DEFAULT REASONING

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

1. Default reasoning

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

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

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

The premise does support the conclusion, but it may nonetheless be true and the conclusion false. A conclusion considered to be correct on the basis of the knowledge we have  now , may turn out to be false later, when further knowledge is gained.

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

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

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

(5) Tweety has highly developed wings muscles

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

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

2. Representation of default reasoning

The reasoning (1) is represented as (2

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

(2)

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

ζ : η — θ

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

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

D (Data) : R (Rebuttal)
—
C (Claim)

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

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

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DEDUCTION

1. In ordinary language

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

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

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

This « deduction » seems to correspond to an argument from natural signs, or if considered as the derivation of an explanatory hypotheses, to an abductive argument, more than to a logical deduction.

2. In Cartesian philosophy

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

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

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

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

3. In logic

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

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

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

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

3.1 Validity and Soundness

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

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

A  → B
A
so, B

The same reasoning can be expressed as an implication which expresses a logical law:

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

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

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

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

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

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

The idea of sufficient condition is also expressed as:

not-(A & not-B)

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

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

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

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

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

All reasoning from natural signs involves this kind of deduction.

4. Paralogisms of deduction

4.1 Denying the antecedent

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

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

Raining, a sufficient condition for the lawn to be wet, was incorrectly assumed to be necessary.

4.2 Affirming the consequent

It is not possible to infer the existence of a phenomenon from the existence of a necessary condition of that phenomenon. The following deduction is invalid:

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

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

5. Pragmatics of deduction

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

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

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

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

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

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DEBATE

Typical Western debates and discussions implement all the facets of argumentative activity: constructing points of view, producing good reasons; interacting with different people and points of view, forming more or less ephemeral alliances, integrating / refuting / destroying the positions of others, supporting arguments by drawing on personal involvement in the issues under discussion. Sometimes the two notions of argument and debate are conflated, with television debates implicitly seen as the prototypical argumentative genre.

This view of argumentation has important limitations. It leaves out argumentation in the workplace, or argumentation in science education. It associates argumentation with polemical debate, which is a non-cooperative form of argumentation. Television debates may try to influence the decision, but they have no decision-making power. Work meetings, family discussions are certainly more representative of the complexity of argumentation. In a work meeting where issues with both short-term and long-term implications are discussed, different types of sequences have to be managed in different episodes: introducing new participants; reading the agenda; giving relevant information is given (to all, to less informed participants), writing down conclusions — not to mention the episodes devoted to interaction management, including digressions and jokes. The level and nature of argumentation of these episodes can vary greatly.

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

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

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

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

2. Criticism of debate

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

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

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

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

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

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

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

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

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

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CRITICISM, RATIONALITIES, RATIONALIZATION

1. Rationalities

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

Ordinary discourse in action embodies different kinds of rationalities.

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

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

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

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

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

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

2. Discursive and argumentative rationality

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

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

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

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

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

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

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

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

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

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

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

4. Rationality and rationalization

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

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

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COUNTER ARGUMENTATION

The term counter-argumentation can be used to refer to any kind of discourse, argued refutation or objection, that openly opposes an argument. A simple “No!” can be considered as a counter-argumentative move, even a non-verbal expression of rejection that is clearly interpretable as such.

In contrast to 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, which is incompatible with M:

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

S2 makes a counter-proposition R, which is 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 that is incompatible with M, serves as a reason for not doing M. Any good reason for supporting R is seen as a counterargument to M.

The argumentation / counter-argumentation structure can 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 an existing counter-argumentation. Such a strongly assertive strategy avoids the paradoxes of refutation, but can be seen as a kind of contempt for the argument of the opposing party, see Question; Contradiction; Antithesis; Dismissal.

As with weak refutations, a weak counter-argumentation strengthens the position being attacked. In the following passage, Noam Chomsky considers that his opponent, the philosopher Hillary Putnam, has failed to develop a counter-argument, not 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]

Praising one’s opponent as an « exceptional philosopher » is a characteristically eulogistic and perfidious accompaniment to this kind of refutation:

By refuting you, I’m not refuting just any philosopher, but a Master – and therefore, a fortiori, all the philosophers who oppose 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.
[Discussion of Putnam’s Comments. In Piattelli-Palmarini M. (ed.). Language Theory, Learning Theory.]

