I tend to use either/or rather than just using or. It seems more explicit, suggesting that neither & both are not acceptable alternatives. I suppose that it might be better to use some phrase like “choose one & only one.” The latter phrase is sometimes awkward and/or sounds snobbish when used with certain people, although mathematicians are happy with the phrase. At least I believe that "Tom or Dick" includes the possibility of Tom & Dick, while "either Tom or Dick" excludes the possibility of Tom & Dick. In some contexts the or construct might include the possibility of neither, while I would expect the either/or construct to imply excluding the possibility of neither. Example: Bill, help me decide who to assign as leader of the XYZ project. Tom or Dick are reasonable choices for that task, implying that other choices might also be reasonable. Either Tom or Dick are reasonable choices for that task, implying that other choices are not reasonable. On my better days, I would add some phrase to the above either/or construct to explicitly state that Tom & Dick are the only reasonable choices if that were my intent. What are the implied semantics of the either/or construct when there are three choices? Does "Either Tom, Dick, or Harry" imply one & only one of the three, while “Tom, Dick, or Harry” implies any, all, or none? As shown in many threads at this forum, English has some problems constructing precise/unambiguous statements. It seems to result in all sorts of semantic confusion. For example: Read some of the Religious Forum Threads relating to atheism/theism/agnosticism. Some seem to claim that "Believing god does not exist" is different from "Not believing god exists." There are definitions of weak or strong atheists, but no medium strength atheists. A weak atheist is not an agnostic. Are there natural languages who handle the above semantics better than English? I am especially interested in either/or constructs in other languages.
In computer languages and other applications of rigorous logic, that's called an exclusive or. If "Tom," "Dick," and "Tom and Dick" are all valid solutions to the formula, that's an inclusive or. As Timur points out, the computer/logician shorthand for exclusive or is XOR. Unfortunately it's neither easy to say nor euphonious to hear so I'll be surprised if it catches on in speech. That's invalid. "Either" is binary. It comes from the same Anglo-Saxon root as "whether," which is also binary. "Whether" is more intuitively obvious because one of its most common uses is the construction "whether or not." And of course people misuse both words. But we're talking about proper English here so both "either" and "whether" must have two and only two objects. As must "both," which amazingly enough is also sometimes misused. Ditto for "neither."
The only thing I can think of off the top of my head where you couldn't just yank it out of the sentence and preserve all the meaning would be something like "We can take either vacation, but not both." In most common usage it seems extraneous. "We can eat either chicken or fish," vs. "We can eat chicken or fish."
That's a slightly different definition of "either," so it doesn't work the same way. For starters, in this case it's an adjective, whereas in the "either-or" usage the dictionary claims it's a conjunction. I agree with the previous comments, that there is a subtle difference of meaning. The first sentence gives me an impression that the only things you can eat tonight are chicken and fish, perhaps, for example, because you've looked over the menu and those are the only entrees that satisfy your dietary laws, or perhaps you're allergic to red meat, or maybe you belong to some bizarre animal rights organization that only respects mammals. The second one sounds more like a helpful suggestion.
English isn't my first language. I actually thought that: A or B means these options are possible: 1. A 2. B 3. A and B and that either A or B means these options are possible: 1. A 2. B and that either A, B or C means these options are possible: 1. A 2. B 3. C Fraggle Rocker suggested that 'either' is binary. I don't think about it as binary at all, only that it denotes exclusiveness. In German, for example, there is: A oder B. 'A or B; one, the other or both.' Entweder A oder B. 'Either A or B; only one of them.' Entweder A, B oder C. 'Either A, B or C; only one of them.'
