The slippery slope argument is another name for the argument of gradualism and direction. It consists in saying that such a controversial action, A, apparently convincingly backed by such and such arguments, should not be accepted, even if it might seem reasonable, because, if it were, the same principles and reasoning could be used to argue in favor of another action of the same kind A+, which is much more controversial, and then for another action A++, that one would find quite unacceptable. In effect, accepting A removes all possible limit, “when started, you cannot stop”. The slippery slope counter-argument is based on the precautionary principle, aimed at preventing a risk of extension of the decision adopted.

In a debate about the legalization of drugs, a participant proposes to legalize hashish:

AC. — [Legalization, or rather domestication] will not eliminate the problem of drugs. But it is a more rational solution, which will eliminate the mafias, reduce delinquency, and also reduce all the fantasies that feed drug taking itself and are part of drug marketing.

The opponent counters this pragmatic argument with a slippery slope argument,

If you legalize hashish, you will have to legalize cocaine, then heroine, then crack and cocaine, and all the worst dirty things that man can find.
Le Nouvel Observateur [The New Observer][1], 12-18 Oct. 1989

For a refutation of the same position based on its perverse consequences, S. Pragmatic Argument; for a refutation based on the very wording and definition of the project, S. Related Words.

This argument is based on the following operations. The question is:

Question: — What should we do about the issue of drugs?
S1 — We should legalize hashish, for such and such reasons.

The opponent S2 is reluctant to accept this proposal, even if the reasons presented by S1 are not entirely unacceptable. S2, however, refuses to become involved in S1’s process of reasoning on the basis of the following analysis of the situation.

(i) Consider the broader graded category including the object concerned, S. Categorization; Classification:

The category “drug” covers hashish, heroin, crack cocaine and so on.
Heroin is worse than hashish, and crack cocaine is worse than heroin

So, hashish is the low point, the weak point by which one enters the graded category of drugs.

(ii) An evaluation
The decision to legalize hashish may be debatable, but the legalization of heroin would clearly be unacceptable, and the legalization of crack cocaine would be unthinkable, even outrageous. This gradation mirrors gradation (i).

(iii) A driving mechanism
The decision to legalize hashish is related to those to be made in relation to heroin and crack cocaine; the same question will inevitably arise about these harder drugs:

Should heroin be legalized? Should we legalize crack cocaine?

Legalizing hashish would set a precedent; the same arguments justifying the legalization of hashish (“eliminate the mafias, reduce delinquency, and also reduce all the fantasies about drug taking”) may well be used to legalize heroin, and even crack cocaine. Given the success of these arguments to justify the legalization of hashish, it would be near impossible to dismiss these arguments if they were to be used to justify the legalization of heroin and crack cocaine. A precedent has been set. In short, by accepting A, one has taken a decisive step toward accepting A+ and A++.

(iv) Conclusion: Let’s reject the legalization of hashish

 

The structure of the slippery slope argument parallels that of the argument from waste:

Slippery slope: Don’t get started, you won’t be able to stop!
Argument from waste: Since you started, you must go on!

The gradualist strategy and the slippery slope argument consider a hierarchized class of elements, S. Gradualism. The question is whether the status of these elements should be changed? The Gradualist is in favor of a change of status, and engages in a step-by-step, progressive modification of the existing hierarchy. The opponent considers that the status of the top elements can in no way be altered, and will use a slippery slope argument to counter the gradualist by opposing any change, however slight, in the status of the lower element.

