Indirect self-reference
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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."[1]
Indirect self-reference can be defined rigorously in terms of cycles in a graph of reference relationships.[2]
An example of this is the postcard paradox, in which a sentence refers to another sentence which in turn references the original one.[1]
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.[3]
See also
[edit]
- 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 logic
References
[edit]- ^ a b Bolander, Thomas (2024), Zalta, Edward N.; Nodelman, Uri (eds.), "Self-Reference and Paradox", The Stanford Encyclopedia of Philosophy (Fall 2024 ed.), Metaphysics Research Lab, Stanford University, retrieved 2025-12-05
- ^ Bolander, Thomas (2005). "Self-reference and logic" (PDF).
- ^ Silva, Matheus (December 1, 2025). "On the circularity of Gödel's incompleteness proofs". philarchive.org. Retrieved 2025-12-05.