One of the key tragic elements of William Shakespeare's "Julius Caesar" is the way in which characters dismiss their own feelings and loyalties in favor of public duty. Brutus, for instance, ignores his friendship with the title character in order to kill him for what he deems to be the common good. He even refuses to trust his own wife, Portia, with the details of his plan.
In this way, Brutus is seen to lose his humanity while pursuing what he imagines to be a higher end.
This dismissal of humanity is remarked upon by Caesar, specifically in reference to Cassius. He tells Mark Antony that he cannot trust Cassius because he is too concerned with his public persona; he has no inner life to keep his ambition in check.
However, Caesar himself is also tragically misled by the grandeur of his public image. Identifying with his symbolic omnipotence, he comes to believe that he is invulnerable, ultimately blinding him to the threat posed by his closest allies.
This monumental fall from a high estate to a position of misery or, in this case, death, is a driving characteristic of classical, Aristotelian tragedy, which Shakespeare would have become familiar with through Latin adaptations.