Ignoramus et ignorabimus  

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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.


Hilbert's reaction

On the 8th of September 1930, the mathematician David Hilbert pronounced his disagreement in a celebrated address to the Society of German Scientists and Physicians, in Königsberg:

"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!')"

Even before that he said: "In mathematics there is no ignorabimus." D. Hilbert, 'Mathematical Problems: Lecture Delivered before the International Congress of Mathematicians at Paris in 1900', bulletin of the American Mathematical Society, 8 (1902) p437-79 (445)

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 establishing limits on mathematical knowledge.

Seven World Riddles

Emil du Bois-Reymond used ignoramus et ignorabimus in discussing what he called seven "world riddles", in a famous 1880 speech before the Berlin Academy of Sciences.

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.

Sociological responses

The sociologist Wolf Lepenies has discussed the ignorabimus with a view that du Bois-Reymond was not really retreating in his claims for science and its reach:

— 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 Stefan George circle. 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.

See also

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