Parameterizing Axioms; Operators on Spaces of Rules

Abstract

We now have the conceptual units of our analysis, the axioms. Let’s discuss what we do with them. Many issues have to be addressed. First, I’ll discuss how to choose among axioms. Who should choose anyway? Also, an axiom seems to be a very inflexible concept: It is satisfied or it is not satisfied. It would seem desirable to express the ideas underlying them in a more nuanced way. I’ll explain that this can often be done through parameterizations. Parameterized axioms can help us obtain a detailed tracing out of the boundary between what’s possible and what’s not, the central objective of axiomatic work. Then, I’ll talk about structuring the space of rules by operators. I’ll distinguish between different types of operators, structural operators, improvement operators, extension operators, compromising operators, and enlargement operators. I’ll also discuss the preservation of properties by operators. So, we have a busy day ahead of us.