The "Dust Theory", by Greg Egan, states that...
... there is no difference, even in principle, between physics and mathematics, and that all mathematically possible structures exist, among them our physics and therefore our spacetime. These structures are being computed, in the manner of a program on a universal Turing machine, using something referred to as "dust" which is a generic, vague term describing anything which can be interpreted to represent information; and therefore, that the only thing that matters is that a mathematical structure be self-consistent and, as such, computable. As long as a mathematical structure is possibly computable, then it is being computed on some dust, though it does not matter how much, only that there can be a possible interpretation where such a computation is taking place. [wikipedia]
There's a similar theory advanced by Max Tegmark [The Mathematical Universe, 2008]:
All structures that exist mathematically also exist physically. That is, in the sense that "in those [worlds] complex enough to contain self-aware substructures [they] will subjectively perceive themselves as existing in a physically 'real' world".
Most of the arguments against this kind of rationale base themselves on the impossibility of asserting claims in a kind-of-MUH [Stoeger et al.]:
... in a true multiverse theory, "the universes are then completely disjoint and nothing that happens in any one of them is causally linked to what happens in any other one. This lack of any causal connection in such multiverses really places them beyond any scientific support".
Despite epistemological concerns, the most plausible argument against the dust theory is given by Greg himself:
However, I think the universe we live in provides strong empirical evidence against the “pure” Dust Theory, because it is far too orderly and obeys far simpler and more homogeneous physical laws than it would need to, merely in order to contain observers with an enduring sense of their own existence. If every arrangement of the dust that contained such observers was realised, then there would be billions of times more arrangements in which the observers were surrounded by chaotic events, than arrangements in which there were uniform physical laws. [Permutation City FAQ]
Which is a kind of distorted anthropomorphic principle; since we are observers, it would be much more probable that the laws of physics would be less strict than those we observe, just to support us as conscious observers.
Suppose the dust theory is testable (Egan may already be drafting something along this line, by arguing that a kind of statistical reasoning may point to its own improbability). What would one expect to see in a dust-theory consistent (multi-)verse that we don't observe in our own, and thus render it invalid?