In metaphysics, Williamson defends necessitism, according to which necessarily everything is necessarily something, in short, that everything exists of necessity. Necessitism is associated with the Barcan formula: it is possible for something to have a property only if there is something which has that property. Thus, since it is possible for Wittgenstein to have had a child, there is something which is a possible child of Wittgenstein. However, Williamson has also developed an ontology of bare possibilia which he argues alleviates the worst consequences of necessitism and of the Barcan formula. It's not that Wittgenstein's possible child is concrete; rather, it is contingently non-concrete.
