> [!Cite]- Metadata > 2025-07-22 20:26 > Status: #concept #philosophy > Tags: `Read Time: 3m 8s` ### One-Sentence Summary > Coextension is the state or condition in which two or more terms, objects, or concepts have the same extension, meaning they apply to exactly the same set of entities or occupy the same range in space or duration. --- ### Definition(s) and Key Terms - **Extension:** The set of all objects or instances to which a term or concept applies. - **Coextension:** Mutual relation of two or more terms having the same extension; i.e., they refer to exactly the same things or cover the same spatial or temporal range. - **Intension:** The intrinsic meaning or concept of a term, distinct from its extension. - **Coextensive terms:** Terms that have identical extension but may differ in intension. - **Reference:** The actual entities in the world that a term stands for. - **Equality of extension:** Another phrase referring to coextension, meaning equal range or coverage. --- ### Core Components or Principles - **Mutual sharing of extension**: Two or more terms cover the exact same objects or region. - **Equality in space or time:** Coextension can apply to physical extension (occupying the same space or time) or logical extension (same set of instances). - **Non-identity of intension:** Coextensive terms may differ in meaning or definition but still refer to the same entities. - **Logical relation:** Used especially in logic and philosophy of language to analyze reference and meaning. --- ### Origins and Historical Context - The concept dates back to early modern philosophy and logic, with roots in the distinction between intension (conceptual content) and extension (referential domain). - The term coextension combines the Latin prefix co- ("together") with extension, reflecting equal or shared extension. - First documented in English usage in the late 1600s; later formalized in logic and semantics during the 19th and 20th centuries. - Prominently discussed by logicians and philosophers such as Carnap, Quine, and Kripke, particularly in relation to meaning, reference, and extensionality vs intensionality. --- ### Interdisciplinary Connections | Discipline | Connection / Application | | -------------------------- | ---------------------------------------------------------------------------------------------------------------- | | **Logic** | Analysis of terms, predicates, and propositional extension in formal semantics. | | **Philosophy of Language** | Study of meaning, reference, synonymy, and the distinction between intension and extension. | | **Mathematics** | Concerned with set theory where coextensive sets have identical elements. | | **Linguistics** | Semantics of words and phrases that are coextensive but differ in connotation or context. | | **Law and Politics** | Coextension of rights or powers over individuals or bodies politic[](https://www.wordnik.com/words/coextension). | --- ### Critiques and Debates - **Equivalence vs. meaning:** Coextension shows that identity of reference does not guarantee identity of meaning (intension), raising issues about synonymy and conceptual content. - **Non-intensional contexts:** In some logical or linguistic contexts, coextensive substitution can fail (e.g., belief reports), highlighting the limits of coextension for explaining meaning. - **Extension vs. Intension debate:** Critics emphasize that coextension neglects the cognitive or conceptual differences despite referential equality. - **Practical ambiguity:** In real-world usage, terms may appear coextensive but differ subtly, leading to disputes over the precise range or applicability. --- ### Applications - **Semantic analysis:** Understanding how different linguistic expressions relate by their referents. - **Logical equivalence:** Identifying coextensive predicates helps simplify or analyze logical formulas. - **Philosophical argumentation:** Used to clarify issues like identity, substitution, and the nature of truth conditions. - **Legal reasoning:** Coextension of rights or jurisdictions clarifies extent of authority or responsibility. - **Taxonomy and classification:** Grouping objects or concepts by identical extension even if named differently. --- ### Case Studies and Examples - "The Morning Star" and "The Evening Star" are coextensive terms because both refer to the planet Venus, despite differing in linguistic intension or conceptual meaning. - "Cicero" and "Tully" – different names (intensions) but coextensive since both denote the same individual. - "Triangle" and "Three-sided polygon" are coextensive classes in geometry. - Legal powers in bodies politic may be coextensive regarding individuals authorized to exercise them, despite different conceptual definitions. - **Logical predicates:** If predicates A and B pick out exactly the same objects in a domain, they are coextensive even if defined differently. --- - What surprised me? - How does this reshape my thinking? - What new questions arise from this? --- ### **Resources** [coextension - definition and meaning](https://www.wordnik.com/words/coextension) [COEXTEND Definition & Meaning | Dictionary.com](https://www.dictionary.com/browse/coextend) [Coextensive - Philosophy Dictionary of Arguments](https://philosophy-science-humanities-controversies.com/listview-list.php?concept=Coextensive) [COEXTENSION definition and meaning | Collins English Dictionary](https://www.collinsdictionary.com/dictionary/english/coextension) [Coextension Definition by Webster's](https://www.smartdefine.org/coextension/definitions/1988739) [coextension, n. meanings, etymology and more | Oxford English Dictionary](https://www.oed.com/dictionary/coextension_n?tl=true)