Serial argumentation (Beardsley 1975, quoted in Wreen 1999, p. 886) also called subordinate argumentation (van Eemeren and Grootendorst 1992), is traditionally known as polysyllogism, S. Sorite; Epicheirema. A serial argumentation is an argumentation where an established conclusion is used as an argument for a new conclusion, up to an ultimate conclusion. Each argumentation which contributes to the global serial argumentation has its own structure, either simple or convergent. It might correspond to any kind of argument scheme.

Serial argumentation is schematized as follows:

Arg_1 => Concl_1 = Arg_2 => Concl_2 = Arg_3 => … Arg_n => Concl_n

Serial or convergent?

Difficulties can arise in the reconstruction of concrete argumentations, as shown in the following an example from Bassham (2003, p.72):

Peter is stubborn, he is a Taurus, he will not know how to negotiate.

1. First Interpretation, as a Serial Argumentation

(A) Peter is a Taurus so he is stubborn; (B) being stubborn, he will not know how to negotiate.

Peter is stubborn (indeed, since…) he is a Taurus; so, he will not know how to negotiate.

(A) First argumentation:
(1) Peter is a Taurus, so (2) he is stubborn

(Ai) — Technical definition of “being a Taurus”: “the Taurus sticks to his or her positions without being willing to change them”[1]
(A.ii) — Instantiation of the definition: “Peter remains on his positions without being willing to change” and conclusion of the first argumentation
(A.iii) — Lexical definition of stubborn: “who is obstinately attached to his opinions, and his decisions; which is insensitive to the reasons and arguments against it.”
(A.iv) — (A1) and (A.iii) are in a paraphrase relationship.
(A.v) — Conclusion: (2) Peter is stubborn.

(B) Second argumentation:
(2) Peter is stubborn; therefore (3) he will not know how to negotiate

(B.i) — Technical definition of negotiation “negotiation involves the confrontation of incompatible interests on various points that each interlocutor will attempt to make compatible by a set of mutual concessions.” (Wikipedia, [Negotiation])
(B.ii) — According to the above (A.iii) lexical definition, “being stubborn” and “making concession” are opposites.
(B.iii) — Opposites cannot be predicated upon the same subject, Peter.
(B.iv) — Conclusion: (3) Peter will not know how to negotiate.

This is a serial argumentation

Arg_1 => Concl_1; so [Concl_1=Arg_2] => Concl_2

2. Second Interpretation, as a Convergent Argumentation

In convergent argumentation, two arguments back the same conclusion.

(C) First argumentation (1) Peter is a Taurus, (3) he will not negotiate

(C.i) — The two technical definitions (A.i) and (B.i) are contradictory.
(C.ii) = (Biii)
(C.iii) — Conclusion: (3) Peter will not know how to negotiate.

Or:

(C.i’) — Technical definition: “the negotiator must remain flexible, calm, and exercise self-restraint.”[2]
(C.ii’) — “The Taurus’ promptness to accumulate feelings and grudges also makes him capable of strong anger”[3]
(C.iii’) — (C.i’) and C.ii’) are contradictory
(C.iv”) = (Biii)
(C.v’) — Conclusion: (3) Peter will not know how to negotiate.

(D) Second argument, (2) Peter is stubborn, (3) he will not negotiate

(D.i) — (A.iii) and (B.i) are opposites, see (B.ii).
(D.ii) = (Biii)
(D.ii) — Conclusion: (3) Peter will not know how to negotiate.

This is a convergent argumentation:

[1] http://www.astrologie-pour-tous.com/taureau.html (09-20-2013)
[2] Jean-Paul Guedj, 50 Fiches pour négocier avec efficacité [50 leaflets to negotiate effectively], Paris: Bréal, 2010, p. 123.
[3] www.astronoo.com/zodiaque/zodiaqueTaureau.html (09-20-2013).

Self-evidence is a sentiment of immediate certainty about a state of things; when expressed, the corresponding statement is obvious, that is, it does not require justification, and should be accepted as such, S. Dismissal.

The term aperception is used to designate this form of knowledge as produced by a conscious perception, and accompanied by reflection. Knowledge by aperception is opposed to knowledge by inference, and therefore to knowledge acquired through argumentation, which is a kind of inference. Three kinds of aperception, that is to say three main sources of evidence, can be identified and distinguished form one another:

— Self-evidence as the fruit of the divine revelation of a transcendental reality.
— Perceptual self-evidence of sense data.
— Intellectual self-evidence given by intuition.

The simplest way to legitimate an assertion is to invoke one of these three sources, S. Argument-Conclusion.

The certainty manifested in a direct, simple affirmation corresponds to the certainty associated with aperception, S. Repetition:

Pure and simple assertion, kept free of all reasoning and all proof, is one of the surest means of making an idea enter the mind of crowds. The more concise an affirmation, the more destitute of every appearance of proof and demonstration, the more weight it carries. The religious books and the legal codes of all ages have always resorted to simple affirmation. Statesmen called upon to defend a political cause, and commercial men pushing the sale of their products by means of advertising are acquainted with the value of affirmation.
Gustave Le Bon, [The Psychology of the Crowd]. [1895][1]

Inferential argumentative belief might be considered inferior to belief based on any kind of evidence: this observation is at the root of the paradoxes of argumentation.

1. Dogma: Revelation as a source of certainty

Believers consider the revelation gathered in the sacred books as a source of certainty. This revelation, which took place in the sacred time of the origins, can be renewed by a particular revelation, such as that which Blaise Pascal has described in what is now called his Memorial, producing an immediate and absolute “certitude”:

The year of grace 1654,
Monday, 23 November, feast of St. Clement, pope and martyr, and others in the martyrology.
Vigil of St. Chrysogonus, martyr, and others.
From about half past ten at night until about half past midnight,
FIRE.
GOD of Abraham, GOD of Isaac, GOD of Jacob
not of the philosophers and of the learned.
Certitude. Certitude. Feeling. Joy. Peace.
GOD of Jesus Christ.
My God and your God.
Your GOD will be my God.
Forgetfulness of the world and of everything, except GOD. […]

Pascal, Memorial. [2]

2. Self-evidence of the sense data

The direct physical perception of a state of affairs immediately legitimates a claim. There is no need to argue to see and claim that the snow is white. As the adage says “facts are the best arguments”; the question “Is snow white?” is not debatable (“a-stasic”, S. Stasis; Evidentiality).

