Brouwer–Hilbert on the Limits of Mathematical Knowledge

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dc.coverageSTUDIA UBB PHILOSOPHIA, LXX, Special Issue, 2025 (p. 27-46)en-US
dc.creatorFEDEROVICI, Silviu-Constantin
dc.date2025-12-30
dc.date.accessioned2026-02-21T10:40:53Z
dc.descriptionBrouwer famously challenged the limits of mathematical knowledge by arguing that classical formalism obscures intuitive evidence. Hilbert, by contrast, considered that intuitive insights could safely be ignored as long as formal systems remained consistent and complete. Such a disagreement created a paradigmatic tension between intuitionism and formalism in how the foundations of mathematics should be regarded. This paper evaluates Hilbert’s eventual pragmatic dominance and explores, via a shared Kantian heritage, how intuitionistic insights might coexist with formal approaches. Focusing on axioms, the analysis reveals how neglecting certain epistemic values while admitting alternative forms of evidence shapes our understanding of mathematical limits.en-US
dc.formatapplication/pdf
dc.identifierhttps://studia.reviste.ubbcluj.ro/index.php/subbphilosophia/article/view/9978
dc.identifier10.24193/subbphil.2025.sp.iss.02
dc.identifier.urihttps://hdl.handle.net/20.500.14637/1324
dc.languageeng
dc.publisherBabeș-Bolyai University / Cluj University Pressen-US
dc.relationhttps://studia.reviste.ubbcluj.ro/index.php/subbphilosophia/article/view/9978/9615
dc.rightsCopyright (c) 2025 Studia Universitatis Babeș-Bolyai Philosophiaen-US
dc.rightshttps://creativecommons.org/licenses/by-nc-nd/4.0en-US
dc.sourceStudia Universitatis Babeș-Bolyai Philosophia; Volume 70, Special Issue, December 2025; 27-46en-US
dc.source2065-9407
dc.source10.24193/subbphil.2025.sp.iss
dc.subjectphilosophy of mathematicsen-US
dc.subjectBrouwer-Hilbert controversyen-US
dc.subjectepistemic limitsen-US
dc.subjectKantian heritageen-US
dc.titleBrouwer–Hilbert on the Limits of Mathematical Knowledgeen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typePeer-reviewed Articleen-US
dc.typetexten-US

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