There are two types of actions that God cannot do (see The Coherence of Theism, p.164):
T1. Actions that are logically impossible for any being to perform.
T2. Actions that are logically possible for some beings to perform, but logically impossible for God to perform.
No being, including God, could produce or discover a four-sided triangle. No being, including God, could produce or find a married bachelor. No being could produce or identify an even number that is greater than 1 but less than 2. No being, according to Swinburne, can change the past. These are actions of Type 1. Let’s call these intrinsically impossible actions.
There are many actions that I can perform, but which God cannot perform. These are actions of Type 2. For example, I can snap my fingers, brush my teeth, scratch my head, clear my throat, chew gum, close my eyes, eat a cheeseburger, wash my face, put my fist through a window, kick a soccer ball, throw a stone, and pinch myself, but God is not able to do any of these things, because God is a spirit, a bodiless person. I can do some things that God cannot do, because I have a body, and God does not. Some actions can only be performed by persons who have a body.
There are other examples of actions of Type 2. God cannot forget someone’s name, because God is omniscient. God cannot try to move some object but fail, because God is omnipotent. God cannot do something that is evil, because God is both omniscient and perfectly good. God cannot cause himself to cease to exist, because God is eternal. These are all actions that are possible for some beings to perform, but not for God, because of some property (divine attribute) that God possesses and which some other beings do not possess. Let’s call these actions extrinsically impossible actions.
Actually, it would be logically possible for God, who is a bodiless person, to brush his teeth, scratch his head, etc. if the property of being bodiless was just a property that God happened to have but was not an essential or necessary property of God.
If God is in fact bodiless, but things could have been otherwise so that God had a body, then logic would not constrain God from performing actions that require the possession of a body. So long as God remains bodiless, he will be unable to perform actions that require having a body, but if it is logically possible for God to have had a body or to become embodied, then it is logically possible for God to brush his teeth, scratch his head, etc.
Many theists and most theologians, however, want to claim that divine attributes, such as omnipotence, omniscience, perfect goodness, etc., are essential properties of God; that is to say, it is logically impossible for God to exist but to lack some of the divine attributes.
In any possible world in which it is true that ‘God exists’, the being who is God possesses all of the divine attributes or properties (Swinburne’s analysis of ‘God’ includes nine such properties). If the divine attributes are essential properties of God, then it is not just the case that God is in fact unable to brush his teeth or to forget a name, but it is logically impossible for God to brush his teeth or to forget a name.
To be continued…