Previously I defined a property as simply a particular causal disposition. And in turn a causal disposition was defined in terms of a hypothetical ideal observer which was both sensitive to that particular causal effect and could compare its past states to its current one without error (in order to determine if a particular causal effect was the same as another). This works for most properties, but space, time, and existence remain problematic cases, which aren’t easily treated as simply a particular causal disposition.
The problem with space and time as properties is that they aren’t independent of other causal effects. Rather they come along with them; we say that a particular causal effect happens at a particular place and at a particular time, and from those happenings we construct space-time in general, as part of a mathematical theory about how the universe is structured as a whole. But this doesn’t help us pull the property of being at a particular space-time point away from the other causal effects, and identify it with some unique causal disposition of its own.
So instead of trying to define a space-time location as if it were just a normal property let us simply accept that it isn’t; that it needs to be treated differently. Let us take every point (or region) where a causal effect occurs and label it as a distinct space-time point (or region). This takes care of part of the problem; now we know what it means to say that a property it at a particular space-time point (or region), it simply means that it is identical to one of our labeled points (and I am going to stop adding “or regions” from here on out). But this solves only part of the problem; we also want to be able to talk about the structure of space-time, specifically the spatial-temporal relationships of one of these space-time points to another.
I am going to say that those relationships are a matter of convention, but only in one specific sense. I do not mean to imply that the way the universe actually works, or the actual structure of natural law, is a matter of convention. However, I do claim that how we actually relate various space-time points is a matter of convention (and that they way we relate them in convention may not, therefore, match up with the way that they are “really” related). Let’s say that we have one of our ideal observers in hand, which is sensitive to a number of causal effects. And let us further suppose that our ideal observer can take a number of actions and has an internal “clock” (by internal clock I mean that the observer is simply put into one characteristic state every so often, perhaps regularly, perhaps not). Such an observer (if it was intelligent) could construct the property of time by simply deciding that each interval between those characteristic states represented one unit of time, and then labeling the time it sensed a particular effect based on how many of those units of time had passed. Obviously this will give the observer only a very rough sense of time. But by noting patterns in the external effects that it is sensitive would allow it to develop further “theories” about time. Eventually it may even decide that its internal “clock” is not a very good measure at all, and may decide on some more precise way of measuring the time property. The same developments could be carried out for space, the observer finding some characteristic actions that when taken in sequence seem to change and then restore the effects that it is sensing. (Moving away from and then back to the same place.) And from there the observer could develop a similar theory about space, again, eventually replacing its initial way of measuring space with a better one.
Obviously we are not such observers. We come born with a “theory” about space and time, albeit an unconscious one. However, we, like our hypothetical observer, have replaced our initial theories with a more complex one that better fits with what we have observed (general relativity). My point is this: the relations between one particular point of space-time and another are not something that we are sensitive to, or can become sensitive to, like we can with causal dispositions in general. Instead we must deduce these connections through a theory. Of course this leave us with some doubt about whether our current theories about space-time relationships match up with the real ones (the ones that actually play a role in determining the outcome of events). But our instinctual theory has been selected for by evolution, and a theory that wasn’t mostly right wouldn’t be very conductive to survival, and we have improved upon this theory substantially. So we have the right to be confident that if our current way of looking at space-time isn’t completely correct then at least it is close. This is all really beside the point, but I wanted to put to rest any skeptical doubts that may have been raised by the investigation into these matters.
And this gives us a workable theory of how space and time are connected to properties. They aren’t properties themselves, but rather ways of talking about particular instances of the effects of properties and their relations. So let me turn then to the nature of existence. Existence too is not the kind of thing that is easily described as a property. Fortunately the case of existence is actually easier to deal with (perhaps surprisingly). Simply think about what it means to exist. If something exists it must have some properties, because to have no properties would to be nothing, and hence not to exist. So we can say that to exist is simply to have some property, any property.
And this gives us an unusual argument for causal closure: To exist is to have at least one property. But to have a property is to be located in space-time, because the individual instances of the effects of those properties can be labeled as individual space-time points. Now consider the relation of this existing thing to the physical world. If it has a causal effect on the world then there must be some causal chain leading from its properties to the physical world. But if there is such a causal chain then it is spatially-temporally related to the physical world (every time something has a causal effect on something else we can say that they were co-located, or at least adjacent, instantaneously, which follows from any principle of causal locality, my favorite of which being the the speed of light / relativity, which says that no effect may travel faster than the speed of light, and hence that at the moment of the effect the two objects must be at a distance of zero). On the other hand, it may not be related by a causal chain to anything physical, and may then exist in a completely separate space-time. But then the physical world is causally closed with respect to it. Thus with respect to everything that exists the physical world is causally closed, and of course non-existent things can’t have effects, and hence can’t violate this causal closure.