Let’s set aside, for the moment, Richard Swinburne’s critique of Ayer’s Logical Positivist argument for the incoherence of theism, and consider Swinburne’s concept of “God”. I’m jumping ahead to the second book in Swinburne’s trilogy on theism (The Existence of God, 2nd edition).
There are two kinds of explanation according to Swinburne: scientific and personal. Swinburne argues that the existence and the most general features of the universe are best explained by theism, which amounts to a personal explanation: some person performed some action or actions in order to acheive some purpose or purposes.
The core concept of “God” in Swinburne’s view derives from that of the simplest personal explanation. Simplicity is a key criterion for evaluation of any type of explanation, whether scientific or personal.
A person must have some degree of power and awareness, and so a person cannot have absolutely no power and no awareness (the quantity of zero power is excluded). Swinburne states that the simplest quantitiy of something is either zero or infinity. Since a person must have some degree of power and awareness, the complete absence of power and awareness is excluded for persons. Thus the simplest sort of person is one that has infinite power and infinite knowledge. Therefore, the simplest sort of person to hypothesize in a personal explanation is a person who is omnipotent (unlimited in power) and omniscient (unlimited in knowledge).
Persons can also have various degrees of freedom, and Swinburne again postulates a person of unlimited freedom, meaning that only rational considerations influence such a person’s choices, not any extraneous influences such as instincts or desires.
So, the core concept of “God” for Swinburne is an omnipotent, omniscient, and perfectly free person. The other properties of God are logically derived from these properties. Thus, God is also perfectly good, because God always knows which actions are wrong or right, better or worse, and being completely free God always chooses to do what is right or best.
God is omnipresent because God is unlimited in power and unlimited in knowledge, and being present in a location means being able to influence objects and events in that location and being aware of objects and events in that location. Since God’s knowledge and power is unlimited, God knows about and can influence objects and events in any and every location.