Knowing knowledge

The following four rules explain what it is to know something. X knows the proposition p if and only if:

1. X believes p;
2. p is true;
3. if p weren't true, X wouldn't believe it;
4. if p were true, X would believe it.

Why do we need the fourth condition? To eliminate what are called Gettier counterexamples. This one is due to Quine:

Four men set sail from Boston on 8 November 1918 with the justified false belief that the War in Europe was over (because reports to that effect had been circulated in the newspapers). They arrived in Bermuda four days later with no further information, but now their belief was true. However, it did not count as knowledge, because the justification and the truth were entirely independent of each other.