What is your distinction between ‘statistical’ and ‘discrete’? And what are you responding ‘no’ to?

Logic in the everyday sense (that is, propositional or something like first-order logic) is indeed ‘discrete’ in a certain sense since it is governed by very simple rules and is by definition a formal language. But ‘mathematical logic’ is a completely different thing. I don’t think it’s discrete in the sense you are imagining. It’s much more akin to a mixture of formal derivations massively guided and driven by philosophical and creative — you might say ‘statistical’ — hunches and intuition.