# Understanding Linguistic Functions

Speaker: Amie L. Thomasson
Course: Making Metaphysics Functional
Watch: https://ergo.org/videos/amie-l-thomasson-do-numbers-really-exist
Transcript: https://ergo.org/videos/amie-l-thomasson-do-numbers-really-exist/transcript/
YouTube: https://www.youtube.com/watch?v=mVeb1ZHrDww

When quoting, name the speaker and link to the watch URL.

In this third lecture, Amie L. Thomasson argues that philosophy has gone astray by ignoring the different functions that various parts of language serve in human life. She draws on tools from systemic functional linguistics to examine how features like mood, modality, and nominalization work, and why they evolved in language. Thomasson distinguishes between mere uses and proper functions, drawing on evolutionary and system-based accounts of function. She pays special attention to nominalizations, explaining how they enter language and why they have generated persistent philosophical puzzles about abstract entities. Along the way, she considers other approaches to linguistic function, including Matthieu Queloz's needs-based method, which asks what we could not do without certain terms and concepts. The lecture sets the stage for applying these insights to debates about morality and truth in the lectures that follow.

## Introduction and Lecture Overview

Welcome to lecture three, Understanding Linguistic Functions. In the prior lectures, I talked about the ways in which I think recent work in metaphysics has become dysfunctional. It's especially become dysfunctional by ignoring the different kinds of functions that different parts of language serve in our lives. And I also suggested in the second lecture that we can do better by rethinking metaphysics, thinking of it not as if it's trying to discover some deep and hidden truths about the world, but rather thinking of it in terms of conceptual engineering, which involves both the projects of trying to understand how our language and conceptual scheme work and what functions they serve, and then making forward-looking choices about what we should do with them. We should retain them, revise them, make any changes in our linguistic or conceptual scheme.

Now, in both of those parts of the project, the notion of function plays a really central role. It plays a role in avoiding the mistakes of recent work in metaphysics by not assuming that all language serves the same function and trying to figure out what functions they do serve. And it plays a big role in forward-looking conceptual engineering. It plays a role there because we have to, in making these changes, understand what kinds of functions we want our terms to serve going forward. So the notion of linguistic function is really important here.

What I'll do in this lecture is to try to show how we can understand the notion of linguistic function, how we can determine what the functions are of different parts and aspects of language, and then what difference this makes to work in metaphysics. And towards the end of this lecture, I'll illustrate that with two examples. One, old problems about talk of numbers and metaphysical problems about what numbers are and if numbers exist, and problems about properties, what properties are, do they exist, et cetera, and how these problems look really different once we understand the functions of these types of discourse.

## Can We Identify Linguistic Functions?

Some people have expressed skepticism about the idea that we can say what functions different parts of language have, thinking of it as a hopeless project. But I don't think it's at all hopeless, and I don't think we should throw out talk of functions. We need an ability to talk about and to determine what functions are in other fields, too. In archeology, for example, if you find an ancient artifact, the archeologists are going to try to figure out what functions it served in the lives of the people, in anthropology, and so on.

So we need a way to identify linguistic functions, and actually, we can get some help in this kind of project from work in linguistics, as I will try to show. When I ask what linguistic functions are, one thing will probably be clear to you if you've heard the prior two lectures. I'm not thinking of this as a metaphysical project of detecting truly what a function is and what its identity and persistence conditions are. Instead, what we need is a notion of linguistic function that's going to help us in doing the work we need to do in conceptual engineering, both reverse engineering and constructive or forward-looking engineering. What kind of notion of function do we need here?

## Uses vs. Functions: The Penny Analogy

Well, the first thing to say is, when I'm talking about linguistic functions, I don't mean to be talking about the way we use language on one occasion or the other. Of course, we use language in all sorts of different ways to order food, to insult each other, to make a contract, whatever. That's all really interesting, and it's a topic that's dealt with more in speech act theory. But obviously, the uses of something can vary a whole lot while the function remains the same.

So think about a penny. You can use that as a screwdriver. You can use it as a way of drawing circles. You can use it in an electric circuit. But that doesn't tell you that any of those are its function. What we want to know is, what's the enduring function that explains why we have these things?

