INDUCTION

There are three types of classical inference: analogy, deduction, and induction. Induction goes from the particular to the general. It generalizes the knowledge and information gathered from a limited number of cases to all cases.

I take a marble out of the bag; then a second marble, … then still another marble…
Even though the bag is not empty, I conclude that this is a bag of marybles.

Examining all the remaining objects one by one would be necessary to be sure, but that would take a long time.
A trade-off must be made between 1) the margin of uncertainty I can tolerate and 2) the time it would take to check the entire bag. I choose to save time, I check a few more items and conclude, “this is a bag of marbles.”
The induction is based on the similarity of the individuals, possibly based on just one feature, that I consider relevant.

An induction based on a single case is an example.

1. Forms of Induction

Complete induction — Induction is said to be complete and its conclusion is positive (valid, certain), if one proceeds by an exhaustive inspection of each individual. Such a procedure is possible only if one has access to all the members of the set. See definition by enumeration, §2.2.2

Induction from a representative subset to the set — A proposition found to be true in a carefully selected sample can be tentatively extended to the whole:

Forty percent of a representative sample of voters say they will vote for candidate Joni.
Therefore, Joni will receive forty percent of the vote on election day.

Depending on whether the sample is truly representative, and whether the respondents gave sincere answers, as well as assuming they don’t change their minds, the conclusion varies from almost certain to vaguely probable.

Induction from an essential property — Generalizing gfrom an accidental property of one sample to all other samples is risky. If the generalization is based on an essential property, the conclusion is positive, see example:

This is an ordinary Syldavian passport.
This passport mentions the holder’s religious affiliation.
Therefore, all Syldavian passports mention religious affiliation.

2. Refuting induction

A conclusion reached by induction is refuted by showing that it is based on a hasty generalization, i.e., on the examination of an insufficient number of cases. This is done by showing members of the collection who do not possess the that does not possess the desired trait. However, these cases can be considered exceptions, see proof by fact.

3. Induction in Mathematics: Recursive Reasoning

In mathematics, recursive reasoning is a form of induction that leads to positive conclusions (Vax 1982, [Mathematical induction or recursive reasoning]). It is effective in domains such as arithmetic, where a relation of succession can be defined between numbers. First, show that the investigated property holds for 1. Then, demonstrate that if it holds for an individual “i”, it also holds for its successor “i + 1”. The conclusion is that all the members have the tested property.

4. Induction as a Positive Method in Literary History

An inductive argument involves postulating a general law or tendency and testing it on a large number of cases. This process is typical of the positivist science of literature and ideas.

§ 2 The Diffusion of Irreligion among the Nobility and the Clergy
The diffusion of irreligion among the high nobility is considerable. General testimonies abound. Lamothe-Langon says, « Atheism was universal in what was called high society; to believe in God became ridiculous, and we were careful to protect ourselves. » The Memoirs of Ségur, those of Vaublanc, those of the Marquise de la Tour du Pin confirm what Lamothe-Langon writes. At Madame de Hénin, the Princess de Poix, the Duchess of Biron, the Princess of Bouillon, and in the officers were, if not atheists, at least deists. Most of the salons members were “philosophers”, who adopted the spirit of the philosophers, and the great philosophers were their most beautiful ornaments. This can be seen not only in the salons of the philosophers themselves, at d’Holbach’s, Madame Helvetius’s, Madame Necker’s, Fanny de Beauharnais’s (where we find Mably, Mercier, Cloots, Boissy d’Anglas), but also among the great nobility. At the Duchesse d’Enville’s, one meets Turgot, Adam Smith, Arthur Young, Diderot, Condorcet. At the Count de Castellane’s, D’Alembert, Condorcet, and Raynal. At the salons of the Duchesse de Choiseul, the Maréchale de Luxembourg, the Duchesse de Grammont, Madame de Montesson, the Comtesse de Tessé, the Comtesse de Ségur (her mother) Ségur met or listened to Rousseau, Helvétius, Duclos, Voltaire, Diderot, Marmontel, Raynal, Mably. The Hôtel de la Rochefoucauld was the meeting place for the more or less skeptical and liberal noblemen, Choiseul, Rohan, Maurepas, Beauvau, Castries, Chauvelin, Chabot, who met with Turgot, d’Alembert, Barthélémy, Condorcet, Caraccioli, Guibert. Many others that could be mentioned here: the salons of the Duchesse of Aiguillon, who was « very much in love with modern philosophy, that is to say, with materialism and atheism »; Madame de Beauvau, the Duke of Levis, Madame de Vernage, the Count of Choiseul-Gouffier, the Vicomte de Noailles, the Duke de Nivernais, the Prince de Conti, etc.
Daniel Mornet, [The Intellectual Origins of the French Revolution], 1933[1]

The claim to be justified asserts that, “the diffusion of irreligion is considerable in the high nobility”. It is supported by an explicit testimony, accompanied by three others, that are merely evoked. This assertion is followed by a similar statement, “most of the members of the salons are “philosophers” and philosophers are their most beautiful ornaments”, supported by twenty-eight names of philosophers. The lists of names are open;  note that the last quoted name is never preceded by a final « and ».
The argument is compelling, but ad nauseam; reading the lists  can be tedious.

The strength of the asserted principle depends on the number of cases considered. A small number gives reason for skepticism:

It hasn’t been sufficiently appreciated how insignificant is the number of these historical examples is on which the “laws” are claimed to be valid for all the past and future evolution of mankind. [Vico] claims that history is a succession of alternations between a period of progress and a period of regression; he gives two examples. [Saint-Simon] says that history is a succession of oscillations between an organic epoch and a critical epoch; he gives two examples. A third, [Marx], that it is a succession of economic regimes, each of which violently eliminates its predecessor; he gives one single example!
Julien Benda, The Treachery of the Clerks, [1927].[2] Our emphasis.

