A Principle-based Analysis for Numerical Balancing

The more recent philosophical literature concerned with foundational questions about
normativity often appeals to the notion of normative reasons, or considerations that
count in favor or against actions, and their interaction. The interaction between reasons is standardly conceived of in terms of weighing reasons on (normative) weight
scales. Knoks and van der Torre [8] have recently proposed a formal framework that
allows one to think about the interaction between reasons as a kind of inference pattern. This paper extends that framework by introducing and exploring what we call
numerical balancing operators. These operators represent the weights or magnitudes
of reasons by means of numbers, and they are particularly well-suited for capturing
the intuition of aggregating and weighing reasons. We define a number of concrete
classes of balancing operators and explore them using a principle-based analysis.