
“Probability fractions arise from our knowledge and from our ignorance.”
Source: The Emergence Of Probability, 1975, Chapter 14, Equipossibility, p. 132.
Source: Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets
“Probability fractions arise from our knowledge and from our ignorance.”
Source: The Emergence Of Probability, 1975, Chapter 14, Equipossibility, p. 132.
Variant translation: The more we learn about the world, and the deeper our learning, the more conscious, clear, and well-defined will be our knowledge of what we do not know, our knowledge of our ignorance. The main source of our ignorance lies in the fact that our knowledge can only be finite, while our ignorance must necessarily be infinite.
Conjectures and Refutations: The Growth of Scientific Knowledge (1963)
Context: 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. For this, indeed, is the main source of our ignorance — the fact that our knowledge can be only finite, while our ignorance must necessarily be infinite.
The Whig Interpretation of History (1931)
The Ethic of Freethought (Mar 6, 1883)
“The science of probability gives mathematical expression to our ignorance, not to our wisdom.”
Time Considered as a Helix of Semi-Precious Stones (1968)
Context: If everything, everything were known, statistical estimates would be unnecessary. The science of probability gives mathematical expression to our ignorance, not to our wisdom.
“The greater our knowledge increases the greater our ignorance unfolds.”
1962, Rice University speech
Address to his household, Yverdon, Switzerland, on his seventy-second birthday (1818-01-12)
Source: The Christian Agnostic (1965), p.77-78, (Paul Tillich: The Shaking of the Foundations. 1963. Pelican Books. p. 164