Talk (Work in Progress): Máté Szabo (Lorraine)
Pepis' and Kalmár's arguments against Church's Thesis
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. In this talk I consider two early arguments against it. Pepis criticized Church’s Thesis already in 1937 in his dissertation and in a letter written to Church. I will display recently found documents showing Pepis’s stance. The main focus of the talk will be László Kalmár's famous An Argument Against the Plausibility of Church's Thesis from 1959. As this paper is quite short, my aim will be to present Kalmár's argument and to fill in missing details based on his general philosophical thoughts on mathematics and his writings published on these issues in Hungarian.