Tags:Axiomatic Method, Constructive View of Theories, Semantic View of Theories and Univalent Foundations
Abstract:
Univalent Foundation (UF) has been recently proposed as a novel foundation of mathematics. We explore a possibility of using UF beyond the pure mathematics as a general formal semantic framework for representing scientific theories. This project is parallel to the project of formal semantic representation of theories by means of Bourbaki-style set-theoretic foundations of mathematics and Tarski-style Model theory, which has been started by Suppes back in 1950-ies and is presently known under the name of “semantic view of theories” . We argue that UF as a prospective representational tool for science and technology has important advantages since it allows for a uniform mathematical representation of various extra-logical methods, which are abound in these fields. This leads us to a new view of theories that at the absence of a better name we call constructive. According to this view a scientific theory is essentially characterised by its methods including the methods of verification and justification of its theoretical statements.
Univalent Foundations and the Constructive View of Theories