Abstract
In his Doppelvortrag (1901), Edmund Husserl introduced two concepts of “definiteness” which have been interpreted as a vindication of his role in the history of completeness. Some commentators defended that the meaning of these notions should be understood as categoricity, while other scholars believed that it is closer to syntactic completeness. A detailed study of the early twentieth-century axiomatics and Husserl’s Doppelvortrag shows, however, that many concepts of completeness were conflated as equivalent. Although “absolute definiteness” was principally an attempt to characterize non-extendible manifolds and axiom systems (different from Hilbert’s axiom of completeness), an absolutely definite theory has a unique model and, thus, it is non-forkable and semantically complete (decidable). Non-forkability and decidability were formally delimited by Fraenkel and Carnap almost three decades later and, in fact, they mentioned Husserl as precursor of the latter. Therefore, this paper contributes to a reassessment of Husserl’s place in the history of logic.
Highlights
The history of completeness during the first decades of the twentieth century has been extensively researched
In light of the discussion above, the conclusion is, I think, a mixed assessment of Husserl’s Doppelvortrag. This Doppelvortrag has been largely neglected by the analytic tradition, so the commentators could not give a full explanation of the development of the notion(s) of completeness
Husserl adressed different questions regarding the completeness of the axiom systems in the context of the problem of imaginary numbers
Summary
The history of completeness during the first decades of the twentieth century has been extensively researched. The work of the Hilbert school in Gottingen, specially Hilbert’s lecture notes to the winter semester 1917–1918 (cf [31]) and Bernays’s Habilitationschrift (cf [6]), is one field of investigation.. A second important topic was the discussion on the writings of Huntington Winner of the Spanish Prize of Logic 2021 and candidate for the Universal Logic Prize 2021. Winner of the Spanish Prize of Logic 2021 and candidate for the Universal Logic Prize 2021. 1Cf., for instance, Moore [47], Zach [70], Ewald [15] and Ewald and Sieg [16]
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