When I was in high school, I wrote a short, humorous poem about my potential future career; it was titled Weather or Not. Unless you’re reading that poem, which is highly unlikely since it’s never left the back of my closet, you should never say whether or not when using the other whether.
Whether, in this instance, is being used to introduce multiple alternatives, such as I don’t know whether I should stay, go to the store, or go to the bank. There are three alternatives (staying, going to the store, and going to the bank), and whether introduces them.
It has become widely accepted to use whether or not as a shortcut, such as saying I don’t know whether or not I should go instead of I don’t know whether I should go or stay. In the former example, whether is not being used correctly since the alternative has not been introduced, but since it’s implied, you’re certainly not going to hear many people complain about its use in this way, especially in informal situations; in the latter example, whether is used as intended, introducing two well-defined alternatives.
What is clearly incorrect is using whether or not with well-defined alternatives, such as I don’t know whether or not I should go or stay since this example introduces more possibilities than intended. In the example, it introduces four alternatives: going, not going, staying, and not staying, as opposed to the intended two. This example mirrors some of the other entries that Sherry and I have discussed in the blog. Enough people use whether or not with well-defined alternatives for it to have gained acceptance; however, acceptance of something that is not logical is not the best way to communicate.