Ignoramus et ignorabimus
The Latin maxim ignoramus et ignorabimus, meaning "we do not know and will not know", stood for a position on the limits of scientific knowledge, in the thought of the nineteenth century. It was given credibility by Emil du Bois-Reymond, a German physiologist, in his Über die Grenzen des Naturerkennens ("On the limits of our understanding of nature") of 1872.
|“||We must not believe those, who today, with philosophical bearing and deliberative tone, prophesy the fall of culture and accept the ignorabimus. For us there is no ignorabimus, and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: Wir müssen wissen — wir werden wissen! ('We must know — we will know!')||”|
Already in 1900, at the International Congress of Mathematicians at Paris he said: "In mathematics there is no ignorabimus."
Hilbert worked with other formalists to establish concrete foundations for mathematics in the early 20th century. However, Gödel's incompleteness theorems showed in 1931 that no finite system of axioms, if complex enough to express our usual arithmetic, could ever fulfill the goals of Hilbert's program, demonstrating many of Hilbert's aims impossible, and specifying limits on most axiomatic systems.
Seven World Riddles
He outlined 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." However, depending on the interpretation of "ultimate nature" and "origin," it is possible to consider some of these as partially or completely solved. For example, the sensory systems for the traditional senses (sight, hearing, taste, smell, touch) are now mostly understood, including some of the associated neural processing.
- — 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.
- Hilbert, David, audio address, transcription and English translation.
- 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.
- William E. Leverette Jr., E. L. Youmans' Crusade for Scientific Autonomy and Respectability, American Quarterly, Vol. 17, No. 1. (Spring, 1965), pg. 21.
- Lepenies, Wolf (1988). Between Literature and Science: the Rise of Sociology. Cambridge, UK: Cambridge University Press. p. 272. ISBN 0-521-33810-7.