Abstract

In this paper two paradoxes of infinity are considered through the lens of counterfactual logic, drawing heavily on a result of Fine (2012b). I will argue that a satisfactory resolution of these paradoxes will have wide ranging implications for the logic of counterfactuals. I then situate these puzzles in the context of the wider role of counterfactuals, connecting them to indicative conditionals, probabilities, rationality and the direction of causation, and compare my own resolution of the paradoxes to alternatives inspired by the theories of Lewis and Fine. Here is a quick overview of the paper. Sections 17.1 and 17.2 introduce two paradoxes of infinity that rest on certain principals concerning the logic of counterfactuals. Section 17.3 considers three possible ways to weaken the counterfactual logic that would resolve these paradoxes, and examines three concrete theories of conditionals which make those weakenings — Lewis (1973), Fine (2012a) and Bacon (2015). With the first two theories found wanting, Sect. 17.4 develops my preferred solution in (Bacon, 2015) a little further, and provides some simple models to show that the paradoxes can indeed be resolved in that framework.