To me there's no other way to interpret it, really, except as one function. The if-then part of it is part of the function definition. The example is genuinely

To me there's no other way to interpret it, really, except as one function. The if-then part of it is part of the function definition. The example is genuinely confusing to me because of the igtheism problem: the idea that the question of whether God exists is a poorly posed one, because God is undefinable. It's like dividing by zero or a type error or something. This was Bertrand Russell's perspective, for example. Maybe the intent of the example is "here is a function whose inputs are unknown" but for me it was more like "here is a function whose outputs depend on an undefinable input." The second example didn't seem much better for the same reason. Knowing that the output is prime regardless of the input — a logical conclusion from the "meta evaluation" of the function — doesn't seem to me to be the same as asking whether the function is computable. To me it's like having the function depend on a contingency sort of like "if the color blue tastes like cheese, then..." It doesn't make sense. If the example was meant to incorporate an unknown state (as opposed to an undefinable one), it would have been better off with a random unseen event or something, like a person flipping a coin in a different room. Or a particle decay in a box, but then that leads to quantum issues maybe which leads to the same sort of problem possibly.