Alice and Bob is Married

Several friends of mine are taking Symbolic Logic this semester, and one of them has brought to my attention something somewhat bizarre. His textbook, it seems, treats “and” as if it is never equivocal. Just intuitively, this seems wrong.

Take these two examples: firstly, “The lines A and B are parallel,” secondly, “Alice and Bob are Moroccan.” In normal English, the first example almost always means that the lines A and B are parallel to each other; re-phrased unambiguously, one would say “The lines A and B are parallel to each other.” But in normal English, the second example almost never intends any connection between Alice and Bob, except for their both being Moroccan; it could be re-phrased “Alice is Moroccan and Bob is Moroccan.”

Even worse, though, there are some words that can be taken either way by a reasonable person. Take the sentence “Alice and Bob are married.” Usually this means “Alice and Bob are married (to each other).” But I could imagine a situation where it meant “Alice and Bob are married (to Charlie and Deborah, respectively).” The word “and”, it seems, can be ambiguous even knowing the definitions of all the words in the sentence – while the textbook writer for this Symbolic Logic class wants to claim it is never ambiguous, ever!

It took a few minutes of thinking for me to figure out exactly how to phrase the ambiguity formally, but here it is. “A and B are C” can mean one of two things. Either “A and B are C” = “A&B are C” = “(A is C)&(B is C)”, or “A and B are C” = “{A,B} is C” – the collection of objects {A,B} possesses a quality, namely C. This is what we mean when we say “line A and line B are parallel,” or “Alice and Bob are married (to each other).”

In other words, we use “and” to do two different things – to apply attributes to multiple things at a time (what we do when we mean “A&B are C”), and to associate things into groups, and then talk about the groups (what we do when we mean “{A,B} is C”). And there’s no way to distinguish between the two without context.

There’s an easy way to fix this, of course. Change the grammar so that when we mean “{A,B} is C”, we don’t say “Alice and Bob are married” – we say “Alice and Bob is married.” It makes sense; after all, we don’t mean “Alice is married and Bob is married,” we mean they can be considered as a unit – “Alice and Bob” – and that unit is married. Is. Not are, because it’s one thing. It’s a set containing two elements, but it’s still a single set.

of course, we’ll never actually talk like this. It sounds stupid. “Alice and Bob is married”? But it does eliminate considerable ambiguity. It’s worth thinking about.