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Maximality and ontology : how axiom content varies across philosophical frameworks

Maximality and ontology : how axiom content varies across philosophical frameworks

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BARTON, Neil, Sy-David FRIEDMAN, 2020. Maximality and ontology : how axiom content varies across philosophical frameworks. In: Synthese. Springer. 197(2), pp. 623-649. ISSN 0039-7857. eISSN 1573-0964. Available under: doi: 10.1007/s11229-017-1336-9

@article{Barton2020Maxim-52660, title={Maximality and ontology : how axiom content varies across philosophical frameworks}, year={2020}, doi={10.1007/s11229-017-1336-9}, number={2}, volume={197}, issn={0039-7857}, journal={Synthese}, pages={623--649}, author={Barton, Neil and Friedman, Sy-David} }

<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/rdf/resource/123456789/52660"> <dc:contributor>Barton, Neil</dc:contributor> <dc:language>eng</dc:language> <dc:rights>Attribution 4.0 International</dc:rights> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/52660/1/Barton_2-1bt5bi4nyhg7m8.pdf"/> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/52660"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/40"/> <dcterms:title>Maximality and ontology : how axiom content varies across philosophical frameworks</dcterms:title> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/40"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-02-01T12:19:43Z</dcterms:available> <dc:creator>Barton, Neil</dc:creator> <dc:contributor>Friedman, Sy-David</dc:contributor> <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:issued>2020</dcterms:issued> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/52660/1/Barton_2-1bt5bi4nyhg7m8.pdf"/> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-02-01T12:19:43Z</dc:date> <dc:creator>Friedman, Sy-David</dc:creator> <dcterms:abstract xml:lang="eng">Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology.</dcterms:abstract> </rdf:Description> </rdf:RDF>

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