The Problem of Analogical Inference in Inductive Logic

TL;DR

This paper addresses the longstanding problem of analogical inference in inductive logic, proposing a new probabilistic approach based on de Finetti's ideas to improve reasoning under uncertainty.

Contribution

It introduces a novel inductive logic framework that incorporates probabilistic symmetries to solve the problem of analogical inference, extending Carnap's paradigm.

Findings

The new logic provides a consistent method for analogical reasoning.

It demonstrates properties aligning with intuitive inductive inferences.

The approach integrates probabilistic symmetries into Carnapian inductive logic.

Abstract

We consider one problem that was largely left open by Rudolf Carnap in his work on inductive logic, the problem of analogical inference. After discussing some previous attempts to solve this problem, we propose a new solution that is based on the ideas of Bruno de Finetti on probabilistic symmetries. We explain how our new inductive logic can be developed within the Carnapian paradigm of inductive logic-deriving an inductive rule from a set of simple postulates about the observational process-and discuss some of its properties.