Article ID: CBB001211006

“Metamathematics” in Transition (2011)

unapi

In this paper, we trace the conceptual history of the term `metamathematics' in the nineteenth century. It is well known that Hilbert introduced the term for his proof-theoretic enterprise in about 1922. But he was verifiably inspired by an earlier usage of the phrase in the 1870s. After outlining Hilbert's understanding of the term, we will explore the lines of inducement and elucidate the different meanings of `metamathematics' in the final decades of the nineteenth century. Finally, we will investigate the earlier occurrences and come to the conclusion that the conceptual prehistory of the Hilbertian notion of metamathematics dates back to 1870, whereas the history of the word starts in 1799 at the latest.

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Authors & Contributors
Sieg, Wilfried
Vrhovski, Jan
Gambetta, Emanuele
Ausejo Lifante, Elena
Zach, Richard
Stillwell, John
Journals
Perspectives on Science
History and Philosophy of Logic
Studies in History and Philosophy of Science
Revue d'Histoire des Sciences
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Historia Mathematica
Publishers
Kluwer Academic
Gangemi Editore
Raffaello Cortina Editore
University of British Columbia (Canada)
Springer
de Gruyter
Concepts
Mathematics
Logic
Philosophy of mathematics
Physics
Geometry
Formalization (philosophy)
People
Hilbert, David
Leibniz, Gottfried Wilhelm von
Kronecker, Leopold
Gödel, Kurt
Cantor, Georg Ferdinand Ludwig
Zermelo, Ernst
Time Periods
19th century
20th century, early
20th century
20th century, late
18th century
17th century
Places
Germany
China
Institutions
Tsinghua University
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