Explanation
The paradox originates from the fact that the volume of the immersed part of the object is important, not the actual volume of water that is displaced by it. In other words, no fluid needs to be actually displaced for Archimedes' principle to take effect. The object merely needs to be surrounded by the fluid.
One method offered to visualize the solution to the paradox is to conduct a simple thought experiment. Instead of a ship suspended in the water, imagine a lightweight bucket filled with water. Since the density of the bucket of water is the same as the water in the dock, the bucket would remain suspended, or floating. Nothing changes hydrostatically by replacing the bucket with a ship of equal or lower density than water (which it would have to be or else it would sink in open water anyway), therefore the ship would also float.
Another way of looking at it is that the buoyant force is the integral of the ambient pressure over the surface. In this model the volume is not directly relevant. When the object is immersed at the interface between two fluids, there is a different pressure distribution with depth on the parts exposed to the different fluids.
Read more about this topic: Archimedes Paradox
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