 

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COOPERATIVE PRINCIPLE

According to H. P. Grice, the intelligibility of the conversation is governed 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 in 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 may cover the rejection of obscurity of expression and action; of ambiguity (the first of the Aristotelian fallacies); of the unnecessary verbosity, corresponding to the fallacy of verbiage.

Grice claims 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: Respect 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” (ibid., p. 48; capitalized in the text).

These four principles can be compared with those of normative theories of argumentation, see Rules.

A statement that violates Grice’s principles is not eliminated as fallacious, but is understood as an indirect speech act. When a participant notices that something does not conform to a conversational rule, the response is not to accuse the partner of making an irrelevant or irrational contribution, but to engage in an interpretive process to determine why he or she has violated the conversational rule. The analysis of fallacies returns to this interpretive orientation whenever it adds to its logic pragmatic considerations that take into account the contextual conditions of the exchange.

In an argumentative situation, the concept of cooperation is a strategic issue that is 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, as long as the partners are aware that they are in such a deliberately opaque context, see Politeness. Rational, reasonable, as well as honorable rules for discussion are intended to restore or strengthen cooperation in such antagonistic contexts.

CONVERSION

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, see Proposition, §3.2

2. Grammar and argumentation

In grammar, the conversion transformation can be applied to any binary structures. Restructuring an expression of the opponent, that is, playing with his or her words, can help to reverse the global orientation of his or her discourse, according to the mechanisms of the antimetabole, see Orientation Reversal.

Well, you know, this talk about the so-called pleasures of retirement is just empty talk to cover up the retirement of pleasures.
Personally, I’d prefer a frightful/terrible end to this endless fright/terror.
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 he did it!

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

CONVERGENT, LINKED, SERIAL Argumentation

The conclusion of an argumentation is usually expressed in a single statement, possibly expanded in a short closing speech, see Argument – Conclusion.
The arguments, i.e., the part of the argumentative discourse that supports and sometimes surrounds the conclusion, can be considerably developed along quite different lines:

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

— Linked argumentation, also called coordinate argumentation consists of several statements that combine to form an argument.

— Serial argumentation, also called subordinate argumentation consist of a sequence of argumentations, such as the conclusion of the first one is taken as an argument to support a second one and so on, see sorite.

One caveat: these categories are logical categories; they assume that arguments correspond to clean-cut, continuous explicit linguistic segments, just like premises in a logical reasoning. This is not the case in ordinary language, where arguments can be intertwined, an argument can contain another argument,  and episodes of expository language can take a distinctly argumentative turn. See Tagging.

CONVERGENT argumentation

Convergence is a basic mode of organization of complex discourse to support a conclusion, S. Convergent, Linked, Serial.
Two or more arguments are convergent when they independently support the same conclusion. The arguments are said to be co-oriented, and the argumentation is said to be convergent or multiple.
“Two reasons are better than one”: In a convergent argumentation, a claim is defended on the basis of several arguments that, taken separately, may be relatively weak, but, taken together, combine to make a stronger case: “My computer is getting old, there are discounts on the price of my favorite brand, I’ve just got a bonus, I’m going to buy one! ”.

 

The above diagram shows each argument is represented as a whole. The following diagram spells out the transition laws according to Toulmin’s proposal, S. Layout; compare with linked argumentation:

As well as pro-arguments, counter-arguments can converge to refute a claim, see Script.

This open structure defines the argumentative network, in contrast to the demonstrative chain. In the demonstrative chain, each step is necessary and sufficient; if one step is invalid, the whole construction collapses. In the case of the argumentative net, if one link in the mesh is broken, the net can still be used to catch fish, at least the biggest ones.

In a convergent argumentation, the organization of the sequence of arguments is relevant. If the arguments are of a very different strengths, a ridiculous or a weak argument next to a strong one risks damaging the whole argumentation, especially if that argument ends the enumeration:

He’s a great hunter, he killed two deer, three wild boars and a rabbit.