Now, another common notion of function that people often come to and draw on is the notion of intended function. If I'm an inventor and you want to know what's the function of my new gizmo, I will report to you what I intend it to be useful for. And again, that's cool, and that's useful in some contexts. But it's not going to be super helpful for language, because most of the language that we've inherited and that we learned to speak when we're very young wasn't really intentionally created by anyone for any purpose. It's something that's evolved through our common use.

Or even where it was intentionally created, if it was intentionally created by someone many centuries ago, we may have no access to their intentions, and the functions it serves for us now may be very different than whatever was originally intended. So intended function, it can be a useful notion for the kind of constructive, forward-looking engineering. If we want to be explicit about what we want our new conceptual linguistic item to do for us going forward, we can get explicit about that. But it's really not going to be very useful for reverse engineering, certainly, and we have to build on that even in doing constructive engineering.

All right, so what else is there? Well, there was a general problem about how to understand the notion of function. In the religiously dominated tradition that was common in Europe, certainly through the Middle Ages, up through parts of the modern period, there was a temptation to understand all functions as intended functions. What's the function intended by God? As that worldview waned, there was a need to get an understanding of function that could be useful in fields like biology, if you want to talk about the functions of the heart or the pancreas or something like that, in ways that don't presuppose a theological assumption about God and his purposes.

## Proper Function: An Evolutionary Account

To fill this gap, this was really a bit of conceptual engineering itself. The philosopher Ruth Millikan developed a notion of what she called proper function, and she thinks of this in roughly evolutionary terms as whatever functions members of this type have played historically that helped explain why they, in biology, reproduced and stuck around in the population. On that model, you can say the function of the heart is to circulate blood, and what explains why we have hearts now is because it did that for our deep evolutionary ancestors and thereby helped enable them to survive and reproduce. Now, even Millikan applies this also to cultural creations. Why did these parts of culture survive and stick around? What did they serve? What functions did they serve in human life that explains why they stuck around?

The notion of proper function that we can get out of the work of Ruth Millikan is really useful here to try to understand functions in a non-theological, non-intentional way, where we can use that to analyze what, whatever it is, these kinds of things do for us in human life that explains why they have perpetuated and stuck around. Now, a couple of caveats on that. If you're getting a notion of proper function, that doesn't necessarily mean that was the only way to do it. We could talk about the proper function of a fork, even if we could have also just eaten with chopsticks. It doesn't also have to mean that the function is something that was useful or good or helpful for absolutely everyone.

Sometimes, what sticks around is what's functional for those in power or who have the power to perpetuate the culture. So we have to be on the lookout for those kinds of things. The proper function approach is really helpful here.

There's also a little bit of a reservation about that. That is, if you're going to make interventions in engineering, conceptual or otherwise, then you want to know not just what things like this have evolved to do, but also what it's doing now. Functions can change over time. If you have a building, you could have a column that was originally just decorative, but after an earthquake, comes to be load-bearing. And you want to know that before you decide whether you should remove it. So we also want to know what, in our case, this part of language does for us now, even if that's not the full evolutionary story of where it came from.

## System Functions and Current Functions

We also want to know what it does in the linguistic system as a whole. I think too often in working conceptual engineering, people have focused just at the level of an individual word, even if they've taken a functional approach, and not everybody does that. Asking things like, "Well, what's the function of the concept of woman?" As if there's only one, and as if we can look at this word in isolation. But again, pull out to analogies with other kinds of questions about function. You're not going to answer a question about what's the function of the pancreas if you just pull it out of the body and you lay it on a tray and you try to study it in isolation. You have to understand how it works within all of the bodily systems.

Similarly, if you're trying to reverse engineer some ancient piece of machinery that you've just discovered, just pulling out one gear and putting it on a tray is not going to enable you to do it. You have to understand how the whole works. So this idea that to understand functions, we need to understand the broader systems, the function of the whole system, and then what the relevant subsystems do that contribute to the workings of the whole. It's a notion called system function that was suggested by philosopher Rob Cummins.

So what I want to do in moving forward and talking about linguistic functions is to use a combination of talk about proper functions, what did it do that explains why it's here, and system functions, where we explicitly look to the way in which these linguistic facilities and grammatical forms, what do they play, what role do they play in the language as a whole, and in the functions of language as a whole.

