DEMONSTRATION AND ARGUMENTATION

To demonstrate comes from the Latin demonstrare “to show, to point out”. The verbs to demonstrate and to show verbs are synonymous in some contexts: “In what follows, I’ll show (= demonstrate) that… ».
In ordinary life, people make demonstrations of friendship, solidarity, affection… they make an exhibition, a show of their feelings, 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 background.

In rhetoric, the word demonstration is used with two completely different meanings, in addition to the meaning of “proof”:
— A demonstration is a vivid representation of an event or a state of affairs as a picture, for an audience or a reader, who is 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, together with 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 taken as a defining characteristic of argumentation. However, its content 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, the ideal of proof?

In logic, a demonstration is a discourse that proceeds from axioms to a theorem, according to specified rules of deduction. 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 is formalized when it can be presented as a mathematical demonstration. Formal proof is seen as characteristic of science as pure calculus, and is sometimes seen as the ideal of proof. This view contrasts with science as a description of reality (geography, zoology), or as a combination of calculation, observation and experiment (physics, chemistry).

In the sciences, a demonstration is a discourse, based on true propositions: (true by hypothesis; or as a result of observations or experiments carried out according to a validated protocol; or as a result 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 involves many non-formal linguistic, cognitive or material operations, other than demonstration. Such operations might include grasping a situation, formulating a  problem, or a hypothesis, setting up an experiment, manipulating the objects and instruments, selecting, observing and describing the relevant data, making quantitative measurements and related calculations, checking the results, imagining new experiences, drawing conclusions, preparing the results for oral communication and publication, responding to the colleagues’ objections, revising the claims, and so on. We could add to this all the professional argumentative situations in which researchers have to apply for new funding, write or evaluate a research project or to recruit 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. Natural language argumentation plays a key role in all these mixed activities.

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

Argumentation is concerned with what is to be believed, with the question of proof and demonstration, but goes beyond this. The exploratory function of argumentation extends beyond its epistemic role, to the practical discussion (internal or external) of what,  would be the most sensible next step given one’s current interests. One might ask for example, “should I apply for this or that job, buy this or that car, ignore or accept offers of negotiation”. And human affairs go even further, beyond the realm of practical decisions; generally speaking, argumentative situations arise as soon as any kind of choice is possible. Thus, argumentative situations can arise in relation to antagonistic feelings, to what is really worthy of admiration or love, see Emotions. In these areas the language of proof and demonstration does not make sense, whereas the language of argument does.

One might think that in the case of certain matters involving true beliefs and accurate scientific predictions, doubt is provisional, and that any doubt will be removed in the light of scientific progress. However, when considering situations involving human agents, however, doubt is an essential component. In such situations, it is often impossible to remove doubt completely, and it is legitimate to ask what would have happened if …

We turn to argumentation when the data are incomplete or of poor quality and the assumptions and laws are imperfectly defined; the conclusions are, therefore, subject to a constant principle of revision. As the last resort, we turn to the question of time: an argument is a bet. Combined with urgency and occasion, argumentation is a time-limited process, in contrast to the unlimited time afforded to the philosophical or scientific demonstration. There are essential differences in the modus operandi of argumentation and demonstration, in their fields of application and in the nature of the problems to which they can be applied.

When it operates in the field of knowledge, argumentation has an exploratory and creative function that goes beyond its demonstrative and critical function, see Abduction. Argumentation generates hypotheses, opens discussions and triggers the critical process of verification and revision.

Demonstration is by definition related to a domain; argumentation can combine heterogeneous evidence. Argumentation is the art of hierarchizing not only values^,, but also types of evidence and articulating levels of demonstrations. If one wants to explore the possibilities and economic interests of a major environmental management project, such as, the construction of a canal between the Green and the Yellow Oceans, for example, then the technical evidence, solutions and objections of geologists, economists and ecologists must be articulated and confronted with those of neighbors, citizens, investors and politicians. Negotiation will take place in the face of calculations and technical evidence each as unique as the next, and argumentation in natural language will have to fully exercise its synthetical function.

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

Several theories of otherwise very different orientations come together in order to oppose argumentation to demonstration. Historically, the notions of demonstration and argumentation inherited by the Western tradition were developed in ancient Greece. Demonstration in science and mathematics (Archimedes, Euclid) was constructed without reference 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 in use:

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 examining 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, persuasive rhetorical argumentation is characterized by its differences from valid logical demonstration (and probable dialectical deduction). Since then, argumentation has been conventionally associated with logical demonstration, to argumentation-demonstration, rather than to argumentation-proof such as exemplified in the practices of scientists, practitioners, historians, police investigators, etc. Argumentation is most closely associated with these practices, because of its non-formal nature and its relation to practical action. For example, the essential concept of the argumentative question is derived not 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 action are suspended.

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

4. Demonstration versus argumentation?

Demonstration and logical proof are classically opposed to argumentation on the basis of their premises and modes of inference. But it goes much deeper than that. Natural language and discourse are inherently subjective, i.e. self- and we-related, focused on the “here” and “now”, see Subjectivity. Words allow for synonymy, homonymy and polysemy; their meaning depends on context. Syntactic constructions need to be interpreted. Discourse is figurative. Meaning and reference are negotiated and managed through principles of relevance. These processes are stigmatized as inherently “vague and elastic”; but the polymorphism of language should also be praised for its adaptability to new situations and its capacity to change the rules

On a more general level, it should be noted, first, that there is no reason to favor elementary logical demonstration over other scientific activities, of which it is certainly a prominent member. Secondly, oppositions only make sense only if the opposed fields are comparable. Experimentation, mathematics, computerization, have moved apart the techno-sciences worlds, and it makes little sense to compare an article in a scientific journal publishing cutting-edge research with arguments developed in a newspaper column..

