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.