Welcome to the deep dive. Today, we're diving into something huge, really fundamental. It's about where are our most complex ideas? Think about things like infinity or evolution or even just the concept of seven. Where do they actually come from? It's a massive question. Right. Are they built up bit by bit from what we see and hear? Or is the mind sort of preloaded? ready for them. Well, that's exactly what we're digging into today. We're moving past the old armchair philosophy, looking at the actual science, the cognitive development research. And what it strongly suggests, especially the work on concept origins we're discussing, is that the blank slate idea, it just doesn't hold up. OK. So our mission, really, is to get clear on this relationship between our built -in mental structures, this core cognition, and how we get to mature abstract thought, and critically, how language fits in. Because it seems language isn't just for communication, it's somehow crucial for building these more complex concepts. Language is a tool for thought itself. Exactly. We want to figure out what the mind starts with, what its initial limits are, and then how language helps it leap over those limits. OK, so let's map this out. We'll start with the basics. What is this core cognition? Then we'll look at how we handle quantity numbers before language comes into the picture. They're these two fascinating systems. Powerful but limited. Right. And then the main event. Yeah. How language acts is this. This bootstrapper, creating new ways of thinking. And we'll use learning to count, learning about natural numbers as our big case study. That's the plan. It really showcases the process. All right. So for a long, long time, the dominant idea, you know, Locke, Hume, the empiricists, was that we start with just basic sensations, a flash of red, a loud noise, and everything else. All our complex ideas are just combinations of these. But this core cognition idea challenges that head on. It really does. The claim isn't that the mind is empty waiting for data. It's that the mind starts with these, well, highly structured, innate mechanisms. Think of them like specialized apps pre -installed on a computer. Apps for what, specifically? Apps designed to build representations about specific things in the world. Core domains like objects, knowing what a physical thing is and how it behaves. Or agents understanding things that act with intention. and even basic number or quantity. They're essentially domain -specific learning devices. So not just raw processing power, but tools tailored for specific jobs. Precisely. They're evolutionary solutions. The world reliably contains objects and agents, so evolution gave us a head start in understanding them. And this isn't just about simple reflexes, right? We're talking actual concepts. Yes, that's key. These systems produce representations with specific content. Take the indigo buntings example from the source material. It's a fantastic illustration outside of humans. Ah yes, the songbirds that navigate by the stars. Tell us about that. Okay, so these tiny birds migrate thousands of miles. How? They use the stars. But evolution couldn't just hardwire a star map because the sky changes over time, right? Right, precession and all that. Exactly. So instead, evolution gave them an innate computational mechanism. It's specifically designed to look at the pattern of the night sky's rotation and identify the center point of that rotation. And the center point is? North or very close to it. So the bunting doesn't just learn a pattern of lights. It computes and represents north an abstract direction. It's a conceptual representation generated by a mechanism tailored just for celestial navigation. That's core cognition in action. Wow. Okay, so it's a specific computation leading to a concept, but How is that different from the concepts we adults have? If the bunting has a concept of north and an infant has a concept of object, how does that differ from, say, my concept of democracy or calculus? The crucial difference seems to be the format of the representation and its expressive power. Core cognition representations are thought to be largely iconic or analog. Like a picture? Sort of, yes. Or like a mental model that resembles what it represents. Think of the bunting's north representation, maybe like an internal compass needle, or the infant's object representation like a little mental simulation of the object's trajectory. It's tied closely to perception and action. Mature concepts, though, the ones we build later, often rely on discrete arbitrary symbols. Like words, or mathematical symbols. Exactly, language -like symbols. These symbols aren't constrained by resemblance. The word dog doesn't look like a dog. its power comes from its relationship to other symbols in a system, the rules of grammar, logic, mathematics. So you can have a picture of round, maybe, but not a picture of electron or the number 3 ,462 ,179. For those, you need symbols. Precisely. Evolution equipped us to perceive roundness directly. But concepts like electron or large exact numbers require these symbolic systems, built through learning, social interaction, complex reasoning. things that fix what those symbols refer to. So core systems are conceptual, but limited. The bunting nose north, but it doesn't have a theory of astrophysics, you know? Right, it's a practical, constrained concept. Okay, this difference in format really hits home when we look at the object concept again. Piaget thought babies built