First-order logic is a formalism whose representational flexibility and well developed theory motivates its adoption for representing complex probabilistic models. Probability has often been presented as a replacement for logic-based methods, but much of the new work in AI is both logical and probabilistic: seeking to exploit the strengths of both approaches in a hybrid framework. Logic-based approaches (often based on logic programming) also provide a method of implementing probabilistic programming languages. Combined logical-probabilistic frameworks are very old; often the result of grand attempts to formulate a calculus of general reasoning. A careful account of the assumptions and achievements of these systems provides understanding of what is significant and novel in contemporary logical-probabilistic frameworks. This paper aims to provide such an account drawing particularly on the pioneering work of Boole. We find two major strands in this work. There are attempts to address Hume's problem of induction by devising an inductive logic and then there is work with the more modest aim of formalising probabilistic reasoning using a logic of probability.