Quite deaf; or so inattentive as not to hear what is said. One might as well speak to a gate-post or log of wood.
Deaf as a white cat.
It is said that white cats are deaf and stupid. None so deaf as those who won't hear. The French have the same locution: “Il n'y a de pire sourd que celui qui ne veut pas entendre.”
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894