 Thus, e.g., Russell and Whitehead introduced type theory (which might in some sense be considered a theory of categories) to avoid a certain form of paradox found in Fregean set theory (where we must consider the putative set of all non-self membered sets, which is a member of itself if and only if it is not a member of itself), liar’s paradoxes (“This sentence is false”, which is true if and only if it is false), etc. On their analysis, paradoxes like these arise from the attempt to form an illegitimate totality by trying to collect into a single totality a collection that has members that presuppose the existence of the totality. To avoid such paradoxes, we must accept that “Whatever involves all of a collection must not be one of the collection” (1913 [1962], 37) and thus that such totalities (involving all of a collection) must be of a higher type, making, e.g., classes of sets of a higher type than are sets of individuals, and so on, leading to an infinite hierarchy of types. The type-mixing paradox-generating claims are rejected as ill-formed and meaningless (1913 [1962]).