# Binding theory - coindexes that produce grammatical sentences

Binding Principle C states that an R-expression must be free.

Consider the following sentence:

[Steven King]i is [Richard Bachman]i.

(Richard Bachman is Steven King's pen name)

The sentence is grammatical, but violates Principle C.

How can binding theory explain this? I was thinking that context and extra syntactic information might have something to do with it, or perhaps that the indices are not necessary.

• That is not a binding problem, because both expressions are referential. In Frege's terms, [Steven King] and [Richard Bachman] have different senses, but the same meaning/reference/denotation, as they point to the same person, but in slightly different senses. Commented Sep 26, 2014 at 8:09
• Equative sentences like your "Steven King is Richard Bachman" aren't a problem for binding theory. You correctly state that an R-expression must be free. To be free is to not be bound. An R-expression is bound if it is c-commanded by a co-indexed expression. Since 'Richard Bachman' is c-commanded by an expression indexed 'i', condition C dictates that it must be given a distinct index, say 'j'. Expressions refer by way of a function which maps their indices to entities in the world. There is nothing preventing the function from mapping both 'i' and 'j' to the same entity. Commented Sep 28, 2014 at 15:13
• To sum up my previous comment, binding theory is stated in terms of co-indexation, not co-reference. Co-reference follows from co-indexation, but contra-indexation is compatible with both co-reference and contra-reference. Once this is acknowledged, the problem dissolves. Commented Sep 28, 2014 at 15:14

Thomas Gross' comment above is on target. Nouns and pronouns (and other linguistic categories) have both identity of sense and identity of reference. The default situation sees a pronoun adopting both types of identity from its antecedent, e.g.

` A. Fredi likes hisi meal.`

The definite pronoun his takes both types of identity (reference and sense) from its antecedent Fred. The traditional binding theory (Principles A, B, and C) from the 1980s was developed to address the distribution of pronouns (reflexive, reciprocal, and personal), whereby the theory was not generally distinguishing between these two types of identity.

Definite pronouns (e.g. he, she, it, etc.) have an identity of reference that they adopt from another entity in context, and the standard case is for them to also adopt identity of sense from the same entity. There are many cases, however, where there is divergence, i.e. the pronoun adopts the identity of reference of an antecedent (or postcedent), but it does not adopt the identity of sense of that antecedent, e.g.

``` B. Shei is my friendi.

C. My friendi is heri. (Pointing at someone across the room)```

Example B violates principle C of the traditional binding theory, and example C violates principle B thereof. These violations are, in fact, not really violations because they involve a divergence of the two types of identity. In each sentence, the coindexed expressions have the same identity of reference, but they have distinct identities of sense.

The word one in English is the stereotypical example of a pronoun that takes only identity of sense from its antecedent (or postcedent), e.g.

`````` D. Tom read a book, and Sam read one, too.

``````

Sentence D has the indefinite pronoun one adopting just the identity of sense from its antecedent a book (a book, but a different book), whereas sentence E has the definite pronoun it adopting both the identity of sense and the identity of reference from a book (the same book).

The example in the question illustrates this same divergence of the two types of identity:

`````` F. Steven King is Richard Bachman.
``````

The two names Steven King and Richard Bachman have the same referential identities, but distinct identities of sense. The traditional binding theory, when it is presented in a superficial manner, does not distinguish between these two types of identity. This is the source of the confusion expressed in the question.

A purely syntactic answer starts by pointing out that Principle C of binding theory, as the other ones, should not be confused with a law of nature. It is more properly a rather vague description of a general tendency of human languages and it is in the course of trying to formulate it more precisely that we expect to find interesting phenomenons, examples and counter-examples.

Now onto your more precise question. Nowadays, the formalization of linguistics which consider the questions of binding to be important have (unanimously, as far I know) rejected the use of indices except as convenient book-marking device, and this is especially true of the most direct descendant of the theory which produced the principles of binding theory you refer to in the first place (minimalist syntax). So you are right that indices are not necessary (and might even be misleading). As to how your example would be treated, my first remark is that the current implementation of binding theory that I consider the best ultimately relates binding phenomenon to the properties of transitive verbs so does not consider binding effects (or the lack thereof) in equative sentences as reflecting the same fundamental properties.

Nevertheless, you could have a look at chapter 3 and 4 of this book for interesting comments on the structure of equative sentences and in particular for the claim that such equative sentences in fact involves inversion of a complex structure and (roughly and informally) always have the structure of

What Stephen King is, is Richard Bachman.

If you are convinced by this proposition, then it follows that such sentences are not clear cut violations of Principle C, just like

Feeling proud of himself, he left the room.

is not a violation of Principle A. Further enquiries (within that framework) would entail investigating the syntactic properties of the functional head Den Dikken calls a Relator; an interesting syntactic question, in fact.