Abstract Model Theory for Logical Metascience

Abstract

The application of logic to the metatheoretical study of mathematics, i.e. metamathematics, has produced many results of great significance, including Gödel's celebrated incompleteness theorems. The same cannot be said, however, of the field of metascience: notwithstanding a century of effort, a viable framework for the formal analysis of science has yet to emerge. In this thesis, I investigate the possibility of reinvigorating metascience by using tools from the field of abstract model theory, as originally proposed by philosopher-logicians David Pearce and Veikko Rantala. After providing an extensive overview of the most important metascientific frameworks as well as the formalism of abstract model theory, I discuss the existent methodology for bringing these two together. Subsequently, I argue that this methodology does not fully utilize the potential offered by abstract model theory and show how a number of recent developments within this field suggest a new manner in which to apply model-theoretic methods to the analysis of science.