Rethinking Intuition in Constructive Mathematics

Bibliographic Data

ID20142084
AuthorsBruno Bentzen (0000-0002-5987-7806, School of Philosophy Zhejiang University Hangzhou China, corresponding author)
Year2025
Volume91
Issue5
Publication date2025-10-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueTheoria (JOURNAL)
Journal identifiersISSN: 0040-5825 • E-ISSN: 1755-2567
PublisherWiley (PUBLISHER • GB)
DOI10.1111/theo.70031
OpenAlexW4412152882
LanguageEN
References cited44

I propose an account of intuition for Bishop's brand of constructive mathematics, where constructions are person programs determined by their computational meaning. Past attempts to elucidate intuition by Parsons and Tieszen drawing on views put forward by Hilbert and Husserl, respectively, have failed to accommodate Bishop's ideas. I argue that, starting from premises building on the works of Brouwer and Heyting on the intuition of units and pairs and their causal sequences, we can explain how we intuit constructions by how their computational meaning is captured by causal relations we project on units and pairs. My exposition of these premises builds on Heyting's reinterpretation of Brouwer's thought and further develops a diagrammatic interpretation proposed recently with the introduction of computations through protentions

Constructive · Diagrammatic reasoning · Epistemology · Exposition (narrative) · Intuition · Intuitionism · Linguistics · Reinterpretation · Computer Science · Mathematics · Philosophy · Philosophy and History of Science · Philosophy and Theoretical Science · Quantum Mechanics and Applications

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