Here are some thoughts I put together a few weeks back on Omnipresence, and especially a recent article by Hud Hudson. I stress that they are preliminary (including parenthetical notes to myself!), but I would welcome any comments you might have.
Divine Omnipresence and Primitive Existence
Hud Hudson recently has presented a method of understanding the divine attribute of omnipresence in contrast to that of classical theism. For the classical theist, such as Anselm or Aquinas, omnipresence, the relation of being present to all things, is understood in terms of God’s knowledge or power. Hudson proposes, in continuity with several contemporary non-classical theists such as Hartshorne and Swinburne, that God’s being present to all things involves occupation of all things, which means that God has some sort of body. We can see, then, that the contrast in the ‘being present at’ relation is between a non-occupation and occupation account. Non-occupation accounts are motivated by the understanding that God is incorporeal whereas occupation accounts are motivated by the thought of omni-presence.
[something should be said to flesh out the classical accounts, and recent non-classical accounts]
Recent work in the metaphysics of occupation gives us four options, in contrast to the classical options. That is, we might understand divine presence to creation in terms of pertension (the analogue of pedurantism), entension (the analogue of endurantism), spanning, and multiple location. Pertension is to be understood as:
‘x pertends’ = df. x is an object that is wholly and entirely located at a non-point-sized region, r, and for each proper subregion of r, r*, z has a proper part entirely located at r*.
Entension is to be understood as:
‘x entends’ = df. x is an object that is wholly and entirely located at a non-point-sized region, r, and for each proper subregion of r, r*, x is wholly located at r*.
Notice that the relevant difference between entension and pertension being that for pertension an object has proper parts, which are each located at a subregion of space-time, whereas for entension objects are simple and do not have proper parts, and so are wholly located at every region and subregion of space-time. Spanning is to be understood as:
‘x spans’ = df. x is an object that is wholly and entirely located at exactly one non-point-sized region, r, and there is no proper subregion of r, r*, such that any part of x is located at r*.
Notice that the difference between spanning and entesion being that a simple, for spanners, does not occupy any subregions but does, for entenders. Multiple-location can be seen as a combination of the previous three options, given a liberal construal of a principle of recombination regarding relations. As such, multiple-location should be understood as:
‘x multiply locates’ = df. (1) x is an object that is located at more than one region, and (2) x is not located at the fusion of the regions at which x is located.
X would not be located at the fusion of the regions given that, if we assume it is a simple object, it must be wholly located at each region. But if it is in distinct regions it cannot be at the fusion of those regions, else they would not be distinct.
Hudson commends ubiquitous entension as the proper presence relation of God to creation. That is, God is present to every region and sub-region by wholly located there and, if we assume divine mereological simplicity (which we want to do as theists) God fulfills this. This allows the literal presence of God to creation, to every region, rather than through a non-occupation relation in terms of divine power or knowledge, or power/knowledge.
Hudson is able to evade six classical puzzles for any theist who would go occupational rather than non-occupational. As already seen, ubiquitous entension is compatible with mereological simplicity. Pertension is ruled out by simplicity, since pertending objects are not simple. Spanners and multiple-locaters are not in all regions, they are excluded from some even if they are simple. So they are out. A concern for multiple-location is met, given that entending simples can be multiply located. God need not be contained by creation, and so un-free, given that containment is not essential to God. Were there no creation, God would not be present to it. Hence, God remains essentially free and unconstrained. God could remain atemporal, outside time, in one of two ways: either by occupying no regions or by entending all of space-time (the maximal set of space-time). If God entends no regions then, trivially, he is outside of time and atemporal. If he entends all of space time then he is within all of time and not limited to some portion of space or time, and so atemporal. Further, as in meeting the constraint concern, being atemporal could remain essential to God while being in time would be merely accidental.
Two further puzzles are more difficult to answer, however. Classically, God is taken to be incorporeal. But, if God literally occupies regions of space-time does he not thereby have a body? Perhaps one could solve this by holding God to have a body accidentally, but not essentially (akin to Swinburne’s thesis). Christian materialists will have no problem here, but a further concern is not so easily avoided, and returns us to divine simplicity. Corporeality is classically understood to contain admixtures of actuality and potentiality, matter and form, which are metaphysical distinctions in corporeal beings. Beings with metaphysical distinctions of act and potency, however, are not metaphysically simple in the way that God is. This is because any admixture of potency and act represents contingency: in principle, the being depends upon another for existence. If that is the case, then clearly God, who creates all, cannot also contain an admixture of potency and act. But then, God cannot have corporeality. But then, God cannot have a body and be literally present to creation. The remaining worry is that of co-location: how can two objects (simple or otherwise) occupy the same region? Perhaps they can if they are of fundamentally distinct kinds. But, what counts as fundamental, as a fundamental distinction of kinds?
