[oleganza]

This reminds of an idea in math that proofs by construction are better than proofs by contradiction. Or making artificial grammars (e.g. PLs) with recursive descent parsers instead of context-sensitive grammars with Turing-complete parsers.

If you can build something step-by-step with a clear hierarchy and easy to trace causes and effects, the result seems to be more convincing/reliable than a process involving a bunch of logical roundabouts. Of course, if that's at all possible for a problem at hand.

[leephillips]

That’s what made Paul Gordon complain after he read a proof by David Hilbert, of his own conjecture, that “This is not mathematics. This is theology.”