this idea slowly. But the core cognition view says... It says Piaget was mistaken about the timeline. Modern research using clever methods shows that even very young infants, we're talking two to five months old, already represent objects as solid continuous things that exist even when out of sight. Object permanence way earlier. Way earlier. And they understand basic physical rules like solidity two objects can't be in the same place at the same time. How do we know that? The rotating screen experiment is the classic, isn't it? It is. It's elegant. Basically, you show an infant a screen rotating back and forth like a drawbridge. Simple enough. They get used to it. OK. Then you place a solid block behind the screen where the screen should stop. In the possible event, the screen rotates and stops when it hits the hidden block. Makes sense? Uh -huh. In the impossible event, the screen appears to rotate right through the space where the block is hidden. And infants look reliably longer at that impossible event. Why? Because it violates their expectations. Exactly. To be surprised, they must have represented the block continuing to exist behind the screen, and they must have expected it to stop the screen's motion because of solidity. This understanding is present so early, it has to be part of that initial core cognition toolkit. It fundamentally challenges the idea that object understanding is slowly constructed or purely dependent on language. So... When older babies fail tasks like the A not B error, where they reach for a toy where it used to be hidden, that's not because they lack the object concept. It seems not. It's more likely an issue with immature executive functions, difficulty inhibiting a prior action, or managing complex search plans. The concept is there. The performance is the problem. Making that distinction is absolutely vital. The foundation for understanding physical objects seems to be innate. Okay, objects are innate. Now let's pivot to quantity, to number. Most people probably think number comes from learning to count, right? One, two, three. But the research shows we have ways of dealing with quantity before we learn number words. Two distinct systems, actually. That's right. And understanding these two pre -linguistic systems is crucial because their limitations are precisely what creates the need for language to step in later. Let's break them down. What's the first one? The first is often called the parallel individuation system or the object file system. Its job is basically to track individual things. Like keeping tabs on specific objects? Exactly. It creates a kind of temporary mental workspace with one file or token for each distinct individual you're paying attention to. Think of it like having mental pointers aimed at specific things. It's great for tracking who did what to whom or where things are located. Sounds pretty useful for everyday stuff. But you mentioned a catch, a limitation. A very sharp limitation. This system has a hard set size limit. It can typically only handle about three or four individuals simultaneously. Only three or four? That seems long. It is. That's why juggling more than a few items in your head gets difficult fast. Try tracking five unique moving dots. It's almost impossible without grouping them or using some other strategy. The evidence for this limit in infants is striking, especially for manual search tasks. OK. Walk us through one of those experiments. The cracker one is memorable. Right. Feigenstein and Carey's work. Imagine a 12 -month -old watching you place crackers one by one into an opaque box. They love crackers, so they're motivated to get them. Naturally. If you put, say, three crackers in the box and then let the infant reach in and pull out only two, what do they do? They keep searching for the third one? Precisely. They search longer. They seem surprised or frustrated. Their object file system tracked cracker one, cracker two, cracker three, saw two removed, and knows one file is still open. They expect exactly one more. OK, makes sense. Now for the surprising part. Here it is. If you put four crackers in the box and let the infant retrieve only one, they don't search longer. They act as if the box is empty. Wait, even though there are still three crackers left, that's numerically a much bigger difference. Four versus one is easier than three versus two, isn't it? Numerically, yes. The 4 .1 ratio is much easier than 3 .2. But the instant fails. Why? Because the parallel individuation system hit its limit. Once you go past three or four, the system just collapses. It can't maintain distinct files for each item anymore. It's not about the arithmetic ratio. It's about the absolute number of individuals it can track. It proves this system is about tokens, not abstract values. Wow, okay, that's a really fun - limit on our innate ability to handle exact numbers. System one handles small exact sets up to about three, but obviously we can deal with larger quantities. How do we do that without language? How do we know a crowd of 50 is smaller than a crowd of 100? That brings us to system two, analog magnitude representations. This system is almost the opposite of the first one. It's not for tracking individuals, it's for representing approximate quantities or numerosity. estimation. Exactly. Think of it like a mental number line, but it's fuzzy. It can represent a lot versus a little or more versus less, but its precision is limited, especially as numbers get bigger. Its signature constraint is scalar