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 ill