If you are Leibniz, and reduce every piece of matter at a given time to an infinitely small amount, you can get away with giving every so-called piece of matter a simple unique space coordinate, one which consists of a single point in the universe. The required coordinate system need only give every actual point in the universe a unique address. The Star Trek universe, for instance, makes the center of earth the 0,0,0 spot in the universe with every other place radiating out from there. Convenient for earthlings, but not much of an attempt to be universal about it. Some sort of spherical polar coordinates are all that are necessary in any case -- for a given point in time, of course.
Two assumptions made this type of method easy: we look only at a given point in time, and we look at matter as consisting of infinitely small points. Yeah right. Let's get more realistic about this -- and probably lose any reputation as theorists in the bargain. :)
Assumption one goes away: The point we look at travels through all time. I can think of two ways of recording this information, and the difference lies in which way we would find more useful to set up a point in space / time lookup table. Are we more concerned with the particular stuff in the point and where it goes to next? Or, are we more concerned with the coordinate basis remaining the same internally? The latter would allow us to track a point of matter (don't confuse the point of matter with the coordinate point it is at, like I almost did there) [Isn't having your own place to write this stuff out cool?] as it traveled over the coordinate system, much like we can track a car as it traverses the relatively stationary grid of streets. The former would allow us to track the changes in the type of matter at any particular coordinate point. It would not force us to adopt one coordinate layout, as that would be what changed.
Anyway the second is more intuitively obvious, and they would be identical in all but usefulness, so I'll adopt the latter.
So much for assumption one.
Assumption two goes away: Either we can choose to leave the point system in place and with it try to define larger (than infinitely small points!) objects with these points. These objects would have infinite surfaces in a trivial sense as described in such a system. At any point in time, the coordinate system could lay out a 3D grid of points that defined the volume of the object in question. It could be a molecule or a mushroom depending on our concerns. As the object is described through time, the volume described by the points would change, and so too the points themselves. So an object defined as the set of all its space / time points would be a huge entry in the database, but never the less unique.
Wrong! Paradoxes of identity conditions play a huge part in delineating which points are of a specific object. We would have to resolve these, either with convention explication or with real solution to these so called paradoxes. Let me give some examples of identity paradoxes that would apply to mess up this theory a lot:
These paradoxes all arise in the consideration of physical objects. Let's move a step further and consider concepts instead. How do we delimit the concept space? Do we require no overlaps? If not, how can we determine when from within an overlap, we move from one concept and its resident set of connections and assumptions to a different but cohabiting (in that space) concept and its resident assumptions and connections (to other concepts)?
Neatly, some concepts nicely denote some objects, or even more nicely that for every object we delimit from all other objects (ignoring the object paradoxes above), we can provide minimally a label, and more interestingly a concept I think, for than object. However, there are vastly more (if one infinity of concepts can be said to be larger than another infinity of them) concepts that will not denote objects. Some will denote relations between objects, some events, some more abstract "things" such as feelings and epiphenomena of other sorts, and finally some will denote absolutely nothing at all. All sorts of line drawing problems emerge when we consider the relations between conepts as defining continuums of conceptual landscape.
Finally, there are problems in divying up the conceptual space permanently. This is truly an error as our best theories are constantly being bettered, and our understanding of the universe and of concepts expands incredibly. Neat, eh?! We don't evendesire to finalize our list -- unlike for the lis tof all possible objects.