From the philosophical point of view, Descartes has rejected the possibility of founding knowledge on sense data by the hypothesis of the “evil genius” (Descartes [1641], First Meditation).

3. Intellectual intuition

Descartes accepts only intellectual intuition as a source of certainty:

Rule 3 – Concerning objects proposed for study, we ought to investigate what we can clearly and evidently intuit or deduce with certainty, and not what other people have thought or what we ourselves conjecture. For knowledge can be attained in no other way. (Descartes [1628], Rule 3)

“Good intuition” is infallible:

By intuition I mean, not the wavering assurance of the senses, or the deceitful judgment of a misconstructed imagination, but a conception, formed by unclouded mental attention, so easy and distinct as to leave no room for doubt in regard to the thing we are understanding. (Id, Rule 7).

This intuition is that which makes us accept something as “beyond reasonable doubt”. So for example, we can feel fairly certain that by taking a point out of a line one can draw a single second line parallel to this line; or that the square of any negative number is positive. These certainties have been called into question by the construction of imaginary numbers and non-Euclidean geometries.

4. Consequences

4.1 Conflict between sources of evidence

It may seem that the most incontestable kind of self-evidence is the direct evidence provided by sense data. Yet the following text shows that it may be judged inferior to that emanating from the authority of the sacred text. It must be noted that the author’s concluding commentary ratifies this hierarchy.

The first disagreement among the Companions after the death of the Prophet concerned the reality of his death itself. After the Death of the Prophet, ‘Umar ibn al Khattaab, may God be pleased with him, insisted that the Messenger of God did not die, considered any such talk a false rumor spread by the hypocrites, and threatened to punish them for it. This went on until Aboo Bakr appeared on the scene and recited the verse of the Qur’an:

‘Muhammad is no more than a Messenger. Many were the Messengers who passed away before him. If he died or were slain, will you then turn back on your heels? Whoever turns back on his heels, not the least harm will he do to God; but God [on the other hand] will swiftly reward those who [serve him] with gratitude’ (3: 144).

And another verse of the Qur’an:

‘Truly you will die [one day], and truly they [too] will die [one day]’ (39: 30).

When ‘Umar heard these verses his sword fell from his hand and he himself fell to the ground. He realized that the Prophet, may God bless him and grant him peace, had passed away and that the divine revelation had come to an end. […]

Differences over the Prophet’s Burial […] These were two critical issues [about “the reality of the death of the Prophet” and about “the burial of the Prophet”], which were swiftly resolved simply by resorting to the Qur’an and the Sunnah.
Taha Jabir al ‘Alwani, 1993, The Ethics of Disagreement in Islam, p. 35-36.[3]

4.2 Subtracting from doubt

The argument, the basis of the argumentative derivation of a conclusion, is presented as being above doubt. It is conveniently framed as an aperceptive datum, that is to say as something which is as certain as a revelation, as sensible evidence, or intellectual intuition. It follows that the person who refuses to share this data will be considered, as disgraced, infirm or idiotic. It is therefore not necessary to refute him or her, since he or she is already defamed, S. Destruction; Dismissal.
Extended argumentability assumes that any person can be summoned to account for his or her beliefs, and that he or she must justify them, so that it is illegitimate to postulate any kind of a priori certainty. This thesis is difficult to apply to points of view which are considered certitudes of a religious order, such as “there is no God but God”; mathematical, “the square of a positive number is positive”; or simply everyday arguments such as, “I believe that the ground will not collapse under my feet”, S. Dialectic. Self-evidence can be opposed to extended argumentability, S. Conditions of Discussion

[1] Gustave Le Bon (1895). La Psychologie des Foules. Paris: Alcan. Quoted after Gustave Le Bon,The Crowd. A Study of the Popular Mind. New York: Macmillan, p. 126.

[2] Quoted after http://www.users.csbsju.edu/~eknuth/pascal.html (07-09-2017).

[3] Taha Jabir al ‘Alwani, 1993, The Ethics of Disagreement in Islam. Herndon: VA: International Institute of Islamic Thought, p. 35-36. Quoted after:
archive.org/stream/157627041TheEthicsOfDisagreementByTahaJabirAlAlwani/157627041-The-Ethics-of-Disagreement-by-Taha-Jabir-Al-Alwani_djvu.txt

1. Argumentation as a composition of statements

1.1 Argument, claim

Consider a discourse, composed of two statements, {S1, S2}. This sequence is argumentative if it can be paraphrased using some of the following sentences:

S1 backs, supports, motivates, justifies, … S2
S1, so, thus, … S2
E2, because, since, as, given that, … S1

The Argumentation within Language theory formulates the same relation in a way that has proved extremely fruitful: the conclusion, it is what the speaker has in mind or in view, what he or she is getting at, when he or she produces the argument:

The speaker puts forward D1, in order to, with a view to… D2.
The reason why he states D1 is D2.
The meaning of D1, that is the direction towards which it strives, the sense… of D1 is D2.
and, ultimately, “D1, i.e., that is to say, in other words, that means, … D2”
S: — You say you have homework, that means that you will not go out with us tonight?

A conclusion can thus be introduced not by a connector or an indicator of consequence, but by a connector of reformulation. The claim D2 essentially “repackages” the argument, revealing the contextual meaning of the statement as argument. The interlocutor fully understands the statement-argument, only if the conclusion is grasped S. Orientation.

The claim is somehow integrated in the argument. This is why the conclusions may frequently remain implicit.

1.2 Argument, conclusion, inferring license

It is generally assumed that the argument-claim link is provided by a topic, an argument scheme, often left implicit; the consistency of a chain:

The wind is rising, it will rain.

is based on the empirically observed regularity:

Generally, when that kind of wind comes up, it rains.

From an epistemic perspective, there is “more” in the argument than in the conclusion, as far as the argument is more reliable than the conclusion, which is only a hypothetical projection of the argument. From a semantic perspective however, there is “less” in the argument than in the conclusion, to the extent that the conclusion is more than an analytical development of the argument, it is the product of this argument enriched and structured by its combination with a general scheme or topic.

1.3 Argument, conclusion, inferring license, modal

This combination corresponds to Toulmin’s layout of argument, which articulates the argumentative unit around five elements, Data, Claim, the two-level transition principle, Warrant and Backing, and finally, a Qualifier which refers to the argument Rebuttal conditions ([1958], chap. 3).

