[srean]

Indeed. Soundness and completeness are different things.

There are two well accepted definitions of soundness. One of them is the inability to prove true == false, that is, one cannot prove a contradiction from within that axiomatic system.

[lupire]

They aren't completely different, because trying to achieve wine generally harms the other.

[srean]

True, I guess you understood what I meant, that they are different things.

Indeed, as you allude, you cannot have both in an expressive enough system.