4.1 The New Rhetoric

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

The fundamental question of the difference between the language of argumentation, natural language and the language of demonstration, formal language, is not addressed. In the Treatise, the form of demonstration as 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 simplistic image of demonstration encourages the antagonism between argument and demonstration, and leads to the exclusion  from the Treatise of all that concerns sciences :

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 concerns only human affairs only, and demonstration concerns only mathematics and science. The gap between “the two cultures” (Snow, 1961) is thus at the very foundation of argumentation as a discipline.

4.2 The Argumentation within Language theory

This theory argues that the argumentative orientation is an essential feature of the semantic level of language, and concludes that it is impossible to develop arguments 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. Already Aristotle noted that the necessary demonstration of the syllogism contrasts with the incomplete and only probable argumentation of the enthymeme. Perelman, Grize, Eggs insisted on this idea. At first I thought that I was merely following this tradition, and that my only originality lay in pointing out 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 now I am led to say much more. Not only do words not permit demonstration, but they do not permit that degraded form of demonstration which 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).

Argumentation is in language, not in discourse. Since Ducrot’s structuralist framework reduces the order of speech to that of language (Saussurian langue), it is quite coherent to deny any specific principle of organization to reasoned discourse.

5. How to argue the (non-)demonstrative character of argumentation?

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

Interaction studies have taught us a great deal about what everyday discourse can achieve. Short, local inferences are developed in sequences that combine language and action into operational conclusions.. We define, categorize, articulate causes and effects, make analogies,  all of which are more or less inadequate, but all of which are open to criticism and correction. Sometimes, these result in satisfaction for all i.nvolved

WIth a few conventions and adjustments, more sophisticated episodes or reasoning  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 at least allow syllogistic demonstration. Figures and arithmetic are not entirely foreign to natural language, which also allows for some correct geometrical conclusions, so that the tenon fits the mortise exactly. Not only a logic, but also an everyday geometry, arithmetic, physics… underpin linguistic practices, and no metaphysical deficiency prevents them from drawing correct conclusions, as the following little calculation shows:

The Abbé du Chaila was one of the main architects of the repression of the Protestants in the Cévennes, in the south of France. His assassination was at 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 the parish registers. It must have been at the beginning of 1648. In fact, François’s parents, Balthazar de Langlade and Francoise d’Apchier, were married on the 9 April 1643 and had eight boys and two girls in ten years, at a rate of one child per year. François being the fifth child of the family was thus born in 1648, the four previous brothers having been born in 1644, 1645, 1646 and 1647.
Robert Poujol, [The Abbé du Chaila (1648-1702)], 2001[1].

Any claim about the (non-)demonstrative character of argumentation in general is difficult to assess, regardless of the prestige of the authorities supporting it. Arguments from natural signs, case-by-case arguments cannot be treated as appeals to authority or arguments by analogy. Ordinary argumentative discourse can combine quite heterogeneous types of argument and fields of evidence, including technical and scientific episodes. One can argue properly in natural language; sometimes, some truth emerges from legal and historical debates if they are properly framed and managed; and argumentation plays a role in the learning of science.

6. Argumentation in science education

There are other links to be found between argumentation and scientific activities. The golden rule is given by Quine who uses it to construct his formal logic:

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).

By the same token, the teaching and learning of scientific method is necessarily grounded in natural language and everyday argumentation, and departs from it when there is a clear advantage in doing so.
Scientific proof can be seen both as a finished product, impeccably presented in published papers and textbooks; and as a process, that leaves room for dialogue, argument correction and development. Argumentation is on the side of the process, its claims are in the making.

This leads to a focus on argumentation as an instrument for science education (Erduran & Jiménez-Aleixandre 2007). Scientific “enculturation” in general, debates on socio-scientific issues are now key domains of argumentation studies. These research programs on argumentation in science education and argumentation on socio-scientific issues, emerged in the late 1990s and early 2000s. They now represent a key field of development for argumentation studies.

The humanities remain largely trapped in a conception of argumentation based on logocentric discourses, in which anything and everything can be claimed. An antagonism has developed from this conception, with “logical demonstration” serving as a convenient antagonist. The repositioning of argumentation as a complex, combinatorial activity that seeks to manage heterogeneous evidence in possibly complex material contexts allows us to distance ourselves from this traditional logocentric exclusivity. Discussions between two mechanics disagreeing about how to repair a faulty engine, or between two students disagreeing about the shape of the rays coming out of the lens are as prototypical of an argumentative situation as any ideological debate.

