – (4)?

(5) Tweety has highly developed wings muscles

The property of having highly developed wing muscles is linked to having the capacity to fly, which, according to the available information (3), is not true in Tweety’s case. The inference from (1) and (4) to (5) is therefore invalidated. In other words, the conclusion “Tweety has highly developed wings muscles” is deducible not from “Tweety is a bird” but from “Tweety is a flying bird”.

A conclusion C asserted through defeasible reasoning can be rebutted in two ways:
— On the one hand, upon the existence of good arguments for a conclusion inconsistent with C (“rebutting defeater”, Koons 2005), that is to say upon the existence of a strong counter-argumentation.
— On the other hand, upon the existence of good reasons to think that the transition principles usually invoked in the argument do not apply in the case considered (“undercutting defeaters”, ibid), S. Refutation.

2. Representation of default reasoning

The default inference is represented as a default rule:

If Tweety is a bird,
in the absence of information suggesting that Tweety may be a penguin (etc.),
it is legitimate to conclude that Tweety flies.

The sequence is represented as:

Tweety is a bird: Tweety is not a penguin (etc.) — Tweety flies

ζ : η — θ

ζ: Prerequisite: we know that ζ
η: justification: η is compatible with available information
θ: conclusion

The historical origins of the theory of revisable reasoning are sought in dialectical reasoning and the Topics of Aristotle. The restriction “in the absence of information” corresponds exactly to the “modal” component of Toulmin’s layout of argument; the basic intuitions and concepts are the same. Toulmin layout can be schematized as:

D (Data) : R (Rebuttal)
—
C (Claim)

D, Data: Prerequisites, we know that D.
R, Justification: The inference from D to C could be rebutted under the conditions R1… Rn; but we have no information leading us to believe that these rebuttal conditions are actually true.
C, Claim: So, the conclusion C can be accepted; one can work on the basis that C.

Gabbay & Woods (2003) develops a study of practical reasoning combining the insights of and relevance theory and default reasoning theory.

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1. In ordinary language

In ordinary language, the word deduction is homonymous. As a derivative of to deduct, deduction means “subtraction”, and does not directly concern argumentation. As a derivative of to deduce, it can be used as an umbrella term, to refer to any kind of argumentation, that is of derivation of a conclusion from a set of data taken as premises. Deductions are given as valid and sound by the arguer to the other participants.

The well-known Holmesian “deductive method” proceeds as follows:

-Watson visits Sherlock Holmes.
‘In practice again, I observe. You did not tell me you intended to go into harness.’
‘Then how do you know?
‘I see it, I deduce it. How do I know that you have been getting yourself very wet lately, and that you have a most clumsy and careless servant girl?’
‘My dear Holmes, this is too much. You would certainly have been burned, had you lived a few centuries ago. It is true that I had a country walk on Thursday and came home in a dreadful mess, but I have changed my clothes I can’t imagine how you deduce it. As to Mary Jane, she is incorrigible, and my wife has given her notice; but there again, I fail to see how you work it out.’
He chuckled to himself and rubbed his long, nervous hands together.
‘It is simplicity itself,” said he, “my eyes tell me that on the inside of your left shoe, just where the firelight strikes it, the leather is scored by six almost parallel cuts. Obviously they have been caused by someone who has very carelessly scraped round the edges of the sole in order to remove crusted mud from it. Hence, you see my double deduction that you had been out in vile weather, and that you had a particularly malignant boot-slitting specimen of the London slavey.’
Arthur Conan Doyle, Adventures of Sherlock Holmes — Scandal in Bohemia, 1891[1].

The reasoning seems to correspond to an argument from natural sign, or if considered as the derivation of an explanatory hypotheses, to an abductive argument, more than to a logical deduction.

2. In Cartesian philosophy

A deduction is a series of operations linking, according to valid rules, a set of true premises (axioms, true propositions) to a conclusion

Many things are known although not self-evident, so long as they are deduced from principles known to be true by a continuous and uninterrupted movement of thought, with clear intuition of each point. (Descartes [1628], Rule III).

In this sense, a well-led deduction is a demonstration, producing apodictic (incontestable) knowledge, defined as “any necessary conclusion from other things known with certainty” (ibid.).

Valid and sound syllogistic reasoning is a kind of deductive reasoning, sometimes taken as the reference for valid argumentation. Argumentation developing the definition of a word and its implications, or the various forms of argumentation from the absurd, are examples of deductions in natural language.

