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Reasoning Continuously: A Formal Construction of Continuous Proofs

Published version
Peer-reviewed

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Authors

Fisher, Eyal 

Abstract

We begin with the idea that lines of reasoning are continuous mental processes and develop a notion of continuity in proof. This requires abstracting the notion of a proof as a set of sentences ordered by provability. We can then distinguish between discrete steps of a proof and possibly continuous stages, defining indexing functions to pick these out. Proof stages can be associated with the application of continuously variable rules, connecting continuity in lines of reasoning with continuously variable reasons. Some examples of continuous proofs are provided. We conclude by presenting some fundamental facts about continuous proofs, analogous to continuous structural rules and composition. We take this to be a development on its own, as well as lending support to non-finitistic constructionism.

Description

Keywords

Proof theory, Intuitionism, Constructivism, Continuity, Continuous proof

Journal Title

Studia Logica: an international journal for symbolic logic

Conference Name

Journal ISSN

0039-3215
1572-8730

Volume Title

108

Publisher

Springer Nature