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

[2] Arsac Gilbert, Chapiron Gisèle, Colonna Alain, Germain Gilles, Guichard Yves, Mante Michel 1992  Initiation au raisonnement déductif au collège. Lyon, Presses Universitaires de Lyon
Baker M. J. (1996). Argumentation et co-construction des connaissances. Interaction et Cognitions 2, 3. 157-191.
Buty Chr. & Plantin Chr. (2009). Argumenter en Classe de Sciences. Du débat à l’Apprentissage. Lyon: ENS Éditions.
De Vries E., Lund K., & Baker M. J. (2002). Computer-mediated epistemic dialogue: explanation and argumentation as vehicles for understanding scientific notions. The Journal of the Learning Sciences 11, 1. 63-103.
Polo Claire, 2020. Le Débat fertile. Explorer une controverse dans l’émotion Grenoble: Université Grenoble Alpes Éditions

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« PERSUASIVE DEFINITION »

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)

For a definition to be persuasive, in Stevenson’s sense, its descriptive content must be redefined, while its « emotional force » must remain intact, so that it can be applied to the redefined content. Stevenson gives the following example; A and B are “discussing a mutual friend”  – let’s call him Z (id, p. 211.)

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

— B describes Z in a number of positive terms (imagination, sensitivity, 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 “Z is a cultured person” a positive emotional orientation. Moreover, the word culture has a vague descriptive sense; B carves out a new definition from this descriptive sense, and shows that it fits their mutual friend Z. Stevenson analyzes 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 – according to Stevenson – is at point (b):

(a) B wants to value Z.
(b) He redefines culture “within the boundaries of its customary vagueness” according to the qualities his friend possesses;
(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 the cultured person.

Thus, a persuasive definition redefines the descriptive content of a term not on the basis of context-free, objective general considerations, but with a view to applying that term to a predetermined person, a known singular case. This would make it misleading.

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

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 to call him by the name corresponding to this category. In other words, a persuasive definition is an ad hoc definition.

But was this definition dreamed up by B in order to save their friend Z from the very negative assessment he is receiving from his other “friend” A?
Rather, this definition seems to be a step in the evolution of the notion of culture, which will lead to the multiple definitions of the word in the dictionary by 2025, where the traditional definition will take second place see Merriam-Webster, Culture.
This exchange is merely a moment of confrontation between two definitions that will end up side by side

A perfect argumentative situation

It could be argued that A, in order to categorize Z, uses the traditional definition of culture as literary references, etc., also carved out of the vague meaning of « culture », « within the limits of its customary vagueness ». Because of its traditional prestige, this definition of « culture » , is considered true and self-evident, and the common friend is excluded from the circle of the cultivated / cultured people.
So A uses the traditional definition of culture to exclude Z from the cultured category, just as B uses a renovated definition to include Z in that category.
In short, we have a perfect stasis of definition that has created an argumentative situation in which A tries to influence B as much as B tries to influence A in their mutual visions of their friend B.
It should be noted, however, that the narrator, Stevenson, attributes a convincing definition only to B. A is the only partner who does not try to persuade, but simply tells the truth.This is a typical maneuver by an ally of A.

A parallel case could be imagined about the criteria of what constitutes “good schoolwork”.

The teacher’s definition: The value of a schoolwork is determined by its content (knowledge-based assessment)
Parent’s education-based definition: A good schoolwork is one in which students are engaged and working hard. My son spent his weekend working on his history class. He turned in an excellent paper, and deserves a good grade. (educationnally-based evaluation)

The parent’s definition could be considered biased just like B‘s definition of culture was in the previous case. The category “is a good school assignment” has been redefined to apply to Mr. Doe’s son, without regard to the content of the paper, which has traditionally been considered as the deciding factor. The target has been redesigned to fit the arrow, and the archer’s limited skills. Or not.

Clearly the parent also has a good educational case. Some negotiation is needed, as it was in the previous case.

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DEFINITION 3
Argument from DEFINITION

1. Definition in the process of categorization

Categorization is the process by which an individual is identified as belonging to a category, and is given the name of that category, S. Categorization and Nomination. The definition is the reservoir of essential characteristics that allow this identification.

2. Argumentation on the basis of 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 an entity designated by that name. It works 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 that is taken as authoritative.
   3. A conclusion: everything that is said about the D can be really be said of I.

A definition (a definiens) is a rich set of propositions about “what that kind of being is”. It contains doxical assertions based on common knowledge about those beings which are found in the examples that illustrate the definiens as well as in the definiens properly said. To call a being “a D” is to ascribe to it all the properties that define the name “D”, as well as the scripts, duties and obligations associated with Ds. In other words, the definition (the definiens) of “what is a D” is a set 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, see 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 definition machine. Armed with this information, we can draw from the body of knowledge 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 legal treatment will be conducted according to 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. Well, my daughter, you’re like this, and you must act accordingly:
— “This is a Scotch bonnet” so, it is “very aromatic, it is delicious prepared in an omelette”; better still, 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 vacations on your beaches.
— “Mrs. Doe is a mother who lives alone”, so under such and such administrative and financial rules, she is entitled to a single parent allowance of a certain amount.
— “Mrs. Smith is a graduate student” so she enjoys certain rights and must fulfill certain obligations as defined by the Graduate Students Charter in effect at the university where she is enrolled.
— “He’s a bastard” so I don’t trust him.

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

When the criteria used for categorization are defined within a rigorous scientific framework, then argument by definition becomes an essential scientific tool. Similarly, in the field of law, the criteria that qualify an act make it possible to apply the legal syllogism, that provides routine legal decisions by default.