2. Self-argued conclusions

From the perspective of the theory of knowledge, in order to be valid an argumentation must be expressed in a coordinated sequence “S1 (argument), S2 (claim)”, such that the claim is not a reformulation of the argument. It follows that it must be possible to assess each statement independently. This is the case in the following sentence, “the wind has picked up, it will rain”, which expresses two independently observable facts, the fact that there is wind and the fact that it will rain a little later. The first fact is measured by an anemometer, the second by a rain gauge, two devices which operate according to entirely different principles.

In ordinary discourse, not only is the conclusion already present, if not contained, in the argument (cf. §1.1), but the argument statement can also be embedded in the concluding statement in the form of a subordinated clause or somehow integrated in a component phrase of the statement expressing the claim:

These people come to work in our country, welcome them!
→ let us welcome these people who come to work!

Ultimately, the argument is absorbed within the meaning of one key term of the statement,

→ let us welcome these workers!

In this case, the argument is included in the word (Empson [1940]); the statement is self-argued, it expresses a complete perspective, which presents itself as obvious, irrefutable.

Scientific language has one tier of signification, while natural language has several and relies on implicit significations. This essential fact opposes scientific languages and natural language. Arguments loaded with a preordained conclusion they “support” can be considered to be “biased”, fallacious, and censored as such. But this is a rather desperate maneuver. It does not makes much sense to pretend to develop critical thinking about human affairs whilst ignoring or condemning the medium and substance which makes the very stuff of all transactions concerning human affairs, and will continue to retain this function for a long time.

The argumentative script attached to a question includes the set of positions, arguments, counter-arguments and refutations put forward by either party when this issue is debated. They are available to any arguer entering the arena and willing to take a position on the issue.
In the media sphere, when a new issue emerges, the arguments very quickly stabilize in an argument script.

The script corresponds to the state of the argumentative question. It may be implemented any number of times, on a wide variety of forums. It pre-exists and informs concrete argumentative discourses. It develops with the emergence of new issues and arguments.

The argument script can be represented as an argument map.[1]

1. Script and circumstances of the argument

Argument scripts are not the sole component of actual argument. A script essentially consists in a collection of arguments on the matter, on the merits of the case, regardless of the specific circumstances of particular encounters. A script may, however, also include generic characteristics of the speakers intervening in the debate and considerations on the conditions under which it takes place.
The argument “the finances of the country are in a state of crisis” is part of the script relating to refugees, as well as its standard refutation “you lack generosity / let us be generous”. An argument about the person, as “you wear jewels and dare to speak about the financial crisis!” is not part of the script, the interlocutor not necessarily wearing jewels.

2. Script and inventio

The existence of scripts largely modifies the classical concept of inventio, according to which arguments are produced  by the arguer, S. Rhetoric. When an argument concerns an everyday issue, the speaker may have to invent arguments, but when dealing with established socio-political issues, as well as in all disciplines where one can refer to a state of the question, arguments are merely selected from the relevant argument script, then reformulated. In such areas, arguments are not “invented”, they are available for all participant.
The first task of the interested party is to review the script relevant to the issue s/he wishes to discuss, and then to perform one’s score that is, to organize a discourse which updates and amplifies the argument line they have selected. In other words, the arguer must define and follow their path within the parameters of the script.
This conception of argumentative activity has repercussions for argumentation education, and emphasizes, firstly, the necessity of carefully established information prior to the discussion, and, secondly, the importance of individual expression and style in argumentation.

[1] A map of a fraction of the script corresponding to the question “Can computers think?” can be found at web.stanford.edu/~rhorn/a/topic/phil/artclISSAFigure1.pdf (29-09-2013).

The theory of categories lies at the heart of taxonomies. In turn, taxonomies represent a series of coordinated scientific definitions.

Correctly articulated in taxonomies, such definitions mirror valid syllogistic reasoning.

The world organized in a taxonomy represents the deep structure of reality; reading the taxonomy is a reasoned voyage through this world. Until the development of mathematics and their application to experimental sciences in the modern period, and the emergence of formal logic at the end of the nineteenth century, the theory of categories served as an introduction to logical reasoning, that is, to scientific reasoning.

From the point of view of argumentation, this traditional system (category-taxonomy-syllogism) defines logic as an “art of thinking” in natural language. It is the basis for reasoning from categorization and nomination, and definition or analogy either in the explicit form of arguments bearing these names, or implicitly present in other forms of arguments.

The theory of categories was developed by Aristotle in the Topics, re-constructed by Porphyry (c. 234 – c. 305 AD) in the Isagoge, “Introduction”, and transmitted in Latin to the Middle Ages, mainly by Boethius (c. 480-525).

1. Taxonomies

The category system provides the rules for the construction of correct taxonomies. A taxonomy is a reasoned hierarchized classification of beings, a nested system, represented by an arborescence. The position of an entity in a taxonomy corresponds to its definition, and its definition determines its place in the taxonomy to which it belongs.

This “classificatory thinking” has produced impressive results in the classification of natural entities. Every entity is classified at its proper level, in a global, comprehensive hierarchy, on the basis of its common and specific properties. At the very top of this great pyramid of classification, are the plant, animal and mineral kingdoms. Such a kingdom includes a number of orders; an order includes families; a family includes several genuses; and a genus includes several species chanracterizing individuals. producing the following pattern of nested succession:

Kingdom => Order => Family => Genus => Species :: {Individuals}

A species is a set of individuals. It is the basic unit of taxonomy. In the animal kingdom, the individuals which make up a species come from the same, or similar, parents, and they can interbreed.

The above series of categories creates a seven-level taxonomy. Depending on the complexity of the kingdom considered, other intermediary levels must be introduced, for example: Kingdom => Division => Class => Order, etc.

As a knowledge domain, a taxonomy requires a well-made denominative language, which is transparent for the specialist. Latin names are used to that end. The fairy ring mushroom, or mousseron, for example, is known scientifically as marasmius oreades. This name corresponds to the following taxonomy: Genus: marasmius; Family: marasmiaceae; Order: Agaricales; etc.

The simplest taxonomy includes the following three levels:

Beings are identified and designated primarily by the name of their “basic” category, characterized by its frequency or its perceptual, cognitive or cultural salience. Non-specialists first identify an animal as a dog, not as a mammal or a labrador.

The concepts of hyponym and hypernym are used in semantics to refer to pairs of terms in a hierarchic relationship. The hyponym relationship corresponds to the genus to species relation “rose is an hyponym of flower, all roses are flowers”. The hypernym relationship corresponds to the species to genus relation, “flower is hypernym of rose, some flowers are roses”.

