Why can't philosophers agree on a definition of knowledge?

Because the classic definition broke, and no repair has won. The traditional analysis said knowledge is a belief that is justified and true. In the second half of the 20th century, thought experiments, notably Edmund Gettier's counterexamples, aimed to show that some justified true beliefs are not knowledge. Philosophers then proposed many alternative definitions, and there is still no consensus on which is correct. Epistemology, the branch of philosophy that examines the nature, origin and limits of knowledge, has been arguing about it ever since.

The fake-barn case shows the problem. A driver is unaware that the area is full of fake barns. By coincidence, they stop in front of the only real one and form a justified, true belief that it is a barn. Many epistemologists agree this is not knowledge, because the justification is not directly relevant to the truth: they would have believed the same in front of any of the fakes. What went right was epistemic luck, a cognitive success that comes from fortunate circumstances rather than competence.

The proposed fixes pull in different directions. One view says the known fact must cause the belief in the right way. Reliabilism, developed by philosophers such as Alvin Goldman, says knowledge requires reliable sources, moving the focus away from justification. Virtue epistemologists such as Ernest Sosa and Linda Zagzebski look at the intellectual virtues or competences behind a belief. Others require that you would not hold the belief if it were false, or that it not be inferred from a falsehood. And some, like Timothy Williamson, reject the whole project: knowledge, he argues, is a unique state that cannot be broken into simpler parts.

Older divides sit underneath. Skeptics question whether humans can attain knowledge at all, fallibilists say knowledge is never certain, and empiricists and rationalists disagree about whether all knowledge comes from sense experience.