As a ship moves away from an observer toward the horizon, the hull disappears first, then the mast and the main structure, and lastly the antennas or sails. When ships return from sea, the sequence is reversed. The antennas and sails will be seen first, followed by the mast and main structure of the ship, then finally the hull.
If the Earth were flat, the ship would shrink until the entire craft was too small to discern, but this is not the case. Ships do shrink when they are moving away from an observer, but eventually, parts of it disappear piece by piece.
A globe Earth explains this observation perfectly because the ship that is slowly disappearing has traveled far enough that the curvature of the Earth becomes apparent. It's impossible for an observer to see beyond the curvature, so the ship looks like it's slowly disappearing.
There are many reasons why the ship appears to sink as it moves toward the horizon. First, the hull disappears first because its angular size reaches the limit of the human eye before any other part of the ship. Second, the sinking ship effect can be caused by bulges on the surface of the ocean. Third, the sinking ship effect could be a result of refraction. Mirages can appear and disappear over water, which causes the sinking ship effect. 
[P1] The Earth is a globe because ships moving away from the observer disappear piece by piece due to the Earth's curvature.
Rejecting the premises
[P1] There are many reasons that can cause a ship to appear to sink as it moves closer to the horizon.