The correlative concepts of argument scale and laws of discourse have been developed by Ducrot (1973) in the framework of the theory of Argumentation within Language to describe the grammar of co-oriented arguments.
Argument scale translates “échelle argumentative”, word for word “argumentative1 scale”. Argument scales strictly deal with argument1 “good reason” or premise for a conclusion, not with argument2, “dispute”, S. To argue.
1. Cooriented arguments on a scale
An argumentative class is defined as follows:
A speaker places two statements p and p’ in the argumentative class determined by an utterance r if he considers p and p’ as arguments for r. (Ducrot , p. 17)
S: — Your great grandmother spent time in The Two Maggots, she dressed in black, she read Simone de Beauvoir, she was a true existentialist!
S presents three convergent arguments co-oriented towards the conclusion “She was a true existentialist” (a mid-twentieth century popular philosophy). These arguments correspond to features borrowed from the stereotype of what existentialists are and do. S. Categorization.
The word class refers to an unordered and non-hierarchical set of elements. There is no reason to think that “spending time in The Two Maggots” (an existentialist Parisian café) is considered by S as a stronger or weaker argument than “reading Simone de Beauvoir”.
Two utterances p and q belong to the same argument scale (for a given speaker in a given situation) “if the speaker considers that p and q are both arguments for the same conclusion r (they belong therefore to the argumentative class of r), and if he considers that one of these arguments is stronger than the other” (Ducrot, , p. 18).
The following scale represents a situation where q is stronger than p for the conclusion r.
The situation where the speaker considers that “reading Simone de Beauvoir” is a stronger argument than “spending time in The Two Maggots” for the conclusion “to be a true existentialist” is represented as follows:
The scales where the force of the arguments p and q is determined solely by the speaker, are called relative, S. Force.
Scales for which the gradation is objectively determined are called absolute, for example the scale of the cold:
2. Laws of discourse
The functioning of argument scales is regulated by four laws: Lowering Law, law of Negation, law of Inversion, and law of Weakness.
2.1 Lowering law
According to this law “in many cases, (descriptive) negation is equivalent to less than” (Id, p.31).
Negation is asymmetric; it does not exclude just a point on the argument scale, but the whole zone including the denied argument and all arguments which are potentially stronger. Denying an argument which is positioned at a higher point on a given scale implies the affirmation of the lower argument.
Let’s consider the argument scale determined by a positive answer to the argumentative question “should we invite him to our hunting party?”, under the presupposed context “we are ourselves a group of decent hunters”.
In such a context, “he or she is not a good hunter” means, “he or she is a poor hunter”, not “he or she is a first rate hunter”.
The statement “he or she is not a good hunter, he or she is a first rate hunter” (stress on good and first class) involves a very particular form of negation, whereby an earlier statement is refuted, S. Denying. The stronger argument is necessarily expressed, while the weaker argument remains implicit in the unmarked use of negation.
2.2 Law of weakness
According to this law, “if a sentence p is fundamentally an argument for r, and if, on the other hand, when certain conditions (in particular contextual conditions) are met, it appears as a weak argument (for r), then it becomes an argument for not-r (Anscombre and Ducrot 1983, p. 66):
He’s a good hunter: he killed two partridges last year
In particular, the weak argument must be presented in isolation, and not in conjunction with conclusive arguments. Grice’s principle of exhaustiveness can also account for this fact: an isolated weak argument will be interpreted not only as weak, but also as the best possible, which results in the rejection of the attached conclusion, and consequently, in a binary situation, as a good reason to go for the opposite conclusion, S. Cooperation.
From an interactional point of view, putting forward a weak argument might also serve a positive purpose, serving to open a discussion and clarify the positions of the participants.
2.3 Law of negation
The law of negation posits as a regularity that, “if p is an argument for r, not-p is an argument for not-r” (Ducrot 1973, p. 27). If “the weather is nice” is an argument for “let’s have a walk”, then “the weather is not nice” is an argument for “let’s stay at home”. This law corresponds to the argument by the opposite (corresponding to the paralogism of negation of the antecedent).
The following example combines the law of weakness with the law of negation; a weak argument for a conclusion is reversed as a strong argument for the opposite conclusion:
After the Second Iraq War, which began in 2003, Saddam Hussein, former President of the Republic of Iraq, was tried and executed in 2006. Some commentators felt that the trial had not been conducted fairly, and considered that the trial was so rigged that even Human Rights Watch, the largest unit in the US human rights industry, had to condemn it as a total masquerade.
Tariq Ali, [A Well-Orchestrated Lynch], 2007.
According to the author, the Association Human Rights Watch generally approves decisions in the interests of the United States. So, the fact that they approve the sentence is a weak argument for the conclusion “the sentence is fair”. In this case, the fact that even the association has condemned the decision (like other persons or associations more inclined to criticize the United States) is a strong argument for the conclusion that the sentence is unfair.
Inversely, a weak refutation of r reinforces r. This strategy falls within the general framework of the paradoxes of argumentation.
2.4 Law of inversion
If p’ is stronger than p with respect to r, then not-p is stronger than not-p’ with respect to not-r. (Ducrot 1973, p. 239; 1980, p. 27)
— “Leo has a Bachelor’s degree” and “Leo has a Master’s degree” are two arguments for “Leo is a qualified person”.
— “Leo has a Master’s degree” is a stronger argument that “Leo has a Bachelor’s degree” for this conclusion: under normal circumstances, we can say:
Leo has the Bachelor degree and even a Master’s degree.
While “Peter has a Master’s degree and even a Bachelor’s degree” is incomprehensible. One can say, “he has a thesis, and even a Bachelor’s degree”, but with some irony on the value of diplomas S. A fortiori. If one wants to argue against Peter, to show that he is insufficiently qualified, one will say:
Peter does not have a Master’s degree, let alone a Bachelor’s degree.
The negation turns the weakest argument for qualification into the strongest argument for the lack of qualification.
Argument scales can express the argument a fortiori: “He doesn’t have a Bachelor’s degree, a fortiori he doesn’t have a Master’s degree”.
 Tariq Ali, Un Lynchage bien orchestré [A well-orchestrated lynching]. Afrique-Asie, feb. 2007.