Russell did his best to deflect the paradox’s sting by claiming that it was an illusion arising from a naïve misuse of the word “describable” in the context of mathematics. That notion, claimed Russell, had to be parceled out into an infinite hierarchy of different types of describability — descriptions at level 0, which could refer only to notions of pure arithmetic; descriptions at level 1, which could use arithmetic but could also refer to descriptions at level 0; descriptions at level 2, which could refer to arithmetic and also to descriptions at levels 0 and 1; and so forth and so on.
