Metaphysical nihilism
Encyclopedia
Metaphysical nihilism is the philosophical
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

 theory that there might have been no objects at all, i.e. that there is a possible world
Possible world
In philosophy and logic, the concept of a possible world is used to express modal claims. The concept of possible worlds is common in contemporary philosophical discourse and has also been disputed.- Possibility, necessity, and contingency :...

 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 object
Abstract object
An abstract object is an object which does not exist at any particular time or place, but rather exists as a type of thing . In philosophy, an important distinction is whether an object is considered abstract or concrete. Abstract objects are sometimes called abstracta An abstract object is an...

s.

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
David Kellogg Lewis
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...

'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.
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