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Article Dans Une Revue Notre Dame Journal of Formal Logic Année : 2021

The Shaping of Dedekind’s Rigorous Mathematics: What Do Dedekind’s Drafts Tell Us about His Ideal of Rigor?

Emmylou Haffner

Résumé

In this paper, I propose to examine Dedekind's ideal of rigor in the context of some of his mathematical drafts. After a presentation of his ideal of rigor based on statements in his published works, I use drafts from his Nachlass to study his invention of the new concept of Dualgruppe (equivalent to our modern lattice). I question the extent to which these preliminary researches hold up to the same standards of rigor. Focusing on a specific law of Dualgruppe theory, I show that the elaboration of a rigorous work can be the outcome of a process that is not necessarily so. I put forward the trial-and-error and inductive aspects of Dedekind's research practices. I consider whether the Dedekindian ideal of rigor guided mathematical research in its various phases, and what were consequences of such an ideal of rigor, if any, on mathematical research.
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Dates et versions

halshs-03513278 , version 1 (05-01-2022)

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Emmylou Haffner. The Shaping of Dedekind’s Rigorous Mathematics: What Do Dedekind’s Drafts Tell Us about His Ideal of Rigor?. Notre Dame Journal of Formal Logic, 2021, 62 (1), ⟨10.1215/00294527-2021-0001⟩. ⟨halshs-03513278⟩
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