What is the truth-value of the following statement?

(1) “The present king of France is bald.”

The State of Play

In this post I will explain why this kind of sentence does have a truth-value. This is a preliminary response in that I have not read any literature specific to this question. Rather, a while ago the question was posed to me, and it hasn’t been until now that I have taken the time to give it any real consideration.

Trivially, the sentence, “the present king of France is bald” cannot be true. This is because, as we are all well aware in the 21st century, France has no king. Consequently the sentence cannot be true, for it is true if and only if there is a present king of France who is in fact bald. And so we are left with two options. Either the sentence is false or the sentence lacks any truth-value whatsoever.

It is potentially illuminating to consider another, slightly different sentence, for comparison. Assume that that there does not exist an escalator in South College.

(2) “John is on the escalator in South College.”

Now ask yourself, is (2) true, false, or neither? Like (1), (2), trivially, cannot be true, for (2) is true if and only if John is in fact on the escalator in South College, which is impossible as the escalator in South College does not exist. So again we are left with two options. Either (2) is false or else it lacks a truth-value whatsoever.

If your intuitions are anything like mine, you will suspect that (1) lacks a truth-value (and so is not false), while (2) is, in fact, a false statement. We will see if this is so.

On Subjects and Predicates

Before we begin, it is useful to analyze and characterize the relevant subjects and predicates, how they work, and how they relate to each other.

In (1), there is a subject, “the present king of France”, and a predicate, “is bald”. And in (2), there is a subject, “John”, and a predicate, “is on the escalator in South College”. Typically a subject is some kind of individual (or object). A predicate should be thought of as a set, not an object. The predicate, “is bald”, denotes the set of all objects that are bald. So when we say that “the present king of France is bald”, we are asserting that the object denoted by the determinative-phrase, “the present king of France”, is an element of the set of all bald things. Predicates, like “is on the escalator in South College”, may consist in determinative-phrases, such as, “the escalator in South College”. This does not change their status as predicates, for a legitimate set is still defined for which any object may be tested or assessed for membership.

A Closer Look at John and the King of France

As another preliminary matter, we should make explicit the truth-conditions for both (1) and (2).

(1T) “The present king of France is bald” is true iff the present king of France is bald.

(2T) “John is on the escalator in South College” is true iff John is on the escalator in South College.

The present king of France cannot be bald, for there does not exist a referent for “the present king of France”. And John cannot be on the escalator in South College, for that escalator does not exist. Does it follow from this that (1) is false? Certainly not immediately. For if (1) is false, then its negation must be true. The negation of (1), and its corresponding truth-condition, is:

(-1T) “It is not the case that the present king of France is bald” is true iff the present king of France is not bald.

[For the sake of continuity, we include the negation and corresponding truth-condition of (2), as well:]

(-2T) “It is not the case that John is on the escalator in South College” is true iff John is not on the escalator in South College.

Now we ask, is (-1) true? Assuming that (1) is false, it is logically necessary that (-1) is true. But here we run into the same quagmire as (1). It cannot be the case that the present king of France is not bald, because there is no present king of France to which the predicate can be applied. So (-1) is either false or lacks a truth-value. But if (-1) is false, then (1) must we true — and (1) we know to be false. (-1) and (1) cannot both be false, for this flouts the law of noncontradiction. And neither one can be true. This strongly suggests that both (-1) and (1) lack truth-values.

And again for continuity, is (-2) true? Because there exists no escalator in South College, the set defined by “is on the escalator in South College” will necessarily have no actual elements. So John cannot be a member of that set. Consequently, it is true that John is not a member of that set. So (-2) has a truth-value, namely True. Therefore it is logically necessary that (2) is false. Though this is consistent with our initial intuitions, it suggests a nontrivial difference between sentences of kind (1) and sentences of kind (2). We may consider these differences later.

Consideration of Logical Form

But let’s take a closer look at the logical form of (1).

(1L) There exists an x such that x is the present king of France and x is bald. Or .

And its negation:

(-1L) It is not the case that there exists an x such that x is the present king of France and x is bald. Or, .

Now we ask, is (-1L) true? Well it is true that there does not exist an object that is both bald and the present king of France. And this seems to be exactly what (-1L) says. So intuitively, (-1L) is true. But then it is logically necessary that (1L) be false.

