In overturning divine authority and poetic license for rational thought, the Milesians turned single-mindedly to the observation of evidence. They were unreflective empiricists, gathering all their knowledge through experience, collecting the data to be explained. Xenophanes follows in this empiricist tradition, but he is reflective about it. In particular, he notices that it has some dire consequences for the possibility of human knowledge.
When knowledge came from divine authority, the limit of knowledge was just the limit of what the gods wanted to reveal, or the limit of what the imagination could drum up. The philosophers have hit now on a new, improved method of obtaining knowledge: investigating the world for themselves. The only problem, Xenophanes purports to show, is that this method does not actually yield much knowledge; the best it can yield is true belief. This is because most subjects of investigation—the gods, the physis, the derivation of plurality from unity—cannot be observed. These matters go beyond our experience. If the only way to obtain knowledge is to gather data with the senses (which Xenophanes believes it is) then we cannot obtain knowledge about the most important things, theology and science.
In addition, Xenophanes points out, we can even disagree about what is directly perceived. As Xenophanes says, "if god had not created honey we'd say figs are much sweeter" (fragment 21B38). In other words, there is a high degree of indeterminacy to our perceptions, a subjective element in all of our observations. We do not gain access to the true nature of, say, the fig by tasting it. Rather, our perception of the taste of the fig varies with our other experiences. If we have tasted honey, then the fig does not taste so sweet; if we have not tasted honey, then the fig tastes very sweet to us. There is, in other words, a veil of appearances or perceptions that we cannot go beyond in our experience; all that we have access to is our own perceptions and these are subjective: they do not accurately reflect the objective reality of things.
Since we rely on experience to give us knowledge, and experience lets us down in these two ways (first, by not even extending to the most important subjects, and second by denying us access to the real, objective nature of things) we are doomed to be forever without any real knowledge. Xenophanes' final analysis of the human capacity for knowledge is as skeptical as it could be.