Tragic, I think not.

J-B

It has often been said, in our very own English class and elsewhere, that Shakespeare wrote his tragedies, including Julius Caesar, following the principles of Aristotle. (ndlr: Not by me it hasn't!)
Aristotle said that tragedies should all follow a simple plot to be good: they should represent in a limited period of time, with no big gaps in the time continuum, in the same place, for example a room, that there should be no on-stage deaths and that there should be a tragic hero.
This hero should be a basically good and noble man in a high position that meets his downfall by "harmatiea", a tragic flaw, normally "hubris" or excessive pride.
A good example would be Antigonie, a Greek tragedy that probably served as a base for all of Aristotle's ideas.

The French authors applied these as rules and, moreover, not only in tragedies. A good example would be a play by Moliere Le Bourgeois Gentilhomme. The action develops in the main characters house, and in one day. The Bourgeois is basically good and in a high position. He is very rich, and , since it is a comedy, meets not his downfall but a great deal of ridicule by hubris.
These principles are not even remotely applied in Shakespeare's play Julius Caesar. This play treats mostly of the downfall of the Conspirators. It begins at Lupercalia, than continues on a month later at the ides of March, and than starts jumping forward, a year than seven months and so on. The action shifts from one place to another, sometimes a public place, then to a private setting, and then back again all over Rome and finally it goes to a battlefield many miles away.
There are many murders right under our noses in this play, in addition to all the other differences to Aristotle's principles.

With this direct opposition on many points we can conclude that there was a parting of ways between the ideas of Aristotle and Shakespeare. And with this parting can we really talk of tragedies from an Aristotelian point of view?

If we accept that these differences were forced on Shakespeare by reasons unknown, than we can try to find a tragic hero. The possible claimers to the tragic hero title are few, but we can name the main conspirators, Cassius and Brutus, then Caesar and finally Anthony.

The four are already in a high position.
Caesar is basically good, noble and wants the good of Rome. But when he shows his want of power by showing his difficulties to resist the crown, when he shows his hubris he gives Cassius all the arguments to sway the other conspirators to kill him.
But the climax is not clear.
He finally refused the crown three times and, to our knowledge commits no other evil deed, and also he dies in the beginning of the play. He seems a too remote a character to be our tragic hero.

Anthony could be thought of as good in the start but we quickly discover that he is utterly and totally evil. But this could come from his tragic flaw. We cannot know but since he meets no downfall. This rules him out with a comfortable certainty.

Cassius also could be thought of as good and due to his tragic flaw, here jealousy, becomes evil and meets a tragic downfall by his own hand. But he seems too calculating and heartless to be our tragic hero.

And finally Brutus. He, without any doubt, is good and noble, and he fights for a very noble cause, his freedom and the Roman Republic. But he seems to lack a tragic flaw, and these are normally obvious, but here his only error was to be over-kind, by not killing Anthony and by letting him bury Caesar, though some people could call this over-confidence and he meets, like Cassius, his doom by his own hand.

He may be our famed tragic hero but his flaw is so well hidden by appearing right after the excitement of Caesar's death that I do not think he is the tragic hero.

So seeing all these differences from the theories of Aristotle, I think that there is no tragic hero in this play and that this is not an Aristotle type of tragedy.