It should be noted that Benda’s own assertion that, “the number of these historical examples on the basis which a “law” is claimed to be valid for all the past and future evolution of humanity is insignificant”, is supported by three examples.

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[1] Daniel Mornet (1933). Les origines intellectuelles de la Révolution Française, 1715-1787. Paris: Armand Colin, pp. 270-271.
[2] Quoted after Julien Benda, La Trahison des clercs. Paris: Grasset, 1975, pp. 224-225.

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Argumentative INDICATORS

Ancient rhetorical theory does not focus much on the connectives that structure argumentative passages. In contemporary times, neither Perelman and Olbrechts-Tyteca ([1958])  nor Lausberg (1960) pay specific attention to connectives in their respective monumental recreations of the classical system.

However, Toulmin’s “layout of argument” emphasizes the role of linguistic connectives in articulating the elements of the argumentative cell (1958). The warrant is introduced by since; the backing by on account of; the claim (conclusion) by so, and the rebuttal (counter-discourse) by unless. However, Toulmin does not discuss connectives further.
Connectives are a central issue in linguistic approaches to argumentation (Ducrot & al. 1980).

1. Indicators

Argument analysis relies on three levels of indicators:

(1) Boundary indicators, which help to delineate the argumentative sequence.
(2) Internal indicators, which help to identify and articulate the argument and the conclusion within the argument sequence.
(3) Argument scheme indicators, which help identify the argument scheme embodied in a given argument.

Various linguistic tools can be used for these operations and can functionally be considered « argument indicators, » not just discourse particles or full semantic words. This label most often refers to the intermediate level of the argument-conclusion structure, where connectives play a prominent role.

1.1 Multifunctionality of Connective Particles

The terminology of connectives and markers of discursive or argumentative structure is rich. Schematically, the framework for the discussion is as follows.
— In logic, logical connectives build complex propositions from simple or complex propositions.
— In natural language, linguistic connectives belong to the category of discursive particles. Grammatically, these particles include conjunctions, prepositions, adverbs, interjections, etc. Some discursive particles such as well, um, right etc., are particularly associated with conversational speech.
— Natural language connectives are multifunctional. Some connectives retain their non-argumentative functions, even in argumentative contexts. For instance, the enumerative and sequential connectives, « first, second, and finally » can be used to list agenda items or  arguments. In an argumentative context, the “list effect” itself can be argumentative, see case–by-case argument; linked arguments.

Other connectives such as since, because, so, therefore, etc., are particularly useful for marking a segment of discourse as an argument or as a conclusion. However while their argumentative function is predominant, it is not exclusive.

In summary, connectives are multifunctional particles that can signal an argument-conclusion relationship.

1.2 Connective Verbs

The argument-conclusion structure, « A so B » can also be articulated by a complete verbal construction:

[A]; this leads me to conclude that [B]

1.3 Connectives Articulate the Semantic Content of Entire Discourses.

Logical connectives articulate precise sets of well-defined simple or complex logical propositions. In contrast, natural language connectives articulate propositions and discourses of undefined length. In the preceding example, [A] and [B] refer to passages of an unspecified length.

Linguistic connectives articulate meanings inferred from such indefinite spans of discourse. For example, a statement such as “and so [Fr. ainsi] Commissioner Valentin put the whole gang in jail” could conclude a novel. The left scope [1] of the connective so sums up all the events since the beginning of Commissioner Valentin’s investigation. The same is true for the connector but, which does not articulate propositions but rather two semantic-pragmatic contents, see the example below, §3.1). See orientation.

1.4 Multifunctionality of Argument Indicators

Argument indicators are not unifunctional words; not all their occurrences are argumentative. Discourse following so or thus is not necessarily a conclusion, and the discourse following because is not necessarily an argument pointing to a conclusion. Thus and because have non-argumentative uses, and excellent arguments do notnecessarily use therefore or because. This means, on the one hand, that peppering a speech with because and therefore does not necessarily make it a good argument. Aristotle had already recognized this strategy and rightly considered it vain, see expression. On the other hand, an interpreter who waits for a so or  because to realize he is in an argumentative situation lacks argumentative, interpretive and interactional competence. Connective particles limit interpretive possibilities by evoking a potential argumentative structure. However, they are not a summons to rouse a sleepy recipient from interpretive torpor.
The discussion of a particle’s argumentative value relates to the argumentative sequence itself. A passage is clearly argumentative if it can be linked it to an argumentative question that sets out both a discourse and a counter-discourse. The argumentative function of a particle is contextual, it is activated when it appears in argumentative contexts.
This general condition does not preclude the practice of the ars subtilior’s practice of reconstructing implicit arguments and conclusions.

When analyzing the linking phenomenon in natural language, it is important to consider the complexity of the grammar of linking terms or expressions.
— Their grammatical category and their specific semantic and syntactic properties.
— Their multifunctionality as argumentative particles.

2. Thus, therefore, so…, since, because…

So can be a conclusion marker, among many other things.  For instance, it can signal the resumption of the main topic of a text or conversation after it has been temporarily put aside. Complicating things further, this non-argumentative resumptive function can be found everywhere, and especially in argumentative contexts. The following example is taken from a lively debate on the attribution of French nationality to immigrants living in France[2]:

je pense que:: toutes ces personnes- et puis aux personnes aussi qui sont venues donc pendant les trente glorieuses on leur doit quand même une certaine forme de respect.

I think that:: all these people— and then also the people who came therefore [Fr. donc] during the post-war boom years, we still owe them a certain amount of respect.

No participant ever doubted that “these people” came “during the glorious thirties”. The reasoning here is

(Argument) they came as workers [donc = therefore] during the post-war boom years”,
(Conclusion) they are entitled to respect.

In fact, donc (=therefore), resumes a statement that is, functionally, not a conclusion but an argument. The structure is certainly not:

* we owe respect to all these people, therefore [Fr. donc] they came during the post-war boom years.

The following intervention is made by a property manager, M, during a conciliation meeting with his tenant, T. The manager recaps his position: he demands a monthly rent increase of 12€  (a very modest amount)  [3].

