Round 9: Tossup 7

Mereology (“mee-ree-ology”) unproblematically incorporates an analogue of these objects’ rule of unrestricted comprehension, which was originally called Basic Law V (“five”). Type theory was developed to resolve a paradox about these objects, which is often compared to a barber (10[1])who can’t shave himself. Gottlob (10[1])Frege (-5[1])(“FRAY-guh”) defined numbers as these objects, which is also done in Zermelo-Frankel theory. The naïve theory of these objects is subject to Russell’s paradox, which concerns one (10[1])of these objects containing all of these objects that do (10[1])not contain themselves. De Morgan’s laws axiomatize the union and intersection operations on these objects. For 10 points, name these unordered collections of objects. (10[1])■END■

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