Anselm of Canterbury gave the first "modal" ontological argument for God's existence. Here, Brian Leftow defends all premises of this argument save the claim that possibly God exists. He in particular defends the premise that God would exist with absolute or metaphysical necessity against all extant and some new objections, and provides new arguments for it. Leftow contends that Anselm's argument requires the Brouwer system of modal logic, and argues that this is part of the correct logic for "absolute," "broadly logical" or "metaphysical" modality. As part of making clear what Anselm's argument is, he contends that Anselm works with this kind of modality, and argues that Anselm provides adequate truthmakers for claims in this modality.