The short answer is "incompleteness is not a big deal" and the slightly longer answer is "if it's inconsistent, the proof of inconsistency is devilishly hard to

The short answer is "incompleteness is not a big deal" and the slightly longer answer is "if it's inconsistent, the proof of inconsistency is devilishly hard to find." If it does exist, the inconsistent part seems likely to be sufficiently esoteric that it could be "built around."