3. Argument from definition: Lexical definitions as inferential resources

Some basic argumentative inferences embedded in a word are made explicit in its lexical definition and suggested in the examples of its use. Language dictionaries are repositories 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) see Orientation. These inferences are considered rational and persuasive insofar as they are expressions of a shared semantic heritage, the treasury of discursive rationality. Consider the word rich. By collating the definitions of some current dictionaries, we can gain some insight into the elementary “licenses to infer”, diversions, or “drifts” to and from this word, that is, the semantic inferences that characterize a basic understanding of the word “rich”. The following information is taken 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 become rich quickly,  SO, he is likely to become rich

 (ii) He is rich, so… On the same analytical basis, or from the 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 allows for exceptions: He is rich, but …

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

(iii) An implicit principle, the “anyone can get rich” principle, eliminates two objections:

Having a humble background:
Even though he became rich and famous, he never forgot his humble background:

Lack of formal education:
A lack of formal education is not an obstacle to getting rich.

(iv) One main opposition: The rich vs. the poor, allows the application of the topos of the 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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DEFINITION 2
Arguments justifying a DEFINITION

1. Methods for constructing a sound definition

Definitions based on common usage, on the true meaning of the word, on the scientific meaning of the word can be pitted against each other.

There are rules for establishing a correct definition, and therefore, critical rules for evaluating, definitions, see Arguments establishing vs. exploiting a relationship.
These rules depend on the social or scientific fields to which the defined entities belong, and adapt to the different types of definitions. The more general ones are.

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

(ii) Does the definition avoid circularity? If not, it is a vicious circle. Since words are defined by words, the whole dictionary is actually circular. As explanations or arguments in general, definitions should try to avoid circularity as much as possible; that is, the definition (definiens) cannot use the word it is supposed to define (definiendum), nor a (near) synonym of the word. Nevertheless, a definition by synonyms or by the simple negation of an antonym is helpful if one of these defining words is better known than the definiendum.

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

(iv) Does the definition make it possible to distinguish those entities that are called by that name from those that are not? A definition can be criticized for being too broad (it applies to heterogeneous objects or beings) or for being too narrow (it excludes objects or beings that it would be desirable to include). see Definition and Argument, § 2, for the role of ostension and exemplification.

(v) Does it help? That is, does it provide enough information to clarify the meaning of the word, and, if necessary, does it give some functional clues, or point to the scientific or technical uses of the word?

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

(vii) Is the definition objective? Does it exclude the speaker’s value judgments and ideological preferences about the entities or qualities being defined? see Orientation; Persuasive definitions.

Methods and rules such as those mentioned above serve as a guide for making definitions and, consequently, for criticizing them.
— 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 concise, clear, and simple
(vii) It is objective.

— These arguments are mobilized in debates about definitions (Schiappa 1993; 2000), that is, when there is a stasis of definition (see infra), see 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 follow this or that rule.

2. Stasis of definition

A definitional stasis occurs when it appears that discourse and counter-discourse appear to be based on incompatible definitions of the same object:

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

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

Incompatible categorizations lead in a question of definition:

S1:      — Accidental death of a Syldavian diplomat
S2:      — Assassination of a Syldavian diplomat

Classified information has been leaked:
S1:      — A new manifestation of the malfunctioning of the Syldavian services
S2:      — There are traitors within 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, based on legal definitions:

What is murder? What is an accident?
What are the crucial differences between negligence and treason?

The stasis of definition can develop as follows:

S1₁: — Syldavia is now a real democracy now!
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 certainly a true democracy
S2₂: — This definition is bad, and ideologically biased.

— The confrontation between the positions S1₁ and S2₁ raises a question of categorization.
— S1₂ rejects S2₁‘s objection by referring to the dictionary; he or she could just as well have referred to the accepted conventions, international law, consensus, etc.
— S2₂ ratifies the definitional deadlock.

According to Humpty Dumpty, the best way to resolve of a definitional stasis 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)

DEFINITION 1
DEFINITION AND ARGUMENT

1. Defining definition

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

Not only words but also phrases need to be defined. Fixed or semi-fixed phrases, that is idiomatic expressions, (beating around the bush), need to be defined, because their global meaning does not result from the mechanical combination of the meanings of their components.
Moreover, social life produces conventional expressions that are used with a specific meaning  that requires a definition:

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

Depending on the nature of the word and the circumstances of the questioning, these questions ask for the meaning of the word, or for 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 may be in dispute: 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                      =      “mother’s or father’s brother”
[definiendum]       =      [definiens]

The definition establishes a semantic equivalence between a word, the definiendum, “that which is  is to be defined”, the dictionary entry, and a discourse, the definiens “that which defines” (sometimes called “definition” by metonymy).
The definiens is a discourse that answers questions such as “what does the word X mean?” “What is X?”

From a logical point of view, the equivalence definiendum / definiens satisfies 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 interchangable in all contexts, the global meaning of the passage remaining the same.
The definition is substituted for the word defined, when the discourse containing that word needs to be clarified; the word is substituted for its definition when the discourse needs to be shortened.