2. Categories

In the Aristotelian system, the goal of science is to build stable taxonomies of entities according to their common properties and specific differences. The fundamental intellectual problem is how to correctly categorize an individual and hierarchize the various categories of individuals. This task leads to more or less convincing results depending on the kind of entities considered. We already have meaningful taxonomies of mushrooms, for example, whilst we continue to lack a taxonomy of affect, emotions and moods — and we must ask whether building such a taxonomy is possible at all.

Aristotelian theory of categories provides the tools needed to build definitions for situating terms in taxonomies. It distinguishes between five categories: genus-specie-difference-property-accident. The exact logical-metaphysical status of these concepts is disputed, but the problem is clear: which logical-semantic structure can we give to statements like the following?

Suzan is a human.

Humans are animals

Humans are rational.

The horse neighs (horses neigh)

The (this) horse suffers.

The analysis in terms of categories assigns the following structures to these assertions:

— “Suzan is a human” predicates the species, “man”, of the individual, Suzan.

— “Humans are animals” predicates a genus, “animal” of a species, “man”.

— “Humans are rational” predicates a difference, “rational” of a species, “man”. Human and horse are two species belonging to the same genus animal; unlike the horse and other animals, man is endowed with reason, which is the defining difference between man and other animals.

— “Horses neigh”: in its generic interpretation, this statement attached to the species horse, a property, “— neighs”. The property is a non-essential characteristic of a species; that is (all) horses neigh, and only horses neigh. The definition of man as a “featherless biped” is extensionally valid; on this basis, one can tell a human from any other being. Essentialist philosophy reproaches such definitions based on properties for saying nothing of what is, in essence, a human being.

— “This horse suffers” predicates an accident upon an individual. The accident belongs only to individuals, not to species or genus. The horse cannot be characterized, at any level, as “a suffering animal”; a particular horse can suffer or not, depending on the circumstances, it cannot, however, be a mammal or not.

Suppose that the statement “some clouds are grey” and “all sparrows are grey” are true. Color is an accidental property of clouds, whereas it is a common characteristic shared by all sparrows, but not exclusively: elephants are also grey. This property, “being grey” cannot serve as a basis for clouds and sparrows to be classed within the same natural genus. At most, we can say that, in term of their color, indeed, some clouds are like sparrows. If one argues that clouds and sparrows belong to the same category, due to this common property, the analogy would be deemed as misleading, S. Analogy (2) Intra-Categorical Analogy; Metaphor.

An object is known when it has been successfully defined, that is, classified. It is associated with identical objects in the same category, and disassociated from objects belonging to different categories. This knowledge is not attached to it as a particular individual; this is what is meant by the expression “there is no science of the contingent”.

3. Syllogistic arguments and natural taxonomies

Predicates are organized in taxonomies according to their generality. The tree-structure of the system of categories allows for valid syllogistic inferences. A taxonomic space defines a syllogistic space: to reason means here to move in a controlled manner from one branch to the other in a “Porphyrian tree”.

A well-constructed taxonomy relies on definitions and authorizes inferences based on the nature of things: “— is a labrador” implies “— is a dog”, and both also imply “—is a mammal” S. Definitions and Argument. Hence the syllogism:

Labradors are dogs, dogs are mammals, SO labradors are mammals

From the definition

humans_definiendum are [reasonable_difference animals_genus]_definiens

one can construct the valid syllogism:

Conversely, if the genus C includes the species E1, E2, … En, then we immediately infer the truth of the disjunction:

“to be a C” implies “to be either a E1, or a E2 or … or a En”

“X is a mammal” means “X is either a human, or a rat, … or a whale”.

Other implications are based on the fact that the genus is characterized by a set of properties that belong to all the species included within its scope. If “being a mammal” is defined as “being a vertebrate, warm-blooded, having a constant temperature, with pulmonary respiration, nursing the cubs” then all of these properties can be attributed to every mammal, regardless of their differences, that is, regardless of the species they belong to.

4. Arguments destabilizing socio-linguistic categories

Scientific categorization determines the exact position of a particular individual or of a class of entities in a taxonomy, where the terms have been given an essentialist definition from which it is possible to argue syllogistically.

Linguistic nomination-categorization assigns to an individual a current name and the category covered by that name. This operation could be considered to be the basic argumentative technique. The simple and stable system of scientific-Aristotelian categories is replaced by the infinitely complex system of meaning relationships in a given language. The argument can no more proceed by syllogism on essentialist definitions, but must operate by derivations out of the heterogeneous elements assembled in a linguistic definition.

Socio-linguistic categories are said to be fuzzy and poorly defined; they are actually evolving categories, in a process of permanent de-stabilization and re-stabilization under the pressure of historical evolution and language change. They are debatable and adjustable, S. A pari; Analogy (II).

1. Transductive reasoning

The concept of transductive reasoning is developed by Piaget ([1924], 185) to analyze the development of children’s intelligence. Transductive reasoning is characterized as the prelogical and intuitive way of thinking of the young child, which goes directly from an individual or a particular fact to another individual or particular fact, without the intermediary of a general law. According to Grize,

The young child who says, ‘It’s not afternoon because there was no nap’ is based on the daily experience of napping as an ingredient of the afternoon [reasons by transduction]”(1996, p. 107).

Transductive reasoning seems to be the product of a conditioned association “nap = afternoon”, which gives, by application of the scheme of the opposites: “no siesta = no afternoon”. From this perspective, napping is a defining feature of the afternoon.

Grize observes that adults are also likely to use this kind of reasoning:

When we say that we stopped at the traffic light because it was red, […] our thinking does not go through a general law of the kind: “any red traffic light implies stop” (ibid.).

In the latter case, the statement has the form of a “semantic block” (Carel 2011), “Answer because Stimulus”. Yet the adult does not apply the negation in the same way as the child; saying “it is not a red light since I did not stop” would be considered as a denial of reality.

However, it is said that a motorist deeply imbued with respect for the Highway Traffic Act refused to believe that he collided head on with another vehicle because he was driving down a one-way street, implying the material impossibility of a fact from its legal prohibition.

2. Two-term reasoning

In a very different context, Gardet and Anawati speak of, “two-term reasoning” which is characteristic of “a specifically Semitic rhythm of thought which the Arab mind knew how to use with a rare happiness of expression” (Gardet and Anawati [1967], p. 89). This type of reasoning seems to be similar in nature to transductive reasoning.

