Here’s a paradox or riddle that I was confronted with recently – and it’s worth some analysis. If I remember correctly, it was posed by Anscombe. It goes like this:

It is impossible to be told anyone’s name. For if I am told, “that man’s name is ‘Smith'”, his name is mentioned and not used. I hear the name of his name, but not his name.

So now we have a mystery. Clearly we can be told someone’s name – this happens all the time (and often, we think, by saying something like, “My name is ‘Smith'”), but how is this possible, if we only ever hear the name of his name?

It is worth distinguishing between use and mention first. When I say “the cat has a spotted tail” I am using the word “cat” to refer to some object/animal. When I say “‘cat’ has three letters” I am mentioning the word “cat”, but not using it – I’m referring to the word itself, not the ordinary referent of the word. When I am told, “that man’s name is ‘Smith'”, ‘Smith’ is mentioned but not used. This means that I am only hearing the name of his name. Why is this a problem? Because if I am only hearing the name of his name, then how can I possibly learn what his name is? “‘Smith'” isn’t his name, it’s the name of his name – it entails, “‘Smith’ is a way to refer to my name”, but that is not to say what my name actually is. Also note, we do not say, “‘Smith’ went to the grocery store”; we say “Smith went to the grocery store”. The former says that a name (‘Smith’) went to the store, the latter says a person (Smith), went to the store.

Now consider the following two sentences.

(1) That man’s name is “Smith”.

(2) That man’s name is Smith.

If the problem is that in (1) you hear the name of the name, instead of a particular person’s name, then why couldn’t we just write the sentence as (2), remove the quotes and we no longer have to worry about mentioning the name – we just use it? Unfortunately, constructions like (2) will not help solve the riddle. Why? Because in (2) “Smith” and “that man” co-refer. And now look what happens with a little substitution.

(3) That man’s name is that man.

We have substituted “Smith” for a co-referring term, “that man”, and ended up with (3). Clearly (3) is absurd, for my name isn’t me – that man’s name isn’t that man; an individual is not identical to his name.

So it looks like we’re going to have to figure some way to make sense of (1), considering (2) and (3) seem fruitless. But the proposition in (1) names a name, and there doesn’t seem to be any grammatical manipulation we can do (that still preserves the sense/meaning of [1]) to change that.

Here’s the trick. There is a distinction between the truth-conditions on the utterance insofar as what is uttered (which we will call the explicit truth-conditions), and the truth-conditions on the utterance which are not explicitly a part of the content of the utterance (which we will call the background truth-conditions).

Let’s look at the explicit truth-conditions of the utterance “that man’s name is ‘Smith'”. There is (1) “that man’s name” which refers to a name, (2) there is “‘Smith'”, which refers to a name, and (3) there is an identity relation between “that man’s name” and “‘Smith'”. So the explicit truth condition(s) of the utterance will be: “that man’s name is ‘Smith'” is true if and only if “that man’s name” and “‘Smith'” co-refer to the same name. The problem: the name that (1) and (2) refer to is not used in the utterance, so we haven’t heard that name.

Now let’s look at the background truth-conditions of the utterance “that man’s name is ‘Smith'”. One trivial background truth-condition might be that: the speaker is speaking English. For if he was using a different language, then the meanings of the parts of the sentence will change and consequently the explicit truth-conditions of the utterance will be something else. But another, less trivial, background condition will be: all proper names are reflexive. This means that a proper name can be used to refer to itself.

So we now know that “that man’s name is ‘Smith'” is true if and only if (1) “that man’s name” and “‘Smith'” co-refer to the same name, but also that (2) the utterance is in English, and (3) all proper names are reflexive. Condition (3) tells you that “Smith” is reflexive, which means that you use it to name it. This gives us another truth-condition (4): “‘Smith'” refers to “Smith” iff “Smith” refers to Smith. These are all the tools we need to know that we have been told the name. Let’s explain.

Humans are embedded in contexts – so certain background conditions will apply to various utterances at whatever point in time. So when we speak to each other, we are not just attuned to the explicit truth-conditions of an utterance, but also to the background conditions. We hear “that man’s name is ‘Smith'” – but we know that this is true (as per truth-condition [4]) only if “Smith” refers to Smith (the man indicated by the demonstrative ‘that’). So we know that we have heard Smith’s name, provided that the utterance is true.

If we wish to maintain that “that man’s name is ‘Smith'” tells you the name of “that man”, then we must recognize that background truth-conditions, not just the explicit truth-conditions of the utterance, contribute to the meaning of the utterance. When analyzing the meaning of an utterance, we should also assess the background truth-conditions to get the most complete picture.