Modal Structuralism with Theoretical Terms.

In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced...

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Publicado en:Erkenntnis Vol. 88; no. 2; pp. 721 - 746
Autores principales: Andreas, Holger, Schiemer, Georg
Formato: Artículo
Publicado: Springer Nature Feb2023
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Acceso en línea:Ver este registro en EBSCOhost
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        atl: Modal Structuralism with Theoretical Terms.
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          Andreas, Holger
          Schiemer, Georg
        affil:
          Department of Economic, Philosophy, and Political Science, University of British Columbia (Okanagan), Kelowna, Canada
          Department of Philosophy, University of Vienna, Vienna, Austria
      su:
        University of Oxford
        Oxford University Press
        Structuralism
        Philosophy of mathematics
        Semantics
        Poststructuralism
        Arithmetic
        Mathematics
      sug:
        subj:
          University of Oxford
          Oxford University Press
          Structuralism
          Philosophy of mathematics
          Semantics
          Poststructuralism
          Arithmetic
          Mathematics
      ab: In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced in Andreas (Synthese 174(3):367–383, 2010). We will thereby show that the application to Peano arithmetic yields a formal semantics of universal structuralism, i.e., the view that ordinary mathematical statements in arithmetic express general claims about all admissible interpretations of the Peano axioms. Moreover, we compare this application with the modal structuralism by Hellman (Mathematics without numbers: towards a modal-structural interpretation. Oxford University Press: Oxford, 1989), arguing that it provides us with an easier epistemology of statements in arithmetic.
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    language: English
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