Brutus is not as much of a philosopher as he would like others to think. After their violent quarrel in Act 4, Scene 2, he tells Cassius that his wife Portia is dead. Then a short while later Titinius and Messala enter the tent and Messala informs him that he has received word that Portia is dead. Brutus pretends that this is news to him and replies: "Why, farewell, Portia. We must die, Messala. / With meditating that she must die once, / I have the patience to endure it now." Messala comments: "Even so great men great losses should endure." ThroughoutJulius Caesar, Shakespeare demonstrates his cynical attitude about all humanity, regardless of how important and how nobel they may appear to the world. The best example of Brutus showing his Stoicism is on the occasion when he hears of Portia's death, and yet he cannot refrain from posing as more of a Stoic than he really is. Like Caesar, Brutus is an egotist who wants people to think of him as a "great man."
The Stoics were one of the most important sects of ancient philosophers, and Brutus a historical figure who was a proponent of Stoicism. His philosophical positions are recorded in the essay by Plutarch that served as the basis for Shakespeare's play and also Cicero's Brutus. Shakespeare's audience would have been acquainted with Brutus as a historical figure.
Of the major philosophical groups during this period, the Stoics were the only ones that considered political activity compatible with politics, unlike the Epicureans and Platonists, who advocated that philosophers should withdraw from the world. Thus in his activism, Brutus shows himself as a Stoic.
Also, the Stoic philosophy was somewhat distinctive in considering suicide legitimate, and thus Brutus's suicide shows him as a Stoic.
Finally, Stoics possessed a certain degree of fatalism, believing that one should try to understand the course of fate (which represented divine will) and accept it. That meant accepting misfortune rather than railing against it, something Brutus exemplifies. He is also an example in the play of someone who puts his moral beliefs ahead of his personal preferences in killing Caesar, something that would also be an example of Stoicism.