heterological, a.
Of an adjective or other predicate: not having the property it denotes. Hence heterologicality, the property of being heterological.

autological, a.
Opp. HETEROLOGICAL a.

In other words, an autological word is a word that describes itself, and a heterological word is a word that does not describe itself. There are lots of examples of autological words below (the main point of this page); some examples of heterological words: 'long', 'French', 'tentacled'. The first puzzle to look at is: Is 'heterological' a heterological word?

Now you've got that sorted out (or maybe you knew already), a second, more open ended puzzle: Think up some autological words. Its pretty difficult really, not many words describe themselves - there are far more heterological than autological words. Here's a list of more or less good autological words, roughly ordered from most clearly autological towards more dodgy ones. If you come up with some more, send them to me, and I'll add them.

To test the word 'foo', ask the question: "Is 'foo' a foo word?"

Reasonably clearly autological words

polysyllabic
pentasyllabic
English (also Saxon, Afrikaans etc.)
unhyphenated
adjectival
descriptive
understandable (also understood)
(also comprehensible, intelligible)
unambiguous
pronounceable
readable (also read, processed)
writable
used (also useful)
invented (also coined)
common
definable (also defined)
describable
repeatable
translatable
classifiable
memorizable
forgettable
unphonetic
unique
real
existant
ordered (also structured)
spelled
synthetic (also man-made)
known (also well-known)
grandiloquent (also grandiose)
(also bombastic, logorrheic)
formal
olde
post-Renaissance (also postdiluvian etc.)
sesquipedalian
latinate
Hellenic
cool
finite
dactylic
esdrśjula (Spanish)
considerable
uncustomary
inflected
meaningful(although Jacques Barzun would disagree)
attributive(attributes to nouns the property of being attributive)
referential(when used as an adjective, refers to a noun)
adjective(meaning 'dependent', not standing by itself)
avoidable(it is possible to av... er, I mean refrain from using it)
rhyming(rhymes with 'timing' for example)
literary (also published) 
sophisticated (also erudite) 
esoteric (also recondite) 
recherché 
abstract (also intangible) 
sibilant (also hissing?)(vague section of linguistic words starts here)
glottal(depending on dialect)
plosive 
nasal (also orinasal) 
cacophonous 
euphonious 
numberless(vague section of negative words starts here)
asexual(unlike French words, English words are asexual)
inoffensive 
harmless 
uninspiring 
nontrivial 
nonpalindromic(also asymmetric, chiral)
unabbreviated 
heterogeneous(although with all those e's it could be more so)
slang (also slangy)(OED has this as from cant (jargon of a class) origin)
abecedarian 
redundant(is this redundant because superfluous means the same thing?)
superfluous(is this superfluous becase redundant means the same thing?)
supererogatory(another word meaning about the same as redundant/superfluous)
anagramatic(again art mat)
sizeable 
wee(Scottish sense)
li'l(surprisingly, is in the OED)
aforementioned (?)(this has been mentioned before)
time-consuming (?)(it takes time to say, time to decide if its an autological word etc.)
single (?)('single' is a single word)
literal (?) 
chatty (?) 
dreamy (?) 
wishy-washy (?) 
iffy (?) 
fanciful (?) 
quirky (?) 
unemotional (?) 
plain, bland (?) 
boring, stodgy (?) 

Notes: In general, where there are a number of words all claiming to be autological on the same (or similar) idea, I'm including only a couple to avoid more unique examples getting swamped. I'm also preferring words describing concepts that have some content when applied to words. So although strictly, we might say that 'untentacled' is an autological word, its a rather uninteresting concept when applied to words. There are a couple of words of this sort in the above list, in particular 'unique' and 'finite'. I'm pretty sure its impossible to have a word that isn't unique in terms of either spelling or meaning, and there aren't many infinite words around (excepting the discussion on extra-extended lower on this page).