And now we’re in a real pickle. On our first level of analysis we found that a sentence like (1) must lack truth-value. But on our logical level of analysis, we find that sentences like (1) must have a truth-value (namely, False). We cannot have it both ways. And since the disjunction of both analyses exhausts the realm of possibilities, one of the two must be right.

Note we could also express (1) with a universal:

For all x, if x is the present king of France, then x is bald. Or,

And on this rendition, (1) is actually vacuously true! No x is the present king of France, therefore it all x is -Fx which means that the antecedent of the material conditional is always false and so the entire conditional is always true.

We will have something to say about this.

Picking up the Pieces

There must be a difference between (1) and (1L). This difference is in what I will refer to as “the assertive content” of the statements (1) and (1L). Here is the literal translation of 1L:

(3) Something is the present king of France and bald.

And this is a far cry from (1), “the present king of France is bald”. Why? Statement (3) consists in a subject, “something”, and is ascribed a predicate that is the conjunction of two sets, namely the set of present kings of France and the set of all bald things. But (1) consists in a subject, “the present king of France”, and a single predicate, “is bald”. Consequently, these two statements differ in assertive content. (3) asserts the existence of an object which is an element of both the aforementioned sets. (1) does not explicitly assert the existence of a present king of France, rather what is explicitly asserted is just that the present king of France is an element of the set of all bald things. The existence of the present king of France is presupposed (and, consequently, not asserted).

What does it mean to presuppose the subject? Existence is not a predicate. Predicates stand for the properties of subjects, and no subject has the property of existence. A subject either exists or it does not, but its existential status is not a property of the subject qua the definition of the subject. For instance, we can define God as omniscient, omnipotent, and omnibenevolent. But we cannot include in our specification that God, in addition to having the properties of the three O’s, also exists. Defining God to have the property of existence does not make it such that God exists. This is because, in ascribing properties (or predicates) to a subject, we must presuppose the existence of that subject. In order to ascribe the three O’s to God, I must presuppose the existence of God. So the ascription of predicates to entities of dubious existence amounts to something like a conditional statement: If so-and-so were to exist, then it would have such-and-such properties. And this especially highlights the fact existence is not a predicate, for consider: If so-and-so were to exist, then it would have the property of existence. And this is a tautology.

Because no such object exists, contrary to (3)’s explicit assertion, we intuitively found it false. Because the existence of the present king of France is not explicitly asserted in (1), there was no explicit phrase which could entail the falsity of (1) (for [1] seems to presuppose a present king of France prior to [1]’s assertion). (1) and (3) differ in assertive content, this difference accounts for our differing intuitions. But this raises a new question. Are we to interpret (1) in the manner of (3)? That is, if Donald Trump, in conversation with you, said “the present king of France is bald”, should you think you had been told something false or should you think that Trump has said something that is simply neither true nor false?

This question acknowledges our conclusion that the truth-value, or lackthereof, of statements like (1) is determined by the particular level of analysis we bring to bear. But it raises a pragmatic point, on what level of analysis do we interpret the utterances of others in our day-to-day conversations?

The Pragmatic Point

This section marks a departure from our original question. It seems we are headed toward some contemporary debates in pragmatics and the theory of meaning. It is not my intention to wade through any of these arguments. Instead, I will sketch out why I think that, if someone were to assert (1) in conversation, they would assert something false, rather than something sans-truth-value. The following is primarily influenced by John Perry’s theory of meaning. (A theory which I think has many virtues. Though my own views are unsettled.)

Interpreting meaning in conversation is significantly distinct from assessing the meaning (that is truth-conditions [or truth-value, depending on who you ask]) of a statement in isolation. This distinction stems from the interaction of two fields, viz. semantics and pragmatics. Semantics aims to understand the truth-functional structure of language — that is, how each lexical item (or word) in a sentence directly contributes to the meaning of a sentence by way of truth-functional application. Pragmatics, on the other hand, seeks to understand language (and meaning) insofar as a language is a way of doing things with words. Conversation is an activity, not a rigid exercise in isolated truth-functional application. In conversation we try to do things like change each others’ beliefs, get somebody to do something (like pass you the salt), or share information. And when we share information, we do so with the understanding that our interlocutor has a unique set of pre-existing beliefs, modes of presentation, and ways of thinking about the world (that is, the relations between his or her concepts). In light of this, meaning in pragmatics will be more dynamic than meaning in semantics.

