Argument a completudine; Lat. completudo, “completeness”.

The evolution of society can be manifested by the emergence of legal cases that do not find clear solutions in the existing system of laws, whether in national, international or human rights legislations (Tarello 1972, quoted in Perelman 1977, p. 55).
Nonetheless, the judge is under an obligation to judge, that is, he or she must pass a sentence upon all the cases before him or her, S.. Silence. That is to say, he or she cannot refuse to make a decision upon a case by arguing that there is no law applicable to that case, or that no interpretation of an existing law can settle it.
In other words, the principle of completeness assumes that the existing system of law, duly interpreted, can qualify all and any human act as permitted, tolerated, or prohibited.

Meta-principles such as the following complement the system of laws:

In civil matters, in the absence of specific law, the judge is obliged to proceed in accordance with equity. To decide according to equity, he must call on natural law and on reason, or on the usages received, when the primitive law is silent.
Fortuné Anthoine de Saint Joseph, [Concordance between the Foreign Civil Code and the Napoléon Code], 1856.[1]

The argument of completeness is parallel to the topos of the impotent legislator, the nature of things rendering the application of the law impossible, S. Weight of Circumstances.

[1] Fortuné Anthoine de Saint Joseph, Concordance entre les codes civils étrangers et le Code Napoléon, 2nd ed. t. II. Paris: Cotillon, 1856. P. 460.