Rethinking Intuition in Constructive Mathematics.

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 fai...

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Publicado en:Theoria: A Swedish Journal of Philosophy Vol. 91; no. 5; pp. 1 - 16
Autor principal: Bentzen, Bruno
Formato: Artículo
Publicado: Wiley-Blackwell Oct2025
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Acceso en línea:Ver este registro en EBSCOhost
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        atl: Rethinking Intuition in Constructive Mathematics.
      aug:
        au: Bentzen, Bruno
        affil: School of Philosophy, Zhejiang University, Hangzhou, China
      su:
        Constructive mathematics
        Intuition
        Philosophy of mathematics
        Epistemics
        Ontology
      sug:
        subj:
          Constructive mathematics
          Intuition
          Philosophy of mathematics
          Epistemics
          Ontology
      keyword:
        Bishop's constructive mathematics
        Brouwer
        constructive mathematics
        Heyting
        intuition
        intuitionism
        mathematical construction
        mathematical intuition
      ab: 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.
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    language: English
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