In conversation (the domain of pragmatics), we do not interpret only the explicit, assertive content of another person’s utterance. We are sensitive to myriad background and contextual factors in determining speaker-meaning. For example, you exit the airport in the Basque country. A man approaches you and utters the sound “/ninaizdjon/”. He means something by his sounds, but before we can assess the meaning or truth-conditions we need some more information. Suppose I think that the man is speaking English. In that case, I take him to have said “Nina is John”. This is a puzzling statement — it is not often that a person two names, let alone both a feminine and a masculine name. Perhaps we were wrong to think that the man was speaking English. Suppose we had some understanding of the Basque language. When the man says, “/ninaizdjon/”, and I interpret him as speaking Basque, then I will take the man to have said, “Ni naiz John” (which, in English, is “I am John”). Conversation doesn’t enjoy the luxuries of print; in print we can easily determine the language and parse sounds (for they are, more or less, already parsed for us on the page), but in conversation we are subjected to a constant stream of phonemes and so must bring some background, interpretive theory to make sense of an otherwise disorienting stream of sound.

This demonstrates our sensitivity to background conditions and contextual factors. When we place the “is speaking English”-background condition on the man’s utterance, we end up with a sentence that is true if and only if “Nina” and “John” co-refer. But when we place the “is speaking Basque”-background condition on the man’s utterance, we end up with a sentence that is true if an only if the man is named ‘John’. Nothing in the isolated sound “/ninaizdjon/” can help us determine which of the two aforementioned background conditions is salient/relevant/appropriate/what-have-you. We cannot determine the meaning without making this choice; context may affect meaning just as much as isolated semantics. Here is another example. Suppose that some time ago, Quine said “Cicero wrote beautiful prose”. The utterance, “Quine said that Tully wrote beautiful prose”, will true if and only if, as a background condition, Quine believes that “Cicero” and “Tully” co-refer to the same object. For if he did not have this belief, then we would be misattributing a Tully-belief to Quine when Quine has only Cicero-beliefs. If we were attuned only to the explicit content of an utterance, we would miss out on or be mistaken about the actual meaning of another person’s utterance. We would incorrectly assess the truth of the utterance “Quine said that Tully wrote beautiful prose”.

An utterance like (1) presupposes the existence of the subject which takes on a predicate. But in ordinary conversation, that presupposition places a background truth-condition on the utterance. The background truth-conditions of an utterance directly contribute to the judgment of the truth-value of that utterance. So (1) is subject to the following truth conditions.

The explicit (1T): “The present king of France is bald” is true iff the present king of France is bald.

The background: AND iff there exists a present king of France (or, alternatively, there exists an individual uniquely denoted by the determinative-phrase “the present king of France”).

AND iff (1) is a sentence in English

(1) is true iff both the explicit and the background are true. Because the existential-background truth-condition is not satisfied, (1) is not satisfied, and so (1) must be false.

To reiterate, one last time, the findings of this post: In an isolated context a sentence like (1) will not have a truth-value. But language is used in varying contexts, and in its use, there must be some additional background truth-conditions which are not explicitly contained in the assertive content of the sentence. An example of such a background condition will be the existence of the presupposed subject, the present king of France. I hope that my response to our initial question doesn’t come across as a sort of “Well, it does and it doesn’t”. I am more inclined toward pragmatic accounts of meaning rather than semantic; so to be unequivocal: if Trump says, “the present king of France is bald”, he would be asserting something false.

As a sort of post-script, I would like to note that when I began writing this, I intended to argue that sentences like (1) have no truth-values. When I almost finished, I changed my mind and came to the here-written conclusions.

I should also note that there are conversational contexts where one could say, “the present king of France is bald” without necessitating the existential-background truth-condition. If I am in a conversation with Trump, and we have both already acknowledged the fact that there is no present king of France, then later in our conversation, when Trump says “the present king of France is bald”, I will know that he does not mean to assert or imply the existence of the present king of France. (This is because I know that he knows there the present king doesn’t exist, and so will not mean to say as much.) In light of this, one possible interpretation of Trump might be, “if there were a king of France in the present day, he would be bald”. (Perhaps Trump is making a point about the dangers of contemporary aristocratic French diet, or perhaps he means to say that the genetic line of French kings is prone to premature baldness.)