In classical rhetoric, the theory of the general organization of discourse (Lat. dispositio) discussed the supposedly different persuasive effects of the various possible textual arrangements of converging arguments of different strength, S. Rhetoric.

Convergent arguments can be merely listed (paratactic disposition):

Arg, Arg and Arg, so Concl

They can be connected by any listing or additive connective:

first, Arg1; second, Arg2; third, Arg3; so Concl.
Additionally, also, in addition, let alone, moreover, not only, 
besides

Connectives such as besides, not only, in addition, let alone, not to mention… not only add argument(s) upon argument(s), they present them as if each one was actually sufficient for the conclusion, and only added just “for good measure” (Ducrot & al. 1980, pp. 193-232):

No, Peter will not come on Sunday, he has work, as usual, besides his car broke down.

The additive approach holds that each argument contributes a piece of truth, and that these pieces can be arithmetically added together, to form a large, conclusive discourse. Speech activity theory holds that, by default, an argument is presented as sufficient, and that the addition of other arguments actually follows the logic of commercial presentation to consumers (the audience), i.e. the speaker offers the audience a series of arguments he considers equally satisfying and self-sufficient.

Case-by-case argument  — To refute the conclusion of a convergent argumentation, each of the arguments supporting that conclusion must be refuted. Thus, a convergent argument is countered by a case-by-case rebuttal, limited to the cases presented by the proponent.

CONTRARY and CONTRADICTORY propositions

1. Definition

In logic, the « square of oppositions » connects the affirmative and negative propositions, the universal and particular proposition, according to a set of immediate inferences, among which are the relations of contradiction and contrariety, see Proposition §4

— Two propositions P and Q are contradictory when they cannot be simultaneously true or simultaneously false; that is, one of them is true, and the other is false, as shown in the  following truth-table (see Logical connectives)

P	Q	P contradictory with Q
T	T	F
T	F	T
F	T	T
F	F	F

— Two propositions P and Q are contrary when they cannot be simultaneously true, but can be simultaneously false.

P	Q	P contrary with Q
T	T	F
T	F	T
F	T	T
F	F	T

These terms can be easily confused. The easiest way to avoid confusion is to relate the relations of contrariety and contradiction to two kinds of universes, thus defining two kinds of opposites. Let U be a universe containing a number of individuals.

(i) Contradictories — In the case of contradiction, the opposition is within a two-dimensional universe, such as the traditional system of genre: “— is a man” and “— is a woman” are contradictory predicates in this system. In a non-traditional system of genres, they are contrary propositions.

U is a two dimensional universe; two properties P₁ and P₂ are defined upon this universe, such as:
— Any members of this universe possess either the property P₁ or the property P₂:
— None possess both properties P₁ and P₂: neither is both (P₁ & P₂). This is noted (P₁ W P₂), with the symbol ‘W’ for “disjunctive or”.

P₁ and P₂ are complementary properties; they divide the universe U into two complementary (non-overlapping) sets.
— P₁ and P₂ are contradictories (opposites); they are in a relation of contradiction.

(ii) Contraries — In the case of contrariety, the opposition is within a multi-dimensional universe such as the universe of colors. “— has white hair” and “— has red hair” are contrary predicates: one person cannot have both white and red hair (notwithstanding the case of badly dyed hair roots); and he or she may have brown hair.

U is an n-dimensional (more than two dimensions) universe: P₁, … P_i, … P_n.

— Every members of this universe has one of these properties, P_j; that is, is either a P₁ , … or a P_i, … or a P_n.
— None has two or more properties P₁ , … P_i, … P_n, that is, none is both (P_k & P_l).
— P₁ , … P_i, … P_n are contraries; they are in a relation of contrariety.

To sum up, semantically connected predicates, or properties, are opposite if they divide exhaustively their universe of reference into a series of non-overlapping sets. If there are just two such properties, they are said to be contradictory properties; if there are more than two, they are said to be contrary properties. So, contradictories are the limit case of contraries.

