In Infinity, Causation, and Paradox, Alexander Pruss undertakes a sweeping defense of the metaphysical thesis Causal Finitism. According to causal finitists, nothing can be affected by infinitely many causes. Pruss argues for causal finitism by way of a cumulative case: accepting causal finitism allows us to eliminate a large class of paradoxes. There are broadly two types of paradoxes Pruss aims to eliminate. The first consists in paradoxes where an infinity of physical things cooperate to produce a paradoxical situation. The paradigm is the Grim Reaper paradox. The second type involves paradoxes of rationality that can occur in infinitistic situations. The paradigm is a fair countable lottery.
The opening chapters of the book introduce causal finitism and provide an overview of the kinds of situations causal finitism rules impossible. This is followed by a discussion of physical paradoxes in chapter 3. Chapters 4–6 are devoted to paradoxes of rationality....
