Internalism and the Determinacy of Mathematics.

A major challenge in the philosophy of mathematics is to explain how mathematical language can pick out unique structures and acquire determinate content. In recent work, Button and Walsh have introduced a view they call 'internalism', according to which mathematical content is explained by internal...

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Publicado en:Mind (0026-4423) Vol. 132; no. 528; pp. 1028 - 1053
Autores principales: Picollo, Lavinia, Waxman, Daniel
Formato: Artículo
Publicado: Oxford University Press / USA Oct2023
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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        atl: Internalism and the Determinacy of Mathematics.
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        au:
          Picollo, Lavinia
          Waxman, Daniel
        affil: National University of Singapore , Singapore
      su:
        Philosophy of mathematics
        Internalism (Theory of knowledge)
        Logic
        Discourse
        Structuralism
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        subj:
          Philosophy of mathematics
          Internalism (Theory of knowledge)
          Logic
          Discourse
          Structuralism
      ab: A major challenge in the philosophy of mathematics is to explain how mathematical language can pick out unique structures and acquire determinate content. In recent work, Button and Walsh have introduced a view they call 'internalism', according to which mathematical content is explained by internal categoricity results formulated and proven in second-order logic. In this paper, we critically examine the internalist response to the challenge and discuss the philosophical significance of internal categoricity results. Surprisingly, as we argue, while internalism arguably explains how we pick out unique mathematical structures, this does not suffice to account for the determinacy of mathematical discourse.
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    language: English
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