---
tag: KWEV8CBKC9
kind: statement
role: proposition
name: Sloppy versus strict identity in ellipsis
sources:
  - wikipedia: en:147460@r1376140548
    locator: Free variables and bound variables, section Natural language > Sloppy versus strict identity in ellipsis
    note: adopted
    mention: wikipedia://en/147460#H5IR
    sections: [Statement]
inventory: [C0PXRNGVQD]
---

## Statement

The distinction between free and bound variables provides a powerful explanation for certain ambiguities that arise under VP-ellipsis. Consider the following sentence:

John loves his mother, and Bill does too.

This sentence has two distinct interpretations:

1. **Strict identity:** Bill loves *John's* mother.
1. **Sloppy identity:** Bill loves *Bill's* mother.

This ambiguity can be explained by the status of the pronoun *his* in the first clause.

- If *his* is treated as a **free variable** referring to John, the elided (or "missing") verb phrase is interpreted as "loves John's mother". When this is applied to Bill, the result is the **strict** reading.
- If *his* is treated as a **bound variable** bound by the subject of its clause (i.e., *John*), the verb phrase is interpreted as a lambda-abstracted property: `λx.x loves x's mother`. When this property is applied to Bill, the result is the **sloppy** reading.

The existence of the sloppy identity reading is considered strong evidence for the psychological reality of bound variable interpretations in the grammar of natural languages.

Thus, the distribution and interpretation of pronouns and other referring expressions in natural languages are not random but are governed by a sophisticated syntactic and semantic system.

The distinction between free and bound variables is a cornerstone of modern linguistic theory, providing the analytical tools necessary to account for coreference, quantification, question formation, and ellipsis.