3. In logic

According to Kleene, a proof is based on axioms, while a deduction is based on hypothesis:

The proof of theorems, or the deduction of consequences of assumptions, in mathematics typically proceeds à la Euclid, by putting sentences in a list called a “proof” or “deduction”. We use the word “proof” (and call the assumptions “axioms”) when the assumptions have a permanent status for a theory under consideration, “deduction” when we are not thinking of them as permanent” (1967, §9, Proof theory: provability and deducibility, p. 33)

In logic, “a (formal) proof (in the propositional calculus)” is defined as “a finite list of (occurrences of) formulas B₁……B_l such as each of which is an axiom of the propositional calculus, or comes by the ⊃–rule from a pair of formulas preceding in the list” (id. p. 34).

The ⊃–rule is “the modus ponens or rule of detachment”, defined as “the operation of passing from two formulas of the respective form A and A ⊃ B to the formula B, for any choice of A and B […]. In an inference by this rule, the formulas A and A ⊃ B are the premises and B is the conclusion” (ibid.).

3.1 Validity and Soundness

Under such a definition, deduction is taken as a valid and sound deduction. Now, a string of propositions can be advanced by as speaker as a valid and sound deduction without being really so.

To be valid, the deduction has to be led according to the laws of (a well-defined system of) logic. For example, the inference from a false proposition to a true one “P(F) → Q(T)” is valid, but not sound: to be sound, the reasoning has to start from axioms or, generally speaking, from true propositions.

The implication (conditional) is a binary logical connective. A deduction is a chain of operations linking well-formed expressions by means of a rule. For example, the rule of modus ponens (⊃–rule, cf. supra) makes it possible to deduce “B” from the two premises “A →B” and “A” (hypothetical syllogism), by a three-step deduction:

A  → B
A
so, B

The same reasoning can be expressed as an implication expressing a logical law, S. Connective:

“If the implication is true and the antecedent true, then the consequent is true”
[(A → B) & A] → B

Let’s consider a true conditional “R → W”, “If it rains, the lawn is wet”.
W is a necessary condition for R; R is a sufficient condition for W.

3.2 If a sufficient condition for W is met, then W

If the antecedent of a true conditional is true, then its consequent is true.

R → W	R is a sufficient condition for W	If it rains, the grass is wet
R	this sufficient condition is met	It is raining
so W	so W is met	so the grass is wet

This rule proceeds from the affirmation of the antecedent of a true implication. It is also known as the modus (ponendo) ponens rule: the deduction poses (ponendo) the truth of the antecedent R, in order to affirm (ponens) the truth of the consequent W.

The idea of sufficient condition is also expressed as:

not-(A & not-B)

In the ordinary world and natural language, a situation in which it might rain without the grass becoming wet is unthinkable.

3.3 If a necessary condition for R is not met, then R is not met

If the consequent of a true conditional is not true, then its antecedent is not true.

R → W	W is a necessary condition for R	If it rains, the grass is wet
not-W	this sufficient condition is not met	The grass is not wet
so not-R	so R is not met	So it is not raining

This rule proceeds from the negation of the consequent of a true implication, also known as the modus (tollendo) tollens rule, the mode that, by denying (the consequent), denies (the antecedent).

All reasoning from natural signs involves this kind of deduction.

4. Paralogisms of deduction

4.1 Denying the antecedent

It is not possible to deny the existence of a phenomenon on the basis of the absence of a sufficient condition for the given phenomenon. The following deduction is invalid:

R → W	R is a sufficient condition for W	If it rains, the lawn is wet
not-R	this sufficient condition is not met	It does not rain
*so not-W	*so W is not met	*So the lawn is not wet

Raining, a sufficient condition for the grass to be wet, has been incorrectly considered as necessary.

4.2 Affirming the consequent

It is not possible to infer the existence a phenomenon in view of the prevalence of a necessary condition of this phenomenon. The following deduction is invalid:

R → W	W is a necessary condition for R	If it rains, the lawn is wet
W	this necessary condition is met	The lawn is wet
*so R	*so R is met	*So it is raining

To find that the grass is wet is not a sufficient basis to conclude that it is raining.

5. Pragmatic of deduction

The rules of deduction are defined within the framework of a logical system in which all the components of reasoning are explicit and well defined.

Ordinary situations are different; in particular, and ordinary reasoning only makes relevant knowledge explicit. Let us suppose that the lawn could be wet because it has rained, because the lawn has been watered, because a pipe has leaked, or due simply to a heavy dew. If it is contextually evident that the lawn has not been watered (I know what I have done), that there is no water leaking (for the simple reason that there is no water pipe in the garden), and there is no dew (at that time of the day), then I can safely say that if the grass is wet, it is because it rained, or is raining.

