King Lear: Tragedy because of Fate?

In his play King Lear, Shakespeare tackles many problems inherit in human nature. But I wonder if the terrible and unnatural acts are predetermined by a higher being? One of the ideas that was discussed almost daily in class was the idea that certain people and events were either natural or unnatural. A person is either naturally good or naturally bad, right? Likewise, the actions of a certain character are either unnatural or natural. But perhaps they were meant to do certain things because of their fate? For example, Edmund believed that he was entitled to the rights he should have had he not been born a bastard. So was the betrayal of his family going against his nature, or was he merely following the guidelines his fate had set forth? I believe it is a bit of both. Edmund believed he was meant to be above his brother, so he acted in a way to make that possible. In the end, all Edmund really did was help his brother, Edgar, gain more power still. It's almost as if Edmund's fate was used to make Edgar's possible. Edgar was meant to have power, he is just and honest, and Edmund's actions are really what made that possible. 

Furthermore, Reagan and Goneril acted unnaturally when they disowned their own father and fought each other over a man. Both women were not just or virtuous leaders, so it makes sense that their fate caused them to fight, and ultimately ruin, each other. But they couldn't possibly have had that fate determined when they were born, so is it possible for one's fate to change based on their actions, or are all of their actions based on their fate? It seems like one's fate may be adjusted at some point. King Lear was almost punished for the unfair treatment of all of his daughters. He favored Cordelia, so his other daughters were less inclined to put up with him in his madness. So maybe because King Lear sent away the only daughter who cared about him, he was punished. 

Though fate is less openly discussed in this play, it definitely plays into the characters' lives. One could reason that Cordelia was sent away to teach her family, and the rest of society, a lesson. When people go against what is natural in their lives they will be punished. What is natural is fate. When people try to stray away from their fate, and any natural order, their fate keeps them in line. Though Edmund wanted to be powerful, he was not meant to be; his fate kept him in line when he strayed from the path. By creating unnatural situations, banning Cordelia and betraying family, circumstances worsen until the perpetrators regain focus and begin to follow the right path again. Unfortunately, this pretty much ends with death in this play. So the play reiterates the idea that  fate cannot be tricked or changed. It is comforting, though, because if we follow the natural path we are meant to, fate will be pleasant and everything will end up right in the end.