Beyond its semantics and lexicological characteristics, the definition of “fish” as a species of animal draws on the field of natural science. The definition of “democracy”, “citizen” and “citizenship”, combines political science and political and ideological ideals. The definition of “single parent” refers to laws and regulations. The vague concept of a “cultured person” will combine a little of all the arts and letters. Advances in knowledge, history, and variations in usage will change the meaning of the words and the kinds of beings and objects they refer to.

Argumentative situations will destabilize the meaning of words, and the definition of commonly used words may require revision and further clarification.

2. Types of definition

Different methods can be used to construct a sound definition of a word, see Arguments Establishing vs Exploiting a relationship. They suggest criteria that come to the fore when the meaning of a word is at stake, when one wants to destabilize an unsatisfactory definition, or when one wants to justify a challenged one.

2.1 Ostension: Indicating the meaning of a word or a phrase

Ostension is a gesture, the act of showing someone a concrete object. To defining a concrete noun by ostension is to show a sample of the object or beings being referred to:

You 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 know a boletus badius when I see one!

Ostensive definitions can only be applied to concrete beings that are 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 an important tool for defining concrete things. The more 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 critique of definition: Does the definition under scrutiny allow us to refer correctly to all the entities or cases currently referred to by the corresponding name? S. Arguments to justify 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 blonds would disappear by 2202? [1]

The example given, if prototypical, provides a good basis for understanding the meaning of the word.

2.2.2 Definition by enumeration (in extension)

Definitions in extension proceed by the enumerating all the individuals to which 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 because it is on the “Democracy List”.

The 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 proven that a sum of money is ill-gotten by showing that it was neither acquired by work, nor by inheritance, nor is the legitimate product of a financial investment, and so on.

2.3 Definition and instructions for use

2.3.1 Operational definition

An operational definition associates a notion X with a set of operations that make it possible permitting to determine whether or not that individual is an X. An operational definition does not say what X is in essence; it simply indicates how to find all individuals to which X refers.

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

2.3.3 Functional definitions

As operational definitions, functional definitions do not consider the ature, or the technical design of the named instrument. The referent is characterized in terms of its functions, goals, objectives. Knowing what a compass is, is knowing that, it points (magnetic) north, 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 the next genus and specific difference” (Chenique 1975, p. 117).  An individual is given the name of its category, identified by a set of generic characteristics common to its parent genus and differentiating characteristics that specify its species, see Classification.

Essentialist definitions work well for natural species. In general vocabulary, the contrast is between central and peripheral characteristics. A dictionary of Syldavian institutions would include an entry “President of the Syldavian Republic (SR)”, defined by his or her mode of election, constitutional role etc. These core elements can be supplemented 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 (it applies to him or her and only to him or her, the condition of substitutability is fulfilled), but doesn’t contribute to the clarification of the meaning of “President of the SR”. From the Aristotelian point of view,, free accommodation at the Parnassus Palace is not an essential characteristic of the office of President of the SR.

Essentialist definitions try to express the true meaning of the word, which corresponds to the very nature of the things it designates, i.e. 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 governed by a methodology, based on an “intuition of the essence of the thing”, S. Classification. Ancient dialectic was the instrument used to construct 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 seeks to establish the ideal, essential characteristics of democracy, sometimes condemning current uses of the word in the name 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 Lexicographic definition

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

— Collect all the words and idioms of a language (or the vocabulary used at a given time).
— Provide a description of their various meanings, their usage in speech, and their stereotypical figurative usage.
— Give the typical contexts of use associated with these meanings.
— Give the syntactic constructions that correspond to these meanings.
— Locate them in the different semantic fields to which they belong, i.e. indicate their relationships with their (quasi-) synonyms and antonyms, and their position in their derivational families.

The dictionary is a highly legitimated and legitimating institution. From the perspective of argumentation studies, since lexical meaning is inferential, the dictionary should be seen first and foremost as a vast store of “inferring principles”, S. Argumentation based on a definition (3).

Linguistic definitions draw simultaneously on different kinds of definitions. Knowledge of words (lexical definitions) and knowledge of things (encyclopedic scientific definitions) are theoretically clearly separated. However, they are, inextricably linked for current terms that have an encyclopedic definition. “When the barometer falls, the weather turns bad”: is this deduction supported by a meteorological physical law that expresses knowledge about the variations in atmospheric pressure? Or is it contained in the linguistic meaning of the word? To knowi 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 that have “plenty of being” are worthy of scientific knowledge, and are registered in the encyclopedia. The boundary between the two categories is unstable and depends on the state of research; conversation, once considered a futile and elusive thing, has been fruitfully conceptualized  by conversation analysis and ethnomethodology. These sciences have given “more being” to their object.

 2.4.3 Scientific definition of concepts and lexicographic definition 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 may use a redefined common term, (see infra stipulative definitions). The the physicist’s mass is not the dictionary’s mass:

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).

In common 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 that establish a scientific definition of things are domain dependent. It took an astronomy conference was necessary to redefine the term planet, and end the controversy over the status of Pluto.

