Some mathematicians and philosophers have adopted finitism not merely as a methodological viewpoint, but also as a metaphysical one. Finite objects, like numbers and sentences, exist (in whatever sense mathematical objects exist), but infinite objects (like the completed set of all the natural numbers, or even arbitrary irrational numbers represented by Dedekind cuts) don’t. Versions of this view are often attributed to the 19th century number theorist and algebraist, Leopold Kronecker, who is q