## What Does Language Do in Human Life?

Here's what I found to be a useful angle. Start more holistically. Ask questions about what functions language serves in human life. And there, I think we'll find, as figures in systemic functional linguistics have found, that in human life, language serves a multitude of functions. It's not just there to communicate ideas or content, as a lot of people instantly come to that as an answer to the question of what the function of language is.

But we also use it in establishing interpersonal relationships of dominance or supplication or question or an answerer. We use it in setting up our social world. We use it in establishing regulations for behavior in the law or in the classroom or whatever, and many, many other things.

So what we'll do is then start from the look at these functions that language serves in human life, and then ask what different capacities and subsystems in language contribute to that, and this is going to help us to get a clue about then what functions things like having noun terms for numbers or property language does for us. So there's three parts of language that I'll focus on because I think they're really helpful to us philosophically.

## Mood, Modality, and Nominalization

One is a mood system. The mood system in language is what enables you to utter, say, imperatives versus interrogatives versus declarative sentences and so on. Then there's the modal system. The modal system is broadly what, at least classically, it involves modal verbs like what you must, may, could, or should do. And then there's this capacity for forming nominalizations, from moving from saying things like, "They danced" to "They did a dance."

So I'll talk about each of these three broad features of language and what they contribute to the functions of language as a whole, and what understanding that can do to help us with philosophical problems. In each case, I want to move ahead by asking questions like this. Well, look, what couldn't we do or couldn't we do as well or efficiently, or couldn't some of us do as well if we didn't have a language with a way of marking different moods, the interrogative versus the declarative or the imperative? What couldn't we do as well without, or maybe we couldn't do at all, without a modal system or without a capacity to form nominalizations out of simpler forms of speech?

Bearing in mind that doesn't mean it's the only way to do it, and it doesn't have to be only one thing. I think it's also a mistake to think in terms of the function rather than many functions of whatever you're talking about, really. But language is what I'll be talking about.

## Evidence for Determining Linguistic Functions

How can we answer these questions? Really, this is a matter for linguistics, and this is a nice case in point of how we need a cooperation between philosophical work and work in linguistics and also in psychology and cognitive science, though I won't be doing that today. This is nice because it's non-mysterious. There's a lot of work we can draw on in terms of trying to understand linguistic functions, and we can do it in a way that's empirically responsive, that's not just trying to purport to discover some deep metaphysical truth.

How can we do it? There's many different kinds of evidence we can draw on. Some of it is what I would just call analytical work. I mentioned yesterday that by having noun terms for properties, for example, we can ask general questions like, what properties did the most seriously affected COVID-19 patients have in common? And we can state generalized scientific laws, like the ideal gas laws that appeal to the relationship between the pressure, volume, and temperature of a sample of gas. All these require nominalizations. You can just see that they do this by looking at these forms of speech, and then it's open to any objectors to say how else we could do it, and would that be simpler. But of course, this may just be the way we've found to do it. It doesn't have to be the only way. So that's analytical evidence.

But we can also look to language development. We want to know what we can do by, say, having a language with a modal system, with modal verbs like must, should, can, that we couldn't do without it. How can we answer that question? Look, there's real live people who speak some language but don't have the modal system. Those are the three-year-olds. The modal system is typically acquired relatively late in language development, between about ages two and four. So you could actually look at language development and get evidence of what the children can't do at that stage that they can do later.

You can also look to linguistic history and linguistic evolution, where you can get evidence about this. And there have been some recent languages, including forms of sign language, that have developed where you can watch this kind of development. And then you can see what kinds of facilities are brought into being by these new linguistic developments that weren't there before. You could also look in the historical development of our living old languages, like English, and ask things like, well, what were the actual historical pressures that were going on that might have led to the development of, say, racial terms, or led to the massive proliferation of, say, nominalizations in our language. And we can use that as evidence as well.

So all of this is, in principle, empirically tractable. It doesn't mean we've got all the answers now, but we've got some things to go on. Sometimes we will just end up addressing counterfactual questions. What couldn't we do or couldn't we do as easily if we didn't have a capacity for nominalization or a truth predicate or whatever?

