According to the dictionary, the word "but" appears to be a multi-tasking word. It can be used as an adverb (albeit awkwardly) as in, "Get out of here but fast!", a preposition as in, "Nobody said so but me", a conjunction as in, "They went to the store, but I stayed home and did laundry", and a noun, meaning a kitchen in a small dwelling (only in Scotland, though).
Alas, the word "but" seems to be mostly used as an attempt to lessen the severity of a situation, as in, "I had an affair with the woman, but, I didn't love her."
The word, "but" is also used to try and negate any opinion that has come before, such as, "You, know, I don't mean to be so blunt, but, you are an ass".
See, I really meant to be blunt, except I used the word "but" to hide my intentions, lamely. So, let me rephrase, slightly.
Mr. Former Politician Who At One Time Ran For Vice President, you are an ass. By your use of the word "but", you have tried to justify your actions.
The English Language. Use it wisely. Use it responsibly. Don't be an ass.
EDIT: It has been reported that Edwards had came out to his family in 2006 about the "liason" as he put it, so I do not know in where in the frame of time the above words were used...but the toothpaste can't be put back in the tube, and all that.