The driving mechanisms invoked (often implicitly) on stage 4 can be very different:
— Psychological:“he who steals an egg will steal an ox”.
— Organic, causal: The slippery slope designation is metaphorical, and clearly illustrates the physical movement of an ever faster physical fall. One could also evoke a domino effect, where the first falling domino pushes the second, the significance of each falling domino becoming greater and greater.
— Strategic: The key point is the attribution of bad intentions to the proponent. The opponent may consider (as in our example) that the proponent is well intentioned, and that his or her public goal is indeed the authentic goal, and that he or she does not see the potential extreme consequence in which this might result. In this case, the proponent is portrayed as a naive or idealistic arguer, who doesn’t see the consequences of what he or she is promoting, but nevertheless maintains his or her moral integrity. This development reflects Hedge’s recommendation, not to attribute to the adversary hidden and manipulative intentions (sixth rule for honorable controversy, S. Rules). Nonetheless, maybe with a polemical intent, the proponent might be framed as a Machiavellian character with the active intention of developing a gradualist strategy, with the manipulative intention of implementing step-by-step, the most extreme measure beginning with the relatively benign one; hashish would be the bait initiating a priming strategy. So, the opponent will cast upon the proponent a suspicion of private, ugly intentions, S. Motives and Reasons.

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[1] Le Nouvel Observateur is a French weekly political and cultural newspaper.

The word sorite comes from the Greek word soros, meaning, “heap”.

A sorite is a discourse progressing by reiteration of the same syntactic form.

1. Sorite paradox

The sorite of the heap is one of the famous paradoxes proposed by Eubulide, a Greek philosopher, contemporary of Aristotle:

A grain of wheat is not enough to make a heap of wheat, nor two grains, nor three grains, etc.
In other words, if n grains do not make a heap, n + 1 do not make a heap either.
So no amount of grains of wheat can make up a pile of wheat.
Similarly, and if you take a grain out of a heap of wheat, you still have a heap of wheat, and so on, down to the last grain. So, a grain of wheat is itself a heap of wheat. [1]

This paradox can be illustrated by any collective name: cluster, crowd, flock, army, collection, bouquet, collective…

2. Rhetorical sorite

A rhetorical sorite (gradatio, climax) is a discourse progressing by the reiteration of the same cause-effect, begetter-begotten relation, or simply temporal succession of linked events, building up to a climax, as in the following poem:

 Cursed be
The father of the wife
Of the blacksmith who forged the iron of the ax
With which the woodcutter fell the oak
In which was carved the bed
Where was born the great-grandfather
Of the man who drove the car
In which your mother
Met your father!

 Robert Desnos, [The Dove of the Ark], [1923]. [2]

3. Logical sorite: a chain of syllogisms

In logic, the term sorite refers to a chain of syllogisms such that the conclusion of the first serves as a premise for the following one.
The sorite is also called polysyllogism:

A polysyllogism is a series of syllogisms chained together in such a way that the conclusion of one serves as a premise for the next. (Chenique 1975, p. 255).

Serial or subordinate argumentation are other names for polysyllogistic argument, and for this kind of sorite, S. Serial Argumentation.

The term sorite may also refer to an abbreviated polysyllogism “in which the conclusion of each syllogism is not expressed, except the last” (Chenique 1975, pp. 256-257).

The critical problem with the polysyllogism is the stability and reliability of the reiterated inference. In a formal system, the transmission of the truth is flawless, while in a default argument chain, as the reasoning progresses the cogency of the conclusions weakens. In such series, everything happens as if the weights of the rebuttals grow exponentially, up to the point where the chain will break.

Other kinds of reasoning engage in the sorite paradox, for example:
— Analogy: A is analogous to B, B to C, … and Y to Z. But is Z always analogous to A? S. Analogy.

— Causal chains, when the expected, theoretically perfect, “domino effect” is counteracted.

— Interpretive reasoning; which is why some Arabic legal schools refuse to interpret the sacred text of the Koran. They consider that only the starting point, the letter of the Sacred Text can be considered certain, and that engaging in interpretation would trigger a slippery slope process, leading to some unpredictable result, potentially contradictory with the undisputable content of the Sacred Text.

