Husserl and Hilbert on completeness, still

dc.contributor.authorda Silva, Jairo Jose
dc.contributor.institutionUniversity of the State of São Paulo
dc.date.accessioned2022-04-28T19:01:24Z
dc.date.available2022-04-28T19:01:24Z
dc.date.issued2016-06-01
dc.description.abstractIn the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas.en
dc.description.affiliationDepartment of Mathematics University of the State of São Paulo, Av. Quatro, 436, apt. 52
dc.format.extent1925-1947
dc.identifierhttp://dx.doi.org/10.1007/s11229-015-0821-2
dc.identifier.citationSynthese, v. 193, n. 6, p. 1925-1947, 2016.
dc.identifier.doi10.1007/s11229-015-0821-2
dc.identifier.issn1573-0964
dc.identifier.issn0039-7857
dc.identifier.scopus2-s2.0-84937061195
dc.identifier.urihttp://hdl.handle.net/11449/220407
dc.language.isoeng
dc.relation.ispartofSynthese
dc.sourceScopus
dc.subjectCompleteness
dc.subjectDefiniteness
dc.subjectHilbert
dc.subjectHusserl
dc.subjectImaginary elements in mathematics
dc.titleHusserl and Hilbert on completeness, stillen
dc.typeArtigo

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