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Everything about Extensionality

Logic principle

In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal definitions of objects are the same. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: ExtensionalityA 5-minute orientation
  2. Skim a recent paper: Identity and Extensionality in Boffa Set TheoryInfluential work since 2022
  3. Pick up a classic book: Understanding MediaThe most-reprinted book on the subject
  4. Read the landmark paper: Suppositions, extensionality, and conditionals: A critique of the mental model theory of Johnson-Laird and Byrne (2002).Cited 90 times
  5. Go sideways: Homotopy type theoryA closely related topic
  6. Go sideways: Uniqueness of identity proofsA closely related topic

📖 Definitions

Noun The principle that objects are equal if and only if their observed properties are the same, regardless of internal processes that lead to those properties.

Noun The principle that functions are equal if and only if they operate on the same domain and for any given element of the domain the result of each of the functions is the same.

Noun The principle, codified in the axiom of extensionality, that sets are equal if and only if they contain the same elements.

🗂️ The subject at a glance

  1. In mathematics
  2. Extensionality principles
  3. Example

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics