Do you think I believe you hope…? The power of recursion


In my previous post, I wrote about recursion – self-same replication, when a rule or procedure is applied to its own successive results. Some linguists argue that recursion is a defining aspect of human language: our grammar allows us to combine words into more complex structures, which are in their turn combined into even more complex structures, similar to Matryoshka dolls. I, however, argued that recursion in grammar does not quite live up to its current central status in theory of language as this hierarchical use of rules is present in most if not all aspects of life. But does this mean that recursion is something trivial and boring? By no means! Like a magic wand, it allows us, notoriously social animals, to understand and communicate with each other in a very efficient and flexible way.

Your cat will never ask you “huh?” It just doesn’t care.


We can read each other’s minds
Unless you are very thick-skinned, you have probably spent sleepless nights, wondering why your boss or friend might have reacted in a strange way. “Did he think that I insulted him by saying that?”, “Does she really believe that rumour that I envy her?” When we hold beliefs about beliefs about beliefs and so on, we perform, using the terminology from Michael Tomasello and other psychologists, recursive mind-reading. Some of them even claim that we can understand up to seven levels of such recursive thinking: having thoughts about thoughts about thoughts about thoughts… etc.!

Even very simple words require mental recursion
Many linguists and psychologists believe that recursive mind-reading is crucial for communication. When we speak, we think about how the hearer will interpret our words. When we listen, we think about what the speaker wants us to understand.

How does it happen? Imagine that the Dutch prime-minister says on TV: “The COVID-19 infection rates were high last week”. He expects that the viewers have sufficient background knowledge to understand what the word high means – not three, or ten, or a million, but most likely, a couple of thousands of people. Language use is full of vague expressions like this. We use them all the time because we expect that other people know what those words mean, and can infer what we intend to say. A very detailed model of this complex process, Rational Speech Act Theory, was formulated by Michael Frank and Noah Goodman (see figure 1 below).

Figure 1. Recursion in human communication (adapted from Goodman & Frank 2016).
Imagine Sue (Speaker) and Leo (Listener) are watching three people. One wears glasses, another one wears glasses and a hat, and the third one wears neither. Suddenly, Sue says, “My friend has glasses”, and she means only one person. What will Leo do? Leo constructs a simplified internal representation of Sue in his head, which we will call “Simplified Sue”, who should have a simplified model of Leo’s reasoning, or “Literal Leo”. This simplified model is a naïve interpretation of the utterance based only on its literal meaning. Literal Leo reasons, “OK, the label ‘glasses’ applies to two persons, while ‘hat’ would apply to only one”. Based on this, Simplified Sue would have used “hat” when intending to speak about the person with glasses and a hat because that expression would have identified him with 100% certainty. But she chooses “glasses” instead. Thus, Leo concludes that Sue means the person with glasses, but without a hat.

Even ordinary function words like but, not, actually and because require a fair amount of mental recursion. For example, when the current U.S. President Joe Biden once said, “I’m Irish but not stupid”, many Irish people were not amused. Why? The use of “but” signals that the speaker thinks that both he and the addressee are familiar with the cultural stereotype that Irish people are generally stupid. From that, the Irish concluded that Biden actually thinks that the addressee shares the stereotypical belief that the Irish are stupid. You see that you need a lot of prior background knowledge and do quite some mental loopings to fully grasp the meaning behind a simple sentence of only a few words.

Although there are good reasons to believe that language users are pretty lazy mindreaders, who use different kinds of short-cuts and tricks to save cognitive effort, there is evidence (check here) that we take into account the listeners perspective most of the time. In particular, we adjust our language depending on whether or not the listener has access to the same information as we do.

What did you say?
The ability to think about the thoughts, beliefs and desires of other people is called theory of mind. Is it only us, humans, who have it, or do other animals have it, too? This issue remains controversial. But even though our closest relatives, great apes, can understand another’s point of view, as some researchers claim, there is still one thing that they cannot do. An animal cannot signal to another animal that it doesn’t understand its message. Humans, on the other hand, do it all the time. Consider an interesting fact: all languages seem to have a word like “huh”, which signals the speaker that the utterance wasn’t understood (check this study). By using it, we communicate about another person’s attempt to communicate. Animals don’t have such a communicative strategy: if your cat doesn’t understand what you said, it’ll just ignore you (this is what cats normally do, anyway). So, if we want to pinpoint one type of recursion that is uniquely human, speaking about speech (another person’s or your own) is probably the best candidate.

Gossip is good for you
The queen of recursion is gossip, where someone speaks about what someone said, and so on… Take Vicky Pollard, a teenage girl from the sketch comedy show Little Britain. Vicky’s gossip, in combination with high speech tempo, is both very recursive and very confusing:

“No but, but yeah, but no, because you know Albany, well she said I’ve been going around saying Samina’s got a moustache, which she has, but I never said it.”

Gossip doesn’t have a very good reputation, but some evolutionary psychologists like Robin Dunbar think that gossip allowed us to build bigger groups and to become the dominant species as a result. It’s a tool for sharing valuable social information and building mutual trust. It is also a powerlifting exercise for recursion!

The glory of recursion
To sum up, recursion indeed plays a crucial role in human language and culture, but not in the sense some linguists think about it (see Part I). The most amazing thing is that we can think about what others think, and can speak about what others say. Our ability to ‘read’ each other’s minds allows us to have very flexible vocabulary and grammar (think, for instance, of the word “square”. It means something different when we speak about a square table, a square jaw or a square pyramid, but we understand what it means easily in each phrase). Our need for cooperation and bonding has created many language tools, from small words like huh? to complex structures like Do you think I believe you hope… These tools have helped us achieve incredible things as a species.


I’m sincerely grateful to Arie Verhagen (Leiden University) for insightful comments on an earlier version of this post.


Read more
– Blakemore, D. 2002. Relevance and linguistic meaning: The semantics and pragmatics of discourse markers. Cambridge: CUP.
– Dingemanse M., Roberts S.G, Baranova J, Blythe J, Drew P, Floyd S, et al. 2015. Universal principles in the repair of communication problems. PLoS ONE 10(9): e0136100. Link.
– Frank, M. C., & Goodman, N. D. 2012. Predicting pragmatic reasoning in language games. Science 336(6084), 998–998. Link.
– Goodman, N.D., & Frank, M.C. 2016. Pragmatic language interpretation as probabilistic inference. Trends in Cognitive Sciences 20(11). Link
– Sperber, D., and Wilson, D. 1986/95: Relevance: Communication and Cognition. Oxford: Blackwell.
– Tomasello, M. 2008. Origins of human communication. Cambridge, MA: MIT Press
– Verhagen, A. 2005. Constructions of Intersubjectivity: Discourse, Syntax, and Cognition. Oxford: Oxford University Press.


– Figure 1: own production


Writer: Natalia Levshina
Editor: Melis Cetincelik
Dutch translation: Eva Poort
German translation: Natascha Roos
Final editing: Merel Wolf