According to Étienne Gilson, for Aquinas, 'Infinity … excluding all limits, refusing all determinations … becomes one of the primary characteristics of the Christian God, and the one which, after Being, most clearly distinguishes Him from all other conceptions of God'; 1 and, again, that he made 'the very foundation of this doctrine … the universally accepted doctrine in medieval theology … that God is infinitely above anything we can think and say about him'. 2 Similarly, Maritain wrote that the first Four Ways of Aquinas 'effect a transition to the infinite' by moving from the finitude of created beings to an Infinite First Cause, 3 and Eric Mascall, that Aquinas's doctrine of analogy was 'vital' to him, 'not merely' as an attempt to show how our knowledge of finite things could somehow be extrapolated to yield some knowledge of an infinite God, but how this possibility is 'conditioned by the fact that the finite order is dependent for its very existence on the fiat of the infinite and self-existent God '. 4 Are these readings justifiable? Apparently not, according to a number of recent treatments: Brian Davies's recent comprehensive survey, The Thought of Thomas Aquinas, 5 not untypically, makes virtually no mention of it. Yet, in the Summa Theologiae, 6 immediately after proving God's existence, Aquinas announces the intention of demonstrating five 'modes' of the divine being of which the third is infinity, and in ST 1a 7 and elsewhere, he certainly develops a more detailed treatment of the divine infinity than any previous Christian thinker. On the other hand much traditional scholarship on Aquinas's doctrine of analogy has arguably laboured under serious misapprehensions. In each of his mature treatments of analogical predication (Summa contra Gentiles 32; Compendium of Theology 27; De Potentia 7.7; 7 ST 1a 13) the problem, contrary to the claims of Mascall and many others, is not said to be one of how finite intellects can conceive the infinite, but how human beings, geared to the cognition of composite beings, can discourse intelligibly of an absolutely simple God.