variability, which follows Weber's law. Wimber's Law, that sounds technical, break it down for us. It basically means your ability to tell two quantities apart depends on their ratio, not the absolute difference between them. So distinguishing 10 dots from 20 dots, a 1 .2 ratio is relatively easy, but distinguishing 110 dots from 120 dots is much harder. even though the absolute difference is still 10, because the ratio 11 .12 is much closer to 1 .1. The fuzziness of the representation increases proportionally with the magnitude. So the bigger the numbers, the harder it is to tell them apart, unless the difference is also proportionally bigger. You got it. You can easily see the difference between five sheep and 10 sheep. But telling 100 sheep from 105 sheep just by looking, very difficult. Your analog magnitude system gives you a rough sense, but not exact precision. And we see this system in animals too, right? Absolutely. Classic studies, like with rats discriminating sequences of tones or light, say, learning to press a lever after two flashes, but not after eight. They can do it, but their accuracy follows Weber's law perfectly. Their timing or counting gets proportionally sloppier for larger numbers. It shows this is a very old shared system for approximate quantity. OK, so let's recap. We have system one, exact tracking, but only up to three or four items, and system two, approximate estimation for larger quantities. limited by ratio. Neither of these, on their own or together, can give us the concept of, say, exactly seven, or the idea that numbers go on forever, the successor function. That's the crucial gap. Neither system can represent the precise cardinal value of sets beyond three or four. Neither system understands that for every number n, there's always a next number n plus one. There's no concept of infinity, no basis for formal arithmetic. And that limitation, that's where language becomes essential. It's the cognitive bottleneck. To get beyond these core systems to the world of integers and mathematics, we need something else. And that something else appears to be language or at least symbolic representation. So we've hit the limits of our innate toolkit. To get to concepts like seven or infinity, we need language. Now there was this really strong view associated with Quine that language basically creates our whole way of seeing the world, our ontology. Does the research we're looking at support that really strong form of linguistic determinism? No, and not in its strongest form. The idea that language creates our understanding of basic things like objects existing over time or cause and effect. That seems too strong. Core cognition gives us those foundations innately. Right, we already established that. However, language is absolutely critical. The sources argue we need to distinguish between, let's say, two levels of linguistic influence. There's a weaker kind, and then there's this much more powerful, transformative mechanism. Okay, let's start with the weaker one. How does language influence a concept that's already kind of there? This is where language might increase the salience or help deploy an existing innate distinction. Think about singular versus plural. one thing versus many things. OK, baby seems sensitive to that difference non -verbally. They do. But some studies, like Barner's work, found something interesting. Toddlers around two years old only start reliably using this one versus many distinction in non -verbal tasks, like if you ask them to grab the keys. versus the key from a box after they start actually using plural markers like S in their own speech. So learning the word keys helps them consistently apply the concept of more than one, even when not speaking. It seems so. The language highlights the distinction. It makes an existing conceptual contrast more available, more robust for problem solving. The concept was there innately, but the linguistic label sharpens it, brings it to the foreground. That's like tuning up an existing engine. But then there's the big one. Quinian bootstrapping. This is supposed to build entirely new engines, right? Concepts the old system couldn't even imagine. That's the idea. This is presented as a uniquely human ability, the really strong mechanism of conceptual change. It's about creating a new representational system. Let's call it Conceptual System 2, or CS2, that is qualitatively different from and more powerful than the initial core cognition system, CS1. And you used the term incoherent before. The new concepts can be incoherent from the old perspective? Yes, that's a key aspect. It means the new system, CS2, might rely on distinctions or principles that literally cannot be expressed or represented within the old system, CS1. Consider a young child's early concept of heaviness. OK. Initially, they might conflate what adults distinguish as weight and density. A big fluffy pillow is heavy, and a small metal weight is heavy. They don't grasp why one floats and the other sinks. The adult concept of density. mass per unit volume requires relating weight and size in a way their initial undifferentiated heaviness concept simply doesn't support. From the perspective of that simple heaviness concept, density is kind of incoherent. It involves variables the child isn't tracking yet. So to build that new concept of density or concepts like exact number, you need something CS1 doesn't provide. Precisely. And this is where language or other symbolic systems are proposed to come in. They provide placeholder