3. Chinese sorite

The expression « Chinese sorite » or « Confucian sorite » is used by Masson-Oursel ([1912], p. 17) to designate « arguments [argumentations] expressing a sequence of means implemented by human activity in view of an end » (1912, p. 20). Eno (2016, p.11) speaks of “sorite” or  “chain syllogism”[2].
The sorite posits a desirable state and considers the stages along the way to achieving it. The progressive sorite starts from the first  stage and proceeds to the ultimate goal. The spring of the progression can be considered as causal, instrumental or indeterminate, in this case the succession seems purely temporal. The regressive sorite states the goal and enumerates the stages backwards to the first, basic stage.
In the brief Confucian treatise The Great Learning (Dàxué), a regressive sorite is immediately followed by a progressive sorite on identical contents. Regressive sorite:

In ancient times, those who wished to make bright virtue brilliant in the world first ordered their states; those who wished to order their states first aligned their households; those who wished to align their households first refined their persons; those who wished to refine their persons first balanced their minds; those who wished to balance their minds first perfected the genuineness of their intentions; those who wished to perfect the genuineness of their intentions first extended their understanding; extending one’s understanding lies in aligning affairs.
The Great learning, R. Eno, p. 12

In the progressive sorite, « the first condition spreads, so to speak, into new conditions which arise from each other. Thus, in Mencius IV, 1, § 27, each term unites with the next by the expression: ‘the main fruit (chĕu) of A is B’. » (Id., p. 19). The previous regressive sorite corresponds to the following progressive sorite:

Only after affairs have been aligned may one’s understanding be fully extended. Only after one’s understanding is fully extended may one’s intentions be perfectly genuine. Only after one’s intentions are perfectly genuine may one’s mind be balanced. Only after one’s mind is balanced may one’s person be refined. Only after one’s person is refined may one’s household be aligned. Only after one’s household is aligned may one’s state be ordered. Only after one’s state is ordered may the world be set at peace.
The Great Learning. R. Eno, p. 12

The difference between progressive and regressive sorite is purely in the textual organization of the stages that compose them. These steps are listed in the form of a parallelism: « when A, then B« . This expression belongs to the « if… then… » family, used to note the logical implication, which gives the sorite an appearance of reasoning. Masson-Oursel proposes a second formulation expressing the progression (or regression) characteristic of the sorite:

Each step forward represents an anticipation that is justified afterwards, thanks to the formula: « in view of B, there is a way, a path to follow (yeou tao); A being given, then (seu) B is given. (Masson Oursel, 1912, p. 20).

The sorite proposes a path to follow, a way on which successive stages are marked. It would be more a question of method or path to follow than a logical or causal inference.

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[1] The concept of a heap is three-dimensional, typically pyramid-shaped. Two or three grains cannot constitute a heap because they do not fit, or fit badly, on top of each other, the heap is not stable.   On the other hand, it is possible to constitute a heap of four grains, from a base of three grains. We could therefore say that the heap is possible from four objects on.

[2] Robert Desnos, La Colombe de l’Arche, 1923. In Œuvres [Works]. Paris: Gallimard, Quarto, 1999, p. 536.

[3] http://hdl.handle.net/2022/234242

 

Lat argument a silentio or ex silentio, from silentium, « silence ».

1. Forms of silence

As in any interaction, in an argumentative interaction, a ratified participant may remain silent, that is to shut up. Overlapping indicate an urge-for-talking, which can be more or less controlled depending on the culture and personality of the participant. A silent participant is not a participant who does not have the floor, but a ratified participant who is expected to speak and does not speak.

1.1 Motivated silence

During an argumentative interaction, third parties are non commited participants, expected to speak as arbitrators at specific times, according to the specific rules of the interaction. The silence of a participant expected to talk as a party sometimes can be argumentatively interpreted as having an argumentative orientation.

For example, “I don’t want to participate”, as an expression of this intentionnally silent attitude can be justified by different forms of the argument of tranquillity (ad quietem argument, S. Calm:

… because we don’t have to discuss that here, now…

another reason alleged to keep silent is that

the  issue is already satisfactorily settled

either because the doxa already provides a satisfactory answer, or because the speaker has a strong stance on the issue, and do not want to question it. This is a stasic move, tending to substitute the issue “should we discuss P?” to the actual discussion of P.

