This just seems like a pretty straightforward problem of definitions... You get inconsistencies when you define an object by its atomic components, but the problems disappear when you re-define it by its structure or physical properties, or at least constraints on such things. Insofar as anyone cares, we can adjust that definition of an object. A person isn't defined by a shapshot of their cells at any given moment, but as the scaffold on top of which their body type, hair length, personality, etc can change over time. A river is a region that undergoes large dWater / dt in a certain area at particular times of year, be it swamped with farm runoff or plentiful fishies. When it runs dry, you re-label it as a former river, with reference to it's historical property of having once carried streams from high to low elevation.