More Debatable/Dodgy:

Pavlovian(rings a bell doesn't it?)
twee (also quaint)(it is annoyingly cute)
lengthier(in comparison with 'longer')
complicated(to say, write... also 'elaborate', 'abstruse')
short(not really that short)
terse(ditto, though tends to be said in a rather clipped manner, unlike 'short')
concise(there are more concise words)
neological(the OED has this as being used in 1800, which isn't that new)
wordy(debatably wordy)
unfinish(not a word)
finished (also whole, complete)(the intended meaning of 'unfinish' is clearer by context)
farnuculent (not a dictionary word, and as with 'protologism' below, if it became one it wouldn't be autological)
prefixed('pre' is the thing that gets prefixed, not the whole of the word)
in-bloody-fixed(replace 'bloody' with favourite intensifier)
mispelt(not a word)
sdrawkcab(ditto)
aaabcehillpt(ditto)
vwllss(ditto)
contiguous(not that often a word applied to words)
disc ontinu ous(not a word)
ebg-13'q(rot 13'd - definitely not a word)
rot-26'd(this isn't in common usage anywhere)
l33t(very not in the dictionary)
awkward(seems awkward with that 'wkw')
awkwardnessful(is definitely awkwardfulness, but isn't a word)
Americanized(was this originally spelt 'ised' but Americani(z/s)ed?)
Anglicised(was this originally spelt 'ized' but Anglici(s/z)ed?)
floccinaucinihilipilificatious(doesn't mean 'worthless', more 'relating to the act of estimating something as worthless')
self-explanatory(is it? yes if you know what 'self' and 'explanatory' mean)
constant(but it might change in the future?)
weird(few words break the "i before e except after c" rule. Not very self-explanatorily autological)
dictionary(in the Countdown (UK tv program) sense)
hurtful("you're hurtful", although it can be used in non-hurtful ways. Similarly 'unfair' as in "that's unfair"?)
typeset(in Notepad...)
tall (also thin)(depends on font)
CAPITALISED(depends on how its written rather than the word itself)
pǝddılɟ(ditto)
legible(ditto)
red(ditto)
hidden(or should that be found?)
written(only if written, not if spoken)
alphanumeric(ditto)
spoken(only if spoken, not if written)
percussive(depends on pronounciation)
staccato(ditto)
smooth(ditto)
mellifluous(ditto)
tinny(ditto)
eloquent(more to do with style of speech than the word itself)
fifteen-lettered (also seventeen-lettered)(not really a word)
hyphen-bearing(ditto)
over-exaggerated(might not be over-exaggerated if its appropriate?)
double-barrelled(only refers to names really?)
verbed(Calvin and Hobbes sense: "verbing" a noun to make a verb out of a noun that isn't normally one)
TLA(acronym)
XTLA(eXtended TLA, a word in common usage, at least around where Stephen Tavener is)
holed(well theres sortof a hole in it...)
parallel(all those 'l's are...)
dwunken, stoopid, etc. 
named(Henry Segerman (08/05/01) has named this word 'Bob')
bibble(where "bibble", as defined by Olly Wilkinson (26/04/01) means "previously unheard of")
gibberishly(is pretty gibberishly)
enigmatic(is enigmatic autological or heterological?)
uncensored(I could have ***ed out bits of it in this list)
acceptable (also fitting)(depends on context. Hmm, I seem to have accepted it for this list)
submitted, sent, suggested(by Ellen Kephart)
emailed, hand-delivered(by Jacob Bien)
added(by me)
considered(and I decided it fits. This one also has a less specific interpretation for which it is also autological)
questionable (also debatable)(it is questionable that this word is in this list)
vetted(I can reject it for this list only by ignoring it entirely)
dodgy 
puzzling(what is this doing here?)
uncalled-for(and this? I didn't ask for this! (?))
repeated 
repeated(inevitable really...)
final(is the final word in this list)

Notes: in parts of this dodgy list, there is a trend for altering an actual word in a way which is described by the original word. Strictly speaking, 'mispelt' is not mispelt, because 'mispelt' doesn't mean anything. However, its clear with minimal interpretation that the meaning the word is supposed to be the same as that of 'misspelt', and all is well. At some point though, the deviation from the original word will become too great, and the original meaning indecipherable or just require too much interpretation to be autological. Whether this is happening by the time we get to 'ebg-13'q' or 'sdrawkcab' is a debatable point.