Only the superficial form of reasoning is fallacious. Full evaluation must take the context into account and re-build the argument explicitly, on a case-by-case basis thereby eliminating the other sufficient conditions, transforming the latter into a necessary and sufficient condition. This is a direct application of Grice’s cooperation principle.

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[1] Quoted after Arthur Conan Doyle, The Penguin Complete Sherlock Holmes. London: Penguin Books, 1981. P. 162.

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Typical Western debates and discussions implement all the facets of argumentative activity: constructing points of view, producing good reasons; interacting with different people and points of view, building more or less ephemeral alliances, integrating / refuting / destroying the positions of others, backing arguments by drawing on personal involvement in the debated issues. Sometimes the two terms arguing and debating are assimilated, with TV debates implicitly considered as the prototypical argumentative genre.

This vision of argumentation has major limitations. This vision of argumentation has major limitations. It leaves aside argumentation at work, or argumentation in science education. Il associates argumentation with polemical debate, which is a non-cooperative form of argumentation. TV debates may try to influence the decision, but they have no decision-making power. Work meetings, family discussions are certainly more representative of the complexity of argumentation. In a work meeting where issues are debated with both short term and long term implications, different kinds of sequences must be managed in different episodes: new participants are introduced; the agenda is read; relevant information is given (to all, to less informed participants), conclusions are written down — not to mention the episodes devoted to interaction management, including digression and jokes. The level and kind of argumentativity of these episodes can be extremely varied.

The form and efficiency of the arguments put forward in a debate depend on the relative power of the participants in the relevant sphere. If taken on a majority basis, the decision compels the minority, whether or not persuaded, and regardless of whether or not the winning argument is the strongest from the point of view of an external evaluator.

1. The informed and properly argued debate as a source of legitimacy

From a foundational perspective, a political decision may be considered legitimate if conforms with, or is derived from an original pact, a social contract that the ancestors, or ideal representatives of the community, freely convened in a mythical original time, or in an ideal rational space.

Democracy values ​​debate. A decision is considered legitimate only if the issue has been publicly argued pro and contra, in a safe, open, free and contradictory space. In principle, the decision should take the results of debate into account; whether or not this decision is really supported by the best argument, is another issue; authority and power play a role. Debate as a form of argument is at the heart of democratic life. At school, it is considered to be the key instrument of “democratic learning”, be it in Citizenship education, in History, or in Science education.

2. Criticism of debate

Debate, however, is not an innocent and miraculous practice which can solve all issues in education, society and uneven development. Debate, particularly debate in the media, or in any public space, is the target of a critical argument that includes the following points.

— Resorting to debate may be merely an artifice of presentation. The topic is framed as an issue, as being the focal point of two antagonistic discourses, as if things were “interesting” only insofar as they radiate some polemical heat.

— Paradoxically, “the debate is open” can be a convenient conclusive formula, when listeners in both camps have got their share of good reasons, as if the main virtue of a debate is furthering the debate, and justifying further debates.

— A dubious and interrogative posture can be very comfortable. Debate merges the variety of positions in one unique global voice saying everything and the opposite; but articulates such unresolved contradictions very well. Correlatively, debate is a fertile field for argumentative personalities to flourish.

— Becoming an end in itself, debate becomes a performance, and loses all connection with the search for truth, clarification of the issues and positions, agreement or exploring and deepening the differences. This is the sophistical ad ludicrum tendency rightly and abundantly condemned as playing to the gallery; a delighted audience consents to its own manipulation, S. Laughter and Seriousness.

— From an educational point of view, debate can promote confrontational forms of argumentation. In fact, debate does not systematically break with symbolic violence, but can simply displace it. Some cultures find open interpersonal confrontation repugnant, or at least rude and counterproductive. Pressing students into a debate can be an educational blunder. Moreover, debates on serious issues divide groups, and can put at risk the reputation and even the security of the individual summoned to expose his or her creeds, networks and communities. Such self-exposure cannot be an option in some communities and cultures.

— Even coming from the best-organized public socio-political forum, the argument deemed the best might differ according to the parties. What is more, once taken, the decision can necessitate a new discussion about how it should be implemented, this being a regulatory or legal issue, in the hands of the current regime. There is a broad open and opaque space between argumentation and decision, and another one between decision and implementation.

— The ideal space in which the debate is held is framed as egalitarian and free. It denies any imbalance of power, at least it puts power relations between parenthesis. But every place has its own rules that impose formal and substantive standards. Such rules of the place apply to all participants. Debate presupposes democracy, as well as it promotes democracy.

Debate is a powerful resource,but debate alone will not resolve all social and individual ills, nor global hardships.

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