Cantor's math proved that an all-knowing mind is logically impossible

The Classical Definition of Omniscience

In classical Western theology and metaphysics, omniscience has long been considered one of the defining attributes of a supreme being. Historically, philosophers such as Augustine, Anselm, and Thomas Aquinas treated an omniscient mind as one that knows everything that is knowable. In contemporary analytic philosophy of religion, this intuition is typically refined into propositional terms: a being is omniscient if and only if it knows every true proposition and holds no false beliefs. On this view, to know everything is to possess an exhaustive cognitive grasp of all facts about the past, the present, the future, and abstract reality.

Underlying this standard definition is a seemingly harmless metaphysical assumption: that there exists a coherent collection of facts to be known. When thinkers formulated claims about knowing all truths, they assumed that reality could be treated as a completed totality. The statements describing the world were presumed to form an identifiable pool of propositions, even if that pool was infinite. If the collection of all truths exists as a determinate whole, then an infinite mind could in principle apprehend every item within that collection without generating any internal contradiction.

Cantor and the Hierarchy of Infinities

In the late nineteenth century, the German mathematician Georg Cantor revolutionized mathematics by demonstrating that infinity is not a single, uniform magnitude. Instead, infinities come in different sizes. Cantor’s theorem established a fundamental principle in set theory: for any given set, the set of all its possible subsets—known as its power set—has a strictly greater cardinality than the original set itself. This remains true whether the initial set contains three elements, three billion elements, or an infinite number of elements.