Description
David Hilbert’s The Foundations of Geometry (1899) is considered a landmark in the history of modern logic and mathematics by philosophers, mathematicians and logicians alike. In his ‘Festschrift’, Hilbert presents consistency and independence proofs for various fragments of his axiomatization of Euclidean geometry and provides a number of methodological innovations that were formative for our current understanding of mathematical theories and the axiomatic method. In reaction to Hilbert, Gottlob Frege, in a series of articles dating from 1903 to 1906, presents a thorough critique of Hilbert’s underlying methodology. In the final part of a paper from 1906 ([1]), Frege eventually develops his own proposal as to how independence must be proved. His suggestions are both radical and puzzling: Frege claims that a ‘new science’ has to be established in order to rigorously prove the independence of genuine axioms. Although some have discussed various aspects of this new science, no systematic account of Frege’s ideas on the matter has been devised so far. The aim of the talk is to sketch out how this lacuna might be filled. More specifically, the aims are to clarify (1) Frege’s motivation for introducing a new science in the first place, (2) what this new science is supposed to look like and how it relates to concepts and methods in (pre-)modern mathematical logic, and (3) how it lines up with Frege’s overall philosophy, what his approach implies for various interpretations of his views on metatheory and what we can learn from his basic approach. [1] Gottlob Frege, Über die Grundlagen der Geometrie, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 12 (1906), pp. 293–309, pp. 377–403, pp. 423–430.| Period | 4 Aug 2015 |
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| Event title | Logic Colloquium 2015 |
| Event type | Conference |
| Location | Helsinki, FinlandShow on map |