The "is" of identity (idea)

Writer "plebius" describes his/her ""The 'is' of identity" as "written entirely in E-Prime" (English without any form of the verb BE).

This description leaves out the fact that plebius' piece contains a BE-form (the word BEING) as follows: "The "is" of identity/The 'is' of identity" ... because ... our definition of 'barber' does not include his being also a man."

Plebius, you could have truthfully claimed that the piece used E-Prime if the clause in question had read: "because calling the individual 'a barber' left out the fact that we can also call him 'a man.'"