I loved Sling Blade. The Billy Bob Thornton that one witnesses today is in no way reflected in the "Karl" character of Sling Blade. Truly an amazing transformation into "becoming" the character and a masterpiece for the writer, director and star. (Won the Oscar, gained 11 nominations and 9 wins in categories!

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1.) No, I do not believe what Karl did was murder, which would go against the original wording of the 6th commandment. ("Thou shalt not murder")
However what Karl did do was commit to stop (in this case kill) the threat Doyle exampled to the innocence of Frank and personal safety of both Frank and his mother Linda. And after repeated warnings from both Karl and Linda as well as measures of interceding on the families behalf by Vaughan. Doyle, despite all this, exampled he would not be dissuaded from being an active part and presence in that family unit of which he was only a peripheral. factor. i.e. boyfriend, not husband, which would have been bad enough.
Further, during the era this was suppose to reflect, there were no such things as "restraining orders" or "orders of protection", to be applied for by Linda on behalf of herself and her son, so as to insure their safety from the reach of this vile man Doyle.
Consequently, before action could be taken legally, Doyle would have to commit an offensive act that would result in legal recourse. Which in the case of his temperament, could boast dire consequences to the family initially, before the law would later afford protection. And that is if the family was alive to petition.
Quite simply as someone I use to know once said; "Some people just ask to be killed!"
And so was the case with Vaughan. Reasoning didn't work. Threats did nothing to dissuade his vicious unstable temperament. So , given the unlimited access he had to accost this woman and her son, what other measures were left to their disposal!? And no, running away was not an option because of the financial issues that attended the family.
2.) I do not think so. I think Karl was pretty much cut and dry and saw life in black and white with no shades of Gray in between. Certainly he did give quarter to the families decision to tolerate Doyle of their own free will. Certainly he did exhibit personal restraint when Doyle accosted him. However when Doyle posed an irrevocable threat to the child Frank, because of the viciousness he displayed in assaulting his mother and the child, I think Karl realized that the white side of remaining on the threshold as a non-commitant observer, altered to the dark side of simply coming to terms simply enough, with what needed to be done because Doyle made it necessary by refusing to leave the family alone and moving on. Doyle was determined to stay, regardless of who he hurt so as to remain in command of that domain which he assumed for himself as that boyfriend, not the homeowner. (*as would have been the case in that era had they been married in most cases).
3.) I think Karl provided the filler for the gap of Franks fatherless life prior to his arrival at the Wheatley property.
Doyle was certainly no role model for anyone to aspire to, much less intent on ever exampling himself a father figure. He was a lush, a violent human being and a waste of space, period! And he was proud of the fact that he intimidated the weaker members of the family and local community, into holding that posture. Had Karl not come into young Franks life at that moment, just before his life changed and he began to grow into manhood, he would have instead had Doyle as an example of abuse and vindictiveness that would have eroded the strength of character and will that young Frank already possessed prior to Doyle's arrival in their life, long before Karls.
Had Karl not come into the picture, as Doyle exampled himself intent to remain in the family no matter what, I can only imagine his overbearing personality, much less size and viciousness, would have overcome Frank either physically (killing him ultimately) or both physically as well as mentally. (Beating him into submission and thereby breaking his spirit).
Karl was the best thing that could have happened to both Frank and his mother. For his mother he freed her from having to be made victim to Doyle till the day he finally killed her. (worst case scenario). And for Frank he was a role model for quiet contemplation, strength of character and of will, which only served to fortify that which was already present in such a young experience. That Karl was there to assist them to overcome the evil that sought to corrupt their family unit, was what provided young Frank's life the opportunity to remain a decent, loving and unscathed boy that would later grow into manhood without the memories of those worst case scenarios I mentioned, having destroyed his innocence and his family. Which was his mother, his only remaining family after his father committed suicide.
And the thing is, Karl accepted full responsibility for his actions. He did not run, he didn't ask Frank and his mother to cover for him after the fact. Indeed he sought to have them well away from the home property before he quite simply did what he believed to be necessary because Doyle's actions gave him no other choice because he was not the type of man, having warmed to the Wheatly family, to walk away and let them endure Doyle as best they could. They gave him a chance, fresh out of the State Mental Hospital knowing full well the skeletons he had in his closet that got him sentenced there in the first place, and so he gave them a chance at life un-scarred by what was clearly one mans intent to destroy it.
And I think he learned the quiet restraint and contemplation about the threat Doyle posed to the Wheatly family, because of those years he spent in that mental hospital for the act he committed against his mother and her lover, when he was about Franks age, compelled it. Whereas had he been of the temperament of his youth, Doyle would have been dead much sooner.
QUOTE
Frank: Ever think of killing yourself on purpose like my daddy done?
Karl: I studied about it. The Bible says you ought not to. It says if you do that, you go off to Hades. Some folks call it Hell, I call it Hades.