Analogical reasoning: a Carnapian approach
With Igor Douven, Steven Verheyen, Shira Elqayam and Peter Gärdenfors.
Abstract Analogical reasoning is a form of non-deductive reasoning that gives special weight to similarity considerations. Here, we pursue an approach to formalizing this type of reasoning that was initiated by Carnap in posthumously published work. In it, Carnap abandoned his long-time project of trying to define inductive and analogical reasoning syntactically and introduced attribute spaces to model the meanings of predicates. While these spaces remain underdeveloped in Carnap’s late work, it is clear that what he envisioned is, or is close to, what are presently known as “conceptual spaces.” We use the conceptual spaces framework as it has been developed over the past two decades to make progress on formally representing analogical reasoning. This will also allow us to address the question of the normative status of analogical reasoning, which was raised by Carnap and others but which has hitherto remained unanswered. Finally, we work out some of the empirical content of our proposal and reanalyze a publicly available dataset to test it.