Reasoning Continuously: A Formal Construction of Continuous Proofs


Change log
Authors
Fisher, E. 
Abstract

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

Funder: University of Cambridge

Keywords
Article, Proof theory, Intuitionism, Constructivism, Continuity, Continuous proof
Journal Title
Studia Logica
Conference Name
Journal ISSN
0039-3215
1572-8730
Volume Title
108
Publisher
Springer Netherlands