Use and Mention

Consider these two sentences:

Paris is a city.

“Paris” has five letters.

They look similar.

They are about different things.

In the first sentence, the word Paris is used to refer to a city.

In the second, the expression “Paris” is mentioned as a word.

This is the use–mention distinction.

It is simple.

It is essential for logic, language, and self-reference.

Using a Word

When we say:

Cats are mammals.

the word:

cats

is being used.

It refers to animals.

The sentence is about cats.

Mentioning a Word

When we say:

“cats” has four letters.

the quoted expression is being mentioned.

The sentence is not about animals.

It is about a linguistic object.

Quotation Marks

Quotation marks commonly signal mention.

Compare:

Snow is white.

and:

“Snow” has four letters.

The first speaks about snow.

The second speaks about a word.

Quotation moves us to a meta level.

Object Language

The language being discussed is called the object language.

Suppose we analyze English grammar.

English expressions are the objects of study.

Metalanguage

The language used to describe the object language is the metalanguage.

If we use English to describe English, the same natural language plays both roles.

The levels are conceptual even if the vocabulary overlaps.

Example

Object-language statement:

Snow is white.

Metalanguage statement:

“‘Snow is white’ contains three words.”

The second talks about the first.

The shift of level prevents confusion.

The Word Is Not the Thing

A word and its referent have different properties.

A tiger has claws.

The word “tiger” does not.

The word “tiger” has five letters.

A tiger does not.

Confusing levels produces absurd conclusions.

Autological Words

Some words describe themselves.

For example:

“English” is English.

“polysyllabic” is polysyllabic.

These are sometimes called autological words.

They blur the ordinary gap between expression and property in playful ways.

Heterological Words

A word is heterological if it does not describe itself.

“monosyllabic” is not monosyllabic.

This leads to a famous paradox when we ask:

Is “heterological” heterological?

The problem resembles the Liar.

Quotation Names

A quoted expression can function as a name of that expression.

For example:

“dog”

is a name for the three-letter word dog.

Formal logic often needs precise naming devices for expressions.

Mention Without Quotation

Quotation marks are not the only way to mention.

We can say:

The word dog is common.

Here, context makes clear that dog is being discussed as a word.

Formal systems use more exact conventions.

Variables Over Expressions

A metalanguage can use variables that range over:

• formulas,
• sentences,
• strings.

This allows general claims about syntax.

For example:

“If formula (A) is provable…”

Now the system discusses expressions abstractly.

Syntax as Object

Once expressions can be mentioned, syntax becomes an object of mathematics.

We can ask:

• Is this string well formed?
• How long is it?
• Is it provable?
• Which symbols occur?

Language becomes data.

Programs as Mentioned Objects

A compiler does not merely execute source code.

It reads code as data.

The source program is mentioned, in a computational sense, by the compiler.

Code can be manipulated before being executed.

Eval

Some programming languages provide operations that turn data into executable code.

A string may be interpreted as a program.

This shifts between:

mention-like representation

and

use-like execution.

Such operations are powerful and potentially dangerous.

Quines

A quine is a program that outputs its own source code.

To do this, the program must somehow bridge:

• code used as instruction,
• code represented as data.

The use–mention distinction becomes computationally concrete.

Natural-Language Confusion

Many everyday misunderstandings arise from confusing words with what they refer to.

For example:

“The word ‘unicorn’ exists, therefore unicorns exist.”

The inference is invalid.

Existence of a word does not imply existence of its referent.

Names and Objects

Likewise:

“Sherlock Holmes” appears in books.

Sherlock Holmes is a fictional detective.

The name exists as a linguistic object.

The fictional character exists in another representational sense.

These levels must be distinguished carefully.

Truth Predicates

Suppose we write:

“‘Snow is white’ is true.”

The inner quotation mentions a sentence.

The outer language applies the predicate:

is true.

Truth predicates create strong interaction between object and meta levels.

This is where paradox becomes dangerous.

Tarski’s Strategy

Alfred Tarski analyzed truth using a hierarchy of languages.

An object language contains ordinary statements.

A metalanguage contains a truth predicate for those statements.

Keeping levels separate helps avoid semantic paradoxes.

We will return to Tarski much later in metalogic.

Self-Mention

A sentence may mention itself indirectly.

For example, a sentence can be constructed to say something about the expression that encodes it.

Formal self-reference often depends on turning expressions into objects that can be named.

Use–mention is therefore foundational to Gödel’s technique.

Labels

Suppose sentence S says:

S is false.

The label S names the sentence.

Now the language can refer to its own statement through a naming mechanism.

Self-reference need not use the phrase “this sentence.”

Type Errors in Philosophy

Some philosophical confusions resemble programming type errors.

A property of a representation is incorrectly assigned to the represented object.

Examples:

map is folded

therefore territory is folded.

word is long

therefore object is long.

Use–mention discipline acts like type checking.

The Philosophical Lesson

Symbols have two lives.

They can be:

• used to refer beyond themselves,
• mentioned as objects in their own right.

Self-reference becomes possible when a system can move between these levels.

Paradox becomes possible when the boundaries are not controlled.

The Next Question

The use–mention distinction points toward a broader warning.

A word is not its referent.

A model is not its target.

A representation is not what it represents.

The next essay expands this principle:

the word is not the thing.