Ignorabimus
Encyclopedia
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
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
Emil du Bois-Reymond
Emil du Bois-Reymond was a German physician and physiologist, the discoverer of nerve action potential, and the father of experimental electrophysiology.-Life:...
, 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 mathematicianMathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
pronounced his disagreement in a celebrated address to the Society of German Scientists and Physicians, in Königsberg
Königsberg
Königsberg was the capital of East Prussia from the Late Middle Ages until 1945 as well as the northernmost and easternmost German city with 286,666 inhabitants . Due to the multicultural society in and around the city, there are several local names for it...
:
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
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of...
showed in 1931 that no finite system of axiom
Axiom
In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true...
s, if complex enough to express our usual arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
, could ever fulfill the goals of Hilbert's program
Hilbert's program
In mathematics, Hilbert's program, formulated by German mathematician David Hilbert, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies...
, demonstrating many of Hilbert's aims impossible, and establishing limits on mathematical knowledge.
Seven World Riddles
Emil du Bois-ReymondEmil du Bois-Reymond
Emil du Bois-Reymond was a German physician and physiologist, the discoverer of nerve action potential, and the father of experimental electrophysiology.-Life:...
used ignoramus et ignorabimus in discussing what he called seven "world riddles", in a famous 1880 speech before the Berlin Academy of Sciences
Prussian Academy of Sciences
The Prussian Academy of Sciences was an academy established in Berlin on 11 July 1700, four years after the Akademie der Künste or "Arts Academy", to which "Berlin Academy" may also refer.-Origins:...
.
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 LepeniesWolf Lepenies
Wolf Lepenies is a German sociologist, political scientist, and author.-Biography:Lepenies was born near Allenstein, East Prussia ), in 1945 his family fled from the Soviet Army's assault on East Prussia to Schleswig-Holstein and from there to North Rhine-Westfalia. He eventually grew up in Koblenz...
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
Friedrich Wolters
Friedrich Wolters was a German historian, poet and translator. He was one of the central figures of the George-Kreis, an influential literary group. Wolters met Stefan George in 1904 and by the 1920s was one of his strongest supporters in the George-Kreis....
, one of the members of the literary group "George-Kreis
George-Kreis
The George-Kreis or George Circle were an influential German literary group centred around Stefan George. Formed in the late 19th Century, the group featured many highly-regarded German writers and academics...
". 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
- HubrisHubrisHubris , also hybris, means extreme haughtiness, pride or arrogance. Hubris often indicates a loss of contact with reality and an overestimation of one's own competence or capabilities, especially when the person exhibiting it is in a position of power....
- Strong agnosticismStrong agnosticismStrong agnosticism or positive agnosticism is the belief that it is impossible for humans to know whether or not any deities exist. It is a narrower view than weak agnosticism, which states that the existence or nonexistence of any deities is unknown but not necessarily unknowable.Strong...
- Unknown unknownUnknown unknown"There are known knowns" are the most well-known words of a statement to the press made by the former United States Secretary of Defense Donald Rumsfeld in February 2002.- Usage :...
- I know that I know nothingI know that I know nothing"I know one thing, that I know nothing" is a well-known saying that is derived from Plato's account of the Greek philosopher Socrates...