More at https://www.philosophytalk.org/shows/alan-turing-and-limits-computation.

Alan Turing was a 20th-Century English mathematician and cryptologist who is widely considered to be the father of theoretical computer science. In 1950, he published a definition of a computer that is both universal, general enough to apply to any specific computing architecture, and mathematically rigorous, so that it lets us prove claims about what computers can and can't do. What does Turing's writing teach us about the bounds of reason? Which thoughts are too complicated for a computer to express? Is the human brain just another kind of computer, or can it do things that machines can't? Josh and Ray calculate the answers with Juliet Floyd from Boston University, editor of "Philosophical Explorations of the Legacy of Alan Turing."