A lesson from the toybox: How children build abstract concepts

Contributed by David Barner (with Katherine Wagner & Katharine Tillman)

Humans can think and talk about many things that we can’t directly see or touch. Neutrinos. Infinity. Justice. The nature of time. But humans are not natural-born physicists or mathematicians. Somehow, we learn these abstract concepts. But how could we learn about things that we can’t directly see or touch? In a forthcoming contribution to a book called “Core Knowledge and Conceptual Change”, dedicated to the inspiring science of Susan E. Carey, we try to solve this problem.

The puzzle of conceptual learning lies at the heart of developmental psychology, and has been around far longer than psychology itself – for at least 2000 years. Currently, it divides developmental science into two somewhat imperfectly defined camps: A first group who begin their investigations by noting the amazingly abstract endpoint of human development, and a second group who begin by noticing that our brains appear to encode information by gradually associating experiences of things that we see, hear, and touch. The first group of researchers, sometimes dubbed “nativists”, often end up concluding that learning couldn’t possibly explain why humans have concepts like “neutrino” – that somehow the thoughts beneath these words must be present in babies as part of their genetic heritage. The second group of researchers, the “empiricists”, conclude that this type of knowledge couldn’t possibly have arisen via known evolutionary processes like natural selection, and thus couldn’t be innate. On this second view, since we know that brains learn by forming associations, it must be possible to go from simple sensory experiences to abstract ideas of justice or infinity.

There are probably many things wrong with this debate. For one thing, we currently have little idea of how even adult brains encode abstract ideas like “neutrino” or “justice”, and thus how brain states are related to mental states. We know that these concepts exist in some form, but not because of neuroscience. Instead, we know they exist because we talk about them and use them to successfully predict and change the world. Also, while we generally know an instance of learning when we bump into one on the street, it’s surprisingly difficult to say exactly what learning is in a principled way, especially when it comes to the problem of learning abstract ideas. It certainly could amount to associating bits of information to one another, but it might also be something entirely different.

Perhaps the most common approach to studying learning is to imagine that the learner begins with a repository of basic – or “primitive” – bits of information that can be combined with one another to create new ideas. One especially influential formulation of this idea comes from John Locke, the British empiricist philosopher, who argued that a concept like “sun” is learned by associating basic perceptual primitives with one another. When we encounter the word “sun” we also encounter a circle that is orange and emits heat. By associating these three bits of primitive information together, we create a new representation – “SUN” – which stands in for these previous experiences, and which can be used in sentences to communicate with others, without having to talk about circles, heat, and color individually. This idea, that complex ideas are constructed from simpler ones, is sometimes called the “Building Block” theory of concept learning.

The building block model has been widely endorsed as a way to think about learning. To understand why, consider the following thought experiment, from philosopher Jerry Fodor. Fodor asks us to imagine a scenario in which our task is to learn a new word, like “blicket”. As a learner, we are presented with training experiences. We see a blue triangle and hear, “This is a blicket”. Then we see a blue circle and hear, “This is not a blicket”. Next, we see another blue triangle and hear, “This is also a blicket.” Soon we are on the way to learning a new concept: A “blicket” is a blue triangle. But have we actually gained something more abstract than what we started with? To this, Fodor replies no: What we have really done is combined simple pre-existing bits of information into a new configuration. Nothing here is new; things have simply been re-arranged. Further, Fodor argues that this is really the only game in town – that there is no way to create new primitive bits and pieces from which to construct concepts. If you don’t have a concept to begin with – or at least the pieces that are needed to build it – then that concept can never be learned at all.

Based on this, Fodor’s suggestion is that the building blocks of thought must not be so simple after all, since it’s impossible to imagine how ideas like justice could be built up from simpler pieces. To understand this, consider a metaphor from the toy box. Most readers are probably familiar with Lego – the classic building block toy. Not all readers, however, will have the same experience of Lego. If you grew up in the 1970’s or earlier, then Lego consisted of a small number of mainly rectangular colored blocks, which could be combined in an almost limitless number of combinations to create just about anything (see Figure 1a). Fast forward 40 years, and Lego has evolved considerably. Now, Lego pieces are exquisitely engineered to build specific, highly constrained, creations, like dragons, spaceships, and ninja robots. For example, a kit for constructing a dragon includes pieces like wings, a tail, and legs (see Figure 1b).


(thanks to Dave at for 1A, and for their OPL content in 1B)

On this metaphor, empiricists like John Locke are playing with old Lego, trying to build complex structures from simple “domain general” building blocks – i.e., simple blocks that can be used to build things from any “domain” of experience. In contrast, nativist philosophers like Fodor are playing with new Lego. They think that the learner is born with a set of highly specialized building blocks that are “domain specific” and can be used for one or two specific functions. Such blocks might include abstract concepts – like “justice”, or “infinity”, or “neutrino”. Or maybe something a degree simpler, but still vastly more abstract than “circle” and “orange”.

Given the widespread acceptance of the Building Block metaphor, it is easy to see why modern psychologists might disagree about the origin of abstract concepts. On the one hand, how could any combination of simple sensory building blocks – colors, shapes, simple motions, etc. – generate abstract ideas like justice or infinity? In response to this, philosophers and psychologists alike have offered up 2000 years of near complete silence, intermingled with loud and embarrassing failures (see here for a great review). Even simple concepts like “apple” have turned out to be notoriously difficult to define, let alone define in terms of only features that we can see, hear, or touch. On the other hand, if concepts aren’t combinations of sensory experiences, how could we ever use abstract words to describe, predict, and change the world. And how could a child ever learn which experiences in the world are related to which building blocks? Even with fully innate concepts available, the problem remains of how such building blocks could become related to experience in the world.

It may well be possible, from the armchair, to resolve this issue. But if it is, it probably won’t turn out to be easy. Fortunately, however, developmental scientists are not confined to their armchairs, and can figure out how human concepts originate by watching them emerge in real time in human children. And after 60 years of continuous empirical research on this specific problem, it seems like some progress may be in the works.

Generally, philosophers and psychologists call the building blocks of thought “primitives”. They’re called primitives because they can’t be constructed from anything else. They are as small as it gets. And if they are made of something else, then it is those things that are primitive. So, if we follow this logic, it’s impossible to learn primitives, since, as Jerry Fodor has noted, by definition these things cannot have structure – they can’t be pulled apart into component pieces – or else we wouldn’t call them primitives in the first place. As long as learning is restricted to the creation of complex concepts by combining simple ones, it follows logically that new primitives can’t be constructed in development. And if we accept this, then we’re stuck with the problem of identifying building blocks that are simultaneously concrete enough to make contact with experience but abstract enough to account for the knowledge that adult humans end up acquiring.

Which makes one wonder: Perhaps the building block metaphor – the idea that concepts are like Lego – is itself the problem. Perhaps things would be different if we dropped the assumption that concepts get their content exclusively from the meanings of their component “blocks”. As developmental psychologists like Susan Carey have pointed out, primitives might be learned if we allowed them to be defined in part by the relations between them, rather than just their internal structure.

Here’s where the developmental science comes in.

Take the case of number words – a case study our lab has explored a lot in recent years. It is now well established that children begin acquiring number words by first learning to recite, by rote, the numbers in their count list. This would appear to be somewhat easy – even 2-yr-olds in the US can be trained to count to 10. What’s surprising, however, is that many of these very competent counters have no clue what number words mean. This has been demonstrated elegantly by former Carey student Karen Wynn, at Yale. Wynn showed that, after learning to recite a partial counting routine, children generally take a few months before they learn the meaning of their first number word, “one”, and are able to give one object to an adult when asked for one. Next, about half a year later (!) they learn the meaning of “two”. Then some months later still, they learn “three”. And then “four. At this point, some type of qualitative shift occurs, and children realize that they can determine the number of items in a set by using the counting routine they learned when they were two. Suddenly, at around the age of 3 ½ or 4, they learn that to give a large number like 8, they should count objects until they reach the number 8 and give all objects implicated in their count.

