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dc.contributor.authorBrunet, T. D. P.
dc.contributor.authorFisher, E.
dc.date.accessioned2020-10-31T16:08:12Z
dc.date.available2020-10-31T16:08:12Z
dc.date.issued2020-01-22
dc.date.submitted2019-08-07
dc.identifier.issn0039-3215
dc.identifier.others11225-019-09892-z
dc.identifier.other9892
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/312306
dc.descriptionFunder: University of Cambridge
dc.description.abstractAbstract: We begin with the idea that lines of reasoning are continuous mental processes and develop a notion of continuity in proof. This requires abstracting the notion of a proof as a set of sentences ordered by provability. We can then distinguish between discrete steps of a proof and possibly continuous stages, defining indexing functions to pick these out. Proof stages can be associated with the application of continuously variable rules, connecting continuity in lines of reasoning with continuously variable reasons. Some examples of continuous proofs are provided. We conclude by presenting some fundamental facts about continuous proofs, analogous to continuous structural rules and composition. We take this to be a development on its own, as well as lending support to non-finitistic constructionism.
dc.languageen
dc.publisherSpringer Netherlands
dc.rightsAttribution 4.0 International (CC BY 4.0)en
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subjectArticle
dc.subjectProof theory
dc.subjectIntuitionism
dc.subjectConstructivism
dc.subjectContinuity
dc.subjectContinuous proof
dc.titleReasoning Continuously: A Formal Construction of Continuous Proofs
dc.typeArticle
dc.date.updated2020-10-31T16:08:11Z
prism.endingPage1160
prism.issueIdentifier6
prism.publicationNameStudia Logica
prism.startingPage1145
prism.volume108
dc.identifier.doi10.17863/CAM.59400
rioxxterms.versionofrecord10.1007/s11225-019-09892-z
rioxxterms.versionVoR
rioxxterms.licenseref.urihttps://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidBrunet, T. D. P. [0000-0002-7609-7254]
dc.identifier.eissn1572-8730


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Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's licence is described as Attribution 4.0 International (CC BY 4.0)