Another approach to looking at linguistic functions has been developed by Matthieu Queloz, a contemporary philosopher, who develops what he calls a needs-based approach to understanding functions of terms and concepts. And he does it in these ways. He really proceeds from addressing these counterfactual questions that say, well, look, what wouldn't we be able to do or do as well if we didn't have terms for truth or knowledge or justice? And he runs these state of nature scenarios to ask what human needs these concepts would provide some kind of solution to and how those might have developed in particular historical circumstances, and even calls this a kind of reverse engineering, the points of these ideas.

So that's also an approach we can take, and I will actually blend these. One thing that I will do is to often begin from a needs-based approach for a basic form of language and then use the work in systemic functional linguistics to understand how we can build through there, through different grammatical developments to add more and more functions to the language.

## Systemic Functional Linguistics: Origins

One really nice source of work on this that I found in, I have these questions about linguistic functions and how to understand them, comes from work in systemic functional linguistics. This is a tradition of work in linguistics that grew out of work in the Prague school of linguistics in the early 20th century, with people like Mathesius and Jakobson, who were lead figures in that circle. It was also strongly influenced by philosophical work by Edmund Husserl's *Logical Investigations* because he was interested in how language works as a system.

But it was also influenced by work in anthropology, especially by the anthropologist Bronisław Malinowski because Malinowski was interested in the functions language serves in human life. And he used that kind of understanding to help him understand distant languages that had never been encountered by Europeans before.

This work in functional linguistics was then developed by people like linguist J.R. Firth and Michael Halliday, especially, and it's been very influential in work in, not surprisingly, in anthropology and also in education because what they aimed to do was to figure out what functional abilities children were lacking who had language delays, who couldn't use language like their peers did.

So I'll be drawing on some of their work here, but a lot of what I have to say about these linguistic functions is really independent of the peculiarities of this or that approach to linguistics. In fact, a lot of the functional theses that I'll draw on here have really been affirmed by people working in different areas of linguistics.

## Stages of Language Development

Here's the approach that I want to take. Let's go through some different stages of language development and ask what we couldn't do before that we can do better after we've acquired that language. So all of us begin pre-linguistically. What problems do we have there? Well, you might say, naturally, we can't communicate. That is certainly true, but also we can't make our needs or desires known.

This is why children who have language delays often get so frustrated and act out in other ways, kicking and screaming because they can't just make their needs known by using their words, as their preschool teachers always say. They also can't be the same part of the social situation. They can't just greet their caregivers or classmates or whatever by saying hello or goodbye. They can't be polite by saying please and things like that. They can't express themselves and their attitudes politely by saying, "I don't like the broccoli." They just have to throw it on the floor, something like that. So there's so many things they can't do.

A lot of this is already taken care of at that first stage of language learning, learning what you might call a proto-language, where these toddlers typically just have one-word utterances or very set phrases without having that kind of grammatical capacity and variability. But now they can do a lot. They can yell, "Milk," when they want milk and make their needs known. They can say, "Yuck," to the broccoli instead of throwing it on the floor. They can greet their caregivers or their classmates and so on.

So that's already a huge move, and notice that it enables the child, even with this very basic proto-language, to serve several different kinds of functions at once to communicate what they think, to express their attitudes, to make requests, and so on. They're certainly not just communicating ideas. The next stage of language acquisition, which often happens around age three, is when a child starts to acquire grammar, and then they get that flexibility that enables them to express their needs in many different ways that may or may not be appropriate, say, in the social situation.

Now, Michael Halliday analyzes each clause in a mature language of a speaker who's acquired grammar as serving three kinds of function at once. He divides these up into the ideational metafunction, which involves expressing a kind of propositional content that's useful for communication and reasoning, interpersonal functions of expressing your attitudes, regulating behavior, showing your level of certainty, and so on, and textual functions of showing how ideas link together.

Now, we don't have to be committed to that exact structure to make use of this idea. What I think is really important here is the idea that each clause in a mature language, when a speaker has acquired grammar, can serve many different kinds of function at once. And again, this reminds us that the question, what is the function of, is a misleading question because we shouldn't assume there's just one. There's often many, and our task is to sort of unravel and untangle them so we can see them clearly.

