“Why do we know what we know and why don't we know what we don't know? What should we know and what shouldn't we know? How might we know differently?”

Rules 2 Rule

As quoted in Walden (1854) by Henry David Thoreau, Ch. 1
Attributed

Confucius, as quoted in Walden (1854) by Henry David Thoreau, Ch. 1
Misattributed

How Children Fail (1964).

Source: Walden

Alvaro De Rujula, quoted in "Large Hadron Collider - The Search For The Higgs" http://www.youtube.com/watch?v=_XbKZwXK-3c; this quote can be heard at approximately 3:55 to 4:15 in the video. It is important to note, it could be taken out of context. It implies that science is what we use when we do not know the answer to something.

Source: Tertium Organum (1912; 1922), Ch. I
Context: The most difficult thing is to know what we do know, and what we do not know.
Therefore, desiring to know anything, we shall before all else determine WHAT we accept as given, and WHAT as demanding definition and proof; that is, determine WHAT we know already, and WHAT we wish to know.
In relation to the knowledge of the world and of ourselves, the conditions would be ideal could we venture to accept nothing as given, and count all as demanding definition and proof. In other words, it would be best to assume that we know nothing, and make this our point of departure.
But unfortunately such conditions are impossible to create. Knowledge must start from some foundation, something must be recognized as known; otherwise we shall be obliged always to define one unknown by means of another.

"Ce que nous connaissons est peu de chose, ce que nous ignorons est immense."
Allegedly his last words, reported in Joseph Fourier's "Éloge historique de M. le Marquis de Laplace" (1829) with the comment, "This was at least the meaning of his last words, which were articulated with difficulty." Quoted in Augustus De Morgan's Budget of Paradoxes (1866).