Anselm of Canterbury, answered from the texts and cited to the page.
God is to be understood as id quo nihil maius cogitari potest — that than which nothing greater can be thought. Even the Fool who says in his heart "There is no God" (Psalm 14:1) must, in saying this, conceive of that than which nothing greater can be thought, and so this conception exists at least in his understanding.12 But a being existing both in the understanding and in reality is greater than one existing in the understanding alone; so what the Fool conceives, that than which nothing greater can be thought, must exist in reality as well as in the understanding, on pain of contradiction.34
A second formulation, developed in Proslogion 3 and sharpened in the Reply to Gaunilo, argues that God cannot even be conceived not to exist: a being that can be thought not to exist is less than a being whose nonexistence is inconceivable; so the greatest conceivable being must be such that its nonexistence is inconceivable.5
But obviously this is impossible. Hence, there is no doubt that there exists a being, than which nothing greater can be conceived, and it exists both in the understanding and in reality.Proslogium, Monologium, Gaunilo's In Behalf of the Fool, and Cur Deus Homo, pp. 8–10
But, if really, nay, since really, he both conceived, because he said in his heart; and did not say in his heart, because he could not conceive; there is more than one way in which a thing is said in the heart or conceived. For, in one sense, an object is conceived, when the word signifying it is conceived; and in an- |f> other, when the very entity, which the object is, is J • understood.Proslogium, Monologium, Gaunilo's In Behalf of the Fool, and Cur Deus Homo, pp. 10–11
So, then, of God alone it can be said that it is im possible to conceive of his non-existence; and yet many objects, so long as they exist, in one sense can not be conceived not to exist. But in what sense God is to be conceived not to exist, I think has been shown clearly enough in my book.Proslogium, Monologium, Gaunilo's In Behalf of the Fool, and Cur Deus Homo, pp. 161–162
BUT, you say, it is as if one should suppose an island in the ocean, which surpasses all lands in its fertility, and which, because of the difficulty, or rather the impossibility, of discovering what does not exist, is called a lost island; and should say that there can be no doubt that this island truly exists in reality, for this reason, that one who hears it described easily understands what he hears.Proslogium, Monologium, Gaunilo's In Behalf of the Fool, and Cur Deus Homo, pp. 158–160
I do not endeavor, O Lord, to penetrate thy sublimity, for in no wise do I compare my understanding with that; but I long to understand in some degree thy truth, which my heart believes and loves. For I do not seek to understand that I may believe, but),JWlnub^jieye in orderwtowJ1^^i£JC•J stand. For this also I believe, — that unless I beleved, 1 should not understand.Proslogium, Monologium, Gaunilo's In Behalf of the Fool, and Cur Deus Homo, pp. 7–8
Held with full force and defended directly against Gaunilo's Pro Insipiente. The Proslogion and the Reply to Gaunilo were circulated together at my own direction, so that subsequent readers would have both the argument and its first major objection. The modern modal reconstructions of Norman Malcolm, Charles Hartshorne, and Alvin Plantinga take up the second formulation in particular and develop it with logical resources I did not have. I welcome these developments as friendly extensions. Karl Barth's fideist reading — that the argument is intelligible only from within faith and does not address the unbeliever — I respect as a reading but do not accept: the Reply to Gaunilo explicitly engages the Fool's conception, and the methodological remark in Cur Deus Homo I.3 explicitly distinguishes arguments addressed to believers from arguments addressed to the impious.