Ignoramus et ignorabimus
The Latin maxim ignoramus et ignorabimus, meaning "we do not know and will not know", represents the idea that scientific knowledge is limited. It was publicized, in this sense, by Emil du Bois-Reymond, a German physiologist, in his publication Über die Grenzen des Naturerkennens ("On the limits of our understanding of nature") of 1872.
Seven World Riddles
Emil du Bois-Reymond used the phrase ignoramus et ignorabimus while discussing what he termed seven "world riddles", in a famous 1880 speech before the Prussian Academy of Sciences.
He defined seven "world riddles", of which three, he declared, neither science nor philosophy could ever explain, because they are "transcendent". Of the riddles, he considered the following transcendental and declared of them ignoramus et ignorabimus: "1. the ultimate nature of matter and force, 2. the origin of motion, ... 5. the origin of simple sensations, a quite transcendent question."
David Hilbert, a widely-respected German mathematician, suggested that such a conceptualization of human knowledge and ability is too pessimistic, and that by considering questions unsolvable, we limit our understanding.
In 1900, during an address to the International Congress of Mathematicians in Paris, Hilbert suggested that answers to problems of mathematics are possible with human effort. He declared, "In mathematics there is no ignorabimus.", and he worked with other formalists to establish foundations for mathematics during the early 20th century.
Answers to some of Hilbert's Program of 23 problems were found during the 20th century. Some have been answered definitively; some have not yet been solved; a few have been shown to be impossible to answer with mathematical rigor.
During 1931, Gödel's incompleteness theorems showed that answers to some mathematical questions cannot be answered in the manner we would usually prefer.
The sociologist Wolf Lepenies has discussed the ignorabimus with the opinion that du Bois-Reymond was not really pessimistic about science:
—it is in fact an incredibly self-confident support for scientific hubris masked as modesty—
This is in a discussion of Friedrich Wolters, one of the members of the literary group "George-Kreis". Lepenies comments that Wolters misunderstood the degree of pessimism being expressed about science, but well understood the implication that scientists themselves could be trusted with self-criticism.
- William E. Leverette Jr., E. L. Youmans' Crusade for Scientific Autonomy and Respectability, American Quarterly, Vol. 17, No. 1. (Spring, 1965), pg. 21.
- D. Hilbert (1902). "Mathematical Problems: Lecture Delivered before the International Congress of Mathematicians at Paris in 1900". Bulletin of the American Mathematical Society. 8: 437–79. doi:10.1090/S0002-9904-1902-00923-3. MR 1557926.
- Lepenies, Wolf (1988). Between Literature and Science: the Rise of Sociology. Cambridge, UK: Cambridge University Press. p. 272. ISBN 0-521-33810-7.