Programming is concrete. Programmers have to reliably determine if their code will halt or not to make functioning software. Mathematics is concrete and mathe

Programming is concrete. Programmers have to reliably determine if their code will halt or not to make functioning software. Mathematics is concrete and mathematicians have to reliably create new consistent axioms to expand our mathematical knowledge. Notice that the fact you too are subject to Gödel's theorem does not entail you are a Turing machine. There is an oracle hierarchy where each level has its own halting problem and a higher level oracle. This does not cause the hierarchy to collapse. So even though humans have their own halting problem does not entail they are reducible to Turing machines. It is a subtle point of logic, but one I see many people miss, even philosophers and computer scientists who attempt to refute oracle arguments.