SelfReference

Self-reference is the relation by which an element refers to itself. It can occur directly, by stating that the sentence or object refers to itself, or indirectly through a chain of references. Self-reference is a common feature across many disciplines, including language, logic, mathematics, computer science, philosophy, and the arts.

In language and logic, self-reference can generate paradoxes. The classic liar paradox asks whether the sentence “This sentence is false” is true or false, leading to a contradiction if it is either. Self-reference underlies diagonalization arguments and Gödel’s incompleteness theorem, where a statement asserts its own unprovability. Philosophical work also examines how truth and meaning operate when sentences refer to themselves, and how truth predicates can be modeled in formal systems.

In mathematics and computer science, self-reference appears in recursive definitions and fixed points. The recursion theorem guarantees the existence of self-reproducing constructs. A well-known computational form is the quine, a program that outputs its own source code. Self-reference also motivates concepts such as bootstrapping and self-hosting compilers in programming languages.

In linguistics, self-reference is studied in pronouns and in autological words—terms that describe themselves, such as “short” when used to describe its own length. In philosophy and aesthetics, self-reference is a motif in self-reflexive art and metafiction, where works draw attention to their status as artifacts rather than merely their subject matter.