  This, then, gives us a first pass at formulating Skolem's Paradox. In the next section, we explain why this simple version of the paradox doesn't constitute a genuine contradiction, and we look at several more-refined formulations of the paradox. In section  3,  we turn to historical and philosophical issues. Section  3.1  looks at Skolem's own understanding of his paradox. Sections  3.2–3.4 look at some more-recent attempts to argue that, even though the paradox doesn't constitute a genuine mathematical contradiction, it still tells us something philosophically important about the nature of our understanding of set theory.