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Vop\v{e}nka's Principle says that the category of graphs has no largediscrete full subcategory, or equivalently that the category of ordinals cannotbe 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 intothe 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 andasked 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 thegeneralization of itself known as Semi-Weak Vop\v{e}nka's Principle.

Weak Vop\v{e}nka's Principle does not imply Vop\v{e}nka's Principle