Scrutinizing the history of mathematics and computer science has led me to the following illustration & line of argumentation, followed by two typical responses and then a question which I pose to my readers. Perhaps the sequel contains a few insights for the reader too; alas, some sections are peppered with nonsense (most of which I have labelled accordingly).
Concerning Cantor's diagonal argument in connection with the natural and the real numbers, Georg Cantor essentially said: assume we have a bijection between the natural numbers (on the one hand) and the real numbers (on the other hand), we shall now derive a contradiction ...
Here's an abstract, entitled: The Turing Machine as a Boundary Object: Sorting Out American Science and European Engineering, co-authored by Erhard Schüttpelz, featuring Marvin Minsky and Edsger Dijkstra in the late 1960s and early 1970s. To be presented this summer in London at the 11th British Wittgenstein Society Conference: Wittgenstein and AI.
Here's a chapter in the making on two very different philosophical positions and computer programming. I engage with Linnebo and Shapiro in connection with classical logical and potential infinity.
Discussions will be held at a Lille workshop in June 2022. A revised chapter will appear in the book What is a computer program? New perspectives, edited by PROGRAMme (i.e., by Liesbeth De Mol, Tomas Petricek, and the rest of the PROGRAMme community).