Indirect self-reference

Indirect self-reference describes an object referring to itself indirectly. For example, the "this sentence is false." contains a direct self-reference, in which the phrase "this sentence" refers directly to the sentence as a whole. An indirectly self-referential sentence would replace the phrase "this sentence" with an indirect reference; and expression that effectively still referred to the sentence, but did not use the pronoun "this."

Indirect self-reference can be defined rigorously in terms of cycles in a graph of reference relationships.

An example of this is the postcard paradox, in which a sentence refers to another sentence which in turn references the original one.

Indirect self-reference was studied in great depth by W. V. Quine and occupies a central place in the proof of Gödel's incompleteness theorem.

See also

• Diagonal lemma – Statement in mathematical logic
• Fixed point (mathematics) – Element mapped to itself by a mathematical function
• Fixed-point combinator – Higher-order function Y for which Y f = f (Y f)
• Gödel, Escher, Bach – 1979 book by Douglas Hofstadter
• Indirection – Computer programming construct
• Quine's paradox – Logical paradox concerning truth values
• Self-hosting (compilers) – Software that can produce new versions of itself
• Self-interpreter – Software that executes encoded logicPages displaying short descriptions of redirect targets