A problem for Hudson, however, and any theist countenancing divine omnipresence as an occupation relation, is that this seems to presuppose and depend upon the debate between substantivalism and super-substantivalism. However, if God is omnipresent through ubiquitous entension, and super-substantivalism is true, then we are committed to pantheism. Hudson is committed, then, to assuming substantivalism true. This debate, however, is plausibly an empirical debate and it is highly curious (and perhaps detrimental!) to have properties of God depend upon an empirical debate. For this reason, then, it would be better (theoretically, metaphysically) to not have God’s omnipresence depend upon how space-time ends up being composed. [more needs to be said here to flesh out the differences and debate] Rather, and if one wishes to keep omnipresence as a presence relation to all creation, a more theoretically parsimonious solution is to posit a primitive existence at relation between God and all domains.
Make a distinction between being located at and existing at a domain. Consider numbers. The number 22 exists at the domain of all possible worlds, but it is not located at any particular possible world. In that case, there is a fundamental ‘exists at’ relation that does not map onto literal location in terms of an occupation relation. It is a primitive existence relation. If numbers can exemplify this relation, then so can God. In this sense, to say that “God is present here” is to say that “God ‘exists at’ here”, in a manner akin to numbers. In that case, we can take an existential reading of omnipresence. God ‘exists at’ all domains, and so is present at/to all of creation but is not located in any of those domains. Domains here take sets, and the set could be the set of all space-time points. Then, trivially, God would possess ubiquitous presence in creation while not possessing a body. ‘Exists at’ is a purely modal relation to all domains (possible worlds, space-time points, etc). In that case, then, God is omnipresent without needing to be located anywhere. This way of construing omnipresence has the theoretical virtue of not being dependent upon the substantivalist/super-substantivalist debate, but rather retains a theoretical neutrality.
I would like to take this existential reading of omnipresence further, with a consideration of divine simplicity. As seen from the discussion of corporeality, it is critical that God have no admixture of potency to act. If that is the case, and for classical theists it is, then we cannot have a relation in God that is distinct from God. So, any primitive relation ‘exists at’ in God, that God has essentially and bears to all creation, must actually be in God as a (non-proper) part of his essence. In that case, given divine simplicity, there are no distinctions in God and that means this ‘exists at’ relation is akin to divine power or knowledge. In that case, and since God’s attributes are identical, omnipresence becomes omnipotence, becomes omniscience. God is omnipresent by existing at every domain, is omnipotent by existing at (and, presumably, giving existence too) every domain, and God is omniscient by virtue of existing at every domain. In that case, this account is far closer, if not identical, to the account given by classical theists such as Aquinas (with the difference that Aquinas explained omnipresence in terms of omnipotence, rather than the other way around). God is not corporeal, nor in time, nor occupies space-time. This has the virtue of being more plausible, over Hudson’s ubiquitous entending, by being more conservative of a theory. It is less of a radical break (or, perhaps not a break at all!) with the classical theist.
 And further understood in terms of divine simplicity.
 Again, concerns of divine simplicity, and the distinction between corporeality and incorporeality, enter prominently here.
 At least, on the account of a classical theist such as Aquinas.
 Is it the concrete/abstract distinction? substance/accident? material/immaterial? divine/non-devine? I prefer the last option, perhaps with an admixture of the others in some way.
 Where substantivalism is the theory that spaciotemporal relations between bodies are parasitic on relations among a substratum of spacetime points that underlie events. As such, however, objects (simples) occupy regions. Super-substantivalism is the theory that objects compose regions, or, rather, are composed by regions. In this way they are not fundamental – objects are literally chunks of space-time.
 I am assuming actualism concerning possible worlds in all discourse herein.
 Caveat: I would hold that God does not bear relations in the same way that numbers do absolutely but analogically, as will be made more clear below.