Moi j’avais d=mandé madame T doit s’en rappeler\ j’avais d=mandé si v=voulez’ ◊ euh: donc euh: quatre vingt francs si v=voulez’ pour arriver à mille trente, par mois, c=qui m=paraissait très raisonnable, très raisonnable’ ◊ vu l’appartement/ et vu son emplacement/ ◊ vous savez qu’un F3 disons tout d=même au deuxième étage’ ◊ relativement confor- table\ […]

[I asked/ Mrs. T certainly remembers\ I asked if you want uh, so [donc] uh: eighty francs f you want to get to a thousand thirty a month=]_claim [that seemed very reasonable, very reasonable]_modal [considering the apartment/ and considering its location/ (..) you know a three-room apartment let’s say all the same on the second floor’ (..) relatively comfortable\ […] ]_argument
Corpus Rent Negotiation (conciliation commission), Clapi Database of spoken French. Our brackets, italics and markings.

T.’s claim is articulated to the context by so [Fr. donc, meaning “so, therefore”], which sounds quite standard. However,  in this claim so does not introduce a conclusion drawn from what comes before, which has already been expressed and repeated.
The so has its classical recall, resumptive function; it just happens that the repeated segment is a claim. Thus, this is an example of a non-argumentative donc = [so, therefore] accompanying a claim, in an strongly argumentative context.  Nonetheless, donc is not here a conclusion marker, but a resumption marker. It just so happens that the repeated segment is a claim.

Other non argumentative functions of so, then, because

can be used to extract and thematize the implicit content of a sentence:
— An encyclopaedic content: All this happened in Greenland, so far up north.

— A semantic content:

S1    — Peter stopped smoking.
S2    — Then you know that he used to smoke?

— An implication of the act of saying something:

S1    — That dress suits you very well!
S2    — Because the others don’t?

3. But

But reverses the argumentative orientation of the propositions it introduces. Nevertheless, no more than so, but is not an inherently argumentative particle, and the argumentative framework and vocabulary cannot account for all its occurrences. In particular but reverses not only argumentative orientations but also narrative and descriptive ones.

3.1 But [Fr. mais], reverses narrative and descriptive orientations.

In general, but is used to reverse any type of orientation: narrative, argumentative, or descriptive. In the following text, but is used to introduce a new narrative development:

August 27: On Friday, I remembered that the annual tax on my car was due to expire. Since I am not one of those people who leave things until the last minute , I went to the tax office to renew it. There was an agent there  for me, or almost. In just a few minutes, everything was done for me over the Internet. I’m all set until next year. But in the meantime…
He walked, and as he walked, tirelessly, with his head held high, swaying to his regular rhythm, dreaming of next year […] ([4])

Such non-argumentative uses of but are quite common. The following passage contains perhaps the most famous occurrence of but in all of French literature. Emma is the heroine of Gustave Flaubert’s novel, Madame Bovary. The entire passage is narrative-descriptive.First, it develops a semantic isotopy: “travel, love, beauty, exotic life, hammocks and gondolas.” But articulates this first isotopy into a second, “husband snoring, children coughing, irritating screeching noises and provincial life”. It would not make sense to impose an argumentative analysis on such a text.

Emma was not asleep; she pretended to be; and while he dozed off by her side she awakened to other dreams.
To the gallop of four horses she was carried away for a week towards a new land, whence they would return no more. They went on and on, their arms entwined, without a word. Often from the top of a mountain they suddenly glimpsed some splendid city with domes, and bridges, and ships, forests of citron trees, and cathedrals of white marble, on whose pointed steeples were storks’ nests. They went at a walking-pace because of the great flag-stones, and on the ground there were bouquets of flowers, offered you by women dressed in red bodices. They heard the chiming of bells, the neighing of mules, together with the murmur of guitars and the noise of fountains, whose rising spray refreshed heaps of fruit arranged like a pyramid at the foot of pale statues that smiled beneath playing waters. And then, one night they came to a fishing village, where brown nets were drying in the wind along the cliffs and in front of the huts. It was there that they would stay; they would live in a low, flat-roofed house, shaded by a palm-tree, in the heart of a gulf, by the sea. They would row in gondolas, swing in hammocks, and their existence would be easy and large as their silk gowns, warm and star-spangled as the nights they would contemplate. However, in the immensity of this future that she conjured up, nothing special stood forth; the days, all magnificent, resembled each other like waves; and it swayed in the horizon, infinite, harmonized, azure, and bathed in sunshine. But the child began to cough in her cot or Bovary snored more loudly, and Emma did not fall asleep till morning, when the dawn whitened the windows, and when little Justin was already in the square taking down the shutters of the chemist’s shop.
Gustave Flaubert, Madame Bovary, [1856][5]

In these two examples, but is not argumentative, it marks an isotopic shift.

3.2 Other Functions of but

But as an Indicator of an Unresolved Contradiction –   In the standard argumentative use of but, the inferred contradiction « E1 but E2″ is resolved in favor of E2, the coordinated construction being co-oriented with E2. In other cases but articulates two opposing arguments without argumentative resolution.

S1    — What should they do today?
S2    — Some want to go to the forest, but others want to go the beach.

Assuming that S2 continues his discourse with a tentative conclusion, conclusion (a) sounds strange, and (b) sounds rather standard:

*(a) So we’re going to the beach.
(b) We don’t know what to do, we’ll have to talk about that.

But as an Indicator of Argumentative Dissociation – The concept of argumentative dissociation was introduced by Perelman & Olbrechts-Tyteca. Dissociation is defined as the splitting of an elementary concept  into two antagonistic meanings, one positive and the other negative, in order to avoid a contradiction ([1958], 550-609), see dissociation.

S1    — I thought you wanted reform?
S2    — We do want reform, but real reform.

Other functions
— Correction: in reference to the “beautiful blue Danube”,

In Vienna, the Danube is not blue, but dirty gray

— Preface to a second turn of speech, aligned with the first.

