The Subtraction Argument in an Infinite World

Metaphysical nihilism can be defined as the view that there might be no con-crete objects. One may argue for this view defining a finite procedure of sub-traction on a set of concrete, contingent objects juxtaposed across possible worlds, which procedure will eventually terminate in an empty possible world. Obviously, this subtraction argument is not applicable if all non-empty possible worlds contain an infinite number of objects. In this paper, I will discuss in detail the limitations of this argument and then investigate whether and how they can be relaxed.