Finite objects are mathematically unproblematic

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 tro