Thursday, April 5, 2012

"John and John"

I just sent out an email to two philosophers whose first name was "John" and the email's first line said "Dear John and John". After I sent the email, I wondered to myself: Is there a fact of the matter as to which token of "John" referred to whom?

Normally, if I write an email to two people, I think about the issue of which order to list their names in, and I typically proceed alphabetically. But in this case, I didn't think about the order of names I was writing down. It is possible that I thought about the one while typing the first "John" and then about the other while typing the second "John". Would that be enough to determine which token refers to whom? Maybe. But I don't know if I did anything like that, and we may suppose I didn't.


  1. John and John are philosophers.
This is true. But I didn't think of a particular one of the two while typing a particular "John" token. It seems unlikely that there be a fact of the matter as to which "John" refers to whom. But the sentence is, nonetheless, true, and hence meaningful.

Is the sentence ambiguous in its speaker meaning? If so, that's a hyperintensional ambiguity, because necessarily "x and y are Fs" and "y and x are Fs" have the same truth value. I am hesitant to say that (1) is ambiguous in its speaker meaning. (I will leave its lexical meaning alone, not to complicate things.)

Suppose that there is no ambiguity in speaker meaning, or at least none arising from the issue of which token refers to whom (maybe "philosopher" is ambiguous). Then this rather complicates compositional semantics on which the content of a whole arises from the content of the parts. For if either token of "John" in (1) has a content, the other token has the same content, since they are on par. But if the content is the same, we're not going to get out of this a sentence that means the same thing as (1) does. Suppose, for instance, the content of each token of "John" is the same as that of of "x or y", where "x" and "y" are unambiguous names for the two philosophers. Then we would have to say that (1) is equivalent to:

  1. (x or y) and (x or y) are philosophers,
but in fact (1) and (2) are not equivalent—all that (2) needs for its truth is that one of x and y be a philosopher.

Maybe the solution is this. Neither "John" in (1) refers. But "John and John" is the name of a plurality. I think not, though. Here's why. Suppose instead I said: "John and the most productive member of my Department and John are all philosophers." Well, "John and the most productive member of my Department and John" is not a name, as it does not refer rigidly.

I am just a dilettante on semantics, and it would not surprise me if this was exhaustively discussed in the literature.


Heath White said...

FWIW: my instinct is to say that the sentence is so to speak semantically underspecified. That is, if there were a fact about which 'John' referred to whom, there would be two possible ways for that to go. On either specification, John and John are philosophers, and (1) is true. Since we don't need to fix reference to figure out truth, we don't always bother. And here we have a sentence where we haven't bothered. So there is no fact of the matter.

Alexander R Pruss said...


I am inclined to the opinion that "p and q" and "q and p" express the same proposition. So there is no ambiguity in the proposition expressed.

Mini argument: Imagine people who communicate only by writing, and their sentences are written in a way akin to our parsing trees. Where order matters for an operator, the tree lines from the operator are marked in some way, but not where order doesn't matter. Moreover, only tree arrangement matters--it doesn't matter what is to the left, to the right, above, etc.

So, for instance, "p and q" is written as "and", with two exactly similar lines sticking out of it leading to "p" and "q". Maybe "if p, q" is written as "if", with a thick line towards "p" and a thin line towards "q".

I am inclined to think that such a language can have all of the propositional expressive power of our "linear" languages. But it is unable to express the difference between our "p and q" and "q and p". So that difference marks no difference in proposition (though it may, and often does, have other communicative roles).

Heath White said...


I don’t disagree about your hypothetical graphical language.

What I was trying to say was that the singular terms (‘John’ and ‘John’) do not refer to anyone, and that is enough to prevent the sentence from, properly speaking, expressing a proposition (= having a definite meaning). However, there are enough contextual constraints on what the singular terms don’t refer to that we can derive a truth value without bothering about specifying reference.

Suppose we run across some token of “The US President is male” where (like your case) there is no fact of the matter about which president we are referring to. Then I want to say that there is no proposition being expressed. However we have enough context to know that the token is true. Or in short: not all sentence tokens with truth values express propositions.

I am filing this kind of case in my “one more reason to be suspicious of propositions” file.

Alexander R Pruss said...


Interestingly, in the graphical language, there is no ambiguity here. For where there is an ambiguity, there is more than one way to disambiguate, say by inserting subscripts. Well, in the graphical language, the sentence "John and John are philosophers" is expressed as a tree. Maybe the way the sentence is expressed is this: At the root of the tree is "and". Sticking out from the "and" are two lines each reaching to "is a philosopher". And then from each token of "is a philosopher" there is a line reaching out to "John". Now, disambiguate the two tokens of "John" with subscripts "A" and "B".

It turns out that no matter how you disambiguate, you get the same sentence type. Here are the diagrams. You can see that the diagrams are exactly the same rooted tree (with root indicated by red text) if the order on page counts no more than font does in written English.

So, interestingly, in the tree language, we can have word ambiguity without sentence or proposition ambiguity. In English, we have word and sentence ambiguity, but no proposition ambiguity, if I am right that "p and q" and "q and p" express the same proposition.

You can also do this without proper names. "Today I sat on the top of a bank (in one sense) and I sat on the top of a bank (in the other sense)." Here, I used parentheses to do a partial disambiguation, clarifying that "bank" is used in different senses, which got rid of two possible readings, but the partial disambiguation is insufficient to result to disambiguate the sentence. However, in the tree language, I could again have total disambiguation if I did this. So, once again, we can have ambiguous tokens but unambiguous sentence.

I think what is going on here may be important. Instead of thinking of sentences in a bottom-up way, formed by applying operators to components as in the Montague approach, one should think of them as analyzable into components, in a top-down way (I am sure real philosophers of language have a name for this approach; I've seen something like this in one paper by Hintikka). In the tree language, sentences whose major operator is conjunction then don't analyze into an ordered pair of sentences, but into an unordered pair of sentences. When we do this with the "bank" and "John" trees, we then get no ambiguity in top-down parsing.

Daniel Hill said...

Thanks very much for this, Alex (and to Heath for illuminating comments too). As it happens I was recently reading Ezra 8: 16:
`Then I sent for Eliezer, Ariel, Shemaiah, Elnathan, Jarib, Elnathan, Nathan, Zechariah, and Meshullam, leading men, and for Joiarib and Elnathan, who were men of insight'.

Now maybe the original readers thought `I know three people called `Elnathan' and only one is a man of insight, so he must be the third-named, whereas the other two are both leading men'. It seems, though, impossible, even for the first readers, to know to which person each of the first two occurrences of `Elnathan' recurs, which means that it seems impossible for the individual words constituting the sentence to be understood. (And it seems very hard for later generations to know which of the three people called `Elnathan' was the man of insight, given the overlap in extension of `leading men' and `men of insight'.) That would suggest, on a compositional account, that one cannot understand the sentence as a whole.