At this point, we might conclude that they have learned the meaning of eight. But in fact, although children can use the word in a routine to reliably find sets of 8, their “concept” of eight is hardly different from their concept of 9 or 10. They do not differ in their internal structure. In fact, the key difference between these words is their sounds, and the position of these sounds in the count routine – i.e., their relations to one another. Although smaller numbers appear to become associated with percepts of 1, 2, and 3 objects, larger numbers only become reliably associated to perception several years after children learn to count, and even then these associations are malleable and context specific, rather than being the source of their immutable arithmetic meanings.

Let’s consider another example: Time. As in the case of number, children begin hearing and using duration words like “second”, “minute”, “hour”, and “day” from very early in development. Time words are among the most frequent words that kids hear. And yet despite this, work from our lab suggests that these same words are not mastered by children until they are 6 or even 7 years of age – around the time when they learn to use a clock. Still, before this, children use the words to discuss time, and know the relative ordering of the words. They know that a day is longer than an hour, that an hour is longer than a minute, and that a minute is longer than a second – and they begin to show evidence of this knowledge by around the age of 4. However, these same kids appear to have little idea of the absolute duration described by each word – how much longer an hour is relative to a minute – and frequently judge that 3 minutes is longer than 2 hours, for example. What they know is how these words are related to each other – but not especially how they are related to experience of time in the world. Much like the case of numbers, children only map time words onto their perception of absolute duration after they have learned their formal meanings in school – i.e., when they are explicitly taught that a minute equals 60 seconds.

And finally, let’s consider a third case study that our lab has explored: Color. Here again, children begin using color words in their speech months – and sometimes years – before they learn their full adult-like meanings. And again, the learning process seems to depend critically on learning how the different color words are related to one another, and how they contrast. Still, color words may differ a little from cases like number and time. In the case of number, the whole system of numbers is anchored to perception by a few “core” meanings – one, two, and three. By being able to quickly perceive and identify 1, 2, and 3 things, kids can begin their counts and build up to larger numbers using their learned procedures and how the higher numbers are related to one another. In the case of time, although hours may be difficult to anchor perceptually, hours are built from minutes, and minutes are built from seconds. And we know that even infants are able to perceive and differentiate events on the scale of seconds. So again, it’s likely that a subset of the words in the domain of time act as anchors for the other words that stray from the realm of direct perception. Color is different, because every word has an anchor – i.e., perceptions that correspond red, blue, and green – but still the full meanings of color words depend on which words the child has learned. If they only know the words “red” and “blue”, then purple hues will be labeled with one of those two words until they learn “purple”. Indeed, in some languages even adults use only 5-6 color words, and these words soak up all of color experience by dividing it up into slightly broader categories. Like the cases of time and number, color words are in large part relationally defined, despite being about as close to perceptually defined as words come.

The lesson of these relatively simple case studies is that many primitive concepts – i.e., concepts that themselves have no discernible internal structure – may actually be learned via their relation to a wider domain of meanings, only some of which are directly anchored to experience. The time for playing with Lego may be over, for better or for worse. Still, a serious challenge remains. How could the type of story we’ve told for number, time, and color words be extended to even more abstract domains like justice, democracy, and infinity? Here we know a lot less, though leaders in developmental psychology, like Susan Carey, have made significant advances by probing children’s conceptual understanding of life, death, causation, growth, the planets, and other people’s minds. It’s now up to the next generation of developmentalists to play with new toys, and leave the building blocks for the kids.

7 thoughts on “A lesson from the toybox: How children build abstract concepts

  1. I fail to see the distinction between Lego and _relationships_: surely Lego includes relationships. Putting brick A over or under brick B are two different combinations; two different relations. Further, in the hypothesis-testing model for acquisition, which to me is the more spelled-out acquisition version (e.g., propose-but-verify of Medina et al) the learner generates propositions that use some sort of relational structure (“grammar”) to generate potentially infinite hypotheses, which are then “tested”. Relations are rife in the Lego model.

    Coming to your examples, each of them can be described by propositions of differing (and maybe increasing) complexity. “Sets differing in cardinality are ordered by cardinality” or “Counting is related to the cardinality of sets” or “My society prefers a modulo-1 system for arithmetic” or “Prioritize cardinality when examining relationships between sets that don’t share obvious sensory features”

    Finally, if you assume that there are some core concepts (like “one”, “cardinality”), then other things like counting and so on can easily be described by their relationships, as you want, simply by inserting them in appropriate propositional structures. “TWO should be ordered after ONE” (assuming TWO,ONE, ORDERING are core concepts, and SHOULD etc mark relationships).