Nouns:

To test the word 'foo', ask the question: "Is 'foo' a foo?"

noun 
word 
thing 
concept (also idea) 
identifier 
string(within many computer systems)
antonym(antonym is the antonym of synonym)
oxymoron 
eggcorn(is now in the OED, see this blog post)
nominalization(nominalization is the nominalization of nominalize)
portmanteau(derives from the two French words porter (to carry) and manteau (cloak or mantle))
dvandva(similar to portmanteau, Sanskrit)
worge (also wombo)(similar to portmanteau, is a word merge (word combo). These seem to be protologisms at the moment)
meme 
abbr. 
iamb 
buzzword 
anagram(a rag man)
cliché(is it by now?)
neologism(as with neological, this isn't that new)
protologism(treads a fine line between being accepted enough to be a real word, and becoming so accepted that it is no longer autological)
spondee/trochee(apparently having both of these might seem to be inconsistent treatment of lightly stressed syllables)
daktylos(in ancient Greek)
Poem(by Ossie Manners)
Parody(of Ossie's 'Poem', by Olly Wilkinson - Note same first letter and identical word structure)
Pastiche(by Rick Rubenstein, a latecomer to this genre)
lingo(in the OED as a colloquial word)
hippopotomonstrosesquippedaliophobia(this is certainly a scary word, but it isn't a phobia itself, it's a word...)
one(this doesn't quite pass the test sentence...)
itself(ditto)
letters(ditto)
faux amis(it doesn't really mean a false friend)
question(can be asked as a question, with the right tone of voice)
t-bloody-mesis(replace 'bloody' with favourite intensifier)
semordnilap(not in the OED)
zigzag(sortof mentally zigzags, and the 'z's help too...)<
password(based on empirical evidence)
element, also entry(in this list)
lagniappe(a bonus word for this list)

This, Here, Is

'This' isn't an adjective or a noun, but is certainly autological in some sense. 'Here' and 'is' also. They seem to fit a test question something like: "Is 'foo' foo?"

'Autological' itself

Following 'heterological' around on itself to try to find out if it is autological or heterological leads to contradictions either way. 'Autological' on the other hand is consistent both ways, so cannot be proved to be either autological or heterological using that method.

However, in a different sense, it is autological: the word itself is a constructive expression, meaning "self-sensical". In other words, the components of the word (and hence the word) describe the word. Which is precisely the meaning of the word 'autological'.

In a way, this is very similar to the case of 'self-explanatory', and similarly, 'autological' is autological if you are willing to assume knowledge of what the components 'auto' and 'logical' mean.

Words meaning 'relating to foo'

Two examples of this would be 'morbid' and 'erotic'. But it's debatable whether the word itself is related to the concept in a strong enough way to justify it being autological.

Interesting Non-Autological Words

The word 'extra-extended' is not extra-extended. The word there that is extra-extended is the word 'extended'. Similarly 'extra-extra-extended' is not extra-extra-extended, it is 'extra-extended' that has been extra-extra-extended. And so on, '(extra)n-extended' is (extra)n+1-extended to form '(extra)n+1-extended'. Perhaps then 'extended' with infinitely many 'extra's on the front is autological?

We could also consider words of the form '[foo]-containing' where [foo] is to be replaced with one's favourite letter. Then of course all of these would be autological. Alternatively we could replace [foo] with a favourite word, so for example 'word-containing' is a word-containing word. Likewise 'word-containing-containing', 'word-containing-containing-containing', and in general '[foo](-containing)n' is autological.

