Kalmar's Argument Against the Plausibility of Church's Thesis

摘要

In his famous paper, An Unsolvable Problem of Elementary Number Theory, Alonzo Church (1936) identified the intuitive notion of effective calculability with the mathematically precise notion of recursiveness. This proposal, known as Church's Thesis, has been widely accepted. Only a few papers have been written against it. One of these is Laszlo Kalmar's An Argument Against the Plausibility of Church's Thesis from 1959. The aim of this paper is to present Kalmar's argument and to fill in missing details based on his general philosophical thoughts on mathematics.