Anselm of Aosta (1033–1109) was born in Italy, joined the monastery of Bec in Normandy, and eventually became Archbishop of Canterbury. He is the most systematic thinker of the pre-Scholastic period, working under the principle of 'faith seeking understanding' (fides quaerens intellectum) — believe first, then understand with reason.

In the Proslogion (c. 1078) he sets out his famous argument. God is defined as 'that than which nothing greater can be thought' (id quo nihil maius cogitari possit). Anyone holding this concept must, Anselm argues, think of a God who exists in reality, because: existing only in the understanding is less than existing both in the understanding and in reality. If God existed only in thought, a greater could be thought — namely one that also existed in reality. That is a contradiction. Therefore God exists in reality.

The conceptual structure of the argument was shaken even by his contemporaries — a monk named Gaunilo offered the counter-example of an island 'than which no greater can be thought'; Anselm wrote a reply. In later centuries Aquinas, Kant, Russell, and modern logicians worked it over. Aquinas rejected it; Descartes and Leibniz revived different versions; Kant declared he had refuted it with the dictum that 'existence is not a predicate'; Gödel translated a modal version into the late 20th century. Anselm's achievement is not to have found 'the answer' — that the argument is still in dispute is itself a marker of how much philosophy can do, and where it stops.