soundness of LEM depends on where one originates the source of mathematics I disagree! One of Goedel's many great contributions was the double-negatio

soundness of LEM depends on where one originates the source of mathematics I disagree! One of Goedel's many great contributions was the double-negation translation (later refined by others), and what it does is show that (simplifying a bit) intuitionistic logic and classical logic are equiconsistent! In other words: any contradiction you can derive in classical logic, you can convert into a contradiction in intuitionistic logic. (The reverse direction is trivial because all intuitionistic proof principles are also classical.)