structures. Placeholder structures. Like what? Think of the ordered count list. One, two, three, four. Initially, for a young child, these are just sounds in a specific order. They don't necessarily know what four means in terms of quantity yet. Ah, OK. The meaning at first comes purely from the structure. Two comes after one, three comes after two. It's this external ordered symbolic list that acts as a scaffold. The child can learn and manipulate the structure before fully grasping the numerical concepts it will eventually represent. This symbolic scaffolding allows us to build systems for concepts like division, negative numbers, or the infinite integers things utterly outside the scope of core cognition. So the symbols provide the framework to hang these new initially abstract ideas on. That's the core idea of Quinian bootstrapping. The symbols let you represent relationships and structures that you can't directly perceive or represent with analogiconic systems alone. And this interaction between innate abilities and language isn't just for numbers, right? It applies to basic categories, too, like knowing a duck is a kind of thing. It's complex there, too. The research suggests infants, even by 12 months, do seem to distinguish kinds of things like duck, a sortle down, from simple properties like read an adjective. They use kind membership to track objects. So Quine's idea that language creates the kind property distinction seems wrong. But language still helps. It definitely helps in learning specific kinds. If you label different looking toy animals all as blickets, poddlers are quicker to group them based on their shared kind or shape. If you use an adjective like, look, the fuzzy one, they're more likely to group based on that property, fuzziness. So language doesn't invent the idea of kind, but it powerfully directs attention and helps children figure out which kinds of properties are important in their culture. Let's really focus now on the prime example of this bootstrapping process, learning the positive integers 1, 2, 3, and so on. You said this new system, the integer list, CS2, is discontinuous with core cognition. CS1. Why is that leap so hard? What exactly is missing from CS1? The fundamental discontinuity lies in representing the successor function. Remind us what that is. It's the core principle of counting. For any natural number n, there is always a unique next number, n plus 1, 5 follows 4, 6 follows 5, and crucially, this process never ends. It implies infinity. And our core systems can't handle that. Neither of them. The object file system is stuck at 3 or 4. The analog magnitude system represents numbers as fuzzy estimations on a sort of mental line. It gives you more or less, but not the precise, discrete step of exactly one more, repeated indefinitely. There's no way to build the concept of an infinite ordered sequence from those starting points alone. Which explains why learning to count isn't trivial for kids. If it were just mapping words onto existing concepts, it should be fast. Exactly. But it takes years, typically from age two to four or even five. Kids spend a long time just mastering the sequence and then figuring out what the words actually mean. This prolonged difficulty is strong evidence that they aren't just labeling old ideas. They're constructing something fundamentally new. So how does this construction happen? What are the steps in this bootstrapping process for number? It seems to follow a predictable pattern, often called the subset knower stage. First, as we mentioned, children learn the count list, one, two, three, four, five, mostly as a meaningless chant and ordered sequence of sounds. Like reciting the alphabet before knowing the letters? Precisely. That list... is the crucial external placeholder structure provided by their culture and language. Then they start to connect the first few words in that list to actual quantities. They become subset knowers. A child might first become a one knower. If you ask them, give me one fish, they could do it reliably. But ask for two and they just grab a random handful. Then maybe months later, they become a two knower. They can give you one and they can give you exactly two. But ask for three and they're back to grabbing randomly. They learn the meanings of these first few number words one by one by one. And how are they grounding the meaning of, say, one or two? It seems they map these first few number words onto the representations provided by their parallel individuation object file system. One maps to a mental file for a single individual eye. Two maps to a model with two individuals, I1, I2. Three maps to I1, I2, I3. They use the exact tracking system. CS1, to give meaning to the first few symbols from the list, CS2. But they hit the wall around three or four, just like the object file system limit. Exactly. They might become a three knower, maybe even a four knower, but they're still stuck. They haven't grasped the underlying system of the count list yet. The real breakthrough is what's called the inductive leap, or acquiring the cardinal principle. The cardinal principle. That sounds important. What clicks at that moment? It's the aha moment. The child suddenly generalizes. They realize that the last number of words said when counting a set represents the total number of items in that set, the cardinality. And crucially, they seem to grasp implicitly that every word on the count list refers to a quantity exactly one greater than the previous word they get the successor function. So