post and posting is not just mail.. Post No Bills was one of those phrases that 'got to me' as a child..

post =mail (actually, it equaled the gernund, mailing) no (a negative) Bills (payments do to utilities and stores)

why would someone go to the effort of stenciling that on a fence? why shouldn't i mail off payments for money owed to utilites? and beside a fence wasn't a post office or post box-- so why the sign?