	Two-dimensions opposition: the two opposite properties are contradictories
Opposites
	More than two-dimensions opposition: the more-than-two opposite properties are contraries

2. Refutation by substitution of contrariety to contradiction

It follows that an assertion based on a contradiction can be refuted by showing that the universe under discussion should not be considered as two-dimensional, but multi-dimensional. This seems to be the case in the following example.

In 1864, Pope Pius IX published the Syllabus, that is, a collection or a catalog of the Vatican’s positions on “modernist” ideas. Considered retrograde, the Syllabus was strongly attacked by “the modernists”. In 1865, Mgr. Dupanloup, defended the Syllabus in the following terms; “they” refers to the modernists.
It is an elementary rule of interpretation that the condemnation of a proposition, condemned as false, erroneous and even heretical, does not necessarily imply the assertion of the contrary, which could be another error, but only its contradictory. The contradictory proposition is the one that simply excludes the condemned proposition. The contrary is the one that goes beyond the simple exclusion.
Now! It is this general rule that they have apparently not even suspected in the unthinkable interpretation of the Encyclical and the Syllabus that they have been giving us for the past three weeks. The Pope condemns this proposition: “It is permitted to refuse obedience to legitimate princes” (Prop. 63).
They claim that, according to the Pope, disobedience is never permitted, and that it is always necessary to submit to the will of princes. This is a leap to the extreme of the contrary, and ascribes to the Vicar of Jesus Christ, the most brutal despotism, and slavish obedience to all the whims of the kings. This is the extinction of the noblest of all liberties, the holy liberty of souls. And that’s what they claim the Pope said!
Félix Dupanloup, Bishop of Orleans, [The September 15th Convention, and the December 8^th [1864] Encyclical], 1865[1].

Is the universe of the encyclical binary or multidimensional? Let’s consider a position X.

— If it comes in a binary opposition, “allowed vs. forbidden”, then the proposals “it is permitted (to refuse obedience)” / “it is forbidden (to refuse obedience)” are contradictory: only one of these propositions is true. If we condemn the proposition “it is permitted to refuse obedience to legitimate princes”, then we have to conclude that the contradictory is true, that is to say, “it is forbidden to refuse obedience to legitimate princes”, otherwise said: “we must always bow our heads under the will of the princes.”

Thus, for Dupanloup, the malevolent “modernists” substitute contradictories for contraries, which he describes as “jumping to the last end of the contrary”, which is a proper designation of the contradictories.

He accuses his opponents of reframing the Pope’s position, using a strategy of absurdification (an exaggeration to the point of absurdity), S Exaggeration.

— If the position X enters a three-dimensional universe, as “required / permitted (indifferent) / forbidden” then the proposals “it is permitted / it is forbidden” (to refuse obedience) are not contradictories but contraries: they are not simultaneously true, but they can be simultaneously false, e.g. if X is indifferent. The conclusion “If X is not opposed, X is demanded” is not valid. If we condemn “it is permissible to refuse obedience to legitimate princes” then we can only conclude one or the other of these opposites:

It is obligatory to refuse obedience to legitimate princes.
It is forbidden to refuse obedience to legitimate princes.

As it would be difficult to admit that Pius IX, or anyone else, prescribes a systematic duty of disobedience to the legitimate rulers, we are left with the other member of the disjunction, that is, “X is forbidden.”

— If two or more additional options, “encouraged” and “discouraged” are introduced, we get a five-dimensional universe “required / advised / permitted (indifferent) / recommended / forbidden”. The interpretation “encouraged” is hardly possible, for reasons previously seen; “discouraged” could correspond to the intention of the Syllabus, such as interpreted by Dupanloup. Then one wonders why this sentence seems so solemn : if we admit that what is not recommended is something that one does not do without good reason, it is obvious that one does not disobey the legitimate prince without a good reason.

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[1] Quoted from Félix Dupanloup, La Convention du 15 Septembre et l’Encyclique du 8 décembre [1864]. In Pius IX, Quanta Cura and the Syllabus. Paris: Pauvert, 1967. P. 104-105.