Israel, D. J. and Perry, J. R. and Tutiya, S. Executions, Motivations, and Accomplishments. Philosophical Review, vol. 102, no. 4, Oct 1993.
Brutus wanted to kill Caesar. He believed that Caesar was an ordinary mortal, and that, given this, stabbing him (by which we mean plunging a knife into his heart) was a way of killing him. He thought that he could stab Caesar, for he remembered that he had a knife and saw that Caesar was standing next to him on his left, in the Forum. So Brutus was motivated to stab the man to his left. He did so, thereby killing Caesar.