The common definition can be hardly recognizable under the technical definition. The following definition corresponds 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 twitch (a start);
3. Neurovegetative events, such as tachycardia and decreased skin resistance.
So, I was referring to the “classic” surprise reaction 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 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 names, that is, the arbitrary application of names to things which are clearly designated by perfectly known terms. (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 process of definition begins with a given term and seeks to clarify its pre-established definition, stipulative definitions begin with a clear and well-established meaning (the definiens), and seek a word to refer to that content; it is a baptism. For this purpose, one might choose an ordinary word stripped of its ordinary meaning. By convention, physicists use the word charm to refer 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 the nature of the phenomenon better than yours ”. Since everyone has a preferred terminology, the relatively arbitrary nature of the stipulative neologism can lead to terminological inflation and a “war of words”, that can be overcome by invoking the primacy of the reality of things. Should we call such patterns of argumentation :

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

If no agreement can be reached, the question can be settled radically, “You can 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 constructed argumentatively in reference to a set of rules, S. Argumentations constructing a definition.
These rules generate a set of specific argumentative lines that are exploited when a conflict of definitions arises, such as:

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

Persuasive definitions are definitions that are restructured 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 store 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 naming.

This is a mushroom

3.1.2 Definition used to enrich the description of an individual

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

3.1.3 A discursive trick: Demanding a definition

The demand for a definition can be made with the intention of blocking the development of the opponent’s line of argument, S. Destruction of speech. The following exchange takes place in a discussion about different 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, a stalemate, in which many participants are not eager to participate.
The internal journal of a research institution objects to a traditional claim of laboratories:

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

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[1] 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. [The Unity of mankind)

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DEFAULT REASONING

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 that is not deducible from a set of premises {P1} can be deduced from  {P1} augmented of additional 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 allow for exceptions: in general, birds fly; but penguins (Sphenisciformes, Spheniscidae) are birds and do not fly. Consequently, 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. Nevertheless, in the absence of any information suggesting that Tweety is a penguin (or some other flightless bird), the theory of revisable inference permits 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 we have  now , may turn out to be false later, when further knowledge is gained.

The theory of defeasible reasoning also addresses complex questions 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 wing 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 related to having the ability to fly, which, according to the available information (3), is not true in the case of Tweety. The inferences 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 refuted in two ways:
— On the one hand, by 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 transitional principles usually invoked in the argument do not apply in the case considered (“undercutting defeaters”, ibid), S. Refutation.

2. Representation of default reasoning

The reasoning (1) is represented as (2

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

(2)

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

ζ : η — θ

ζ: Prerequisite: we know that ζ
η: Rationale: η is compatible with available information
θ: Conclusion

The historical origins of the theory of revisable reasoning are to be 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; we can assume that C.

Gabbay & Woods (2003) develop a study of practical reasoning that combine the insights of relevance theory and default reasoning theory.

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DEDUCTION

1. In ordinary language

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

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 slavery.’
Arthur Conan Doyle, Adventures of Sherlock Holmes — Scandal in Bohemia, 1891[1].

This « deduction » seems to correspond to an argument from natural signs, 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 which, according to valid rules, links 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-conducted deduction is a demonstration, that produces apodictic (incontrovertible) knowledge, defined as “any necessary conclusion from other things known with certainty” (ibid.).

Valid and sound syllogistic reasoning is a type of deductive reasoning, that is sometimes used as a reference for valid argumentation. Argumentation developing the definition of a word and its implications, or the various forms of argument 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 hypotheses:

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, a deduction is taken to be a valid and sound deduction. Now, a series of propositions can be advanced by a speaker as a valid and sound deduction without actually being so.
To be valid, the deduction must be carried out according to the laws of (a well-defined system of) logic. For example, the inference/deduction from a false proposition to a true one “P(F) → Q(T)” is valid, but not sound: to be sound, the deduction must start from axioms or, more generally, from true propositions.

The implication (conditional) is a binary logical connective. A deduction is a chain of operations connecting well-formed expressions by a rule. For example, the rule of modus ponens (⊃–rule, see above) 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 which expresses a logical law:

“If the implication is true and the antecedent is 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 satisfied, 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 is based on the affirmation of the antecedent of a true implication. It is also known as the modus (ponendo) ponens rule: the deduction posits (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 in natural language, a situation in which it could rain without the grass getting wet is unthinkable.

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

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 is based on 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 lawn to be wet, was incorrectly assumed to be necessary.

4.2 Affirming the consequent

It is not possible to infer the existence of a phenomenon from the existence of a necessary condition of that 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 satisfied	The lawn is wet
*so, R	*so, R is met	*So, it is raining

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

5. Pragmatics of deduction

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

Ordinary situations are different; ordinary reasoning is not about formal systems, but about causes and effects in the empirical world, see Causality. This world is represented by the body of shared knowledge; it follows that only relevant knowledge needs to be made explicit.

Suppose that the lawn might be wet because it has rained, because the lawn has been watered, because a pipe has leaked, or simply because of a heavy dew. If it is contextually obvious that the lawn has not been watered (I know what I have done), that there is no leak (for the simple reason that there is no water pipe in the garden), and that there is no dew (at this time of the day), then I can safely say that if the grass is wet, it is because it has rained, or is raining.

Only the superficial form of reasoning is fallacious. Full evaluation must take the context into account and reconstruct the argument explicitly, case by case, thereby eliminating the other sufficient conditions and 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 from Arthur Conan Doyle, The Penguin Complete Sherlock Holmes. London: Penguin Books, 1981. P. 162.

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DEBATE

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, forming more or less ephemeral alliances, integrating / refuting / destroying the positions of others, supporting arguments by drawing on personal involvement in the issues under discussion. Sometimes the two notions of argument and debate are conflated, with television debates implicitly seen as the prototypical argumentative genre.

