Aristotle's ideas about tragedy were recorded in his book of literary theory titled Poetics.   In it, he has a great deal to say about the structure, purpose, and intended effect of tragedy.  His ideas have been adopted, disputed, expanded, and discussed for several centuries now.

The following is a summary of his basic ideas regarding the tragic hero:

1.  The tragic hero is a character of noble stature and has greatness.  This should be readily evident in the play.  The character must occupy a "high" status position but must ALSO embody nobility and virtue as part of his/her innate character.

2.  Though the tragic hero is pre-eminently great, he/she is not perfect.  Otherwise, the rest of us--mere mortals--would be unable to identify with the tragic hero.  We should see in him or her someone who is essentially like us, although perhaps elevated to a higher position in society.

3.  The hero's downfall, therefore, is partially her/his own fault, the result of free choice, not of accident or villainy or some overriding, malignant fate.  In fact, the tragedy is usually triggered by some error of judgment or some character flaw that contributes to the hero's lack of perfection noted above.   This error of judgment or character flaw is known as hamartia and is usually translated as "tragic flaw" (although some scholars argue that this is a mistranslation).  Often the character's hamartia involves hubris (which is defined as a sort of arrogant pride or over-confidence).

4.  The hero's misfortunate is not wholly deserved. The punishment exceeds the crime.

5.  The fall is not pure loss. There is some increase in awareness, some gain in self-knowledge, some discovery on the part of the tragic hero..

6.  Though it arouses solemn emotion, tragedy does not leave its audience in a state of depression.  Aristotle argues that one function of tragedy is to arouse the "unhealthy" emotions of pity and fear and through a catharsis (which comes from watching the tragic hero's terrible fate) cleanse us of those emotions.   It might be worth noting here that Greek drama was not considered "entertainment," pure and simple; it had a communal function--to contribute to the good health of the community.  This is why dramatic performances were a part of religious festivals and community celebrations.