Category: logic
Type: paradox
Associated thinker(s): Kurt Grelling, Leonard Nelson
Original publication or approximate period: Grelling and Nelson, “Bemerkungen zu den Paradoxien von Russell und Burali-Forti” (1907; a 1908 reprint is also listed)
Difficulty: Intermediate
Themes: self-reference, semantic paradox, predicates
Related experiments: Russell’s Paradox; The Liar Paradox
Call an adjective autological if it applies to itself: “polysyllabic” has several syllables. Call it heterological if it does not: “monosyllabic” has several syllables, so it is not monosyllabic.
Now ask whether “heterological” applies to itself. If it does, then by definition it does not; if it does not, then by definition it does. The contradiction follows if this definition is allowed to apply to the adjective itself and every adjective must receive a yes-or-no classification.
What assumptions about self-application and classification make this definition paradoxical?
The paradox is semantic, but it has a structure close to Russell’s set paradox: each asks whether an item belongs to a class defined in terms of not belonging to itself. The resemblance is structural; the paradoxes concern different kinds of things.
One historical response, discussed by Ramsey, distinguishes the meaning relation used to define “heterological” from the relation that links the word “heterological” to its meaning. On this approach, the same unrestricted relation is not used to apply the predicate to itself. The Stanford Encyclopedia of Philosophy notes that this proposal anticipates Tarski’s later work on semantic hierarchies.
The contradiction depends on treating “heterological” as a predicate that can apply to itself under the same definition used for other adjectives. The Ramsey-style response blocks that unrestricted self-application by distinguishing levels of meaning. This is one historically discussed response, not a settled proof that every version of the puzzle has the same solution.
The puzzle does not show that ordinary English as a whole is inconsistent. It shows that a particular self-applying definition conflicts with the assumption that it must classify itself as either applying or not applying. Examples about adjectives illustrate the setup; the paradox turns on the definition and its self-application.
Berry’s and Richard’s paradoxes are other puzzles involving self-reference or definability, but they use different constructions. They are comparisons, not identical versions of the Grelling–Nelson argument.
The SEP’s “Paradoxes and Contemporary Logic” entry (§3.3.2) gives a translated formulation, credits the paradox to Grelling within the paper by Grelling and Nelson, and discusses Ramsey’s approach. Its bibliography cites 1908. The PhilPapers catalogue lists a 1907 publication (pp. 300–334) and a 1908 reprint (pp. 301–334). The original paper and its publication volumes were not directly inspected, so the article reports both dates rather than claiming to settle the chronology. The “Self-Reference and Paradox” entry (§§1.1, 1.4) supports the standard self-application setup and its structural comparison with Russell’s paradox. This is an original educational explanation, not expert review or an exhaustive survey.
Research check: 2026-11-01. The consulted sources and passage locations are recorded in the local evidence ledger. Examples are illustrations of the definition, not quotations from the original paper.