The ‘dialectical’ logic, connatural to the Arab genius, is organized according to modes of reasoning with two terms that proceed from the singular to the singular, by affirmation or negation, without a universal middle term. Should we say, as has sometimes been said before, that [this universal medium term], not explicitly understood, is nevertheless explicit in the reasoning mind? We don’t think so. Undoubtedly, two-term reasoning can be ‘translated’ into a three-term syllogism […]. Yet in the logical mechanism of thought, it is indeed the confrontation, by contrast, similarity or inclusion, of the two terms of the reasoning that gives the ‘proof’ its power of conviction. The universal middle term is not present in the mind, even in an implicit form. This is not about establishing a discursive proof, but about promoting a self-evident certainty. (Bouamrane & Gardet 1984, p. 75; my emphasis)

The Arab logician and theologian al-Sumnani has distinguished five rational processes, that is five argument schemes, which are characteristic of two-term reasoning. These five processes are based on

Findings, and then, by a movement of the mind operating either by elimination or by analogy from the same to the contrary, or from the same to the same. It is always a question of passing from the present, actual fact, the “witness” (shâhid) [the argument, cp], to the absent, (gha’ib) [the conclusion, cp]. There is no abstract search for a universal principle. (Gardet and Anawati [1948], pp. 365-367; my emphasis).

1. Schema

The word schema is used to refer to any kind of diagram used to represent and clarify the structure of an argumentative phenomenon: Toulmin’s schema, Convergent argumentation schema, etc.
Toulmin “layout of argument” is also known as “Toulmin Schema” or “Toulmin Argument Pattern” (TAP).

2. Argumentation scheme

An argumentation scheme is an abstract or generic representation of a series of concrete argumentations sharing the same structure (scheme).

3. Schematization

Natural Logic uses the term “schematization” to designate the succession of linguistic and cognitive operations through which a reality is given a linguistic expression by a speaker, S. Schematization.

Arguments can be approached on the basis of very different systems of rules.

— Rules expressing observational regularities.
— Rules expressing norms, imperatives, which are instrumental for argument evaluation.
— Rules as counsels to do things well, how to convince a person to believe or to do something.

1. General rules of interaction

1.1 Rules of interaction

Argumentative interactions in natural language follow the various systems of rules proposed for interaction in general, so for example, the rule of justification of non-preferred sequences is applied:

A dispreferred second part is a second part of an adjacency pair that consists of a response to the first part that is generally to be avoided, and which is likely to be marked by such features as delays, prefaces and accounts. (SIL, Dispreferred second part)

1.2 Cooperative principle

The principle of cooperation expresses not only what the participants actually do (observational regularity), but also what is reasonable for them to do (rational regularity).

1.3 Principles of politeness

The principles of linguistic politeness regulate talk relationships on the basis of the concepts of face and territory. In ordinary conversation, these rules might inhibit the development of arguments. The overriding concern to preserve the relationship means that contradiction is difficult to express and develop.

1.4 Language Sins

A set of commands related to the control of discourse has been developed by the theological tradition inspired by the Bible. The violation of any of these rules is characterized as a sin of language (Casagrande & Vecchio 1991), S. Fallacies as Sins of the Tongue.

2. Rules specifically attached to argumentative speech

2.1 Rules of the Place

Specific codes are attached to specific argumentative places. Parliamentary rules for example apply in Parliament; tribunal proceedings, or classroom interactions develop in line with their own specific regulatory conventions, S. Forum. These regulations are drawn up in accordance with a sui generis procedure and are applied by the competent authorities ruling in the given place. These rules frame the kind of local rationality which characterizes the “genius loci”, the spirit of the place.

In such places, the rules determine the topics to be dealt with, the procedures that will lead to a legitimate decision and conclusion, and the persons qualified to take the floor; they regulate the right to speak, the quantity of speech, and the succession of turns at speech. These rules might, for example prohibit overlaps and interruptions.

2.2 “The Rules of an Honorable Controversy”

Levi Hedge, in his Elements of Logick (1838), presents the following seven “Rules for Honorable Controversy”:

Rule 1. The terms, in which the question in debate is expressed, and the precise point at issue, should be so clearly defined, that there could be no misunderstanding respecting them.

Rule 2. The parties should mutually consider each other, as standing on a footing of equality in respect to the subject in debate. Each should regard the other as possessing equal talents, knowledge, and desire for truth, with himself; and that it is possible therefore that he may be in the wrong and his adversary in the right.

Rule 3. All expressions which are unmeaning or without effect in regard to the subject in debate should be strictly avoided.

Rule 4. Personal reflections on an adversary should in no instance be indulged.

Rule 5. No one has a right to accuse his adversary of indirect motives.

Rule 6. The consequences of any doctrine are not to be charged on him who maintains it, unless he expressly avows them.

Rule 7. As truth, and not victory, is the professed object of controversy, whatever proofs may be advanced, on either side, should be examined with fairness and candor; and any attempt to ensnare an adversary by the arts of sophistry, or to lessen the force of his reasoning, by wit, caviling, or ridicule, is a violation of the rules of honorable controversy.
(Hedge, 1838, pp. 159-162)

Some of these rules sound familiar. Rule 5 corresponds to the accusation of having a hidden motive: “You agree with this proposal not because you approve it but to please the director”. Rule 6 is original, and refers to the problem of the hidden agenda, or even of conspiracy, S. Pragmatic argument. Disputes can be said to be “honorable” in both the intellectual and social sense. This system reintroduces what is socially acceptable in a situation where the participants will not spontaneously apply the common rules of cooperation and politeness. Such considerations join the rhetorical problematic of the prepon and the aptum (Lausberg [1960], § 1055-1062).

In Hedge’s system, social control is the root of the imposition of co-operation. The rules for avoiding the sins of language originate from religion, S. Fallacies as sins of language. In the Pragma-dialectical system, the system of rules avails itself of communicational rationality, in the spirit of Grice, S. Cooperative principle.

3. Pragma-Dialectic rules and the re-conceptualization of fallacies

These rules define “A Code of Conduct for Reasonable Discussants” (van Eemeren, Grootendorst 2004, p. 190), for partners willing to rationally resolve their difference of opinion. A fallacy is defined as a violation of one of these “Ten Commandments for Reasonable Discussants” (id., 190-196), S. Fallacies (I):

Commandment 1, Freedom rule: Discussants may not prevent each other from advancing standpoints or calling standpoints into question

Commandment 2, Obligation to defend rule: Discussants who advance a standpoint may not refuse to defend this standpoint when requested to do so.