This view of argumentation has important limitations. It leaves out argumentation in the workplace, or argumentation in science education. It associates argumentation with polemical debate, which is a non-cooperative form of argumentation. Television 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 with both short-term and long-term implications are discussed, different types of sequences have to be managed in different episodes: introducing new participants; reading the agenda; giving relevant information is given (to all, to less informed participants), writing down conclusions — not to mention the episodes devoted to interaction management, including digressions and jokes. The level and nature of argumentation of these episodes can vary greatly.

The form and effectiveness of the arguments presented in a debate depend on the relative power of the participants in the sphere concerned. If taken on a majority basis, When a decision is taken on a majority basis compels the minority is coerced, whether or not they are persuaded, and whether or not the winning argument is the strongest from the point of view of an external evaluator.

1. Informed and properly argued debate as a source of legitimacy

From a foundational perspective, a political decision can be considered legitimate if it conforms to, or is derived from an original pact, a social contract freely entered into by the ancestors or ideal  representatives of the community in a mythical primordial time, or in an ideal rational space.

Democracy values ​​debate. A decision is considered legitimate only if the issue has been publicly argued for and against, in a safe, open, free and contradictory space. In principle, the decision should take into account the results of the debate ; whether or not that decision is really supported by the best argument, is another matter; authority and power play a role. Debate as a form of argumentation is at the heart of democratic life. In schools, it is seen as the key instrument of “democratic learning”, whether it in citizenship education, history, or science education.

2. Criticism of debate

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

— The use of debate can be a mere means of presentation. The issue is framed as a problem, as being the focus of two antagonistic discourses, as if things were only “interesting” in so far as they radiate a certain polemical heat.

— Paradoxically, “the debate is open” can be a convenient closing formula, when listeners in both camps have their fair share of good reasons, as if the main virtue of a debate were to encourage and justify further debates.

— A doubtful and questioning attitude can be very comfortable. Debate condenses the diversity of positions into a single global voice that says everything and the opposite; but articulates such unresolved contradictions very well. Accordingly, debate is a fertile field for argumentative personalities to flourish.

— When debate becomes an end in itself, it becomes a performance, and loses all connection with the search for truth, clarification of the issues and positions, agreement or the exploration and deepening of 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, see Laughter and Seriousness.

— Pedagogically, debate can encourage confrontational forms of argumentation. In fact, debate does not systematically break with symbolic violence, but may simply displace it. Some cultures find open interpersonal confrontation repugnant, or at least rude and counterproductive. Forcing students to debate can be an educational blunder. Moreover, debates on serious issues divide groups, and can jeopardize the reputation and even the safety of the individual who is asked to expose his or her beliefs, networks and communities. In some communities and cultures, such self-exposure is not an option.

— Even in the best organized public socio-political forum, what is considered the best argument may differ from party to party. Moreover once the decision is made, it may require a new discussion about how it should be implemented, which a regulatory or legal issue, in the hands of the current regime. There is a wide open and opaque space between debate and decision, and another between decision and implementation.

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

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

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CRITICISM, RATIONALITIES, RATIONALIZATION

1. Rationalities

In the modern and contemporary world, scientific rationality, based on experience and shaped by mathematics has taken the upper hand in the current vision of rationality. Scientific discourse is seen as the prototype of rational discourse, while argumentation is seen as the instrument of reason as reasonableness in human affairs. This position has been strongly reasserted by Perelman & Olbrechts-Tyteca ([1958]), S. Persuade, convince; Persuasion.

Ordinary discourse in action embodies different kinds of rationalities.

Rationality as common sense — Rationality as common sense can be defined as the art of thinking according to the rules and intuitions embodied in traditional logic and adapted to social needs through rhetorical argumentation. As a scientific concept, this vision of rationality has been shaken to its foundations by the development of axiomatic thought, as exemplified by non-Euclidean geometries or by the invention of the imaginary unit i, such as i² = −1. In the human sciences, the Freudian invention of the unconscious and the development of studies on ideologies and social determinism, have most certainly challenged the vision of a sovereign subject transparent to itself and consciously in control of its calculations, intentions, discourses and actions. This double crisis directly affects the classical vision of the rational well-intentioned rhetorical speaker.

Rationality as the adaptation of a conduct to a goal — Rationality as the adaptation of behaviour to a goal covers all forms of action guided by a script, a recipe or a pre-established conventional plan. For example, to make a good custard,  it is more rational to pour the hot milk over the eggs than to put the eggs in the hot milk, so that the cream is more homogeneous. This principle of rationality merges with the requirement of consistency between action and goal. It is exploited by all forms of refutation that reveal a contradiction in the opponent’s ideas and actions see Ad hominem; Consistency. Since it is human to pursue several goals simultaneously, the resulting practical rationality is constantly destabilised.

Rationality as the adaptation of an action to a goal is compatible with crime. The Marquis de Sade is an excellent arguer. Hence the possibility of delirious and despotic rationalities serving equally perverse ends.

Rationality in relation to a domain — Rationality depends on domains. A given behaviour (with or without a linguistic component) is said to be rational if it conforms to recognised practices in the relevant domain, technical field, scientific paradigm or tradition of thought, see Rules.