The French word 'adjuster' was adjusted to form 'adjusted', the Old French 'ajoster' was adjusted to form 'adjuster', and the Latin word 'juxta' was adjusted to form 'ajoster'. But is there an autological word in here? I'm not so sure 'adjusted' isn't adjusted now...I think the verb seems to apply (like 'inflected') to either the input or the output.

If we ask: "Is 'quote' a quote.", then I guess we have to say yes, though its not the word 'quote' that is being autological. Its using the test sentence to get itself accepted, reminiscent of how a virus gets itself reproduced?

The words 'four' and '1' are self-documenting in a sense, because they tell us how many letters/symbols they each contain, but it requires too much interpretation to see this for them to be properly autological. See however Autological Numbers.

Richard Forbes notes that the word 'ineffable' (n. incapable of being expressed or described in words) is non-autological in an interestingly contradictory way. By the very existence of the word, the definition does not apply to any object of expression, unless the definition is reworded to exclude 'ineffable' from the words that could (but fail to) express or describe said object of expression.

Co-autological words?

Saul Schleimer points out that 'autological' is pentasyllabic.

Autological phrases

I haven't been collecting autological phrases (as opposed to single words) since there are too many possibilities. However, Simon Tattersall mentions a very nice example in the well-known rock band called "The Band". Bands whose name begins with the word "The" are sometimes called "The" bands, so "The Band" is not only a band, but also a "The" band.

Simon also contributes a poem commenting on Ossie Manners poem: "Poem is a poem". This of course invites further commentary poetry. Similarly, if awareness of autological words becomes widespread, together with the fact that "meme" is autological, might lead to "meme is a meme" becoming a meme. This suggests a further kind of autological notion, with test question: "Is 'foo is a foo' a foo?"

Links

Contributors:

Ossie Manners, Olly Wilkinson, Ian Shaw, Madeleine Mayne, Edward Laird, Jil Segerman, Henry Segerman, Will Segerman, Aron Dumbos, Paul-Olivier Dehaye, Patrick Finglass, Jim Gillogly, Greg ?, Russ Perry Jr, Ewart Shaw, Fred W. Helenius, Keith C. Ivey, Nick Wedd, Andrew Krywaniuk, Patrick Hamlyn, Andy Jakcsy, Ian Hill, Matt Reilly, Jon Wild, Stephen Tavener, Biep, Clay Blankenship, Juho Snellman, Peter Renzland, Stuart Steedman, Daniel Ford, Paul Teale, NeilFred Picciotto, Rick Rubenstein, Adam Booth, Alex Cruise, Robert Beckwith, Ellen Kephart, Sarah Terman, Colin S. McLeod, Jacob Bien, John Vertical, John Martz, hovig, Adam LN, Sandra Emerson, Bill Figeley, William Limratana, Scott Carson, Monica ?, GTBacchus, John Cohen, Joe Mattinson, Mike Nolan, Walter Vulej, Bruno Curfs, Bruno Estigarribia, Isaac Copeland, vexitude, Vince & Rachel, Matt Blackburn, Christopher Landauer, Jake Simon, Gray Symon, Allison Moore, Rowyn McDonald, Chris Simpson, Saul Schleimer, Dan Scherlis, Ralph L. Kohler, Jr., Anthoni Fortier, Richard Forbes, Alicia Krywaniuk, Simon Tattersall, Billy Bodnar, Ionatan Waisgluss.