Commandment 3, Standpoint rule: Attacks on standpoints may not bear on a standpoint that has not actually been put forward by the other party.

Commandment 4, Relevance rule: Standpoints may not be defended by non-argumentation or argumentation that is not relevant to the standpoint.

Commandment 5, Unexpressed-premise rule: Discussants may not falsely attribute unexpressed premises to the other party, nor disown responsibility for their own unexpressed premises.

Commandment 6, Starting-point rule: Discussants may not falsely present something as an accepted starting point or falsely deny that something is an accepted starting point.

Commandment 7, Validity rule: Reasoning that in an argumentation is presented as formally conclusive may not be invalid in a logical sense.

Commandment 8, Argument scheme rule: Standpoints may not be regarded as conclusively defended by argumentation that is not presented as based on formally conclusive reasoning if the defense does not take place by means of appropriate argument schemes that are applied correctly.

Commandment 9, Concluding rule: Inconclusive defenses of standpoints may not lead to maintaining these standpoints, and conclusive defenses of standpoints may not lead to maintaining expressions of doubt concerning these standpoints.

Commandment 10, Language use rule: Discussants may not use any formulations that are insufficiently clear or confusingly ambiguous, and they may not deliberately misinterpret the other party’s formulations.

This system is inspired by the proposals of the Erlangen school for the definition of a rational “ortholanguage”, S. Logics for dialogue. In the spirit of Grice, these commandments introduce or impose cooperation where it would not be spontaneously practiced by the participants. The game is based on the notion of standpoint. It corresponds to a dialectical treatment of the difference of point of view, with a proponent affirming the point of view and responding to the attacks of an opponent who casts doubt upon it. Rule 9 recalls the aim of the game, that being to settle the difference of opinion either by eliminating the unsustainable opinion or by eliminating the doubt about a well-justified opinion.

Such a system of rules accounts for the validity judgments of the speakers (van Eemeren, Garssen, Meuffels 2009). It is also possible to identify the implicit rules to which the speakers refer for their evaluations based on observing their practices (Doury 2003, 2006).

4. On rules

Dialectic

Fallacies (I), Contemporary approaches

Fallacies (II), Aristotle’s foundational list

Fallacies (II), From logic and dialectic to science

Fallacies (IV), A moral and anthropological perspective

Argumentation (II): Key features and issues

Paradoxes of argumentation

1. Argument scheme

An argumentation scheme (argument scheme) is a discursive formula, a generic statement functioning as an argument rule, an inferring license. Concrete argumentations, or enthymemes are its actualization in specific passages.
The concept of an argumentation scheme (argument scheme) captures the specificity of the minimal concatenation of two statements (S1, S2) making up an argumentation (Arg, Concl). An argumentation scheme is essentially a specific kind of sentence connection, a special case of textual coherence and cohesion; that is to say, a general discursive inferential scheme associating an argument with a conclusion.

In Aristotle’s Rhetoric, all the argument lines are expressed as such generic statements, that can sometimes be formulated as proverbs or maxims. The saying, “if you can do the hard things, you can do the easy things as well” corresponds to the “from the biggest to the smallest” (a maiori ad minus) branch of the a fortiori scheme. Typical formulas, such as those proposed by Bentham “let us wait a little, the moment is not favorable” are also complete and perfectly adequate expressions of an argument scheme. S. Juridical arguments: three collections. This scheme can be specified in a discursive domain, S. A fortiori.

In the expression of the scheme, their characteristic indefinite components (subject, predicate) may also be expressed as variables. For example, the a fortiori scheme can be written as (according to Ryan 1984):

If <P is O> is more likely (more recommendable…) than <E is O>,
and <P is O> is false (not plausible, not recommendable)
then <E is O> is false (not likely, not recommendable).

And embodied in the following argumentation:

If teachers do not know everything, students know even less

In the same style, the scheme of the opposite is written as:

If <A is B>, then <not-A is not-B>.

Derived argumentation:

If I was of no use to you during my life, at least my death will be useful to you.

Such presentations should not be taken as a kind of “logical or semantic deep structure” of the scheme. Their unquestionable benefit is to clarify the reference of general terms.

2. Example: Argument scheme and argumentations on waste

To detect a scheme in a text is a key moment in argument analysis. But this identification is not easy, the key semantic components of the scheme being frequently disseminated in the text. How can we identify a scheme in a passage? Experts will say that they just recognize a scheme when they see it; but the non-specialist necessitates a methodical reconstruction, which can proceed along the following basic lines:

— First, an explicit definition of the topic is needed.
— Second, the passage must be clearly delimited.
— And finally, one has to show how the scheme can be projected upon the passage; that is, one has to establish a point-to-point correspondence between the scheme and the passage under analysis. In essence, these links consist in linguistic operations of equivalence and close reformulation.

This method can be illustrated by the case of the argument from waste, as defined and illustrated in Perelman & Olbrechts-Tyteca.

— The scheme:

The argument of waste consists in saying that, as one has already begun a task and made sacrifices, which would be wasted if the enterprise were given up, one should continue in the same direction. ([1958], p. 279)

— First derived argumentation:

this is the justification given by the banker who continues to lend to his insolvent debtor in the hope of getting him on his feet again in the long run. (Id., p. 279)

— Linguistic operations associating the argument to the scheme (bijective association Scheme – Argumentation)

The second enthymeme is more complex:

This is one of the reasons which, according to Saint Theresa, prompt a person to pray, even in a period of ‘dryness’. One would give up, she says, if it were not “that one remembers that it gives delight and pleasure to the Lord of the garden, that one is careful not to throw away all the service rendered, and that one remembers the benefit one hopes to derive from the great effort of dipping the pail often into the well and drawing it up empty”. (Id., p. 279)

— Linguistic operations associating the argument to the scheme (same conventions):

 (¹) Traditional mystic metaphor for “no increase in faith” = no spiritual benefit.

3. Naming the argument schemes

Argument schemes are labeled according to their form or their content.

3.1 According to their specific domain and semantic content

Some famous arguments are named in reference to their precise content.

— The third man argument is an objection made by Aristotle to the Platonic theory of intelligible forms, as opposed to individuals. According to this objection, the Platonic theory implies an infinite regression. It may be seen as an argument from vertigo.

