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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1. Rationalities

In the modern and contemporary world, scientific rationality, based on experience and shaped by mathematics has taken the upper hand upon the current vision of rationality. Scientific discourse is taken 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 complying with the rules and intuitions embodied in traditional logic and adapted to social necessities by rhetorical argumentation. As a scientific concept, this vision of rationality has been shaken to its foundations by the development of axiomatic thinking, as exemplified by non-Euclidian geometries or by the invention of the imaginary unit i, such as i² = −1. In human sciences, the Freudian invention of the unconscious and the development of studies on ideologies and social determinisms, have most certainly challenged the vision of a sovereign subject transparent to him/herself, consciously mastering his or her calculus, intentions, discourses and actions. This double crisis directly affects the classical vision of the rational well-intentioned rhetorical orator.

Rationality as adaptation of a conduct to a goal — Rationality as adaptation of conduct directed towards a goal covers all forms of action guided by a script, recipe or pre-established conventional plan. To make good custard, for example, it is more rational to pour the hot milk on the eggs than to put the eggs in the hot milk, so that the cream will be more homogeneous. This principle of rationality merges with the consistency requirement between conduct and objective. It is exploited by all forms of refutation revealing a contradiction in the opponent’s conceptions and actions S. Ad hominem; Consistency. Since it is human to pursue several objectives at the same time, the resulting practical rationality is perpetually destabilized.

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

Rationality related to a domain — Rationality depends on domains. A given behavior (with or without a linguistic component) is said to be rational if it conforms to recognized practices in the relevant domain, technical field, scientific paradigm or tradition of thought, S. 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 may 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 brought to account for their use.

Is rationality  governed by rules? if one tries to express the preceding conditions as a set of rules, they will have to be hierarchized and context-sensitive in order to integrate various genres and practices.

2. Discursive and argumentative rationality

Language rationality — From a linguistic point of view, a discourse is deemed rational if it is well built, if it is understandable, if the speaker can account for it and if it makes sense in relation to the problem discussed or the task under way.

The reasonableness paradox created 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 discriminate between these answers, theorists of argumentation need a criterion, which would be stronger than meaning, and, to that effect, introduce the notion of rational or reasonable discourse into their models. The different families of theories of argumentation can be related to different visions of rationality.

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

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

Rational discourse as justified and rectified discourse — The definition of rational discourse as a justified discourse develops the idea that a discourse is reasonable insofar as its claim is not asserted on the basis of individual certainty, but openly supported by other propositions, exploiting some kind of public data connected to the claim by some recognized rule, albeit fragile. Its rationality increases if it exhibits its weak points, suggesting the directions that must 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, indicating the potential point of refutation.

The practice of dialogue, whether remote or face-to-face, can be considered to be the exercise of the critical function of language. A speech is more rational if it has been duly criticized, that is, if it has survived a number of contradictory encounters. Criticizing does not mean “denigrating” or “rejecting”, but “passing a judgment”, positive or negative, on an activity. The observation of the data shows that the partners involved in an argument spend much 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 concerned with empirical adequacy must take this critical dimension into account.

For the New Rhetoric, arguments are assessed by the participants in the rhetorical event; the rationality of an argument increases with the number and quality of the interested and competent audiences who accept it. The progression towards human rationality is seen as an evolution from a particular to a universal audience, S. Persuasion.

The dialogue models of argumentation put the critical activity at the center of their concerns. Pragma-Dialectic and Informal Logic develop a critique of argument 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. S. Paralogism; Sophism; Fallacy; Norm; Rules; Evaluation

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

The Argumentation within Language theory of Anscombre and Ducrot and the Natural Logic of Grize make no commitment to rationality; they are not irrational but a-rational. Any discourse being argumentative, the idea of ​​rectifying a discourse in order to improve its argumentativity or its rationality does not make sense. These theories are just concerned with the fact that to be rational a discourse must first be meaningful, S. Schematization; Orientation.

