The substantialists such as Democritus there are fundamental things that persist in time, things like you and me, atoms and boats. A boat is a thing apart from its surroundings, identifiable, nameable.
On the other hand there were processists such as Heraclitus who countered that in a deep sense there are no things, that everything is like a wave: it comes and goes and in its vanishing its water remains but is changed.
They would argue that a ship is not a thing, just a temporary combination of materials, and use a classic thought experiment in their defence:
If you took a ship and one by one replaced each of its components would it be the same ship? If you used the replaced components to build a ship from scratch, which would be the "real" ship?
The process argument has no difficulty here: the ship, for the time it exists, has function, then the materials that comprise it are changed: identity is never complete, but transitory and incomplete.
But what about consciousness? Isn't that pretty separate and whole? Maybe a processist would argue that like a crest of a wave we exist for a moment before being absorbed into the greater sea, but that isn't the point.
So what is the point?
Updated: see the following post