— The argument against miracles: the likelihood that the dead person was resurrected is lower than the likelihood that the witness is mistaken; so we can reasonably doubt that the dead person was resurrected (Hume, 1748, §86 “Of Miracles”). This formally refers to a hierarchy of the probable, and can be represented on an argumentative scale, S. Argumentative scale.

— The ontological argument infers the existence of God from the a priori notion of a perfect being, S. A priori; Definition.

3.2 Depending on their form and content

S. Collections (2): From Aristotle to Boethius
Collections (3): Modernity and tradition
Collections (4): Contemporaty innovations and structurations

On the use of Latin words and expressions, S. Ab Arguments, a/ad — e/ ex — 

3.2 Oriented labels

Usually, the label designating an argument specifies a form or content: the argument refers to the consequences (ad consequentiam), to authority (ab auctoritate), to the consistency of human beliefs (ad hominem), to emotion (ad passionem) or to any particular emotion (ad odium). The speaker may admit, without inconsistency, losing face and invalidating the argument he has just used, that he or she argues by the consequences, ad hominem, ex datis, upon a religious belief (ad fidem), or possibly from the number, ad numerum. These arguments can be assessed in a second, normative, stage.

Some other arguments involving the arguer are designated by oriented labels. An argument cannot be dubbed an appeal to stupidity, to superstition or to imagination without invalidating it; given the current vision of emotion as antagonistic to reason, referring to a passage as containing an appeal to emotion, from ad passiones to ad odium, amounts to a rejection of the argument. Such labels contain a built-in evaluation; there is some confusion between the levels of description and evaluation.

A call to faith will or will not be judged as fallacious depending whether or not one shares the beliefs of the speaker. In such cases, the theoretical language is biased, and normative action becomes ideological.

4. Typologies of argument schemes

A general typology of argumentation schemes is an organized collection of argument schemes. Collections of argument schemes are locally constituted as:

— The set of arguments locally exploited by a particular speaker, in a particular discussion, see « collections”.
— The set of arguments attached to a question, S. Script.

5. Argument schemes in discourse

The concept of the argument scheme anchors the study of argumentation in the material reality of speech and discourse. The capacity to identify an argument from authority, a pragmatic argument, etc. is an essential skill for the production, interpretation and criticism of argumentative discourse, S. Tagging.

Some works, such as the Thomas Aquinas Summa Theologica or texts such as Montesquieu “On the Enslavement of Negroes” can be described as dense and dry successions of arguments. Other texts are more fluid, and seem hardly reducible to circumscribed segments that could be plausibly described as an occurrence of an argument scheme.

The schemes are relatively under-determined by the linguistic expression; there may be several plausible analyses of the same text segment, some invalidating the argument, others not. This uncertainty should not be automatically seen as an indicator of the poor quality of the argument. In this respect, contextual considerations and the kind of editing given to the analyzed passage play a crucial role.

An argumentative text or interaction can be compared to a natural meadow, the most beautiful flowers corresponding to canonical argument schemes. But it is also necessary to wonder about what the dense plant tissue around these flowers is made of. To this end, interaction analysis, discourse analysis and text linguistics serve as crucial analytic instruments, which have to be adapted to the specificities of argumentation analysis. The “scheme approach” comes within a larger prospect, opening with the stance taken vis-à-vis the other’s discourses, the kind of argumentative situation they frame, the determination of general argumentative strategies, taking into consideration a whole range of semiotic phenomena. On a micro-level, one has to consider the operations producing the statements, as well as in their coordination: a good grammar book and a good dictionary are essential if one is to construct a good argument analysis, S. Argumentative Question; Indicator.

The study of schematizations is the defining objective of the Natural Logic developed by Jean-Blaise Grize, a student and subsequently a collaborator of Jean Piaget at the Research Center on Genetic Epistemology in Geneva. This logic is called “natural” as opposed to formal logic: on the one hand, it is a “logic of objects” (1996: 82) and a “logic of subjects” (Grize 1996: 96); on the other hand, it involves processes of thought that leave “traces” in natural discourse.
According to Grize, discourse is essentially argumentative, meaning that all utterances frame the world or the situation, along their subjectively relevant lines, to build a meaningful “schematization”. “Scheme” has here a totally different meaning from “argument scheme”, which would be called a “reasoned organization”, in Grize’s vocabulary, corresponding to the second-level phenomenon of sentence combination, whereas schematization is a first-level phenomenon, that of sentence production.

According to Grize’s favorite metaphor, to argue, is to “give to see” to the audience a situation as “spotlighted” by the speaker. As every speech throws some subjective lighting on the world, argumentation is inherent to speech. In Perelman’s terms, this operation consists in giving “presence” to an object (Perelman & Olbrechts-Tyteca, [1958], p. 116).

In this perspective, an argumentation is not necessarily a set of statements organized in line with the layout proposed by Toulmin. The influence of an argument and its rationality are not attached to a special kind of speech, or to the use of such and such specific “discursive techniques”, as suggested by Perelman & Olbrechts-Tyteca. Any statement, any coherent succession of statements, be it viewed as descriptive, narrative or argumentative, is indeed argumentative, insofar as it builds a point of view mapped into a meaningful schematization. Natural Logic is defined as the study of such schematizations, the cognitive counterpart of sentence construction.

This concept is adapted to a vision of arguing as story telling, as offering a coherent and detailed presentation of the world. This might be of some comfort to all students who find themselves disheartened by the difficulty of giving a dense account of extended texts or interactions in terms of argument schemes, even where these are supplemented by an extensive repertoire of figures of speech.
If persuading is defined as shifting the partner’s representations, and, accordingly, his or her behavior, then any informative statement, such as “It is 8 a.m.” is argumentative. If the addressee has to take the 7.55 train and is savoring a last coffee, thinking it is a quarter to 8, then, the information will dramatically change his vision of the immediate future. Natural Logic is also a theory of generalized persuasion, as just “focusing on the relevant aspect of reality”.

1. Schematization, a step-by-step process of meaning construction

Argumentation is traditionally defined as a combination of utterances. Natural Logic studies argumentation as a cognitive process evidenced in natural discourse, and manifested at every stage of discourse production, from the first elaboration of an idea to the combination of utterances, which is only the final stage of the argumentative process. Schematization corresponds to a representation embodied in a complex discursive unit,

Influencing the interlocutor is to try to modify his or her representations, by emphasizing some aspects of things, concealing others, proposing new ones, and all this by using appropriate schematization. (Grize 1990, p. 40)

Argumentation does not appear to be a chain of statements in a discourse. It emerges progressively at every stage of the production of the utterance, from the first operation of apprehension of content to the construction of a meaningful and therefore “reasoned” discourse. Any statement, any coherent succession of statements, whether or not it is traditionaly considered to be argumentative, narrative, or descriptive … , is indeed argumentative to the extent that it constructs a unique point of view, that is a “schematization”. This conception leads to reconsider all information as argumentation, tending to liken discursive meaning to argumentation, S. Argumentation (I); Argumentation (II).

