Half Face Man: Pushed? Or Jumped? Or even Tripped?

Doctor Who Series 8 went off with a flying start. Peter Capaldi debuted in his first episode called "Deep Breath". Deep Breath saw the return of the Clockwork Robots and the Paternoster Gang. The Clockwork Robots had one leader. The Half Face Man. The Clockwork Robots were going to eventually kill Clara and the Paternoster Gang. Until the Clockwork Robots suddenly collapsed. This was because their leader had died. We see him on the spire of Big Ben. So the question is now, was he pushed? Or did he jump?

Was He Pushed?

On the air ship the Doctor said that he had the feeling that he is going to have to kill him (Half Face Man). The Half Face man was determined to find the Promised Land. The Doctor went onto explaining that the Promised Land was a conspiracy and wasn't even real. Did the Doctor and the Half Face Man get into a big argument about the Promised Land and the Doctor ended up pushing him out of the air ship? The position he is in looks like he was pushed.

Did He Jump?

After being told by the Doctor that the Promised Land wasn't real and was a conspiracy, did the Half Face Man begin to see the future and that he wasn't actually going to end up anywhere? Maybe he felt that as there was no need to go and find the Promised Land because it isn't there, that he felt he wasn't needed anymore? Then ended up jumping out if the air ship? If he jumped then he probably jumped backwards?

What If He Tripped?

We saw the Doctor and the Half Face Man get into a fight on the air ship that involved a lot of pushing and shoving by the door of the air ship. Maybe the Doctor let go of the Half Face Man and he was on the edge of the air ship. Then suddenly the Half Face Man lost his balance and tripped and fell out the air ship?