Why are some old paintings unfinished on the bottom?

Answer 1

As an artist myself, sometimes the answer is simple: the painting was abandoned or put away and never picked up again, the artist lost inspiration, or it was done as a statement within the piece. There are also some examples (such as The Treaty of Paris by Benjamin West) where a painting was commissioned with the expectation the commemorated event would happen, but due to conflicts within the group to be painted the painting was only partially complete.