“Whatever the progress of human knowledge, there will always be room for ignorance, hence for chance and probability.”

This "aphorism" was expressed in different forms by Josh Billings and Socrates. note: Often misquoted as, "The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge," and often misattributed to Stephen Hawking.
Source: Cleopatra's Nose: Essays on the Unexpected (1995).

The Value of Science (1955)
Context: The scientist has a lot of experience with ignorance and doubt and uncertainty, and this experience is of very great importance, I think. When a scientist doesn’t know the answer to a problem, he is ignorant. When he has a hunch as to what the result is, he is uncertain. And when he is pretty darn sure of what the result is going to be, he is still in some doubt. We have found it of paramount importance that in order to progress we must recognize our ignorance and leave room for doubt. Scientific knowledge is a body of statements of varying degrees of certainty — some most unsure, some nearly sure, but none absolutely certain. Now, we scientists are used to this, and we take it for granted that it is perfectly consistent to be unsure, that it is possible to live and not know. But I don’t know whether everyone realizes this is true. Our freedom to doubt was born out of a struggle against authority in the early days of science. It was a very deep and strong struggle: permit us to question — to doubt — to not be sure. I think that it is important that we do not forget this struggle and thus perhaps lose what we have gained.

Probably a paraphrase of this line from De l’Allemagne, Pt. 3. ch. 10. "Goethe has made a remark upon the perfectability of the human mind, which is full of sagacity: It is always advancing, but in a spiral line." Not known from Goethe's works.
Misattributed

Αs translated by William Smith, in The Popular Works of Johann Gottlieb Fichte (1889), Vol. I, Lecture IV, p. 188.
The Vocation of the Scholar (1794)
Context: Upon the progress of knowledge the whole progress of the human race is immediately dependent: he who retards that, hinders this also. And he who hinders this, —what character does he assume towards his age and posterity? Louder than with a thousand voices, by his actions he proclaims into the deafened ear of the world present and to come —"As long as I live at least, the men around me shall not become wiser or better; — for in their progress I too, notwithstanding all my efforts to the contrary, should be dragged forward in some direction; and this I detest I will not become more enlightened, — I will not become nobler. Darkness and perversion are my elements, and I will summon all my powers together that I may not be dislodged from them."

The Ethic of Freethought (Mar 6, 1883)

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 244; Cited in: Michael J. Katz (1986) Templets and the Explanation of Complex Patterns, p. 123

2016

Source: Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets

Why I Am a Muslim: And a Christian and a Jew (2020)