The metalogical hexagon of opposition

The difference between truth and logical truth is a fundamental distinction of modern logic promoted by Wittgenstein. We show here how this distinction leads to a metalogical triangle of contrariety which can be naturally extended into a metalogical hexagon of oppositions, representing in a direct and simple way the articulation of the six positions of a proposition vis-a-vis a theory. A particular case of this hexagon is a metalogical hexagon of propositions which can be interpreted in a modal way. We end by a semiotic hexagon emphasizing the value of true symbols, in particular the logic hexagon itself.