Publikation: Conceptions of Infinity and Set in Lorenzen’s Operationist System
Dateien
Datum
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
DOI (zitierfähiger Link)
Internationale Patentnummer
Link zur Lizenz
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Publikationsstatus
Erschienen in
Zusammenfassung
In the late 1940s and early 1950s, Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as a precursor of the better-known dialogical logic (Notable exceptions are the works of Schroeder-Heister 2008; Coquand and Neuwirth 2017; Kahle and Oitavem 2020.), and one might assume that the same philosophical motivations were present in both works. However, we want to show that this is not everywhere the case. In particular, we claim that Lorenzen’s well-known rejection of the actual infinite, as stated in Lorenzen (1957), was not a major motivation for operative logic and mathematics. Rather, we argue that a shift happened in Lorenzen’s treatment of the infinite from the early to the late 1950s. His early motivation for the development of operationism is concerned with a critique of the Cantorian notion of set and with related questions about the notions of countability and uncountability; it is only later that his motivation switches to focusing on the concept of infinity and the debate about actual and potential infinity.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
Schlagwörter
Konferenz
Rezension
Zitieren
ISO 690
ANTOS, Carolin, 2021. Conceptions of Infinity and Set in Lorenzen’s Operationist System. In: HEINZMANN, Gerhard, ed., Gereon WOLTERS, ed.. Paul Lorenzen : Mathematician and Logician. Cham: Springer, 2021, pp. 23-46. Logic, Epistemology, and the Unity of Science. 51. ISBN 978-3-030-65823-6. Available under: doi: 10.1007/978-3-030-65824-3_3BibTex
@incollection{Antos2021-08-18Conce-56478, year={2021}, doi={10.1007/978-3-030-65824-3_3}, title={Conceptions of Infinity and Set in Lorenzen’s Operationist System}, number={51}, isbn={978-3-030-65823-6}, publisher={Springer}, address={Cham}, series={Logic, Epistemology, and the Unity of Science}, booktitle={Paul Lorenzen : Mathematician and Logician}, pages={23--46}, editor={Heinzmann, Gerhard and Wolters, Gereon}, author={Antos, Carolin} }
RDF
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/56478"> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/56478/1/Antos_2-ea5cgyb2a7si7.pdf"/> <dc:contributor>Antos, Carolin</dc:contributor> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-02-10T07:49:03Z</dc:date> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/56478"/> <dcterms:abstract xml:lang="eng">In the late 1940s and early 1950s, Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as a precursor of the better-known dialogical logic (Notable exceptions are the works of Schroeder-Heister 2008; Coquand and Neuwirth 2017; Kahle and Oitavem 2020.), and one might assume that the same philosophical motivations were present in both works. However, we want to show that this is not everywhere the case. In particular, we claim that Lorenzen’s well-known rejection of the actual infinite, as stated in Lorenzen (1957), was not a major motivation for operative logic and mathematics. Rather, we argue that a shift happened in Lorenzen’s treatment of the infinite from the early to the late 1950s. His early motivation for the development of operationism is concerned with a critique of the Cantorian notion of set and with related questions about the notions of countability and uncountability; it is only later that his motivation switches to focusing on the concept of infinity and the debate about actual and potential infinity.</dcterms:abstract> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/56478/1/Antos_2-ea5cgyb2a7si7.pdf"/> <dcterms:issued>2021-08-18</dcterms:issued> <dc:creator>Antos, Carolin</dc:creator> <dcterms:title>Conceptions of Infinity and Set in Lorenzen’s Operationist System</dcterms:title> <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2022-02-10T07:49:03Z</dcterms:available> <dc:language>eng</dc:language> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/40"/> <dc:rights>Attribution 4.0 International</dc:rights> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/40"/> </rdf:Description> </rdf:RDF>