 Another viewpoint, associated with David Hilbert, is called finitism (see Hilbert 1926). Most finitists accept classical logic, but worry about the consistency of theories of infinite objects. Hilbert’s worries about consistency were fueled by the paradoxes that the new infinitary set-theoretic mathematics was giving rise to (Cantor’s inconsistent sets; Burali-Forti Paradox; Russell’s paradox etc.) Hilbert was convinced that quantification over such infinite totalities was at the root of the troubles. Finite objects, like configurations of strokes corresponding to the natural numbers, and finite sentences of a formal language, are taken by the Hilbertian finitist to be unproblematic, since these objects can in some sense be grasped individually and thus in their (potential) totality. But infinite objects are taken to be problematic: this includes Cantor’s higher ordinals and cardinals, and all the geometric, algebraic, and topological objects of which mathematicians were starting to develop detailed theories at the turn of the 20th century.