Autological Numbers

     Alternatives

!      1, a
bi      Jr
odd      tri
even      four, quad
prime      penta, fifth
phi(7)      notodd, sextet, half12
seventh      noteven, dwarves, wonders
twocubed      twofours, powerof2
composite
triangular      squarefree
twoplusnine      fiveplussix, primenumber
zodiacnumber
superstitious
twoweeksofdays      einhexadecimal, Februaryhalved
fifthtriangular
fourthpoweroftwo      gjashtėmbėdhjetė (in Albanian)
foursquaredandone
fiftyeightmodforty
primeafterseventeen
positionofthelettert      writeatwonexttoazero
sevenandsevenandseven
secondmultipleofeleven
smallestprimeovertwenty
twicetwelveorthriceeight
raisefivetothesecondpower      areaofasquarewithsidefive
halfofastandarddeckofcards      countslettersinthealphabet
multiplythreebythreebythree
theonlytwodigitperfectnumber      theeighthprimenumberplusnine
daysinfebruaryifitisaleapyear
multiplyingthefirstthreeprimes
baskinrobbinshasthismanyflavors
takethesquarerootoftentwentyfour
trentetroiswhentranslatedtofrench      writedowntwothreesnexttoeachother
twothirdsofonemorethanhalfahundred    
multiplytogetherromannumeralVandVII
firstperfectnumbermultipliedbyitself
thinkofanumberbetweenoneandonehundred
inbinaryitbecomesonezerozerooneonezero
writethefirstoddprimenexttoitsownsquare
ninthwhencountingbyfivesstartingwithzero
itspositioninalistofprimesisseenasbadluck
hhgttganswertolifetheuniverseandeverything      dadamsanswertolifetheuniverseandeverything      itstheanswertolifetheuniverseandeverything
fourthprimewithleastsignificantdigitofthree
countbytensuntilyoureachfourandaddtwosquared
threetimesthesquarerootoftwohundredtwentyfive
numberofgoldmedalswonbytheUSin2004plustwosixes
wordsinthepreambleoftheUSAconstitutionminusfive
numberofhoursonananalogclockfacemultipliedbyfour
countyourtoesmultiplytheresultbyfiveandtakeoffone
thenumberofmembersofthejedicounciltimesfivelessten

.
.
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anunreachablepointattheendofaneverendinglinethatrepresentsanunreachablepoint.... (in an ambigram by John Langdon)

The 'test question' for membership in this list is something like: "Is the number of letters in 'foo' foo?". Suggestions to fill in the gaps or alternatives to the usual address.

Induction?

If n>8, and we have a word for n-8, [w] say, then "[w]andeight" is a word for n...thus by induction we now have words for all natural numbers? Well maybe, here's a possible counterexample suggested by Paul-Olivier:

roundtothenearestintegerthecuberootoftwohundredandseventythousand

This has 65 letters, and the cube root of 270,000 is around 64.63304. However, it is very natural to read

roundtothenearestintegerthecuberootoftwohundredandseventythousandandeight

as asking for the integer nearest the cuberoot of 270,008, which is around 64.63368, so we get 65 again. This works however:

roundtothenearestintegerthesquarerootoffourthousandninehundredandeight

However, if we just want to show that every natural number has an autological representation then we can avoid these kinds of issues by using a sensible construction that cannot be so deviously misinterpreted: Matthew Turner supplies such a construction for integers n greater than or equal to 10:

Let k be any natural number (including 0 as a natural). Let any integer of the form:

12 + 6k be written as fiveaddseven (addsix)^k

13 + 6k be written as fivepluseight (addsix)^k

14 + 6k be written as oneaddthirteen (addsix)^k

15 + 6k be written as threeplustwelve (addsix)^k

 4 + 6k be written as four (addsix)^k

11 + 6k be written as fiveplussix (addsix)^k
Then any integer greater than or equal to 10 is congruent to 12, 13, 14, 15, 4 or 11 (mod 6) and we can take the necessary expression. Equivalently (and more helpfully), any integer greater than or equal to 10 is congruent to 0, 1, 2, 3, 4 or 5 (mod 6).

Natural numbers smaller than 10 can be dealt with as in the table above (although not all are determined as precisely as in this construction...)

Links

Colin Rose has a page on Narcissistic Numbers, another way in which numbers can be self-describing.

Contributors

[lots of people from the Stanford Math department], Scott Sheffield, Paul-Olivier Dehaye, Daniel Ford, Henry Segerman, Dave Futer, Elizabeth Meckes, Mark Meckes, Rick Rubenstein, NeilFred Picciotto (lots), Jeff Rissman, Ryan Stewart, Matthew Turner, Mike Naylor