The Model Theory of Falsification

TL;DR

This paper explores the conditions under which theories can be definitively refuted through observations, linking falsifiability to model-theoretic properties like NIP, and broadening the understanding of falsifiability beyond axiomatizable theories.

Contribution

It introduces a model-theoretic perspective on falsifiability, demonstrating that NIP theories are highly falsifiable, thus expanding the scope of theories considered susceptible to empirical refutation.

Findings

NIP theories are highly falsifiable.

Falsifiability is not limited to axiomatizable theories.

The paper connects falsifiability with model-theoretic dividing lines.

Abstract

This paper is concerned with the question of when a theory is refutable with certainty on the basis of sequence of primitive observations. Beginning with the simple definition of falsifiability as the ability to be refuted by some finite collection of observations, I assess the literature on falsification and its descendants within the context of the dividing lines of contemporary model theory. The static case is broadly concerned with the question of how much of a theory can be subjected to falsifying experiments. In much of the literature, this question is tied up with whether the theory in question is axiomatizable by a collection of universal first-order sentences. I argue that this is too narrow a conception of falsification by demonstrating that a natural class of theories of distinct model-theoretic interest -- so-called NIP theories -- are themselves highly falsifiable.