Inductive Reasoning with Multi-dimensional Concepts

Attribute spaces are a type of conceptual spaces which Carnap introduced in his late basic system of inductive logic. This article shows how to extend Carnap's use of them into a full model of inductive reasoning with geometrically represented concepts, extending my earlier work (Sznajder [2017]). The proposed model draws on Bayesian non-parametric techniques in order to define a probability distribution over the attribute space and a way of updating it with data. The model is another example of conceptual and formal continuity of Carnapian inductive logic with subsequent developments in statistics.