## The Mood System and Politeness

Here's an example of how these functions might come together. Suppose somebody gives you some tea and you really want some milk for it. If you don't have language, you can't do much. You could try to just go grab the milk for yourself, or you could scream and hope someone figures out why. Not very effective. If you're a child with a proto-language, you could holler, "Milk!" in a demanding tone, and then get what you want.

But if you're a mature speaker, you probably won't just do that. Imagine you're at the home of an acquaintance here. You would think of that as impolite, too direct. But as a mature speaker, you've got options. The mood options enable you to do things much more subtly. So you could say things like, "I want milk," declarative sentence, or you could be even more polite and say, in an interrogative, "Do you have any milk?" A bit more polite.

Now, if you've mastered the modal system too, you can say it even more politely. You could say, "Might you have some milk?" Or, "Some milk would be lovely." And you then communicate your needs, get what you want, while also setting up the right social relationship with your host.

We're getting some clues already about what you can do with a mood system that you couldn't do without it. By having a mood system, you can make clear if what you're doing is attempting to state a fact, making a declarative, or asking a question, or making a request or whatever, instead of just saying, "Milk," and having whoever you're with not know if you're identifying it, or requesting it, or objecting to it, or what. The mood system is acquired pretty early, usually about around 19 months.

Then there's two other really philosophically interesting language facilities that I want to talk about. That's acquiring the modal system and the ability to cross grammatical categories in a way that typically introduces nominalizations.

## What Are Grammatical Metaphors?

I'll talk about that in my next lecture, about the modal system, because it's very important to understanding moral discourse. So I'll come back and talk about that later. That typically develops around ages two to four.

What I want to talk about for the rest of this lecture is the idea that's referred to by Michael Halliday as grammatical metaphors. Now, I don't love that word because I think it's misleading. It makes it sound like the speech is merely metaphorical. That's not how Halliday means it. The term metaphor comes from the Greek for transfer, and a grammatical metaphor, in his terminology, is a way of transferring from one grammatical category to another.

And this can go in various directions. The ones I'll be especially interested in for our philosophical work are nominalizations, and that's just the capacity to form a noun term out of another part of speech. So we can move from saying, "The apples are red," that's an adjective, obviously, to saying, "The apples have the property of redness," where the property of redness is a noun term. Or we could move from saying, "They danced," verb, to saying, "They did a dance," introducing a new noun term, dance. Or from saying, "There are four cups on the table," where we have a number term and a determiner use, counting things, to saying, "The number of cups is four."

So all of these involve crossing grammatical categories from another part of speech into a noun term. What's really interesting is that most philosophically interesting and problematic terms, or certainly those that have been considered problematic in metaphysics, turn out to be nominalizations.

## Nominalizations as Philosophical Problems

If you start to think about it, the terms that have been problematic include things like terms for properties and numbers, like I've been talking about. Also for meanings, events, states, processes, time, causation, possibility, probability, necessity, thoughts, beliefs, minds, moral requirements. All of these are terms that have been thought to present first-rate metaphysical problems, and they're all nominalizations.

So understanding the functions of nominalizations in our language and how they get introduced can help us unravel many of these metaphysical problems. I'll just give a gesture towards two today. First, let me say a bit more about grammatical metaphors, including prominently these nominalizations.

## How Nominalizations Enter Language

We don't acquire the capacity for completely processing and using nominalizations and other grammatical metaphors until really late in language development, like ages eight to twelve. That's crazy late for language development. We start off when we're little kids learning language, learning observational language acquired in response to what we see in the environment. So you point at the dog, and your parent or caregiver will say, "Dog," and you can learn that word, or point at a tree and say, "Tree," and so on. And you can observe toddlers doing this when they start to acquire language. They'll find some way of encouraging their caregivers to name more and more things in the environment for them, and that's great, and that contributes to their learning about the environment.

Learning terms in this way, these observational terms, requires a kind of causal and observational connection to the environment, or sometimes a less direct one. If you're reading picture books, then you can also get a term for elephant, even if you haven't seen one yourself directly, but there's a causal connection to whoever drew the picture originally. And these kinds of observational terms, they enable us to learn more about the environment and to communicate and express our needs about observable things, and to track the features in an environment as they move. You can track the dogs, you can learn more about dogs as you go on and report on it.

