  Vop\v{e}nka's Principle says that the category of graphs has no large
discrete full subcategory, or equivalently that the category of ordinals cannot
be fully embedded into it. Weak Vop\v{e}nka's Principle is the dual statement,
which says that the opposite category of ordinals cannot be fully embedded into
the category of graphs. It was introduced in 1988 by Ad\'{a}mek, Rosick\'{y},
and Trnkov\'{a}, who showed that it follows from Vop\v{e}nka's Principle and
asked whether the two statements are equivalent. We show that they are not.
However, we show that Weak Vop\v{e}nka's Principle is equivalent to the
generalization of itself known as Semi-Weak Vop\v{e}nka's Principle.