they realize the whole list has meaning, not just the first few words. Yes. The placeholder structure isn't just sounds anymore. It's suddenly understood as a generative rule for representing number. They might not be able to count perfectly to 100 yet, but they understand the principle that allows counting to continue indefinitely. They bootstrapped the integer concept, CS2. Okay, so now they have this abstract, powerful number system in their heads, but does that mean they instantly feel the difference between, say, 7 and 10? Does it connect back to that gut sense of quantity? Not necessarily. And this is another fascinating piece of evidence for discontinuity. The next step is mapping this new abstract integer list, CS2, back onto the old approximate analog magnitude system, CS1. Why do they need to do that? To get quantitative intuition. To know roughly how much 7 is compared to 10. And research shows that children who have just made the cardinal principle leap, so -called CP knowers, are often initially non -mappers. Non -mappers. They know the counting rule. They can tell you that seven comes after six. They might be able to count out seven items correctly, but if you show them two sets of dots, say seven versus ten, and ask which is more, they might guess randomly or rely on visual cues that are subject to Weber's law, just like a pre -counting child would. So they have the abstract rule, but not the connection to magnitude for those larger numbers yet. Exactly. They haven't yet associated the specific symbol seven with the corresponding fuzzy magnitude on their internal number line. That mapping process, connecting the precise symbols back to the approximate sense of quantity, is slow and happens gradually after the cardinal principle is acquired. And that slowness is key evidence. It's powerful evidence. If seven were just a continuous extension of the core concept of three, the mapping should be automatic. The fact that it's laborious and piecemeal strongly suggests that the integer concept was constructed discontinuously. using the linguistic list as a necessary scaffold, creating a system that then needs effortful integration with the older core systems. This really brings home the power of symbolic systems. And it makes you think about cultures that might lack these extensive number systems, like the Pirahan people in the Amazon. The Pirahan case is often cited here, yes. Reports suggest their language lacks number words beyond maybe one, two, and many. And studies testing their ability to mask quantities exactly for sets larger than three show their performance immediately drops off and looks just like the signature of the analog magnitude system, approximate and ratio dependent. So without the symbolic tool, the count list, they seem to rely solely on the core cognition systems for quantity. That's the interpretation. It provides a stark illustration. The development of exact large number concepts seems deeply reliant on having that specific linguistic or symbolic scaffolding in place. That's the interpretation. It provides a stark illustration. Hashtag tag outro. So pulling all this together, what does it tell us? It paints a picture of the human mind, starting with a surprisingly rich foundation. These innate core cognition systems for understanding objects, agents, space, and approximate number. They give us continuous intuitive grasp of the basic structure of the world. But that's not the whole story. Not at all. To get to the truly powerful abstract concepts that define human thought, formal mathematics, science, complex planning, we need something more. We need this remarkable process. quitting and bootstrapping. It uses language or other symbolic systems as essential placeholders. Scaffolding to build something new. Exactly. Scaffolding that allows the mind to make these inductive leaps, constructing new conceptual systems, CS2, that are qualitatively different, more powerful, and sometimes from the perspective of the original system, CS1, even seem incoherent initially. Yeah, that idea of incoherence is really striking. Learning isn't just adding information. It can be about fundamentally restructuring your way of thinking, like the child moving from simple heaviness to distinguishing weight and density, or from tracking three items to understanding the infinite integers. It's hard work, because the new framework might not even make sense from the old point of view. It is hard work. And it highlights how the very structure of the symbolic systems we learn the grammar of our language, the notation of mathematics, shapes the conceptual landscape we can build. These tools don't just express thoughts. They seem to enable certain kinds of thoughts in the first place. Which leaves us with a really provocative final thought, doesn't it? If the specific structure of language, like having a count list, is necessary to bootstrap a concept as basic as exact number. Well, it makes you wonder, right? Think about the language or languages you use every day. What complex ideas may be about time or consciousness or causality or perhaps dimensions beyond our immediate perception? What concepts might currently be hovering just beyond our conceptual reach? Because we lack the right words, the right symbols. Perhaps. Because we haven't yet collectively built the necessary symbolic scaffolding, the placeholder structures that would allow our minds to make the next great inductive leap, what potential conceptual systems remain unbuilt, waiting for the right linguistic tools?