Lewis' paper "Anselm and Actuality" 1 contains one of the most penetrating modern treatments of Anselm's so-called "ontological" argument for the existence of God as formulated in ch. 2 of his Prostogion. ~ Nevertheless I think there is a serious difficulty with Lewis' analysis. I shall first explain the problem I see and then give a different analysis of the argument, one which avoids the problem but which retains much of the spirit of Lewis' analysis.
Lewis' paper falls neatly into two main parts: (i) an analysis of Anselm's ch. 2 argument, leading to (ii) an "indexical" theory of actuality. ~ His reconstruction of the argument is based on three main premisses:
- Whatever exists in the understanding can be conceived to exist in reality. (p. 176) That is, for any understandab]ke being x, there is a world w such that x exists in w. (177) 2. Whatever exists in the understanding would be greater if it existed in reality than if it did not. (176) That is, for any understandable being x, and for any worlds w and v, if x exists in w but x does not exist in v, then the greatness of x in w exceeds the greatness of x in v. ( 178) 3. Something exists in the understanding than which nothing greater can be conceived. (176) See below. and an uncontroversial fourth premiss: 4. The actual world is a world. (180) 1 Nous 4 (1970), 175-188. . 2 The further argument in ch. 5, the arguments in Anselm's reply to Gaunilo, and the quite different ontological argument in the Cartesian tradition must be kept carefully distinct from the argument in Anselm's oh. 2. ~ For a criticism of the "indexical" theory of actuality, see Robert Merrihew Adams, "Theories of Actuality," Nuns 8 (1974), 211-231.