S1    — Once again, Peter has failed to graduate
S2    — But that’s just like me!                                             

4. Other Constructions Bring an Argument to a  Conclusion

An argumentative thus can be paraphrased using a set of verbal constructions that link the argument to the conclusion:

[left context]

therefore, from there, hence, that is why, this means, proves, clearly shows that…   one can (then) conclude that…

[conclusion]

4.1 Connective predicates

Markers of argumentative structure would thus be unduly restricted to “small connective words.” Other constructions, combining anaphoric terms, verbs, or nouns can exlicitly play this role.
Some verbs predicate a conclusion on an argument or an argument on a conclusion. These connective predicates are, in fact, the only undeniable and unambiguous argumentative indicators. We must distinguish between two cases.
In what follows, argument is taken in the sense that it has in the theory of argumentation, not in the sense of “argument of a mathematical function”, see argument)

(1) Conclusion predicate: the conclusion is predicated on the argument.
Subject (argument) + Predicate (conclusion)

— from [argument] I infer (that) [conclusion].

V = to conclude, to infer, to deduce…

— [argument] makes it possible to deduce (that) [conclusion].

V = to induce, to show, to demonstrate…

— [argument] proves [conclusion]

V = to prove, to show, to demonstrate, to support, to corroborate, to suggest, to go in the direction of, to motivate, to legitimate, to justify, to entitle, to believe (say, think…)

(2) Argument predicate: The argument is predicated on the conclusion.
Subject (Conclusion) + Predicate (Argument)

[conclusion] ensues from [argument]:

V = to ensue, to result, to follow, to derive…

To argue is not a conclusion predicate, but rather a simple verb denoting speech activity. In “X argues for such-and-such a conclusion”, the subject X must be [+ human]; it cannot be an argument, or a description of a state of affairs. This construction contrasts with the construction “X suggests such-and-such a conclusion” where X can be a discourse or a human being, see (to) argue.

Failing to recognise these distinctions can be particularly damaging in the teaching of argumentation.

4.2 Constructions that Frame Argumentation

All words used to talk about arguments and argumentation can serve as markers of argumentative structure and argumentative function. This class of nominal indicators includes the entire lexicon of argumentation, i.e. the metalanguage of argumentation:(counter)argument, (counter-)conclusion, point of view…, premise, objection, refutation…

This is my conclusion, a consequence, a serious objection, an argument to be considered.

[D1, argument] is given as a good reason to admit, to do [D2, conclusion]
[D1, argument] is stated, stated for the purpose of making [D2, conclusion] acceptable or convincing.

the conclusion, the premise, the objection that…;
against this point of view…

We can be sure that “to build the school here, the land is cheaper” is an argument, because it can be satisfactorily paraphrased as follows:

A good reason to build the school here is that the land is cheaper.
The fact that the land is cheaper justifies the decision to build the school there.

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[1] The left scope of a connective is the left segment of discourse taken into account for the semantic interpretation of the passage; the same applies for the right scope.
[2] Corpus Debate on Immigration, Clapi Database of Spoken French
http://clapi.univ-lyon2.fr/V3_Feuilleter.php? Num_corpus = 35]. (09-30-2013)
[3] Corpus Negotiation on rents – conciliation commission), Clapi Database of spoken French. Our brackets, italics and markings. http://clapi.univ-lyon2.fr/V3_Feuilleter.php?num_corpus=13]. (09-30-2013)
[4] http://impassesud.joueb.com/news/mali-pendant-ce-temps-la-il-il-marchait]. 07-28-2010. Our emphasis.
[5] Quoted from Gustave Flaubert, Madame Bovary. Trans. by Eleanor Marx-Aveling. Ebook, 2006. http://www.gutenberg.org/files/2413/2413-0.txt

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IMITATION, PARAGONS, MODELS

1. Paragons

When it comes to political thought, some events serve as paragons: Munich and the diplomatic defeat of democracies in the face of Nazi expansionism, the genocide of Jews, Gypsies and homosexuals, are all great analogues that function as an anti-model for all current conflicts. For the United States before the Iraq war, Vietnam was the great analogue called to the rescue when it came to opposing military intervention abroad. Paragons serve as “models” for understanding the new events; they work on the principle of precedent, S. Analogy (II); Precedent; Example.

The paragon, person or event, creates a class by analogy, see Categorization; Analogy (I).

A “great analogue” can stage characters that are a source of antonomasia. The antonomasia is the figure of speech by which a member of a category is designated by the name of the paragon of that category: a Daladier or a Chamberlain is a politician who capitulates to a dictator instead of fighting him. This references the behavior of the European politicians Edouard Daladier and Neville Chamberlain in Munich in 1938, as they dealt with Hitler.

Anti-models such as Chamberlain or Daladier represent everything one should not do (Perelman, Olbrechts-Tyteca [1958], p. 362).

Anti-models typify negative authority; the “Model of the Anti-Models” is Hitler, S. Authority §6: Refutative uses of authority.

2. Model

The model is the single most valued member of a hierarchical category.

— It functions as the root of the class, generating the other members of the class.
— It is the most representative element of the category.
— As such, it is the criterion for evaluating the other class members and for integrating new individuals into the category.
— It is considered to be the ideal form, towards which all members of the class tend.

The argument by the model supports the conclusions of the type “this is (not) a good (real, true) X” by comparing the item to evaluate and reference.

In classical culture, the doctrine of imitation is based on the authority of a model. Literary genres are defined by the relationship of their members to a founding model, a founding “father”: Thucydides for history; Aesop and La Fontaine for fables; Aristotle and Cicero for argumentation, etc.

3. Imitation

When an individual identifies with another person this person becomes his model.

Reciprocally, A model is an individual worthy of imitation.