The Argumentation within Language theory proposes a radical criticism of the capacity 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, which are denounced as biases by fallacies theories, in search of a referenced, neutral, objective language. Rephrased in the language of fallacies, this amounts to the claim that argumentation in natural language is circular, so fallacious. It results that argumentation as a rational process is a “dream of discourse” (Ducrot 1993, p. 234). Following this metaphor, the rational pretension of argument (as found in Perelman, for example) will be seen as a “rationalization of the dream”, and the criticism of the arguments, as a “criticism of the dream”, whereas dreams can only be exposed and interpreted as such. S. Demonstration.

4. Rationality and rationalization

Psychoanalysis uses the terms rationalization or intellectualization to refer to discursive constructions claimed to be rational by the subject who tries to account for his or her actions, representations, feelings, symptoms or delirium. Psychoanalysis objects to such reconstructions that the subject has no conscious intellectual access to their true source (Laplanche and Pontalis, 1967, art. [Rationalization]):

Whenever possible, [the ego] tries to remain in good terms with the id; it clothes the id‘s unconscious commands with its preconscious rationalizations […] In its position midway between the id and reality, it only too often yields to the temptation to become sycophantic, opportunist and lying, like a politician who sees the truth but wants to keep his place in popular favor. (Freud [1923], p. 55).

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The expression counter-argumentation can be used to refer to any kind of discourse, argued refutation or objection, going openly against an argumentation. A mere “No!” can be considered as a counter-argumentative move, even a nonverbal expression of rejection clearly interpretable as such.

Unlike direct refutation, a specific “argumentation vs. counter-argumentation” situation occurs when the refutation is reciprocal and indirect:

— Speaker S1 argues for proposition M.
— Speaker S2 counter-argues for proposition R, incompatible with M:

S1 — Let’s built the new school here, the land is cheaper.
S2 — Let’s built the new school there, the students will waste less time commuting

S2 makes a counter-proposition R, providing an alternative to M.

Argumentation and counter-argumentation play a reciprocal role in refutation. In such a polarized situation, the fact of providing a reason for doing R, incompatible with M, serves as a reason for not doing M. Any good reason for supporting R is seen as a counter-argument to M.

The argumentation / counter-argumentation structure may correspond to an emerging argumentative situation, or to the moments when the participants present and argue their position without considering the antagonist’s proposal, which can occur at any time in a concrete argumentative situation.

An argued position can be presented in isolation in an autonomous text without refuting or even mentioning any existing counter-argumentation. Adopting such a strongly assertive strategy avoids the paradoxes of refutation, but can be seen as a kind of contempt for the argument put forward by an opposing party. S. Question; Contradiction; Antithesis; Dismissal.

As is the case with weak refutations, a weak counter-argumentation will reinforce the attacked position. In the following passage, Noam Chomsky considers that his opponent, the philosopher Hillary Putnam, has failed to develop a counter-argumentation, even a counter-proposal, and argues that this shows that he, Chomsky, must be right:

So far, in my view, not only [Putnam] has not justified his positions, but he has not been able to clarify what these positions are. The fact that even such an outstanding philosopher fails to do so, may allow us to conclude that…
Noam Chomsky, [Discussion on Putnam’s Comments], 1979.[1]

The praise of the opponent as an « exceptional philosopher » is a characteristically eulogistic and perfidious accompaniment to this kind of refutation:

By refuting you, I’m refuting not just any philosopher, but a Master – and therefore, a fortiori, all the philosophers who are opposed to my views.

S. Politeness; Ignorance; Paradoxes.

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[1] Noam Chomsky, Discussion sur les Commentaires de Putnam. In Piattelli-Palmarini M. (ed.). Théorie du Langage, Théorie de l’Apprentissage. Paris: Le Seuil. 1979. P. 461.

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According to H. P. Grice, the intelligibility of the conversation is ruled by “a rough general principle which participants will be expected (ceteris paribus) to observe”, namely:

‘Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged’. One might label this the Cooperative Principle. (1975, p. 45; capitalized in the text).

This “Principle of Cooperation”, is specified under four forms, “Quantity, Quality, Relationship and Manner” (ibid.).

