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Neo-kantians or empiricists: who coined the term “Metamathematics”?| old_uid | 7398 |
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| title | Neo-kantians or empiricists: who coined the term “Metamathematics”? |
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| start_date | 2009/10/05 |
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| schedule | 14h-17h |
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| online | no |
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| location_info | bat. Condorce, site Rive gauche, salle Klee |
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| summary | The term ? metamathematics ? is an artificial word. It is a creation of scientific discourses and received its ultimate meaning through the use of David Hilbert. It is well known that Hilbert used the word ? metamathematics? as a name for his proof-theoretic foundations of mathematics. Hilbert?s program was a twofold foundational program : whereas on the object-level the program called for a formalization of classical mathematics, on the meta-level (in metamathematics) there should be carried out finite consistency proofs for every formalized branch of mathematics. The talk deals not with Hilbert?s program but asks for the origins of the term ? metamathematics? and consists in a philosophico-mathematical quest going back more than a half a century. Hilbert was philosophically open minded and sympathized with some Kantian notions. In the first two decades of 20th century he read not only through the works of Kant but also publications about some crucial topics discussed by the leading neo-Kantians and Empiricists ? especially the epistemological status of Euclidean geometry in the light of non-Euclidean alternatives. In these contexts the term? metamathematics? became famous as the summarizing name for the meta-reflections about the formal and philosophical questions concerning the geometries. But whereas in the last two decades of 19th century the frequency of the use increased notably, it is much more difficult to retrace the days before Hermann von Helmholtz authorized the concept in 1878. The talk sheds some light on these very early days and will end off with some conjectures. |
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| responsibles | Pataut, Dubucs, Panza |
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