Church and Turing did not prove their papers with the words, they described the math proving their statements in them and what that math implies (which is why the ending summary would not be math, it must already have been shown to be a summary). In however many comments you have certainly used a lot of words to describe your thought but have given nothing in the way of the math used to base the difference in your claim between that of Church/Turings.
A psychologist could just as well assert the halting problem contains math applicable to any system and therefore blue cars mathematically make us angry. The doubt would then not be on Turing but on the psychologist to show how on Earth they are mathematically linking what they are saying with what Turing actually showed. That they don't see a requirement in having the chain of math rigorously define and prove the claim when they make it is precisely why they are a soft science - they can just claim it seems to relate by less rigorous means. Defend that kind of approach if you wish, it does not make it more rigorous.
I expect we'll soon hear words about more mathematicians and scientist, related to the current problem or not, rather than math. Perhaps I've allowed myself baited by hope again on the mention of what math is needed being discussed.
A psychologist could just as well assert the halting problem contains math applicable to any system and therefore blue cars mathematically make us angry. The doubt would then not be on Turing but on the psychologist to show how on Earth they are mathematically linking what they are saying with what Turing actually showed. That they don't see a requirement in having the chain of math rigorously define and prove the claim when they make it is precisely why they are a soft science - they can just claim it seems to relate by less rigorous means. Defend that kind of approach if you wish, it does not make it more rigorous.
I expect we'll soon hear words about more mathematicians and scientist, related to the current problem or not, rather than math. Perhaps I've allowed myself baited by hope again on the mention of what math is needed being discussed.