What happens when we introduce grammatical metaphors like nominalizations isn't that we observe something new. It's that we learn to make a certain kind of licensed grammatical shift, and these shifts are licensed across languages. So the people in systemic functional linguistics have evidence that this capacity for shifting grammatical categories is universal across the languages they've studied anyway, and for good functional reasons, as we'll see. It'll vary from language to language, like which ones are the most common and how frequently they're used in different kinds of discourse, but they always have this basic ability.

So what happens there is that a meaning that, this is a quote from Halliday, "was originally construed by one kind of wording, comes to be construed by another." So you might start by observing a scene and saying, a man's washing a car, and say, "Man wash car," if you're three. But then if you learn to introduce nominalizations, you can come to say things like, "The man gave the car a good wash." Or you could say things about the car wash, like, "The car wash was a very messy enterprise." Or, "The children did a car wash all afternoon on Saturday to raise funds for their trip," whatever. Now, introducing these new nominalizations enables linguistic speakers to do new things.

## Why Nominalizations Matter for Science

What are the functions of these kinds of nominalizations? One is we can use it to make these kinds of grammatical shifts that help us identify the topic of the sentence and what's new information about it. We could say things like, "They danced." That's fine. That's just observational. But if we introduce the noun form, the dance, instead, we can put that at the beginning of the sentence and say, "The dance was the hardest part of the whole show for Christy," or whatever. Now you attract attention to what we're talking about by putting it at the start with a noun.

More importantly, by introducing these new noun terms, we add expressive power to the language, so we can do things with the language that we couldn't do before or otherwise. We can, for example, qualify events and processes in ways that we couldn't before. We could say things like, "This very difficult Latin American dance," and now we can talk about the dance and add adjectives to that because now it's in the noun place. We can also quantify events and processes in new ways. So instead of just saying, "They danced," we could say, "They did three dances in the second act of the show," and count them.

Also, and I alluded to this in the prior lecture, bringing in these kinds of nominalizations is really important to developing general theories and bureaucracies. Only by having noun terms, instead of saying things like, "The gas was really hot," we can talk about the relationship between the temperature of the gas and the pressure and the volume, all of those being nominalizations. And only with these kinds of nominalizations at our disposal can we formulate general scientific theories.

You can get some neat evidence of this also in historical linguistics. As I was saying, sometimes you can get nice evidence from historical linguistics, and Halliday has brought out the ways in which the use of nominalizations just exploded in the scientific revolution in Europe. The density of nominalizations and the number of new ones that were introduced increased dramatically as we started engaging in systematic scientific theorizing.

But it's not just there. We also need these kinds of nominalizations in order to lay out systematic bureaucracies. If you look at any contract in your files or read the terms and conditions for once, they're just absolutely full of nominalizations. You can't state generalized laws, say, that establish the relationship between your debt, your income, and your taxation rate without a whole slew of nominalizations at your disposal. We need this to form generalized laws as well as generalized theories.

Again, interestingly, what kinds of evidence you can get developmentally, Halliday says, since we need a real capacity for forming and understanding grammatical metaphors, including nominalizations, in order to even understand and process general scientific theories, that's why we don't start teaching children serious science until they get to about middle school, because they need that capacity. We certainly don't start teaching them serious law then either. So that's a brief overview of some of the functions that are served by this general ability in language to cross grammatical categories and introduce, mainly I focused on noun terms, from terms of other grammatical categories and what this does for us.

## Debates About Abstract Entities

Why does it matter to metaphysics? Why should a metaphysician or anyone interested in metaphysics care about it? What I'll do now is turn to give a couple of brief illustrations of this. There have been age-old debates, really since ancient philosophy, about whether or not abstract entities exist or how we should think of them. Abstract here gets used in many ways, but roughly entities that aren't in space and time, that you can't just observe, touch, tell exactly where they're located. Central among these are numbers and properties, like the property of redness or being red.

So people have long debated questions. Are there any such things? As I mentioned at the beginning, metaphysics has often thought of itself as centrally involved in addressing questions about what exists. So do abstract entities exist? Do properties exist? Do numbers exist? If so, again, metaphysicians have pressed questions like, how could we find a place for them in the natural world? If they don't have a space-time location and so on.