Democratic rationality — Democratic rationality is a quality of societies and groups where information is accessible; where free and contradictory examination of socio-political positions and oppositions can develop with a view to effective decision-making; where there is a right of reply; and where the safety of the opponents is ensured. It is a form of society in which the holders of legal power and violence are held accountable for their use.

If the above conditions are to be expressed as a set of rules, they will have to be hierarchical and context-sensitive in order to integrate different genres and practices of rationality

2. Discursive and argumentative rationality

Linguistic rationality — From a linguistic point of view, discourse is considered rational if it is well constructed, if it is understandable, if the speaker can explain it, and if it makes sense in relation to the problem discussed or the task under way.

The paradoxes that arises in an argumentative situation driven by a question is that each of the competing discourses taken in isolation makes sense, but, taken together, they become contradictory. To distinguish between these answers, argumentation theorists need a criterion, that is stronger than meaning, and, to this end, introduce the notion of rational or reasonable discourse into their models. The different families of argumentation theories can be associated with different conceptions of rationality.

Discourse rationality and discourse types — Argumentative discourse is not the only container of discourse rationality. There is not one, but several discursive rationalities: argumentative rationality, narrative rationality, descriptive rationality, and so on. Irrationality manifests itself in incoherent and delirious narratives, descriptions or prescriptions; in any ill-conceived installation diagram that can be called irrational, because it is useless.

Rational discourse and effective rhetoric — Effective rhetoric, focused on persuading an actual, relevant audience is a case of goal-adaptive rationality. It is compatible with verbal and non-verbal manipulation.

Rational discourse as justified and revised discourse — The definition of rational discourse as a justified discourse develops the idea that a discourse is rational-reasonable insofar as its claim is not asserted on the basis of individual certainty, but is openly supported by other propositions, using some kind of public data linked to the claim by some recognised, albeit fragile rule. Its rationality increases when it shows its weaknesses and suggests the directions to be taken to improve it; as Bachelard says, there is no truth, only rectified errors. The Toulminian layout meets these requirements: the Claim is based on Data, according to a Warrant, itself supported by a Backing, and duly Qualified. The critical instance is represented by its trace, the Rebuttal, which indicates the possible points of refutation.

The practice of dialogue, whether at a distance or face to face, can be seen as the exercise of the critical function of language. A speech is more rational when it has been duly criticized, that is, when it has survived a series of contradictory encounters. Criticising does not mean “denigrating” or “rejecting”, but “passing judgement”, positive or negative, on an activity. Observation of the data shows that the partners involved in an argument spend a lot of time evaluating their partner’s arguments (Finocchiaro 1994, p. 21). Argumentative speech is evaluated in a meta-discourse, produced under any conditions, face to face or at a distance in space and in time. Any approach to argumentative discourse that is concerned with empirical adequacy must take this critical dimension into account.

For the New Rhetoric, arguments are evaluated by the participants in the rhetorical event; the rationality of an argument increases with the number and quality of the interested and competent listeners who accept it. The development of human rationality is seen as an evolution from a particular to a universal audience, see persuasion.

The dialogue models of argumentation place critical activity at the center of their concerns. Pragma-Dialectic and Informal Logic develop a critique of argumentation based on the notion of fallacy. To detect fallacies, pragma-dialectics uses a system of rules, while informal logicians use the technique of critical questions, see paralogism; sophism; fallacy; norm; rules; evaluation

3. Rational argumentation, as a “dream of language”

Anscombre’s and Ducrot’s theory of argumentation within language and Grize’s natural logic make no commitment to rationality; they are not irrational but a-rational. Since every discourse is argumentative, the idea of ​​correcting a discourse in order to improve its argumentativity or its rationality makes no sense. These theories are only concerned with the fact that to be rational a discourse must first be meaningful, see schematization; orientation.

The Argumentation within language theory proposes a radical critique of the ability of discourse to achieve any kind of rationality. Conclusions are seen as mere semantic developments of the arguments, the argumentation process being driven by the linguistic orientations of the utterances; the discourse develops according to the orientations of natural language, denounced as biases by fallacy theories, in search of a referential, neutral, objective language. In the language of fallacies, this amounts to saying that argumentation in natural language is necessarily circular, i.e., fallacious. It follows that argumentation as a rational process is a “dream of discourse” (Ducrot 1993, p. 234). Following to this metaphor, the rational claim of argument (as found, for example, in Perelman) is seen as a “rationalization of the dream”, and the criticism of the argumentation, as a “criticism of the dream”, whereas dreams can only be exposed and interpreted as such. see Demonstration.

4. Rationality and rationalization

Psychoanalysis uses the terms rationalization or intellectualization to refer to discursive constructions that are claimed to be rational by the subject in an attempt to explain his or her actions, representations, feelings, symptoms or delirium. Psychoanalysis rejects such reconstructions because the subject has no conscious intellectual access to their true source (Laplanche and Pontalis, 1967, art. [Rationalization]):

Whenever possible, [the ego] tries to stay in good terms with the id; it dresses up the unconscious commands of the id with its preconscious rationalizations […] In its position halfway between the id and reality, it all too often yields to the temptation to become sycophantic, opportunistic and lying, like a politician who sees the truth but wants to keep his place in the popular favor. (Freud [1923], p. 55).

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