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evasion is not applicable because the rules of
English uniquely determine its meaning from that of "autological". A similar slight modification to the definition of "autological" (such as declaring it false of "nonautological" and its synonyms) might seem to correct that, but the paradox still remains for synonyms of "autological" and "heterological" such as "self-descriptive" and "non–self-descriptive", whose meanings also would need adjusting, and the consequences of those adjustments would then need to be pursued, and so on. Freeing English of the Grelling–Nelson paradox entails considerably more modification to the language than mere refinements of the definitions of "autological" and "heterological", which need not even be in the language for the paradox to arise. The scope of these obstacles for English is comparable to that of
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of objects to which that adjective applies. So, for example, the adjective "red" is equated with the set of all red objects. In this way, the adjective "pronounceable" is equated with the set of all pronounceable things, one of which is the word "pronounceable" itself. Thus, an autological word is
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The
Grelling–Nelson paradox arises when we consider the adjective "heterological". One can ask: Is "heterological" a heterological word? If the answer is "no", then "heterological" is autological. This leads to a contradiction, for in this case "heterological" does not describe itself: it must be a
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One may also ask whether "loud" is autological or heterological. If said loudly, "loud" is autological; otherwise, it is heterological. This shows that some adjectives cannot be unambiguously classified as autological or heterological. Newhard sought to eliminate this problem by taking
Grelling's
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The paradox can be eliminated, without changing the meaning of "heterological" where it was previously well-defined, by modifying the definition of "heterological" slightly to hold all nonautological words except "heterological". But "nonautological" is subject to the same paradox, for which this
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This is the opposite of the situation for heterological: while "heterological" logically cannot be autological or heterological, "autological" can be either. (It cannot be both, as the category of autological and heterological cannot overlap.)
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if it does not describe itself. Hence "long" is a heterological word (because it is not a long word), as are "hyphenated" (because it has no hyphen) and "monosyllabic" (because it has more than one syllable).
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heterological word. But if the answer is "yes", then "heterological" is heterological. This again leads to a contradiction, because if the word "heterological" describes itself, it is autological.
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All adjectives, it would seem, must be either autological or heterological, for each adjective either describes itself, or it does not. Problems arise in a number of instances, however.
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if we say that "autological" is autological and then ask whether it applies to itself, then yes, it does, and thus is autological;
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yes → "heterological" is heterological → "heterological" does not describe itself → "heterological" is not heterological,
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arises from the question of whether the term "non-self-descriptive" is self-descriptive. It was formulated in 1908 by
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One may also ask whether "autological" is autological. It can be chosen consistently to be either:
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Grelling, K.; Nelson, L. (1908). "Bemerkungen zu den
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The first instance of the word "blue" is autological, while the second is heterological.
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in the following way. First, one must identify each adjective with the
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One hundred years of
Russell's paradox: mathematics, logic, philosophy
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Ramsey, Frank P. (1926). "The
Foundations of Mathematics".
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In logical terms, the situation for "autological" is:
496:Newhard, Jay (October 2005). "Grelling's Paradox".
414:The Grelling–Nelson paradox can be translated into
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561:. Hamburg: Felix Meiner Verlag. pp. 95–127.
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603:. Berlin: Walter de Gruyter. pp. 501–516.
472:Weyl refers to it as a "well-known paradox" in
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383:while the situation for "heterological" is:
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257:"Grelling–Nelson paradox"
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557:Nelson, Leonard (1974).
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889:Paradoxes of set theory
454:Use–mention distinction
123:Grelling–Nelson paradox
377:A if and only if A, a
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498:Philosophical Studies
423:understood as a set,
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1255:Kavka's toxin puzzle
1027:Income and fertility
238:improve this section
43:improve this article
914:Temperature paradox
837:Free choice paradox
701:Fitch's knowability
1354:1908 introductions
1290:Prisoner's dilemma
976:Heat death paradox
964:Unexpected hanging
929:Chicken or the egg
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32:This article
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1280:Preparedness
1112:Productivity
1092:Mandeville's
884:Opposite Day
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807:Bhartrhari's
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135:Hermann Weyl
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41:Please help
36:verification
33:
1210:Condorcet's
1062:Giffen good
1022:Competition
776:White horse
751:Omnipotence
504:(1): 1–27.
480:Ramsey 1926
298:August 2023
189:homological
187:(sometimes
184:autological
153:. It is an
99:August 2018
1343:Categories
1285:Prevention
1275:Parrondo's
1265:Navigation
1250:Inventor's
1245:Hedgehog's
1205:Chainstore
1188:Population
1183:New states
1117:Prosperity
1097:Mayfield's
939:Entailment
919:Barbershop
832:Epimenides
610:3110174383
568:3787302220
529:References
268:newspapers
69:newspapers
1300:Willpower
1295:Tolerance
1270:Newcomb's
1235:Fredkin's
1122:Scitovsky
1042:Edgeworth
1037:Easterlin
1002:Antitrust
899:Russell's
894:Richard's
867:Pinocchio
822:Crocodile
741:Newcomb's
711:Goodman's
706:Free will
691:Epicurean
662:paradoxes
555:Also in:
545:cite book
518:170827394
379:tautology
225:does not
179:adjective
1328:Category
1225:Ellsberg
1077:Leontief
1057:Gibson's
1052:European
1047:Ellsberg
1017:Braess's
1012:Bertrand
990:Economic
924:Catch-22
904:Socratic
746:Nihilism
716:Hedonism
676:Analysis
660:Notable
431:See also
155:antinomy
1230:Fenno's
1195:Arrow's
1178:Alabama
1168:Abilene
1147:Tullock
1102:Metzler
944:Lottery
934:Drinker
877:Yablo's
872:Quine's
827:Curry's
790:Logical
766:Sorites
756:Preface
736:Moore's
721:Liberal
696:Fiction
282:scholar
246:removed
231:sources
161:Paradox
83:scholar
1137:Thrift
1107:Plenty
1082:Lerner
1072:Jevons
1067:Icarus
997:Allais
959:Ross's
797:Barber
781:Zeno's
726:Meno's
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1240:Green
1220:Downs
1152:Value
1087:Lucas
954:Raven
862:No-no
817:Court
802:Berry
582:. 2.
514:S2CID
460:Notes
289:JSTOR
275:books
90:JSTOR
76:books
1318:List
1142:Toil
857:Card
852:Liar
605:ISBN
563:ISBN
551:link
261:news
229:any
227:cite
149:and
129:and
121:The
62:news
588:doi
506:doi
502:126
420:set
240:by
181:is
177:An
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45:by
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