Wolfgang Schwarz

The property of being two meters away

I believe that there is such a property as being two meters away. -- Not two meters away from me, or from somebody else, or two meters away from something or other. Just two meters away.

Admittedly, there is a sense in which something can be two meters away only relative to some point of reference. But compare properties like being empty and being bent. There is a sense in which, strictly speaking, persisting things can be empty or bent only relative to a time: this cup here is empty at the present time while it was full 5 minutes ago. Likewise, at least prima facie many things are empty or bent only relative to worlds: the cup is empty at the actual world, but full at other possible worlds. That's why properties are often modeled as something like functions from worlds and times to sets of objects.

Besides relatively intrinsic properties such as being empty and being bent, there are more extrinsic ones: being two meters away from something empty, arriving at a bus stop two minutes after the last bus left. These properties, too, apply to things only relative to times and worlds.

Lewis would model all those properties as classes of time-slices of world-bound individuals. This construction doesn't work any more for properties such as being a famous philosopher and having ceased to exist 2 minutes ago because things can have these properties at times (and, in the former case, worlds) at which they don't exist. So even Lewis would model these properties as functions from worlds and times to sets of objects (as I've argued here).

Now why not add locations into the domain of these functions, turning them into functions from centered worlds to sets of objects?

One argument for this is the obvious parallel between time-relativity and location-relativity: just as things can be empty at one time and full at another, things can be bumpy at one place and flat at another. Germany, for example, is bumpy in the South and flat in the North.

Moreover, every argument I can think of against location-relative properties applies equally well to time-relative properties. Such as:

if being two meters away was a property, we should be able to distinguish between the things that have this property and the things that don't. So what are the things that have it? The things that are two meters away from you? But then isn't this alleged property of being two meters away really just the harmless property being two meters away from you?

You can say exactly the same against having ceased to exist two minutes ago, arguing that this is really just the property of having ceased to exist two minutes ago relative to the present time (and the actual world).

By this kind of reasoning, being famous and being bent will also turn out to be ultimately relations to times and worlds: being bent at t and w, being famous at t and w. This is of course exactly what Lewis would say; and he would insist that at least some properties are not ultimately relations to times and worlds.

Whether or not Lewis was right about this -- that is, whether or not all properties are ultimately reducible to properties that are not time- and world-relative, I think he was wrong when he claimed that all the relative properties do not deserve the name "property". It is perfectly okay to say that this cup (not just its present timeslice) has the property of being empty, or that Plato has the property of being a famous philosopher. Sure, these are time- and world-relative properties, but properties nonetheless.

So being bumpy and being two meters away are location-relative in addition to their time- and world-relativity. But they are still properties, on a par with being empty and being a famous philosopher. In fact, it doesn't seem very unnatural to me to say that Alpha Centauri has the property of being 4.3 light years away.

One last argument for introducing the location-coordinate: as relativity theory undermines any principled distinction between time and space, it is quite unclear what a function from worlds and times to sets of objects is supposed to be. By contrast, functions from centered worlds (pairs of worlds and spacetime-points, if you will) to sets of objects are unproblematic.