From http://www.scottaaronson.com/papers/pnp.pdf p. 3 since I had the link handy from another thread:

Have you ever lay awake at night, terrified of what would happen were the Zermelo-Fraenkel axioms found to be inconsistent the next morning? Would bridges collapse? Would every paper ever published in STOC and FOCS have to be withdrawn? ("The theorems are still true, but so are their negations.")