 

In this cases, the question is “why did you keep silent?” and ask for a justification of silence, while in the following one the issue is “what should we infer from this silence?”, silence is now an undisputed fact which to be interpreted, that is, from which some conclusion should be drawn, S. Natural sign; Interpretation.

1.2 Silence as an argument

Such a silence can be argumentatively exploited according to the rules and the goal of the specific interaction underway:

— In the case of written text, by a classical argument from silence (§2), which applies along the same lines, to modern media (§3).

— During a police interrogation, the accused remains silent (§4)

— The law is (apparently) silent about the case before the judge (§5)

2. The classical argument from silence

The classical argument from silence argues from the fact that a text says does not mention an event that might have happened in the real universe corresponding to its textual universe, to conclude that the event did not happen.
Chroniclers record all the outstanding events of their time; if they do not mention in their Chronicles something that normally should have attracted their attention, the argument from silence concludes that such an alleged event never occurred.
This can be considered as an application of the completeness principle applied to the work of these chroniclers.

Did Syldavia face terrible flooding during a given period? If such an event had occurred, the chroniclers would have mentioned it, let alone if they regularly mention less important events. But they do not mention anything of the sort. So, there was no devastating flood during this period.

The value of the argument depends on the quality and quantity of the relevant documentation available for the relevant period. It increases considerably if we know that chroniclers regularly record atmospheric events. In the following example, the argument of the historiographers’ silence argument carries its weight:

Metz is perhaps the only city where the Crusaders did not dip their hands in the blood of the Jews. Louis the Younger, leaving for Palestine, assembled his army there, and yet it is not mentioned that they received any outrage there. The silence of history in this regard is worth a positive proof, considering that Metz then had historiographers.
Abbé Grégoire, [Essay on the physical, moral and political regeneration of the Jews], 1789. [1]

 

If a fact is not mentioned, it maybe because it is irrelevant to the intention of the text under consideration. The argument of silence is sometimes answered with the argument of the camel: there is no mention of camels in the Qur’an. So, there were no camels in 7th century Arabia, which is absurd. The rebuttal is nice, but there are several references to camels in the Qur’an. S. also Borges, Gibbon….

A better example would perhaps be:

The book [The history of Belgium for dummies]  does not mention French fries. Therefore, the Belgians never knew about fries. [2]

 

The argument of silence is used to date literary works. Marie de France wrote the Lais (poems whose theme is courtly love) towards the end of the 12th century. Can we specify the date? The editor of the Lais argues as follows (according to Rychner, 1978 [3]):

1) “To date more precisely the Lais, they should be placed in relation to other works of the time”.
2) To do that, he invokes “an argument ex silentio, to use with caution but [which] should not be overlooked”
3) First, “there is no evidence in the Lais of Marie having read Chrestien de Troie Eneas”, a courtly novel, published in 1178
4) Second, “it is difficult for me to imagine that, having read [Eneas], she would have been able to remain so completely herself and so different from him, in her style and general inspiration.”

The conclusion follows: the Lais must have been written before 1178.

 

The argument from silence is an indirect proof, which can only be used by default, in the absence of all proof or direct information.
Even if we admit, for the sake of the reasoning, that there is no camel in the Koran, it would not be a proof of “inauthenticity” of the Book, (whatever one may mean by “authenticity”), since we cannot play an indirect proof against strong direct ones. Direct proofs rebut indirect ones.

3. Argument from the silence of the media

The argument from the media silence is a variant of the classic argument of silence: Nothing happened since all the media (the main trend media, my influencer…) do not say anything about it.
The counter-argument goes along the following lines:

the media are silent because they are silenced
the media are silent because they share the same political agenda
you’ll find all the information you need on the social media

4. Argument of silence and right to silence

Applied to the case of the suspect who refuses to cooperate and to answer the questions of the police officer, the common adage  » If you do not speak up, you do not object« , leads to interpret the silence of the accused as an admission of guilt.
The right to remain silent « derives from the principle of the presumption of innocence« , according to which the prosecution must prove guilt (Dalloz, [Right to be silent]) [4])
It follows that the accused does not have to collaborate in the search for the truth, has the right to remain silent and not to contribute to one’s own incrimination (id.).

