There Might Be Nothing: The Subtraction Argument Improved
1 . The nihilist thesis that it is metaphysically possible that there is nothing, in the sense that there are no concrete objects, has been denied by philosophers like Armstrong (1989), Lewis (1986) and Lowe (1996). Van Inwagen (1996), although he has not denied it, has argued that it is as improbable as anything may be. In a recent paper Thomas Baldwin (1996) presents and defends what he calls the subtraction argument , designed to establish the nihilist thesis. When defending the first premiss of his argument, Baldwin introduces failure to satisfy the identity of indiscernibles as the ‘mark of concreteness’. He uses this to disqualify as concrete sets whose members or ur-elements are concrete. Such disqualification must be made somehow; otherwise, as will be made clear below, the first premiss of Baldwin’s argument collapses. But, as I shall argue below, Baldwin’s first premiss does indeed collapse. I shall then present another version of the subtraction argument which is free from difficulties, and whose premisses stand firm. But let me start by summarizing Baldwin’s argument.