The more we learn about the world, and the deeper our learning, the more conscious, specific, and articulate will be our knowledge of what we do not know, our knowledge of our ignorance

[The aim of science is] to explain what so far has taken to be an explicans, such as a law of nature. The task of empirical science constantly renews itself. We may go on forever, proceeding to explanations of a higher and higher universality.

No number of sightings of white swans can prove the theory that all swans are white. The sighting of just one black one may disprove it.

All we can do is search for the falsity content in our best theory.

There will be well-testable theories, hardly testable theories, and non-testable theories. Those which are non-testable are of no interest to empirical scientists. They may be described as metaphysical.

While differing widely in the various little bits we know, in our infinite ignorance we are all equal.

Our aim as scientists is objective truth; more truth, more interesting truth, more intelligible truth. We cannot reasonably aim at certainty. Once we realize that human knowledge is fallible, we realize also that we can never be completely certain that we have not made a mistake.