5. Argument from the silence of the law

The argument from the silence of the law is put forward by the judge to justify a refusal to judge such an action, arguing that the Code of laws does not contain any article applicable to the action in question, which cannot therefore be legally qualified.
The argument of silence is declared invalid by a meta-principle which imposes on the court the obligation to judge, under penalty of committing a denial of justice:

The judge who refuses to judge, under the pretext of the silence, obscurity or insufficiency of the law, may be prosecuted as guilty of denial of justice (Dalloz, [Prohibition of denial of justice] [5].

Obligation is made to the judge to interpret the law, that is, to find in the existing body of law an article applicable to the case before him.

 

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[1] Abbé [Henri Jean-Baptiste] Grégoire, Essai sur la régénération physique, morale et politique des Juifs. Preface by R. Badinter. Paris, Stock, 1989, note p. 179.

[2] I owe this example to Michel Goldberg, who pointed out to me that the Dictionary (2018) reproduced the traditional mistake about camels and the Koran.

[3] Jean Rychner, Introduction aux Lais de Marie de France, Paris, Champion, 1978, p. X-XI

 

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

Serial argumentation is schematized as follows:

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

Serial or convergent?

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

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

1. First Interpretation, as a Serial Argumentation

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

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

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

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

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

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

This is a serial argumentation

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

2. Second Interpretation, as a Convergent Argumentation

In convergent argumentation, two arguments back the same conclusion.

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

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

Or:

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

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

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

This is a convergent argumentation:

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

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

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

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

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

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

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

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

1. Dogma: Revelation as a source of certainty

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

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

Pascal, Memorial. [2]

2. Self-evidence of the sense data

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

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

3. Intellectual intuition

Descartes accepts only intellectual intuition as a source of certainty:

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

“Good intuition” is infallible:

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

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

4. Consequences

4.1 Conflict between sources of evidence

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

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

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

And another verse of the Qur’an:

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

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

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

4.2 Subtracting from doubt

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

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

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

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

1. Argumentation as a composition of statements

1.1 Argument, claim

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

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

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

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

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

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

1.2 Argument, conclusion, inferring license

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

The wind is rising, it will rain.

is based on the empirically observed regularity:

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

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

1.3 Argument, conclusion, inferring license, modal

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

2. Self-argued conclusions

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

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

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

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

→ let us welcome these workers!

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

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

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

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

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

1. Script and circumstances of the argument

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

2. Script and inventio

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

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

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

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

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

 

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

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

1. Taxonomies

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

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

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

 

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

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

 

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

 

The simplest taxonomy includes the following three levels:

superordinate category:	“— is a mammal”
basic category:	“ — is a dog”
subordinate category:	« — is a Labrador”.

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

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

2. Categories

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

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

Suzan is a human.

Humans are animals

Humans are rational.

 

The horse neighs (horses neigh)

The (this) horse suffers.

 

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

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

 

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

 

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

 

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

 

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

 

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

 

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

3. Syllogistic arguments and natural taxonomies

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

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

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

All L are D	Labradors are dogs	Labrador is a species of genus_1, dogs
All D are M	Dogs are mammals	Genus_1 is a sub-genus of genus_2, mammals
All L are M	So, Labradors are mammals	Labrador is a sub (subspecies) of genus_2 mammals

From the definition

 

humans_definiendum are [reasonable_difference animals_genus]_definiens

 

one can construct the valid syllogism:

all H are A	Human are animals
all H are R	Human are reasonable
SO, some A are R	O, some animals are reasonable

 

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

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

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

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

4. Arguments destabilizing socio-linguistic categories

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

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

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

1. Transductive reasoning

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

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

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

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

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

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

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

2. Two-term reasoning

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

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

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

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

1. Schema

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

2. Argumentation scheme

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

3. Schematization

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