If they don't make any sense, if we can't make sense of things that aren't physical and spatiotemporally located, then some have said we should just do without them and try to find a way of understanding science without numbers, as Hartry Field aimed to do, or speak not in terms of abstract properties, but individualized tropes, like the blackness of this particular chair without thinking of that as an abstract property.

Others have worried, if there were numbers and properties, and they're not entities we're causally related to that we can observe, how could we possibly ever come to speak of them because we don't have a causal connection? How could we have knowledge of them if we can't be causally connected? We learn about dogs and bears by having causal relations to them, by observing them or hearing from others who've observed them, but we can't do that for numbers or abstract properties, and so on. How could we even come to acquire the language at all?

So these have all been enduring sources of skepticism about whether we should say that properties or numbers really exist. Now let's pause from that and step back and see how understanding the ways in which terms like this enter language and the functions they serve can shed new light on these ancient problems.

## Easy Inferences and Ontology Made Easy

I've already talked a little bit about how terms like this come into language. They don't come into language by observing a number or observing an abstract property. They come into language by making these kinds of grammatical shifts from terms in other categories. And what functions do they serve? Well, look, we're able to make these grammatical shifts, and the capacity to make these grammatical shifts is available across languages for really good reasons, because they enable us to qualify and quantify events and processes, and to state general theoretic and bureaucratic laws.

Let's return to the metaphysical questions. Are there, or some people say, are there really properties? Are there really numbers? Well, in my 2015 book, *Ontology Made Easy*, I argued that we can actually answer these questions through what I called easy inferences. That is, they're inferences that take us through really simple steps from a statement nobody disagrees with to conclude that there are numbers or properties. So you can start by looking at the barn in my yard and observing and saying, "The barn is red." No one who's not colorblind and comes to my yard is going to disagree with that. That's fine. That's uncontroversial.

But then you can just move from that to make this grammatical shift and say, "So the barn has the property of redness." This is just a licensed grammatical shift that enables you to introduce a new noun term. But if the barn has the property of redness, then there is a property of redness the barn has, and so we conclude, yes, there are properties. There's one, redness.

Or similarly, as neo-Fregeans in the philosophy of mathematics, like Bob Hale and Crispin Wright, made a sort of similar move for numbers. I'll do it in slightly different terms than theirs. But suppose you start from a simple observation no one would disagree with. Say there are three glasses on the table. Anybody can come and check that. But then from that, you can move to say the number of glasses on the table is three. Again, that's just a sort of trivial inference that moves you into using a noun term for numbers. And then you can say, "So there's a number."

In the book, I respond to a whole range of objections against these easy inferences. That's not where I'm going to go now. But what I want to say is, what was really interesting to me when I discovered this work on linguistic functions is that we can say more now to support the idea that these really are just trivial inferences that entitle us to answer these existence questions in the only sense that has sense, the sense these nominalizations have.

So, when I wrote the book, a lot of people said to me, "No, look, the inference can't be that easy. It would be stupid to have language that's just that redundant and long-winded to introduce to go from the barn is red to the barn has the property of redness. That would just be redundant. There must be something more that's really required for there to really be properties." Well, now I can see, actually, no. It's trivial, but it's not just redundant. We have this capacity to introduce nominalizations, and it doesn't require that we observe some new thing, some new kind of abstract entity, or that we intuit a number.

Instead, we have this ability to introduce the new noun term, and it's there for good reasons. It's not just redundant. It's there for new functional reasons. It enables us to do new things with language. Because now we can talk about the property of redness and how it's related to properties of having certain microtextual features or of wavelengths of light and so on.

So we can see then, I think, why there are these kinds of rules that enable us to make the kinds of trivial inferences that I had alluded to before, why they're in language for good reason, and why nothing new is required, and you make a mistake if you think you've got to also observe some abstract entity in order to be licensed to introduce terms for properties or for numbers.

## Dissolving Traditional Metaphysical Worries

You might say at that stage, "Well, but look," and various metaphysicians have said this to me, "that doesn't address the problems with numbers. Aren't they just spooky, numbers or properties? Aren't abstract entities spooky? How could we possibly come to know them if we're not causally in contact with them?" Well, again, I think once we understand the entry rules for and the functions of this terminology, we can see why those kinds of objections are a mistake. There's no need to causally interact with an abstract entity to be able to know the truth of certain property statements or to know that the number of cups on the table is three. Instead, we can come to this knowledge by making certain kinds of inferences from other statements that we already accepted. Sometimes it gets very complicated in the mathematical case, but you can see how that's going to go.

