Brian Leftow. Anselm’s Argument: Divine Necessity. Oxford: Oxford University Press, 2022, 317pp.

According to Brian Leftow, Anselm of Canterbury's best argument for the existence of God rests upon the assertion that a perfect being must exist necessarily if it exists at all.Further, and still, according to Leftow, Anselm offers us a metaphysical theory of the truth-makers of modal claims, which supports this argument by providing the modal-logical axioms required to turn the argument into a valid proof.In the book Anselm's Argument: Divine Necessity, Leftow puts forward a reconstruction of Anselm's argument and his modal metaphysics and argues at length that the principle at work, "Perfect Being Necessity," is sound and unassailable.The book offers a thoughtprovoking and potentially widely useful discussion of modal metaphysics, which should appeal to any philosopher of religion with an interest in perfect being theology, modalities, and modern analytic metaphysics.The book is also a very challenging read.The first few chapters of the book focus on Anselm.In chapters 1 and 2, his account of modality is reconstructed in modern terms based on textual evidence.We find in Anselm a metaphysics of modal notions based on powers inherent in real objects.Leftow argues that this modal metaphysics constitutes an account of absolute necessity and possibility specifically.Further, Anselm's metaphysics can be modelled using standard modal logic with possible worlds semantics.In this logic, axiom 4 is required, and so a logic as strong as S4 is required.It is important to note in this context that while we may here talk about possible worlds, they should be considered merely a façon de parler since Anselm (like Leftow himself) is a realist but not necessarily a realist about worlds: the truth-makers of modal talk are real powers, not worlds.In chapter 3, Leftow raises and responds to some objections to the reconstructed account.In Leftow's view, Anselm's modal metaphysics grounds and elucidates Anselm's "ontological" argument, and in particular the Perfect Being Necessity principle which the argument includes as a premise.The argument in question Leftow draws not from the Proslogion but from Anselm's Reply to Gaunilo.In chapter 4, Leftow presents a formal reconstruction of it and then of a different, strengthened or refined argument.In chapter 5, the last chapter to focus on Anselm apart from perhaps the very last chapter, chapter 17, Leftow argues that Anselm is committed to an S5 logic, since an S4 logic was already in place, and we need the Brouwer axiom to make a premise of the reconstructed argument (necessarily) true.As Leftow notes, if we have S5, we need only the Perfect Being Necessity principle and a premise saying that a perfect being is