With the comeback of metaphysics on the agenda of analytical philosophy a renewed interest for modalities and their specific properties was not lagging far behind. Yet, their indispensability in debates, say for example on identity and essence, stands in marked contrast to the explanatory meagerness when modalities are introduced by reference to ‘possible worlds’. However, what is required for an appropriate understanding of modalities is not, or so I try to argue, a philosophical account in any ambitious sense of the word but rather a specification of their ‘structural’ properties, which allow us to differentiate between various types of modalities. The proper framework for such a specification is conveniently offered by proof theory, and here specifically by Gentzen methods. Therein we find not only all that is needed to understand modalities, modalities are thereby also handed back to where once they originated: logic.
Keywords: modalities, modal logic, possibilities, possible worlds, proof-theoretic meaning