Human-Effective Computability†

Abstract

We analyse Kreisel's notion of human-effective computability. Like Kreisel, we relate this notion to a concept of informal provability, but we disagree with Kreisel about the precise way in which this is best done. The resulting two different ways of analysing human-effective computability give rise to two different variants of Church's thesis. These are both investigated by relating them to transfinite progressions of formal theories in the sense of Feferman.

The open texture of ‘algorithm’ in legal language

“…) are the intended scope of our intuitive notion of algorithm (cf. Antonutti Marfori and Horsten 2018;Piccinini 2015;Shagrir 1997Shagrir , 2022Gurevich 2019;Maley 2023)?…”