When a model is chosen by an individual, the model is not necessarily conscious of being a model, and the situation is not clearly argumentative, S. Example

In order to get an individual to do something, one can proceed argumentatively, that is  discursively, by arguing through the model, by giving as an example important people, either real or fictional, who have done the same deed. This “argument from exemplarity” can be seen as variant of the verbal argument of authority, a metonymic exemplum.

In addition, one might set an example in order to demonstrate to the other what is desired. For example, one might stop smoking to encourage a friend to stop smoking. Metaphorically speaking, this is an “argument by example”, just as one speaks of an “argument by strength” (appeal to force) when trying to open a stubborn can with a screwdriver.

The strategy  of example can be applied to any forms of behavior we wish to change; how to eat properly, how to speak properly, how to live a dignified life worthy of reward in the afterlife. During this process, there may be some kind of persuasion, i.e.,a  change in belief that correlates with the change in behavior, but not all persuasion comes from argument, see ‘You too’.

By setting an example, the person hopes to set in motion alignment mechanisms. The argument by the example given, plays on nonverbal mechanisms of social imitation, ripple effect, identification, empathy, charisma. Seduction and repulsion are forces distinct from argumentation that push individuals to align with or to distance themselves from another person.

The ethotic argument combines with the argumentation by example, thereby pushing the audience to fully identify with the orator as a model, to commit themselves to full belief in what he or she says and doing what he or she does, see Ethos; Consensus; Ad populum.

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Argument From IGNORANCE

1. Argument from Ignorance and the Legitimacy of Doubt

Locke defines the argument from ignorance [1] as one of the four basic forms of argument, see collections 2:

Secondly, another way that men ordinarily use to drive others, and force them to submit to their judgment, and receive the opinion in debate, is to require the adversary to admit what they allege as a proof or to assign a better. And this I call argumentum ad ignorantiam. ([1690]; Vol. II, p. 410-411)

This argument is considered fallacious:

It proves not another man to be in the right way, nor that I ought to take the same way, because I know not a better. (Id., p. 411)

The following dialogue schematizes a situation in which S1‘s conclusion is based  on S2‘s ignorance:

S1₁  – A, therefore C
S2₁   – This is a bad argument. I do not accept that A proves C.
S1₂  – Do you have any reason to conclude anything other than C?
Do you have a better argument for C?
S2₂   – No.
S1₃   – Then you must accept my proof and conclusion.

(i) First round: S1₁ suggests the justified proposition C.

(ii) Second round: S2₁ refuses to ratify the claim C.

(iii) Third round: S1₂ asks S2 to explain his reasons for doubt. According to the conversation principle which requires justification for non-preferred second turns, S1 is perfectly justified in asking for an explanation. S2 could respond by:

(a) refuting S1₁‘s argument outright, or  raising objections to it;
(b) constructing a counterargument that provides what Locke calls “a better proof.”
Since the text does not specify the conclusion, so the following two cases can be assumed:

(b1) inferring from A something different from C;
(b2) providing a “better proof” than A for C.

(iv) Fourth turn: S2₂ admits that he cannot elaborate on (a), (b1) or (b2).

(v) Fifth turn: S1 may:

(a) acknowledge S2’s reluctance, while maintaining his argumentation: “Okay, this is not a very good argument, but it is interesting, In fact, it is the only one we have.”
(b) Ask S2 to accept his argument (A, C), and use S2 inability as second-order evidence to strengthen to his previous argument A. This would be an ad ignorantiam fallacy, even if his previous argument is not so bad.

A pure ad ignorantiam fallacy would be based solely on the partner’s failure “to assign a better [proof]”. In a conversation, when S2₁ does not ratify S1₁’s turn, this situation prompts S1 to clarify and elaborate on his proposal. S1‘s crude dismissal seems  too abrupt: “Since you can’t articulate anything against my argument, you must accept it in its entirely.”
From S2’s perspective, this situation also seems bizarre, a borderline case, where S2 only has his inner conviction to oppose the argument. Under normal conditions, a conversationalist–and a fortiori a dialectician–knows how to elaborate on a strong inner conviction. Locke seems to ascribe a radical clause of conscience to S2.

Leibniz moderates Locke’s radical position:

The argument ad ignorantiam is valid in cases of presumption where it is reasonable to hold to an opinion till the contrary is proven. ([1765], p. 576)

Presumption concerns the burden of proof. Although S1‘s presumption may be exaggerated and misleading, his argument still creates a preference in this area. In practice we can adhere to this preference until something else is proven.
This “for want of anything better” reasoning seems to be the standard in practical argumentation when a decision must be made and a possibly urgent action must be taken:

S1_i:     — On such-and-such a basis, I propose 1) that we take such-and-such a disposition;
2) that we explore such-and-such a hypothesis. Now, the floor is yours.

S2:        [Long silence]

S1_j     — Nothing to say? Silence means agreement.
1) In the absence of objection, my proposal is adopted.
2) In the absence of any other hypothesis, mine will serve as the working hypothesis.

It is difficult to disagree with S1_j’s conclusions. He does not claim that his proposal is the only viable one, nor that his hypothesis is true.

2. Ignorance and the Principle of the Excluded Middle

Regardless of the quality of the argument, an argument from ignorance can be defined as an illegitimate application of the principle of the excluded middle.

P is true, because you cannot prove that it is false.

The argument is inconclusive. If we consider that “not-P is not proved” is equivalent to “not-(not-P)”, then we can apply the principle of the excluded middle and conclude that P is true. However, the two negations are not of the same kind: “not-P is not proved” does not mean “not-P is false”, which would confuse what is true (alethic) with what is knowable (epistemic), see absurd.

3. Ignorance, Burden of Proof, Precautionary Principle

I am innocent, because you cannot to prove that I am guilty.
You are guilty because you cannot prove your innocence.

Admitting that P is true, or acting “as if” it were true in the absence of proof that it is false is a decision incumbent upon the institution empowered to discuss and decide such matters in the relevant field. In the law, the presumption of innocence places the burden of proof on the prosecution and gives the benefit of the doubt to the accused.