Well, others would say, "But look, we shouldn't really posit numbers or properties, these kinds of abstract entities, into our ontology because they don't add any explanatory power to our theories. They can't causally explain anything," as the neo-Quinean program would say. But once we understand the functional role of this vocabulary, that it's not there to provide causal explanations, but instead to enable generalizations and qualifying and quantifying events and processes, and enabling us to theorize and bureaucratize, in general terms, then you can see that there's no reason to reject or deny that there are these entities because they don't have explanatory power. They were never supposed to do that. That's not the kind of term they are.

Well, how can they be placed in the world if they don't have a spatiotemporal location? How could we refer to them if we aren't causally connected to them? Again, once we understand the functional differences, we can see that all these problems arise by a mistaken analogy to the kind of language we learn first when we talk about dogs and trees and stuff, and we can just observe them, and we are causally interacting with them. And we better be, if that language is to be legitimate. But that's just not how this kind of language, these nominalizations, work. It's not how they're supposed to work.

So the traditional metaphysical objections to properties and to numbers all rest on a kind of failed presupposition. This is the functional monist presupposition that I talked about in prior lectures. A presupposition that these terms for numbers and properties, maybe other abstract entities, work or should work the same way as observational terms like dog and tree do to pick out things we can causally interact with in the environment and track them.

Now, for terms like that, for these observational terms, it is indeed a problem if you don't have a causal connection to them. So this is where unicorn and Bigfoot go wrong. If you try to use them as names for creatures in the environment, there's no causal connection to an actual horned horse-like creature or an actual giant, furry human-like creature. And so these terms fail. But that's not what terms for properties and numbers are supposed to do. That is not how they're introduced. There's no such expectation or requirement here, and we don't have to learn about these things by being causally connected to them. Instead, we just have to master this kind of linguistic ability to introduce nominalizations out of these other grammatical categories.

Now, I don't mean to suggest this solves all the old problems in philosophy about numbers or properties or how we can know them. That would require a whole lot more discussion. But I do hope to have convinced you that at least we can undermine a whole lot of what have been thought of as great barriers to saying that there really are such things, that they would just be spooky or weird or would lack explanatory power, and so we shouldn't have them. I think we can see why those standard kinds of complaints and objections and hesitations just lead us astray once we really understand how the language works, what functions it serves, and how we introduce it.

## Summary and What Comes Next

In this whole series of lectures, I've been aiming to make metaphysics functional. What I've tried to develop here is a kind of first example, or two examples if you like, of why avoiding a functional monist assumption, the assumption that all of our language works to connect us causally with observable features of the environment and track them, that all language works like terms for dogs and trees work. Why this leads us astray. And then I've used this to try to engage using work in linguistics in a kind of reverse engineering of some of the centrally metaphysically interesting or problematic terms, terms for numbers, terms for properties.

In some cases, I've suggested once we understand how these terms get introduced to language and why we have rules like this that entitle us to introduce them, then we can see how to answer old questions about what exists. Do properties and numbers exist easily by trivial inferences that are perfectly legitimate and that are in language for good functional reason. In other cases, I've tried to show how understanding the functions of the language and its entry rules can enable us to dispel old metaphysical worries or concerns, reasons people have given for thinking that numbers or properties would just be spooky and we should just deny their existence or remove them from our ontology. We can show the mistake here by showing that these problems rely on a false presupposition about how this form of language works, the presupposition that arises from a kind of functional monism.

So these are just examples, and I've treated them relatively briefly here, but just to give a sketch of the way in which this kind of functionally oriented reverse engineering work can shed new light on old problems in metaphysics. Plenty more remains to be said about both topics, but you can probably see already how this kind of approach might generalize to other metaphysical debates, say about whether there really are events or states of affairs or processes and so on. All of these have been debated in metaphysics.

I'll turn to discuss other kinds of metaphysical problem next and show how some of this work in linguistics can really help us reverse engineer and better understand the problems and where to go in resolving them, talking about moral language and morality more generally, and about truth. So I'll turn to those in the next two lectures.