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.
[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