You are partly right, I made a mistake, I meant to say that contradiction is when we can derive both a statement and its negation, indicative of inconsistency.

You are partly right, I made a mistake, I meant to say that contradiction is when we can derive both a statement and its negation, indicative of inconsistency. You are correct to point out that incompleteness is not a flaw, but a natural property of sufficiently complex systems and does not detract from their validity or usefulness. I must admit, I don't know enough about ZFC and the Continuum Hypothesis, but I did not mean to imply that all systems were incompatible.