Grize defines Natural Logic as “the study of logical-discursive operations that make it possible to construct and reconstruct a schematization” (1990, p. 65); “Its task is to account for the operations of thought allowing a speaker to construct objects and to predicate upon them at will” (1982, p. 222).
The concept of schematization defined as a “[discursive representation], oriented towards an addressee, of what the author conceives or imagines of a certain reality” (1996, p. 50), “of what it is all about” (1990, p. 29). A schematization is a discourse that focuses the listener’s attention upon a “micro-universe” given as “an accurate reflection of reality” (id., p. 36), which constructs or “structures” (id., p. 35) a synthetic, coherent, stable meaning. The purpose of schematization is “to show something to someone” (Grize 1996, p. 50; my emphasis); “to schematize […] is a semiotic act: it is to give to see” (id., p. 37; my emphasis). The object of Natural Logic is the study of the operations constructing such images.
The functioning of schematization is particularly clear in classical argumentative situations, when a discourse directly confronts a counter-discourse; the same reality is given two antagonistic descriptions:

S1 — These replacement workers, you will pay them with the strikers’ money!
S2 — Not the strikers’ money, the taxpayers’ money.

2. Operations constructing a schematization

Natural Logic postulates the existence of “primitive notions”, of a pre-linguistic nature (Grize 1996, p. 82), linked with the culture and the activities of the speakers. These pre-notions are the place of “cultural pre-constructions”, i.e., received ideas and current, accepted ways of doing things. The language “semantizes” these primitive notions turning them into “objects of thought” associated with words (Grize 1996, 83).
Schematization operations are anchored in these “primitive notions” (id., p. 67) and are constructed by a series of operations; “primitive notions” are actually noted by words between brackets. The following sequence is formed of the primitive image and fuzzy notions /fuzzy/ and /image/:

It’s unfortunate that the edge of the image is blurry, and it needs to be corrected. (Ibid.)

This construction follows these steps:

(a) The process of discourse construction begins with the selection of relevant primitive notions, to produce the objects of discourse; here “image, edge of the image” as well as the predicative pair “to be blurred, not to be blurred”. The objects thus schematized will evolve with the development of the discourse, S. Object of discourse.
(b) Then, the operation of characterization produces “contents of judgments” that is predications, and these are accompanied by modalizations, carried out on the objects of discourse. Here, the content of judgment is, “that the edge of the image be quite blurry”.
(c) A subject then asserts (positively or negatively) the preddication, and produces a statement, “it is unfortunate that the edge of the image is quite blurry”.
(d) Operations of configuration then connect several utterances and so build a discursive chain, “a reasoned organization”. The preceding statement for example, is connected to another statement, “this must be corrected”, which is produced according to the same mechanism:
It’s unfortunate that the edge of the image is blurry, and it needs to be corrected.

These different linguistic-cognitive operations can be likened to the vision of language and mind developed by the philosophy of traditional logic, S. Logic.

(a) Apprehension of content by the mind;
(b) Predication, constituting unasserted propositions;
(c) Judgment, expressed in an assertion, which can be true or false;
(d) Concatenation of judgments, i.e. discourse construction.

The aim of this approach is to emphasize that all operations relevant to the genesis of the utterance have an argumentative import. Argumentation is as much a sentence construction process as a sentence connection process.

3. Shoring

The concept of shoring developed in Natural Logic is defined as,

a discursive function consisting, for a given segment of speech (whose dimension can vary from a simple statement to a group of statements having a certain functional homogeneity), to accredit, to make more likely, to reinforce, etc. the content asserted in another segment of the same discourse. (Apothéloz & Miéville 1989, p. 70)

This concept corresponds to the classical problematic of argumentation as a composition of statements, a statement-argument supporting a statement-conclusion. To refer to the same phenomenon, Natural Logic also uses the expression “reasoned organizations”:

Many statements are made merely to support, to shore up the information given. This is part of the general process of argumentation, and allows us to envisage more or less extensive blocks of discursive sequences as reasoned organizations. (Grize 1990, p. 120)

The study of reasoned organizations is an instrument for the study of representations, defined as “a network of articulated contents” (id. p. 119-120). It should be emphasized that, for Natural Logic, the reasoning process is not limited to the combination of utterances but includes the whole dynamic process of structuring the utterance, whether it will function as argument or conclusion in a reasoned organization.

4. Schematization and communication

Schematizations refer to a particular communication situation. They are the product of “the activity of speech [which] is used to construct objects of thought” (1990, p. 22); these objects being part of a dialogue where they are used “as shared references for interlocutors” (ibid.). The communication situation envisioned is intended to be “essentially dialogical in nature” (1990, p. 21), but it is actually analogous to that of rhetorical address. It never considers the possible interactions between the respective schematizations of the participants.

By [dialogal] I don’t mean the interweaving of two discourses, but the production of a speech between two parties, a speaker [orator] … addressing a listener. Admittedly, in most texts, the listener remains virtual. This, however, does not alter the basic problem: the speaker constructs the speech according to his or her representations of the listener, simply, if the listener is present, he or she can actually say, “I do not agree” or, “I do not understand”. But if the listener is absent, the speaker must indeed anticipate his or her refusals and misunderstandings. (1982, p. 30)

Persuasion is given up, “the speaker can only propose a schematization to his or her audience, without actually ‘transmitting’ it” (ibid.).

5. “Logic of Contents” (Grize) and “Substantial Logic” (Toulmin)

Grize defines his Natural Logic in relation to formal logic:

Alongside a logic of form, a formal logic, it is possible to envision a “logic of contents”, that is, a logic taking into account the processes of thought, the development and interconnection of these contents. Formal logic based on propositions accounts for the relations between concepts, while Natural Logic proposes to highlight the construction and interconnection of the notions. (Grize 1996, p. 80)

This “logic of contents” might remind us of Toulmin’s “substantial logic”, S. Layout. But, unlike Toulmin, who characterizes argumentation as an arrangement of statements without discussing their internal structure, Grize considers that argumentation begins with the basic operation producing the statement itself.