The aim of this paper is to examine whether the possibility of a genuine non liquet is ruled out by a so-called ‘closing rule’underlying public international law. The answer to this question largely determines the relevance of the debate on the legality and legitimacy of the pronouncement of a non liquet by an international court. This debate was recently provoked by the Advisory Opinion of the International Court of Justice on the Legality of the Threat and Use of Nuclear Weapons. In this opinion, the Court held that it could not definitively conclude whether the threat or use of nuclear weapons was contrary to international law in an extreme circumstance of self-defence in which the survival of a state is at stake. Nevertheless, some authors have argued that, since international law contains a closing rule stating that the absence of a prohibition is equivalent to the existence of a permission (or vice versa), the Court had in fact decided the legality of nuclear weapons. By virtue of this closing rule, the pronouncement of a non liquet would be impossible. In our analysis, we have taken issue with this view and claim that there are no a priori reasons for the acceptance of a closing rule underlying international law. It is possible indeed that a legal system is simply indifferent towards a certain type of conduct. Moreover, even if a closing rule would be assumed, this rule would be of no help in determining the legality or illegality of the threat and use of nuclear weapons, since the Court asserted that the current state of international law and the facts at its disposal were insufficient to enable it to reach a definitive conclusion. Nothing follows from this assertion, except the assurance that international law cannot definitively settle the question of the legality of the threat or use of nuclear weapons: to be permitted or not to be permitted, that is still the question. Hamlet's dilemma precisely.