Metaphysical Nihilism

Metaphysical nihilism is the philosophical theory that there might have been no objects at all, i.e. that there is a possible world in which there are no objects at all; or at least that there might have been no concrete objects at all, so even if every possible world contains some objects, there is at least one that contains only abstract objects.

The most common argument for metaphysical nihilism is the subtraction argument. In its simplest form, this runs as follows:

1. There could have been finitely many things.
2. For each thing, that thing might not have existed.
3. The removal of one thing does not necessitate the introduction of another.
4. Therefore, there could have been no things at all.

The idea is that there is a possible world with finitely many things; you can then get another possible world by taking one of its inhabitants away - and you don't need to add any other thing as its replacement; then you can take another thing away, and another, until you're left with a possible world that is empty.

While intuitive, some philosophers argue that there are necessarily some concrete objects. It is a consequence of David Kellogg Lewis's concrete modal realism that it's impossible that no concrete objects exist; for since worlds are concrete, there is at least one concrete object - the world itself - at each world. E.J. Lowe has likewise argued that there are necessarily some concrete objects. His argument runs as follows. Necessarily, there are some abstract objects, such as numbers. The only possible abstract objects are sets or universals: but both of these depend on the existence of concrete objects (their members or the things that instantiate them, respectively). Therefore, there are necessarily some concrete objects.