Ok. If we are being careful, there are different kinds of completeness and we should specify which one we're talking about. Here's a good list: https://en.wik

Ok. If we are being careful, there are different kinds of completeness and we should specify which one we're talking about. Here's a good list: https://en.wikipedia.org/wiki/Completeness_(logic)#Forms_of_completeness https://en.wikipedia.org/wiki/Completeness_(logic)#Forms_of_... The existence of a proof within the logic system for every well-formed formula or its negation is "syntactical completeness".