  This, then, gives us a fairly simple formulation of Skolem's Paradox. Before turning to look at this paradox's solution, a point about motivation is probably in order. From one perspective, there's nothing especially surprising about the fact that a particular model fails to accurately capture every feature of the reality of which it is a model. A mathematical model of a physical theory, for instance, may contain only real numbers and sets of real numbers, even though the theory itself concerns, say, subatomic particles and regions of space-time. Similarly, a tabletop model of the solar system will get some things right about the solar system while getting other things quite wrong. So, for instance, it may get the relative sizes of the planets right while getting their absolute sizes (or even their proportional sizes) wrong; or it may be right about the fact that the planets move around the sun, while being wrong about the mechanism of this motion (e.g., the planets don't really move around the sun because some demonstrator turns a crank!). Given all this, it may be unclear why we should even expect first-order models of set theory to accurately capture the distinction between countable and uncountable sets. Hence, it may be unclear why we should even think that Skolem's Paradox looks paradoxical in the first place.