— Quantity: “I expect your contribution to be neither more nor less than is required” (ibid.).
— Quality: “I expect your contribution to be genuine and not spurious” (ibid.). This can be compared to the requirement of accuracy mentioned in the pragma-dialectical rule 8; the same concern is also found in Hedge’s Rule 1 “For an honorable controversy”, S. Rules.
— Relation: “I expect a partner’s contribution to be appropriate to immediate needs at each stage of the transaction” (ibid.). This concerns in particular the relevance of the turn in relation to the present topic of dialogue and action. Grice recognizes the difficulty of identifying what is relevant in an exchange. The pragma-dialectical “Relevance rule” deals with this same requirement (van Eemeren, Grootendorst (2004, p. 192). S. Relevance; Rules.
— Manner: “I expect a partner to make it clear what contribution he is making” (ibid.). This entry can cover the refusal of the obscurity of expression and action; of ambiguity (the first of the Aristotelian fallacies); of the unnecessary prolixity, corresponding to the fallacy of verbiage.

Grice holds that his principles capture the rational character of conversation:

One of my avowed aims is to see talking as a special case or variety of purposive, indeed rational behavior. (Id., p. 47)

as well as its reasonable character: Respecting these principles is not merely “something that all or most do IN FACT follow, but as something that it is REASONABLE for us to follow, that we should not abandon” (id., p. 48; capitalized in the text).

These four principles can be compared with those advanced by normative theories of argument, S. Rules.

A statement violating Grice’s principles is not eliminated as fallacious, but is understood as an indirect speech act. When a participant notes that something is not in conformity with a conversational rule, the reaction is not to accuse the partner of making an irrelevant or irrational contribution, but to engage in an interpretive process to identify why he or she has flouted the conversational rule. The analysis of fallacies reverts to this interpretive orientation whenever it adds to its logic pragmatic considerations taking into account the contextual conditions of the exchange.

In an argumentative situation, the concept of cooperation is a strategic issue redefined by the participants, who are not necessarily willing to cooperate, for example in their own refutation. There is nothing scandalous or irrational about this, insofar as partners are aware of being in such an intentionally opaque context, S. Politeness. Rational, reasonable, as well as honorable rules for discussion are intended to reintroduce or strengthen cooperation in such antagonistic contexts.

1. Logic

In logic, two propositions are converse (in a relation of conversion) if they swap their subjects and their predicates. “As are Bs” and “Bs are As” are converse propositions. The converse of a true proposition is not necessarily true, S. Proposition.

2. Grammar and argumentation

In grammar, conversion can apply to any binary structures. Restructuring an expression of the opponent, that is, playing with his or her words, can be instrumental in reversing the global orientation of his or her discourse, according to the mechanisms of the antimetabole, S. Orientation Reversal.

Well, you know, this talk about the so-called pleasures of retirement is just empty talk to mask the retirement of pleasures.
Personally, I’d prefer a frightful end to this endless fright.
González, on Kohl ‘He fought for a European Germany, never again a German Europe.” (El País, 07-01-2017)

One can radically counter-argue a proposition by emphatically supporting its converse, S. Causality (II); Analogy:

S1 —     A is the cause of B;
A is like B; A mimics, copies B.

S2 —     Not at all! B is the cause A!
B is like A; B copies A.

In the same way, a sweeping defense strategy consists in converting the roles of accuser and accused, first by applying the reciprocity principle, “it takes one to know one”:

You blame me (for X), I blame you (for Y)
You filed a complaint against me (for X), I file a complaint against you (for Y).

and, second, by converting the position about the same criminal offense:

You are the culprit, you did it, you, who accuse me!

The child’s reply “he who says it did it” converts the accusation, , and justifies the counter-accusation:

S1 — You stole the orange!
S2 — No, you stole it, who says it did it!

The fact that S1 accuses S2 is used by S2 as an argument to accuse S1. S. Reciprocity; Stasis.

The conclusion of an argumentation is usually expressed in a single statement, possibly expanded in a brief conclusive speech, S. Argument – Conclusion. The argument part, supporting and sometimes surrounding the conclusion, can be considerably developed along quite different lines, referred to as:

— Convergent argumentation, also called multiple argumentation, combines several co-oriented arguments, S. Convergence.

— Linked argumentation, also called coordinate argumentation is composed of several statements combining into an argument.

— Serial argumentation, also called subordinate argumentation is composed of a succession of argumentations, such as the conclusion of the first one is taken as argument to support a second one and so on, S. Sorite.