I am reading Simon Singh’s “The Code Book”. Interesting discussion of Alan Turing.
Turning wrote a paper “On Computable Numbers”, published in 1937. In “Breaking the Code”, Hugh Whitemore’s play about the life of Turning, a character asks Turing the meaning of his paper. Turning replies “Its about Right and Wrong in general terms. It’s a technical paper in mathematical logic, but it’s also about the difficulty of telling right from wrong. People think — most people think — that in mathematics we always know what is right and what is wrong. Not so. Not any more.”*
Math has crisply-defined problems, hard standards of proof and mountains of proofs, but it still can’t always know True/False for simple questions in mathematics, clearly and crisply stated.
I think there is no reason to believe that mathematics is more complex than any other part of life, in fact it is probably simpler because it has progressed so far, so fast.
In any case, given our real-world problems of right and wrong, good and evil, to which we apply words with fuzzy edges and analogy as our main intellectual tools, we should expect to have to sweat to decide the most obvious cases.
By analogy, of course.
* “Breaking the Code” was typical Hollywood schlock. It falsified history “to tell a good story”, and the story was lousy, unbelievable on every level. The fact that it got Academy Award nominations is all you need to know about the integrity of that great prize.