Inacceptable, multiword word, ...: fun with autological words

Predictably, I haven't been able to get to the end of Quine's text, short though it is, without getting side-tracked. Grelling's paradox is to blame. The paradox involves the distinction between autological words and heterological words. Autological words are those that describe themselves. For instance, the word word is also a word, the adjective English is English (it's not French, for instance), and pentasyllabic is pentasyllabic itself , as it consists of five syllables. A word is heterological if it doesn't describe itself. Thus, adjective, unlike adjectival, is heterological as it's not itself an adjective, and so are the words monosyllabic, French or long.

Kurt Grelling

The paradox named after Kurt Grelling (1886-1942), now, lies in the impossibility of answering the following question without arriving at a contradiction: What kind of word is heterological? Chances are it's heterological, as most words do not really describes themselves. But if heterological is indeed heterological, then it's actually an autological word, which is the opposite of heterological. In other words, if heterological is heterological, it is not heterological. So, is it autological, then? Let's consider this. If it's the case that heterological is an autological word, then we are forced to say that it is not an autological word, since only adjectives that fit in the frame "X is a(n) x word" (e.g. Short is a short word) can be considered autological. You see? We have a problem either way. If the word heterological is heterological, it's not. And if it's autological, it's not. That's the paradox.

I've risen to Henry Segerman's challenge to think up autological words. Here's a preliminary list, which I'll then send to him.

I'll start with 20 adjectives (or past participles):

1. burbling 
Listen to it. Doesn't this word make a gurgling, bubbling sound itself? I suppose many onomatopoeias are autological.

2. long-winded
If it's meant to convey what long does on its own, it's rather long-winded.

3. polymorhemic 
It's not just polysyllabic but it consists of several morphemes: poly-, morph, -eme and -ic.

4. listed
It's listed here.

5. included
Idem ditto.

6. near-forgotten
I'd almost forgotten about this word.

7. normal
A very normal word. There's really nothing special about it.

8. West-Vlams
That's a West-Flemish word.

9. inacceptable 
It's underlined by my spell-checker. It should be unacceptable. Segerman only accepts existing, correctly spelled words in his main list -- he also has a list of "more debatable/dodgy" ones, such as mispelt, which isn't a word. But since inacceptable really is not acceptable as a word, shouldn't he therefore include it in his list of "reasonably clearly autological words"? What a conundrum.

10. bizarre
Look at it. How many words do you know that end in -arre?

11. random
Could be just any other word, so it's pretty random.

12. decomposable
You can analyse it into its component parts, as in the following word.

13. de-compose-ed
Perhaps compose itself can also be further decomposed.

14. taggedVBN
The word tagged has here been provided with the part-of-speech tag for 'past particle', as used in the Penn Treebank project.

14. infrequent
That's not a very common word, compared to the word common, for example.

15. hyper-infrequent
Only 29 occurrences in Google for this word

16. self-rhyming
There once was a word that was self-rhyming / And that word was the word self-rhyming.

17. finite
All words come to an end, just as this one.

18. ante-penultimate
Wiktionary defines this as: "Two before the last, i.e., the one immediately before the penultimate, in a series."

19. penultimate
I guess you saw that one coming.

20. unexpected
Given the preceding two, this is not the word you had expected here, is it?


Now for some nouns...

1. derivation
This noun is derived from the verb derive.

2. compound noun
It's a noun which is consists of two free morphemes, which is precisely what we expect of a compound noun.

3. multiword word
Similar to the preceding item: any word which consists of more than one word is a multiword word.

4. haplogy
A bit of a linguist's joke: haplogy is an example of haplology, the omission of a syllable when you have two adjacent sounds or syllables in a word.

5. hapax
This is a word which occurs only once in a text.

6. unicum
Also a unique member in this list.

7. example
This word illustrates what an autological word is, doesn't it?

8. list member
It's undeniably in the list, what with having a number and all.

9. twenty-one letter series
Just count the letters.

10. 21-character sequence
Hyphens and spaces included.


If phrases, rather than words (including compound words), can be said to be autological, then it becomes quite easy to come up with autological phrases, such as beginning with a b-, starting with an s-, ending with an -e, but these couldn't be any lamer. Or how about previously ignored? This phrase used to be ignored as an example of an autological phrase, but it no longer is!

Last day of holiday

My kids played a lot with Lego this summer holiday, but this is one thing they didn't construct:

(Peter Lea, from http://ingeniumetars.blogspot.be/2010/11/lego-penrose-triangle.html)

The Ways of Paradox, by W.V. Quine

After checking my email etc., I'm going to sit down today and read the essay The Ways of Paradox by the late Harvard professor Willard Van Orman Quine (free pdf here). From a brief skim of the text, I can see he's dealing with a definition of paradox, and provides lots of useful terms, distinctions and examples. I'll be able to turn to this text whenever I need to talk about any of the following, some of which I'll copy and paste in my labels box in a minute:

definition, barber paradox, Russel's paradox, veridical paradox, falsidical paradox, fallacy, Zeno, Achilles and the tortoise, Grelling's paradox, autological adjective, heterological adjective, antinomy, Epimenides paradox, pseudomenon, Liar paradox, Berry's paradox, Tarski, subscripts, self-membership of classes, Frege, mathematics, general set theory, Gödel's proof, theorem

The text is conveniently short and, since it's a revised version of an article that originally appeared in Scientific American, it should be quite readable.

Superstition brings bad luck

My post this morning about praying to Mary to make it stop hail and thereby inadvertently implore her to make it hail (Hail, Mary!) made me think of a great bit of wit in one of Tom Heremans' columns for De Standaard:

"Zijn mensen op hun hoofd gevallen? Weten ze dan niet dat bijgeloof ongeluk brengt?" (Tom Heremans, De Standaard Weekblad, 9 mei 2015)

 'Have people lost their minds? Don't they know superstition brings bad luck?'

