Unlike first-order logic, second-order logic is not recursively enumerable—less computationally tractable, more fluid, more human. It operates in a space that, for now, remains beyond the reach of machines still bound to the strict determinism of their logic gates.
In what sense is second-order logic “beyond the reach of machines”? Is it non-deterministic? Or what are you trying to say here? (Maybe some examples would help)
Maybe I should have asked: In what sense are machines “fully doing” first-order logic? I think I understand the part where first logic formulas are recursively enumerable, in theory, but isn’t that intractable to the point of being useless and irrelevant in practice?