The Precautionary Principle
In debates about the safety or toxicity of new products, decisions must be made in situations of insufficient knowledge. The presumption of safety would be:

The product may be toxic, but this has not been proven. Therefore, it has no toxic effects / it is deemed safe.

The precautionary principle is easiest to refute when maximized:

Any new product is presumed to be toxic and remains banned until its safety is proven.

In its most common form, the principle simply reverses the burden of proof:

The precautionary principle (or precautionary approach) to risk management states that when an action or policy is suspected of causing harm to the public, or the environment, in the absence of scientific consensus (that the action or policy is not harmful), the burden of proof that it is not harmful falls on those taking an action that may or may not pose a risk.
Wikipedia, Precautionary Principle

4. Argument from Ignorance and Argument from Silence

See silence

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[1] Latin ad ignorantiam argument ignorantia, “ignorance”

GRADUALISM and DIRECTION

The gradual strategy is a progressive approach, also known as a step-by-step or gradual process. It is the opposite of the « one-shot strategy, » in which everything is decided in one go. This process can be manipulative when used to conceal an ultimate negative goal by revealing it gradually from an innocuous initial goal.
The slippery slope argument is used to counter the gradual strategy. It is employed when there is suspicion that a stated goal is only the initial phase of a hidden gradual process.

1. The Stages Device as a General Strategy of Action

This process is implemented when the overall goal is deemed not to be directly unattainable. It is then divided into smaller, more easily attainable goals.
This division corresponds to a to a general strategy of action that is not necessarily manipulative. Experienced explorers explain that when you are lost in the desert and dying of thirst while trying to reach a distant oasis, your ultimate goal, you could set your sights on reaching the next dune, and then the next cactus, and so on, until you finally reach the oasis.
A more relevant example to everyday life is how to carry a heavy weight. If I cannot carry this one-hundred-pound object, I take it apart, when possible, and carry each part separately.
This process of breaking down a global goal into an organized series of small, achievable goals is currently applied to the learning process: for example, one first learns to drive on a normal road, before learning to drive on an icy road.
In these cases, the actor keeps the final goal in mind, and determines and organizes the partial goals in relation to it.

2. The gradual strategy

The gradual process can be used not as a a convenient tool, but as a deliberately opaque, and manipulative strategy,

It is often better not to confront the interlocutor with the entire distance between the current situation and the ultimate goal. Instead, this distance is divided into sections with stopping points indicating partial goals. These partial goals are less likely to provoke strong opposition. (Perelman & Olbrechts-Tyteca [1958], p. 282).

Arguing with the Joneses – The step-by-step strategy, in this second sense, is commonly referred to in sales interaction as the priming strategy:

The newlyweds Jones want to buy an apartment. The real estate agent suggests a modest, perfectly adequate two-bedroom apartment, and they agree to buy it. Now that the agent has his foot in the door, he observes that a baby is on the way; so they really need a three-bedroom apartment is necessary. The Joneses change their minds and agree to buy one. However, the agent notices that Mrs. Jones is starting a business, and needs a private office. Therefore, they need a four-bedroom apartment, and so on.

In arguing with the Lord to persuade Him to withhold His wrath against Sodom, Abraham uses such a priming strategy and step-by-step process-a bit manipulative, but praiseworthy nonetheless. The argument is not from the few to the many but from the few to the very few:

[…] Abraham remained standing before the Lord. Then Abraham approached Him and said: “Will you sweep away the righteous with the wicked? What if there are fifty righteous people in the city? Will you really sweep it away and not spare the place for the sake of the fifty righteous people in it? Far be it from you to do such a thing—to kill the righteous with the wicked, treating the righteous and the wicked alike. Far be it from you! Will not the Judge of all the earth do right?”
The Lord said, “If I find fifty righteous people in the city of Sodom, I will spare the whole place for their sake.”
Then Abraham spoke up again: “Now that I have been so bold as to speak to the Lord, though I am nothing but dust and ashes, what if the number of the righteous is five less than fifty? Will you destroy the whole city for lack of five people?” “If I find forty-five there,” he said, “I will not destroy it.”
Once again Abraham spoke to Him, “What if only forty are found there?” He said, “For the sake of forty, I will not do it.”
Then he said, “May the Lord not be angry, but let me speak. What if only thirty can be found there?”He answered, “I will not do it if I find thirty there.”
Abraham said, “Now that I have been so bold as to speak to the Lord, what if only twenty can be found there?” He said, “For the sake of twenty, I will not destroy it.”
Then Abraham said, “May the Lord not be angry, but let me speak just once more. What if only ten can be found there?” He answered, “For the sake of ten, I will not destroy it.”
When the Lord had finished speaking with Abraham, he left, and Abraham returned home.
Genesis 18:22-33 New International Version.[1]

Unfortunately, the Lord will not find ten righteous men in Sodom.

3. Argument of Direction, or Slippery Slope Argument

The term argument of direction is an alternative name for the slippery slope argument. It is used to prevent the use of a gradualist strategy:

“[it] consists, essentially, in guarding against the use of the device of stages. If you give in this time, you will have to give in a little more next time, and heaven knows where you will stop” (Perelman & Olbrechts-Tyteca [1958], p. 282).

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[1] Quoted from www.biblegateway.com/passage/?search=Genesis%2018:16-33

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Argument from the GENUS

1. Argument from the Genus

This argument [1] is based on an essential definition. It transfers the qualities, duties, representations,and all the characteristics associated with the genus to its species, and finally to the individuals belonging to this genus, see classification; categorization; definition.
From a cognitive point of view the argument from the genus is the same as the argument from the category. From a linguistic point of view the argument from the genus is the same as the argument from lexical definition. Like the genus/species argument, the relation hyperonym/hyponym relationship transfers the characteristics of the hyperonym to the hyponym.

2. Extension to the Genus: the Generic Clause “… and the like”

Generic clauses are phrases such as “… and the things of the same kind”, “… and the like.” The text has the follpwing form:

This provision applies to a, b, c, and things of the same kind.

