The first phase of Swinburne’s case for God is in his book The Coherence of Theism, where he argues that the sentence ‘God exists’ is a meaningful declarative sentence that makes a coherent statement.  The middle section of this book covers his concept of a ‘contingent’ God, which is basically the God of traditional theism minus the problematic belief that God is a necessary being.

I won’t try to give a blow-by-blow account of these important chapters, but will give a general description of how Swinburne goes about defining and defending the coherence of the idea of the idea that a ‘contingent’ God exists.

Definitions are an important part of Swinburne’s defense of the meaningfulness and coherence of the sentence ‘God exists’.  To the extent that Swinburne provides a clear and pausible definition of ‘God’ in ordinary words, he shows that this sentence makes a meaningful claim.  Swinburne provides both a high-level definition of ‘God’ in terms of divine attributes (omniscience, omnipotence, perfect freedom, etc.) and also lower-level definitions and clarifications of each of the various divine attributes in his high-level definition.

Since both Swinburne’s high-level definition and his lower-level definitions appear to be clear and plausible, I don’t see any obvious problem with his conclusion that the sentence ‘God exists’ is a meaningful declarative sentence that makes a claim.  The real question here is whether the claim is coherent, whether there are any internal logical contradictions (i.e. whether any of the individual divine attributes contains a self-contradiction) or any external contradictions (i.e.  whether possession of one or more of the divine attributes logically precludes possession of some other divine attribute).

In addition to providing a high-level definition of ‘God’ and lower-level definitions of the divine attributes, Swinburne considers various objections to the coherence of the claim ‘God exists’ understood in terms of his proposed definitions.  In some cases he rejects the objection and argues that the objection is in error.  In other cases, he accepts the objection and then modifies or qualifies the definition of the problematic divine attribute in order to avoid the problem raised by the objection.

The primary method for establishing the coherence of the claim ‘God exists’ is to show that the claim that a person who possesses some of the divine attributes (which in turn are used to define the word ‘God’) is a coherent claim.  For example, Swinburne tries to show that each of the following sentences makes a coherent claim:

There is a person who is omniscient.
There is a person who is omnipotent.
There is a person who is perfectly free.
There is a person who is eternal.

In order to show these claims to be coherent, Swinburne provides a definition of each of these divine attributes, answers objections about the coherence of each divine attribute, and describes a set of circumstances in which the claim would be true. 

There is a further step required, which is to show that there are no logical contradictions between the various divine attributes (or to qualify the definitions of the attributes as required to avoid any such contradictions).  Swinburne does not do as well in describing a set of circumstances in which many of the divine attributes apply to a single person.  Sometimes this step of imagining a person with multiple divine attributes gets glossed over a bit too quickly.

One objection that Swinburne accepts is the claim that there is a logical contradiction between omniscience and perfect freedom.  If a person is perfectly free, then their future choices cannot be determined in advance.  But an omniscient being (in the sense of completely unlimited knowledge) would know what choices any given person (even himself) was going to make in the future.  Thus, an omniscient being cannot also be a perfectly free being.  Swinburne accepts this objection, but instead of tossing out omniscience or tossing out perfect freedom, he retains both divine attributes in his definition of ‘God’ but modifies the concept of ‘omniscience’ to avoid the logical contradiction.  Roughly speaking, an omniscient person is one who knows everything that it is logically possible to know in view of the constraints placed on knowledge by the fact that one or more beings are perfectly free.

In other words, God’s perfect freedom creates a constraint that limits what God can know about the future.  God, as a perfectly free person, cannot know in advance the choices that God will make in the future.  And, to the extent that humans are capable of making free choices, God also cannot know in advance what free choices humans will make in the future.