Marta Sznajder (University of Groningen/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Inductive Reasoning with Conceptual Spaces: A Proposal for Analogy". Abstract: In his late work on inductive logic Carnap introduced the conceptual level of representations – i.e. conceptual spaces – into his system. Traditional inductive logic (e.g. Carnap 1950) is a study of inductive reasoning that belongs to the symbolic level of cognitive representation (in the three-level view of representations presented by Gärdenfors (2000)). In the standard, symbolic approach the confirmation functions are functions applied to propositions defined with respect to a particular formal language. In my project I investigate alternative approach that is a step towards modelling inductive reasoning directly on the conceptual spaces: considering probability densities (or distributions) over the set of points in a conceptual space rather than traditional credences over propositions.

I will present one way in which analogical effects can enter inductive reasoning, using the tools of Bayesian statistics and building up from Carnap’s idea that analogical dependencies between predicates can be read off conceptual spaces via the distances that encode similarity relations between predicates. I consider a quasi-hierarchical Bayesian model in which the different hypotheses considered by the agent are probability distributions over a one-dimensional conceptual space, representing possible distributions of the particular qualities among a studied population.