1. Modal Versions of the Ontological Argument Based on Alvin Plantingas discussion in God, Freedom, and Evil (1974).

2. (1) It is possible that there is a greatest possible being, B. Possibility here is logical possibility, roughly the absence of any internal contradiction. Greatest possible being entails a being with the properties of omniscience, omnipotence, and moral perfection. So (2) There is a possible being, B, that in some world (W1) has a maximum degree of greatness, a degree of greatness nowhere exceeded. W1W2W3W4 W1 actual

3. (3) A being, B, has the maximum degree of greatness in a given possible world, W1, only if B exists in every possible world (W2, W3, W4). W1 W2 W4 W3 If W1 had been actual, instead of W4, then Bs non-existence would have been impossible. W1 W2 W3 W4

4. (4) What is logically impossible in one possible world is logically impossible in all possible worlds. So (5) Bs non-existence is logically impossible. (from (2), (3), & (4)) W1 W2 W3 W4 Therefore, (6) There exists a being, B, with maximum greatness. (from (5)) Given that B has the properties omnipotence, omniscience, and moral perfection (divine attributes), we must conclude that God exists. W4

5. Problem in the Argument?

6. If (i) it is possible that there is a greatest possible being and (ii) the idea contains the idea of necessary existence, then in fact there is some being that exists in every possible world and in some worlds has a degree of greatness nowhere exceeded. The problem is subtle though apparent on closer examination. in some of those worlds has maximum greatness The original premises only support the conclusion that there is a being, B, who exists in all possible worlds and in some of those worlds has maximum greatness. B in W1 {max-great} B in W2 B in W3 {max-great} B in W4

7. in some world W Mistaken Assumption: Greatness of B in some world W is the only thing that counts towards the greatness of B in W. However, the argument forces us to consider greatness of B across possible worlds. In other words, we must distinguish between the properties that S has in world W and the properties that S has in other worlds. This will require a distinction between two ways of rating a being, in terms of its excellence and in terms of its greatness. EXCELLENCE is concerned with the properties a being has in a particular world. GREATNESS is concerned with the properties a being has across all possible worlds.

8. Let excellence in W be a function of the properties B has in W. B in W1 {a, q, z} B in W2 {a,b,c} B in W3 {a,e,f} B in W4 {r,s,t} Suppose that {a,q,z} involve maximal excellence. B will have maximal excellence in W1, but not in W2, W3, and W4. B might be great in W2, W3, and W4, but B would be surpassed by greatness in W1. We can see here that even if Bs non-existence is impossible (and so B must exist), B might not exist with maximal excellence. If maximal excellence involves omnipotence, omniscience, and moral perfection, then B might exist but without this set of properties. Hence, if God is a maximally excellent being, we cannot conclude that God exists.

9. Let greatness in W be a function of the properties B has across all possible worlds. Let maximal greatness entail maximal excellence in all worlds. (7) It is possible that there is a being, B, that has maximal greatness. So (8) There is a possible being that in some world, W, has maximal greatness B in W1 {g-max} W2W3W4

10. (9) A being B has a maximum degree of greatness in a given world W only if it has maximal excellence in all possible worlds. (10) A being has maximal excellence in a given world W only if it has omniscience, omnipotence, and moral perfection in W. B in W1 {g-max} B in W2 {e-max} B in W3 {e-max} B in W4 {e-max} If W1 had been actual (instead of W4), then B would have had omnipotence, omniscience, and moral perfection in every possible word. If W1 had been actual, then it would be impossible for there not to exist some omnipotent, omniscience, and morally perfect being.

11. (11) What is logically impossible in one possible world is logically impossible in all possible worlds. B W1 B W2 B W3 B W4 Therefore, (12) Bs non-existence as a maximally great being is logically impossible. (from (7), (9), (10), and (11)). (13) A maximally great being B exists, together with the properties of omnipotence, omniscience, and moral perfection.

12. Final Overview of the Argument (14) There is a possible world in which maximal greatness is instantiated. B in W1 {g-max} W2W3W4 (15) Necessarily, a being is maximally great in one world W1 only if B has maximal excellence in every world. B in W1 {g-max} B in W2 {e-max} B in W3 {e-max} B in W4 {e-max}

13. It follows from (14) that there is a possible world W1 such that had it been actual, then there would have existed an omnipotent, omniscient, and morally perfect being. But this being would have had these qualities in every possible world, not just W1. So had W1 been actual it would have been impossible for there to be no such being. (16) What is logically impossible in one possible world is logically impossible in all possible worlds. So (17) The non-existence of a maximally great being, B, is logically impossible. B in W1 {g-max} B in W2 Omnipotence Omniscience Moral Perfection B in W3 Omnipotence Omniscience Moral Perfection B in W4 Omnipotence Omniscience Moral Perfection

14. B in W1 Omnipotence Omniscience Moral Perfection B in W2 Omnipotence Omniscience Moral Perfection B in W4 Omnipotence Omniscience Moral Perfection B in W3 Omnipotence Omniscience Moral Perfection (18) Necessarily a being has maximal excellence in every world only if he has omnipotence, omniscience, and moral perfection in every world. So (19) There exists no omnipotent, omniscient, and morally perfect being is a logically impossible statement. Therefore, (20) God exists. God exists W4 Actual