Complex sentence: In particular, the law of excluded middle, "A" or not "A", is disallowed since one can construct, via Gödel's incompleteness theorems, a mathematical statement that can be neither proven nor disproved.
Split into simpler sentences: In particular, the law of excluded middle, "A" or not "A", is not accepted as a valid principle. Indeed, one can construct, via Gödel's incompleteness theorems, a mathematical statement that can be neither proven nor disproved.