    • Fair question. Let me try to explain. And my apologies if I don’t calibrate my response adequately to your knowledge. Roughly, we can ask what makes two concepts – e.g., CAT and DOG – different concepts. We have several different options that have been around for a long time. Let me draw a simplified picture here: (1) they differ because of their structure (they are composed of different parts or features); (2) they do not differ in their structure, but differ only in their inferential relations to other concepts; (3) they get their content via some form of intentional relation to things in the world. In the lego metaphor, a concept like “CAT” differs from “DOG” because they are composed of different constituent pieces, not because CAT and DOG bear different inferential relations to other concepts. CAT has features (whatever those might be) like “meows”, “has whiskers”, that are *contained* within the concept – i.e., are constitutive of it. On an inferential role semantics this is not the case. But the really critical discussion surrounds primitives. On the building block theory, the primitives must get their content by something like (3) – see Fodor – since they don’t have structure ex hypothesis and aren’t defined by their relations (again, ex hypothesis). On the inferential role account, the primitives do not need to get their content via intentionality – they can inherit their relationship to experience via their relation to other, core, concepts that do have direct intentional relations to the world (again, whatever those end up being). This distinction is, I think pretty well worn.

      The second issue raised is whether we can’t just supplant all of this with propositional structures. The answer to this is yes. The lego metaphor is a metaphor for exactly such a theory. Propositional meanings are just instances of meanings that inherit their content from their constituent parts (say “words” in the language of thought) and how these words are put together. So far so good. Every theory needs propositional structures (and thus relations), whether you’re playing with lego or not. This is how *complex* concepts are born (whether you’re Fodor, Locke, Carey, or whomever). The question is this: What is the nature of those words in which the language of thought is written? How do *they* get their content? Is it purely by their role in the many propositions in which they occur? Or do they get their content via some kind of intentional relation? The propositional account is really not designed to address this issue, and is neutral with respect to the origin of the primitives, at least in principle (though in practice more or less anything is possible).


  2. Thanks for your thoughtful reply! But it’s still not clear 😦
    You say:
    On the inferential role account, the primitives do not need to get their content via intentionality – they can inherit their relationship to experience via their relation to other, core, concepts that do have direct intentional relations to the world (again, whatever those end up being). This distinction is, I think pretty well worn.

    What stops me from reading ‘core concepts’ as ‘primitives’ and ‘relations to experience’ as ‘hypothetical propositions?’ In other words, why are you certain that some of the things you might be studying, like exact numbers like 7, are primitives that are gaining their meaning (to me, out of nowhere), as opposed to what you are calling complex concepts?


    • Core concepts are absolutely primitives on this account (and see Carey, 2009). But it is also possible to create new primitives – which is nice, because absent this we have no theory of how more powerful representational resources might be created (a problem for propositional accounts, recall). How do we know they these initially empty concets are primitives and not propositional and complex? Here is why we do the developmental science – because if you try to solve the problem from the armchair, there are many descriptively adequate intertranslatable accounts. Kids acquire words – placeholders – before they have any content at all, and spend years learning the relations between these words via procedures, which depend on every item in the procedure being known – you need to know the whole system (a signature of these IR accounts). If you want to describe these relations with propositions, that’s fine but for *kids* every word will make reference to every other word, which is not how classical theories (that use propositional definitions contained in concepts) work. And remember too that you are imposing this on a behavior that we know doesn’t have a containment structure for kids. 3 year olds kids who can count up to 8 and give 8 things show no evidence of believing that 8 is defined as 7+1 until some years later (6 or 7 years old). You can describe the behavior this way but it’s not how kids mentally represent it (see Davidson et al., 2012, in Cognition). Time and color present similar issues, wherein kids appear to be using an entire network of placeholders to infer the system of meanings in parallel rather than one meaning at a time. This is what differentiates the theories. Even if propositions can be used to describe children’s behaviors from the armchair this going to turn out to not reflect what is going on in the mind of actual children when we do the science.


  3. Pingback: Great blog — Dave Barner | brain314

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