In his speech What To the Slave Is the Fourth of July?, Douglass argues that the state of Virginia has passed laws that punish slaves if they commit crime. He believes that the fact that these laws exist implies that the government believes slaves to be logical, moral, thinking humans that hold personal responsibility. Moreover, laws are passed against teaching them to read and write. These laws imply that slaves can be taught things, and that they have the capacity to learn. This establishes the "manhood" of slaves.
As the law of the United States has already established that all men have the right to own their own body and to freedom, and black people are, as proven, fully human, then it must be illegal to own them.