1
A description asserts three things
“The F is G” says that something is an F, that nothing else is an F, and that the one thing that is an F is G. All three are part of what is said, and each can fail.
Lesson · Mind, Language and Meaning · Language
Definite Descriptions and the Present King of France
“The present King of France is bald” looks like a sentence about a king, and there is none. Russell reads it as a claim that there is exactly one king and that he is bald. Evaluate that expansion in a model for the three cases, and see where Strawson disagrees about what to call the result.
the F is G = one F, and it is G
there is an F, at most one F, and G
no F: Russell says false
two Fs: false, even if both are G
Strawson: a failed presupposition
A description is a claim, not a name
Core ideas
What this lesson establishes
The previous lesson let a name point at an individual. A description such as “the king” looks like a name, and Russell's claim is that it is not one.
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Three cases
The F can be there once, not at all, or more than once. Only the first can make the sentence true, and the other two make the expansion false by different clauses.
3
Russell and Strawson read the second case differently
Russell calls the sentence false, because its existence clause is false. Strawson says the sentence presupposes a king, and if there is none the question of truth does not arise. They agree about the model, and differ on the name for the result.
The material
Expanding a description
The expansion, the three models that fit it, and the dispute over the empty one.
Definition · Definite description
A definite description is a phrase of the form “the F”, such as “the author of Waverley” or “the present King of France”. It is used to speak of one thing by saying what that thing is like.
On the surface a description behaves like a name: “the King of France is bald” has a subject and a predicate and seems to be about the king. The trouble is that there is no king, and a sentence cannot be about a thing that is not there. If it is meaningful, as it plainly is, then either there is some such thing, or the surface form misleads.
Russell's analysis holds that the surface misleads. “The F is G” is a quantified sentence with three clauses.
∃x ( F(x) ∧ ∀y ( F(y) → y = x ) ∧ G(x) )
Read it as: there is an x that is an F, any y that is an F is that x, and that x is G. The first clause says there is an F, the second that there is no more than one, and the third says what the one is like. The lab takes a phrase of the form “the x such that F holds of x”, followed by the predicate G, and expands it this way.
Three models cover the cases. In the first, the domain has individuals a, b and c; Author holds of b alone, and Scot holds of b and c. The description picks out b, the one and only author. b is a Scot, and the sentence is True, with the description denoting b.
In the second, King holds of nobody, and Bald holds of a. The first clause fails: no x is a king. Whatever the third clause says, the conjunction cannot hold, and the lab prints False. It also reports that the description denotes nothing, which is the fact Strawson builds on.
In the third, King holds of a and of b, and both are bald. The first clause is met. The second is not, since b is a king and is not a, and the lab prints False, reporting that the description is not unique, and naming a and b. That both kings are bald does not help, because the sentence claims there is just one.
Now the dispute. Strawson's observation is about what people say. Asked whether the present King of France is bald, almost no one answers “no”; they say there is no such king. The sentence, he held, presupposes that there is a king, and when the presupposition fails the sentence is neither true nor false. Russell's reply is that the sentence does say that there is a king, so it is false, as “there is a king who is bald” is false. The lab computes only the expansion, so it prints Russell's False in the value tile, and in the tile for the description it prints the fact on which Strawson relies. Which tile to treat as the sentence's status is the philosophical choice, and it is not one the arithmetic makes for you.
What the expansion buys is a way to say that the sentence is meaningful although nothing is denoted: the description was never a name, only a bundle of claims. Its price is a complication for the grammar, since “the King of France” no longer behaves as a single phrase. The next lesson turns that complication into a second reading.
Interactive
Truth in a model
A first-order sentence evaluated over a domain you can edit
Method
Evaluating a description
Five steps. The description tile is the one to read first.
1
Pick out the restrictor
In “the F is G” the F is the descriptive part. List the individuals of the model that satisfy it.
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Count them
None, one or several. This is the case, and it decides which clause of the expansion can fail.
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Apply the three clauses
There is an F; there is no more than one; it is G. All three are needed for True.
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Read the value as Russell does
A missing F and a doubled F both make the expansion False, by different clauses. Say which.
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Say what Strawson would say
For an empty description, the presupposition has failed. State the disagreement as one about what to call the result, not about the model.
The three cases
Score 0 / 0Choose the answer you can justify.
The present King of France is bald
Russell's expansion, applied to a model in which King holds of no one.
claim: ∃x ( King(x) ∧ ∀y ( King(y) → y = x ) ∧ Bald(x) )
model: King holds of nobody, Bald holds of a
clause 1, something is a king: no x, False
the conjunction cannot hold: False
description tile: denotes nothing
Russell: False. Strawson: presupposition fails
Both readings of the same fact are available at once. The expansion gives False because its first clause is false, and the description tile says the same thing in Strawson's words. The lab does not choose between them.
Common mistakes
1
Saying the sentence has no truth value on Russell's accountIn the model with no king the lab prints False for Russell's expansion, because its first clause asserts a king. It is Strawson who withholds a value, and the description tile shows the fact he does so on. The mistake mixes up the two positions, and is common because the sentence still strikes most people as odd to call false.
2
Thinking that a doubled description is true if every F is GWith two kings, both bald, the lab prints False and lists both. The expansion has a uniqueness clause, and “the” is what puts it there. Every king being bald is a different sentence.
3
Treating a description as a name that happens to failA name points at an individual of the model, and a name with no individual is a model error. A description is evaluated by looking at the extension of its restrictor, which may be empty, and an empty one makes the sentence false rather than making it unparseable.
Check your understanding
✓
Finish when you can expand a description and name the clause that fails.
Given a sentence of the form “the F is G” and a model, you should be able to write Russell's three clauses, evaluate them, say whether the description denotes one thing, nothing or several, and state what Strawson would call the empty case.
Note: Whether ordinary speakers use descriptions as Russell says is a question about language use that this lesson does not settle; Strawson and later writers argued it does not fit. What the lesson teaches is the analysis as something with a checkable value.