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Negationless intuitionism

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Abstract

The present paper deals with natural intuitionistic semantics for intuitionistic logic within an intuitionistic metamathematics. We show how strong completeness of full first order logic fails. We then consider a negationless semantics à la Henkin for second order intuitionistic logic. By using the theory of lawless sequences we prove that, for such semantics, strong completeness is restorable. We argue that lawless negationless semantics is a suitable framework for a constructive structuralist interpretation of any second order formalizable theory (classical or intuitionistic, contradictory or not).

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Padova, Via Belzoni 7, I-35131, Padova, Italy

    Enrico Martino

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  1. Enrico Martino
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Martino, E. Negationless intuitionism. Journal of Philosophical Logic 27, 165–177 (1998). https://doi.org/10.1023/A:1004278211254

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  • DOI: https://doi.org/10.1023/A:1004278211254

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