Universal Declaration of Human Rights, Article 2[1].
Everyone is entitled to all the rights and freedoms set forth in this Declaration, without distinction of any kind, such as race, color, sex, language, religion, political or other opinion, national or social origin, property, birth or other status. (My emphasis)

If an object x is not included in the enumeration “a, b, c…” but can be considered part of the category defined by the enumeration, then the generalizing clause “and all beings of the same kind” applies the provision concerning a, b and c to x.
This shows that the enumerated beings are mentioned not only  for their own sake, but also as prototypes from which a new category is to be derived, see Analogy 2.

This rule applies to cars, motorcycles, and all private vehicles.

Cars and motorcycles are regarded as prototypical members of the category “personal transport” to which the rule applies. Note that the particle etc. would also open the list to new subcategories of individuals, but would not indicate the relevant common feature that brings them into a particular genus, as the provision “all private vehicles” provision does.

The generic provision may either create a new category from an enumeration of specific individuals, or it may explicitly mention an existing genus:

You must pay the tax on chickens, geese, and other poultry.
Conclusion: the same applies to ducks and turkeys.

Chickens and geese are mentioned only as prototypical examples of the category “poultry”. One could discuss borderline cases,such as whether a peacock is really a backyard animal or  pet. In any case, rabbits are not considered poultry and are not subject to the levy.

However, the absence of a generic provision limits the application of the measure to the categories that are explicitly mentioned:

You have to pay the tax on chickens and geese.
Conclusion: Not on ducks.

Unless the legislator’s intent is invoked.

The use of the comprehensive clause is not limited to the legal field:

Fixed concrete grill
Caution! Do not use alcohol, gasoline or similar liquids to light or reactivate the fire.

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[1] Latin ejusdem generis argument. Idem, « equal »; genus, « kind ».

[2] Quoted from www.un.org/en/universal-declaration-human-rights/ (01-07-2017)

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Argument of the GENERALITY OF THE LAW

In law, the argument of the generality of the law [1] states that the law must be applied in its entirety, that is, the law is not negotiable.
— We must not make distinctions where the law does not.
— General terms should not be given particular meanings.
— Most important: The law does not discriminate between persons: all subjects of law are equal before the law.

This principle is enshrined in the Universal Declaration of Human Rights of 1789, Article 6, “The law shall be the same for all.”

The Constitution of the 5th French Republic, Article 1, states, « [The French Republic] shall ensure the equality before the law of all citizens without distinction of origin, race or religion.”

A reminder:

Punishment of error does not avoid the great ministers, rewards for good does not overlook commoners
Han Fei (~-283, -233), Han Fei Tzi, Section 6, “On having standards” [2].

Any possible exceptions must be explicitly stated in the relevant regulation. For example, while canna­bis consumption is generally prohibited, it may be tolerated in some specific places that comply with existing regulation.

In public places, people’s behavior must conform to the law plus the specific rules of the place.  When rules are strictly enforced, they also follow the principle of generality. If the school rule states in general terms that “the use of cell phones during class is prohibited ”, then it applies generally, and does not allow for exceptions or distinctions. One cannot argue that the rule applies only to “the lower grades”, or that exceptions should be made for students who “urgently need to manage their bank account”, or for “students who are in good academic standing”, see strict meaning

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[1] Latin a generali sensu; Lat. generalis “general”, sensus “thought, idea”.

[2] Han Fei (~-283, -233) — Han Fei Tzi, Section 6, “On having standards”; quoted and translated by A. C. Graham, 1989; 2 ed. 1991, p. 277.

FORUM

Diversity and specificity of the argumentative forums
Some disputes, such as “Who’s going to take out the trash?” can be resolved quickly and privately. Others cannot be resolved so easily and are brought before established, specialized,  social institutions. An argumentative forum is a more or less institutionalized physical public or private space dedicated to addressing argumentative issues. These spaces may or may not have the capacity to make decisions. Interventions there are governed by the norms and customs that characterize the forum, first and foremost, the specific codification of the turns of speech as defined by the rights to speak. These rules give meaning and consistency to the notion of “local rationality.”

The concept of a forum, along with its institutional accompaniment and its concrete rules, must be considered when analyzing of social argumentation. This approach allows us to move beyond an idealized view of argumentation as an exercise subject only to the law of dialectical reason, which law would suffice to regulate verbal exchanges between artificially de-socialized actors, see roles.
The crucial question of the burden of proof relates not only to the prevailing opinion (doxa) at the time of the discussion, but also to the forum in which the discussion takes place.

Tribunals and political assemblies can be seen are typical forums. There are also many other “marketplaces of argument ”, where points of view are calculated, expressed and traded to inform practical decisions. Such marketplaces are integral to democratic societies.
Consider the dispute over the legalization of drugs in Syldavia, a true participatory democracy. This issue is discussed in many forums, including subway cars, family dinner tables, corner pubs, town hall meeting rooms, commissions that prepare official political party positions, the National Congress Palace, and so on. Some of these forums have the power to make decisions, others simply serve to broaden and popularize the debate rather than conclude it.

« The lack of a truly democratic living environment »
The following passage is taken from a 2002 speech given by Alfredo Cristiani, who was President of El Salvador from 1989 to 1994. In 1992, during his presidency, the Chapultepec Peace Accords were signed, ending a twelve-year civil war between the extreme right and Marxist guerrillas. His 2002 speech was delivered on the occasion of the tenth anniversary of these accords[1].

Welac cannot understand the significance of what has happened in El Salvador if we confine ourselves to the recent past. The crisis that has engulfed the Salvadoran nation in the last decade did not come out of nowhere, nor was it the result of isolated wills. This painful and tragic crisis, has ancient and profound social, political, economic and cultural roots. One fatal flaws in our national way of life in the past was the absence or inadequacy of spaces and mechanisms [de los espacios y mecanismos] necessary for the free exchange of ideas and the organic development of the various political projects stemming from freedom of thought and action. In short, there was a lack of a truly democratic living environment.

