Infinities of Different Kinds: A Medieval Exploration

This study examines Bacon’s critique of the Unity of Matter Thesis (UMT) as articulated in his Opus maius. In this work, he refutes UMT using mathematical reasoning, particularly targeting its implication of material holenmerism. He argues that if prime matter were numerically identical across all things, it would possess infinite potency, which in turn necessitates an infinite essence. The latter would mean equating matter with God, a heretical conclusion. Bacon focuses particularly on the link between infinite potency and essence. He advances three “geometrical” demonstrations that reject the idea of infinite potency of matter. These demonstrations appeal to the paradox of unequal infinities to show that if actual infinities exist, some would be greater than others, violating mathematical principles. Beyond their specific use in discussing UMT, Bacon’s geometrical demonstrations, modelled after the Euclidean proof, not only exemplify his commitment to “mathematical epistemology” in metaphysics, but also prefigure later attempts to replace logic with mathematics.