It's a perfect case of a sentence that bites itself in the tail. It's a self-referential utterance, but one in which the author isn't (or feigns not to be) aware of it. The (second) utterance is about superstition but it is also couched in the stereotypical sentence frame which we associate with superstition: "X brings bad luck". The humour resides in the fact that the author pretends to be superior to superstitious folks but is no better than them. What's more, if it were the case that "superstition brings bad luck", he would ironically bring bad luck upon himself by saying and believing this.

I wonder whether this isn't some remote variant of the Liar paradox, with "S is true" and "S is false" substituted for by "you believe in S" and "you don't believe in S":

- If you believe that "Superstition brings bad luck" (i.e., if you agree that this sentence is true), you are the sort of person who does not want to give in to superstitious fears and you won't accept any general fearmongering delivered in the form "X brings bad luck".
- But if you don't believe that "Superstition brings bad luck" (i.e., if you don't agree that this sentence is true), you are the sort of person who's better safe than sorry, who avoids the sight of black cats and walking under ladders, and who may want to believe people who warn you that "Superstition brings bad luck".

So, the paradox here can be formulated in its purest form as follows: you don't believe statement S when you believe it and you believe it when you don't believe it.

Update: I'm no longer sure Hereman's "Don't they know superstition brings bad luck" is a case of self-reference. I'll have to make sure I find out sooner or later, but rather sooner than later, what exactly is meant by self-reference. Does it just apply to sentences of the form This sentence is/contains/... ?

Hail Mary

Last night there was a tremendous hailstorm over parts of West Flanders. What if someone in the midst of such a devastating tempest called upon the help of the Jesus' mother, praying "Hail Mary full of Grace etc."? Would she then know what to do? Would she make the storm abate or would she, as per what almost sounds like a request, make it hail even more? Of course, weather verbs are only used with it as the Subject and hardly ever occur in the imperative (as in Rain, goddammit, rain!), but higher forces such as the Sweet Mother of God have been implored to influence more than a bit of weather, so she might get confused.

The correct answer is that there's no correct answer

I asked my 8-year-old son to do some simple maths exercises in preparation for the start of the new school year. One booklet we have in the house to make sure the kids can practise at any time contains the following exercise. (I'll just copy it here in Dutch, the language of origin. Just in case you should be an actual person really reading this post and you don't happen to understand a word of Dutch, use Google Translate or some other translation tool if you need help, or just ask me to translate.)

Rekenen met liter. Kleur het bolletje met het juiste antwoord groen. Als het antwoord er niet bij staat, moet je het zelf oplossen!

1. Er is een spannende tenniswedstrijd bezig tussen Kim en Stefanie. Tijdens de rustpauze drinkt Kim veel water. Ze drinkt 2 flesjes van een halve liter, daarna drinkt ze nog een fles van 1 liter. Hoeveel liter water dronk Kim tijdens de tenniswedstrijd? 

O 3 liter                  O 5 liter                 O 4 en een halve liter          

O Het juiste antwoord staat er niet bij.

Ze dronk ............... liter water.

2. ...

My son correctly answered that Kim drank 2 litres of water. However, he forgot to colour in the bullet with the correct answer, which is that the correct answer is not provided. Wait a minute... Isn't that a contradiction? Can't we consider this a paradox? Perhaps. If the correct answer is not provided, we can colour in the bullet that says "The correct answer is not provided". But in doing so, we have coloured in the correct answer, which is provided among the answers! So it is both true that there is no correct answer and false that there is no correct answer.

The English Wikipedia page on paradox informs me that "A paradox that is both true and false at the same time and in the same sense is called a dialetheia." Of course, the question here is whether the statement "The correct answer is not provided" is both true and false in the same sense. It is true in the sense that the right answer is not among those mentioned already, up to now, before the present answer. It is false in the sense that the right answer is among the answers provided in the section with bullets.

The Stanford Encyclopedia of Philosphy has a nice page on dialetheism, where the Liar paradox is mentioned as a case in point. My impression is that the paradox sketched here has much of the flavour of this classic paradox ("This sentence is false"). Yet, the paradox in this maths book is less problematic than the liar paradox. That is because it's clear even to a child that the answers are not of the same kind. The first three name a concrete quantity, while the fourth does not. Therefore, the latter doesn't really count, as it doesn't name a quantity itself but is instead about the answers that do name a concrete quantity. The fourth answer is formulated at a meta-level. It is not wholly unproblematic, however, because insofar as this fourth answer is preceded by a bullet, just like the other ones, and says "The correct answer is not provided", we end up, as we have seen, with the problem that we can't really colour in this bullet without contradicting ourselves. 

Perhaps there is some ambiguity in the use of Dutch er(...)bij, which could mean something like 'among them' or 'among the ones here'. If the fourth bullet had stated, as is usually the case, "The right answer is not provided among the above" (or simply "None of the above"), there would have been no paradox.

By the way... the Wikipedia page about dialetheism provides a link to George Orwell's doublethink. I've recently read that novel (yes, shame on me for not having read it much earlier) and I knew there was a close connection with this whole area of paradoxes. I'll use "Orwell" as one of the labels for this post and will try to write one or more posts about Orwell's penchant for paradoxes later.

Countdown to start of sabbatical

Hello hello. I'm counting down to the start of a half-year sabbatical, starting on 1 September 2015. The sabbatical will be devoted to research on paradoxes in language use and linguistic theory. My intention is to just post some random thoughts here, in the hope of bringing some order to them. Much of what you'll find in this box of paradoxes might be just incoherent ramblings, though. We'll see.