  We close this discussion of the mathematical side of Skolem's Paradox with four final points. First, the discussion in 2.3–2.4 focused on the transitive submodel case of Skolem's Paradox. This case is relatively straightforward to analyze, and (so) it's the case that's been most widely discussed in the literature. But it can also be somewhat misleading. Much of the analysis of 2.3–2.4 turned on the fact that transitive models get a lot of things “right” about the set-theoretic universe (membership, bijections, real numbers, etc.). Most importantly, if M is transitive and m ∈ M, then m = {m′ ∈ M  | M  ⊨ m′ ∈ m }.