Argumentative forums or the banks of the Ilisus river?
According to Plato, sophistry dominates public forums and institutions, especially courts and the assemblies, which are controlled by professional sophists. For this reason, Socratic dialectical interaction, which is solely aimed at searching for truth, takes place in a special, desocialized, argumentative setting: a pleasant place in nature, such as a hot day, by a stream, under a tree with a light breeze and grass to lie down on:

Phaedrus:    — […] All right, where do you want to sit while we read? [2]
Socrates:     — Let’s leave the path here and walk along the Ilisus. Then we can sit quietly wherever we find the right spot.
Phaedrus:    — How lucky, then, that I am barefoot today-you, of course always are. The easiest thing to do is to walk right in the stream. This way, we’ll also get our feet wet, which is very pleasant, especially at this hour and season.
Socrates:     — Lead the way, then, and find us a place to sit.
Phaedrus:    — Do you see that very tall plane tree?
Socrates:     — Of course.
Phaedrus:    — It’s shady, with a light breeze. We can sit or lie down on the grass there if we prefer.
Socrates:     — Lead on, then.
Phaedrus:    — Tell me, Socrates. Isn’t it from somewhere near this stretch of the Ilisus that people say Boreas carried Orithuia away?
Socrates:     — So they say.
Phaedrus:    — Couldn’t this be the very spot? The stream is lovely, pure and clear–just right for girls to play nearby.

Plato, Phaedrus, I229a-c. CW, p. 509.

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[1] archivo.elsalvador.com/noticias/especiales/acuerdosdepaz2002/nota18.html (09-20-2013)

[2] The speech of Lysias, which Phaedrus “[holds] in [his] left hand under [his] cloak”.

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FORCE

The word force is used with three different meanings:

1. 1. Argument from or by force, see threat -promise
   2. Force of circumstances, see weight of circumstances
   3. Force of an argument, see strength
      

The graded concept of the strength of an argument contrasts with the binary notion of valid or invalid argumentation. An argument is strong (or weak) either in itself or in relation to another argument. This strength is evaluated according to different criteria.

1. Inherent strength of an argument scheme

In scientific fields, to be strong an argument must first of all be valid. That is, it must be developed according to a method that is accepted in the given scientific field.
However, an argument can be valid and not so strong, i.e., really relevant and interesting for the discussion of this or that hypothesis.

From a philosophical point of view, one might consider that some argument schemes are inherently stronger than others. The strength of an argument is thus determined on the basis of ontology. An adept of moral realism will consider that an argument based on the nature and definition of things is stronger than a pragmatic argument; a practical mind will think the opposite.

2. Strength and effectiveness

With respect to a goal such as persuasion, the strongest argument will be the most efficient, the argument that most quickly achieves the arguer’s goal, whether it is selling a product or electing a president. A degree of strength can be assigned to the argument based on an impact study carried out on the relevant target population, S. Persuasion.

3. Strength of an argument and acceptability by an audience

The New Rhetoric defines the strength of the argument according to the extent and quality of the audiences that accept it, S. Persuade, Convince.

4. Strength and linguistic reinforcement of arguments

Two arguments that lead to the same conclusion belong to the same argumentative class. Both provide some support to this conclusion; they share the same orientation.
Within the same argumentative class, the strength of an argument may be determined by some objective gradation, such as the scale of temperature, or it may simply be assigned to the argument by the speaker, who values such argument over another. The hierarchization is marked by the means of argumentative morphemes (e.g., even) and realizing or de-realizing modifiers. The resulting arrangements of the arguments on an argumentative scales are governed by the laws of discourse.

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FIGURE

The term figure is used with different meanings in syllogistics, in fallacy theory and in rhetoric.

1. Figures of the Syllogism

The figures of syllogism correspond to the different forms of the syllogism, depending on the position of the middle term in the premises.

2. The “Figure of Speech” Fallacy

The fallacy of a misleading expression is sometimes called the fallacy of the figure of speech.

3. Figures of Rhetoric

Figures of rhetoric are variations in the manner of expression that give discourse « more grace and vivacity, luster and energy” (Littré, Figure). Dictionaries of rhetoric contain entries relevant to the field of argumentation. For example, the Gradus dictionary, devoted to the literary processes (Dupriez, 1984), contains entries such as argument, argumentation, deduction, enthymeme, epicheirema, example, induction, refutation, paralogism, premise, reasoning, sophism, etc..These basic concepts belong to the fields of argumentation studies and literary studies, among others.

The term figure encompasses tropes and figures of speech. Metaphor, irony metonymy and synecdoche are considered the “four master tropes.” As a kind of analogy and model, the metaphor  has a clear argumentative function. The mechanisms of metonymy and synecdoche correspond to those that justify the transition from an argument to a conclusion. Moreover, irony draws on a self-evident situation.

The term figure of speech can actually refer to any significant and recurring form of discursive organization. Thus, the enthymeme can be considered as a figure, the enthymemism, as can refutation and prolepsis. Other figures of rhetoric, ranging from antanaclasis (see orientation) to analogy and interpretation correspond to well-identified argument schemes.

Other figures play a role in constructing argumentative structures. For example, a figure of syntactic disposition, such as parallelism, can organize an analogy or antithesis.

Figures of opposition are all directly interpretable as argumentative, because they correspond to different modes of « discourse versus counter-discourse » confrontation.

Without reducing each and every figure to an argumentative feature, one can be observe that the classical definition of argumentation is based on the idea that it is an attempt to gain acceptance of a discourse (conclusion) based on good reasons (argument). A clear sign of acceptance is when the proposed discourse is resumed, repeated, and developed, especially as fragments or slogans. Things that are repeated must be first memorized, therefore figures of sound and rhetorical puns which are used in catchphrases, can legitimately be considered features of argumentation.

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