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Negationless Intuitionism

  • Enrico MartinoEmail author
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Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 42)

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 formalisable theory (classical or intuitionistic, contradictory or not).

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.FISPPA DepartmentUniversity of PaduaPaduaItaly

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