Infinity, Causation, and Paradox

This monograph presents a sophisticated defense of causal finitism—the thesis that nothing can have infinitely many causes—and explores its implications for cosmological arguments. Pruss develops a systematic framework demonstrating how the acceptance of actual infinities in causal sequences generates genuine paradoxes, thereby providing grounds for rejecting such infinities and supporting theistic conclusions.

The work's central innovation lies in constructing rigorous paradoxes that arise when infinite causal sequences are permitted. Pruss employs formal logical analysis to show that accepting infinite causal histories leads to contradictions involving probability, decision theory, and causation itself. For instance, he demonstrates that certain infinite fair lotteries become impossible if actual infinities exist, and that infinite causal sequences generate problematic scenarios in Newtonian mechanics. These paradoxes are not merely mathematical curiosities but reveal deep conceptual problems with infinite causal chains.

Methodologically, Pruss combines technical philosophical analysis with mathematical precision, engaging extensively with set theory, probability theory, and modal logic. His approach bridges abstract metaphysics and concrete physical scenarios, showing how causal finitism constrains both philosophical theorizing and scientific modeling. The work critically engages with contemporary defenders of actual infinities, particularly those who invoke Cantorian set theory to legitimize infinite collections in reality.

The theological significance emerges through causal finitism's implications for cosmological arguments. If no infinite causal regresses exist, then the universe's causal history must be finite, requiring an uncaused first cause. Pruss carefully develops this connection, showing how causal finitism provides a principled way to block infinite regress objections to cosmological arguments without arbitrary stipulation. He addresses objections from both theistic and atheistic philosophers, engaging with figures like Graham Oppy, William Lane Craig, and Adolf Grünbaum.

The monograph makes several contributions to natural theology. First, it provides a novel defense of a key premise in cosmological arguments through purely philosophical reasoning about infinity and causation. Second, it demonstrates how formal methods from logic and mathematics can illuminate traditional metaphysical disputes. Third, it shows how causal finitism unifies diverse philosophical problems, from Zeno's paradoxes to modern cosmology. The work stands as a significant advancement in analytic philosophy of religion, offering a technically rigorous yet philosophically profound argument that infinite causal sequences are impossible, thereby supporting the existence of an uncaused first cause.