[…]Thinking of the Web servers as “objects” is an extremely bad idea. Objects are repositories of state. Conversations with them are by definition not stateless.[…]
There, Adam appears to confuse object state and application state. The former, object state, refers to the state held by the object, in the “behaviour, state, identity” sense of the word. For example, the state of the current weather in Ottawa is 11 degrees C.
“Application state” refers to the progression of the system during the execution of the application, more commonly (and less confusingly, IMO) referred to as “session state”. In the weather example, “session state” is held entirely by the client as the weather service need not remember anything about my invocation in order to serve it the next time (though that’s obviously a weak example). Any stateless interaction means that application state is maintained by the initiator of that interaction. Any stateful interaction means that application state is, at least in part, maintained by the recipient; this can range from part initiator, part recipient with HTTP+cookies, or full-recipient state in a remote session architecture like VNC.