  Together, these last two points highlight just how central classical first-order logic is to Skolem's Paradox. From a mathematical standpoint, this shouldn't be all that surprising. Lindstrom has shown that the Löwenheim-Skolem theorems play a key role in characterizing first-order logic itself (Lindström 1966; Lindström 1969; Ebbinghaus 2007). Given this, it should be unsurprising that the puzzle that's most closely associated with these theorems also turns out to be tied pretty closely to the peculiarities of the first-order situation. Although, as we've seen, the paradox doesn't constitute a straightforward mathematical contradiction, it does help us to understand the nature and limits of classical first-order logic.