Imagine that I say to you, “Tonight for dinner we’ll be having peas and carrots or green beans.”
What do you think our menu options are? Can we be having both peas and green beans? Are just green beans an option? If we have peas, do we have to have carrots?
What I’m trying to get at is that the phrase peas and carrots or green beans is ambiguous. How you interpret it depends on what syntactic structure, or bracketing, you assign to it.
In this case, there are two different ways you can bracket it. You can have:
So, with the one bracketing you can either have both peas and carrots or you can have both peas and green beans. With the other you can have both peas and carrots or you can have just green beans. I’m afraid that if you want only carrots, you are out of luck. You are only allowed to have them with peas, or not at all. And if you don’t like peas, you’ll have to hope that you’re getting the bracketing on the right, because at least then you stand a chance of getting just green beans. Artichokes are completely out of the question, which is a shame, because I really like artichokes.
Why am I telling you this? Because I like vegetables. Also because this actually relates to my research. The project I’m working on right now is looking at how people produce and perceive ambiguous coordinate structures like these, especially with respect to intonation. Because when you speak, you generally (but not always) give cues to the structure you intend. You may not even realize when you’re saying it that your menu options are ambiguous, but chances are that if you are offering peas and carrots or green beans, you will use aspects of your speech–specifically the timing of what you say and the patterns of the pitch of your voice as you say it–to indicate which structure you mean. Your prosody acts to group the words you say into meaningful chunks so we know what our vegetable options are.
So, what will it be? Do your options look like this?
Or this?
Images by John. Vegetables prepared by me.
(This confusing bit of a post is brought to you by a tired brain, and was in part prompted by a two-month-old request from Nora that I write more about linguistics. I just hope she likes peas.) (At some point, I’ll try to tell you a bit more about what I’m actually looking at, when it doesn’t involve vegetables.)
collecting tokens 
Cool! I would probably ask for clarification if your verbal cues did not make clear which you meant, because I would immediately recognize the ambiguity.
Back when I was teaching college-level mathematics, I had to teach a certain amount of logic, and some of it involved explaining this sort of ambiguity. I’m not sure if I ever gave a vegetable example, but I like vegetables! So I think this is a great explanation. I like the explanatory photos, too.
I would not offer two green vegetables together, so even if my speech was inexact, my children at least would know that the options would not include green beans and peas. Cooked carrots are known to make me gag, so they wouldn’t be a solo offering; therefore, the choice in the Aufiero household would be “carrots and peas or beans.”. If choices were offered, which they are not. Whaddaya think this is? A restaurant?
Most of us who grew up attending public school would assume peas and carrots go together, based on our experience with hot lunch.
Where’s the comma?
More to the point, where’s the salad?
I would understand that as meaning the second option. But I would probably want all three.
We actually learned some of these cues in law school– how phrasing affects people’s choices, and to choose conjunctions carefully to steer people to the choice you want people to make when you’re crafting your language for court. But we never got into it from the linguistic angle. I’d love to hear more about it!
I would think it was option 2 and I would choose green beans…I’d also like to add “and cheese” to the end of the sentence.
Are you breaking this down as a way to help computers learn to talk?
You rock! I love drawing syntactic diagrams. I’m a technical writer and I’m constantly being given ambiguous statements like that from software developers (only notsomuch about peas, carrots and beans). I’ve actually been known to draw little diagrams like that for them to show the various ways in which their text can be parsed. Generally when I do that, the developers look at me like I’ve suddenly grown an extra head. That’s all part of the fun.