# 6.1: Arbitrariness and Compositionality

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To start off, listen to the comedian ISMO's routine about how complicated the word ass is--at least, if you're trying to learn English. (The video is captioned)

## 6.1.1 Arbitrariness and Compositionality, from Sarah Harmon

### Video Script

With respect to arbitrariness and compositionality, there are a lot of the pieces that you're going to see below in what Catherine Anderson wrote that are exceptional, but I think they need a little bit of setup now. When we talk about semantics, one of the things that is kind of important to remember, is the fact that this is really like philosophy in some ways that we're going to talk about really abstract concepts. Meaning is harder to imagine sometimes than the structure of a phrase or how we put a lexicon together with different morphemes. To start off, let me start talking about a few things that are going to be closer to what you may hear in a philosophy class; there's a reason for that and I’ll get to it.

With respect to semantics, we always have to start off in the same place, and that is talking about an ontology. In linguistic terms, an ontology is pretty close to what you hear in a philosophy class: it is a box with all the possible meanings. Each language assigns a lexicon or a phrase to that meaning; that's what we call lexical meaning or lexical semantics. Let's unpack that a little bit, because that might be a little hard to understand. I like thinking of an ontology as a box, a box for each given language and, in many cases, you can say a specific dialect. You can say that that box come has an entire litany all of the possible phrases and lexicons and the meaning associated with it, so they are connected in some way. What happens is that as fluent speakers of a given language, whether it is our native language or one that we have learned, we pull from the items out of that box and we import it into our entailment, our mental lexicon. That mental lexicon that we talked about in morphology comes in here, because that is how we have built our language, we have pulled items from the ontology we have entailed certain other pieces to that and have built up our mental dictionary or mental lexicon. This really encapsulates a lot of what we do in semantics, because everything that we talked about with respect to semantics, and even pragmatics, which we'll get to later, has to do with understanding what are the items in that box, what are the lexicon and phrases, as well as the meaning in that ontology.

We have talked about this gentleman before in chapter one, as well as when we got to morphology: Ferdinand de Saussure. As you can see, he lived from the middle of the 19th century into the early part of the 20th century. We already talked about his Principle of the Arbitrary, but let's come back to that to refresh our minds a bit. It really is the cornerstone of semantics; you have a hard time understanding anything in semantics without understanding the arbitrariness of language. I talked about him briefly earlier; he was Swiss mathematician, logician, and philosopher that used these tools to look at language. He is a fascinating individual; at a different point in time, I might get into it.

For now, his Principle of the Arbitrary is what we need to focus on. I talked about earlier that you have, for example, sofa, couch, davenport; three different terms, and for most of us we use at least two of those to describe the same piece of furniture. Or, we talk about a groundhog or woodchuck and it's the same animal. Even how air, food and water, the three things that human beings need to live, that none of those terms are the same in any two languages. We use different lexicon in every single language to describe the same three things that we all need. That is proof of arbitrariness, that any given language arbitrarily assigned a lexicon or a phrase to a specific meaning. That's exactly what the Principal the Arbitrary is: connecting the reference to the meaning or the sense. Those were Saussure's terms and when he did this; he had a different aspect for us to think about. He described accurately that when we talk about the morning star and when we talk about the evening star. It's the same heavenly body. What does that mean? You may have heard those terms before, the morning star and the evening star and; if not, the morning star is the last heavenly body, the last thing we see in the sky before the sun comes up and makes it so bright that we can't see any stars. The evening star is the first thing we see once the sun goes down is the first heavenly body that we see. It isn't actually a star—it's the planet Venus—but even still, we use this these two terms to refer to the exact same thing. As Saussure described, that is arbitrary; we arbitrarily name it a different thing, depending on the time of day. That this happens in English or maybe used to happen (there aren’t too many people who say morning star and evening star), but arbitrariness does happen in every language.

Really what we're saying is that a reference or a lexicon or phrase that we use is really a set of truth values, meaning that, if it is correctly attaching or entailing to a certain meaning that it's a true reference: it's true for me, it's true for you. If it's not, then it's a false reference. Let me give you an example. If I hold up this device and call it my phone or my telephone or my mobile phone or my cell phone, all of those are true references, meaning that in any dialect of English this thing would be considered a ‘phone’. It could be any or all of those lexicons. But if I hold this thing up and I call it a pencil, that's going to be a false reference, because in no dialect of English does this apparatus get connected to or entailed to a ‘pencil’; it just doesn't happen. Let me give you another example. If I say, that is a true reference, because this thing that in English we call ‘sky’, it's the thing that is above us when we go outside right; get rid of the clouds and what you see is the sky. That thing up there that thing has a color to it, or at least that we perceive and that color is associated that hue is associated to the term blue, so that's a true reference. If I say the sky is green, for most all of you, that would be a false reference, because in no way does that color get correlated to the term ‘green’. I will say, though, if you are from an area or have spent time in an area that is prone to tornadoes, then you know what that phrase means. If you have the unfortunate instance of being in an area when a tornado is about to drop, the clouds look green; the light bounces off the clouds in such a way that it looks green, and so you say the clouds are green or the sky is green. In that specific reference, it would be true, but for most everybody else, it would be false.

If we talk about Saussure here and the Principle of the Arbitrary, then we have to include Gottlob Frege, who also came from Switzerland. He's also a mathematician, logician, and philosopher of language and he worked alongside Ferdinand de Saussure. He came he came up with the Principle of Compositionality and it is equally important when we talk about semantics; you can't talk about semantics without either the Principle of the Arbitrary or Principle of Compositionality. This principle is actually pretty straightforward and I probably don't need to explain it very much. It is that the meaning of the whole is determined by the meaning of the parts and the way they combine. The components help to form and shape the meaning of the overall. That pretty much makes sense, but I’ll give you a couple of examples. If we think about this morphologically, then certainly if we have a term unbelievable. All we need to do is look at the individual morphemes that are associated with that lexicon, note the meaning of the different morphemes, and we can put together the meaning of the full lexicon. In the term unbelievable, we have a root belief, we have a prefix un-, which means ‘not’ and it's a negator, and we have a suffix, a derivational suffix, that means ‘able to’, -able. ‘Not’ ‘believe’ ‘able’; ‘to not able to believe’—that's what unbelievable means.

It even helps us to understand the history of how certain terms or certain phrases get changed over time. For example, if I say holiday, you have a certain image in mind for most English speakers, that means just a day off. It may include a vacation; certain dialects of English equate a holiday to vacation. However, if I told you that, historically, that it was a sacred day or a holy day, that may not be the meaning of it now, but you can see the history of that, and you can understand how it could come to mean that. These are examples of the Principle of Compositionality: the parts and the way they combined inform the meaning of the whole.

We can also talk about when there is a lack of compositionality. We already have in the previous chapter, when I talked about grammaticality and I talked about the statement that Noam Chomsky came up with: colorless green ideas sleep furiously. We talked about how it is a grammatical sentence structurally; it follows the phrase structure rules of English. Why it doesn't make sense is because it lacks compositionality; the meaning of the individual pieces, that they don't work together. In semantics we call that anomaly; an anomaly is when there is a lack of compositionality. Most of the time, anomaly produces a lack of understanding; you don't understand what somebody is trying to communicate.

However, there are times that anomaly can be massaged a little bit; it can be understood, given a context. One example is, metaphors. If I say there is a fork in the road, what I’m saying has nothing to do with an eating utensil in the middle of the roadway. In that sense, there is anomaly, because there's a lack of compositionality. As an English speaker, you understand what I’m trying to say; I’m describing a situation in which a single road forks or splits into two or more subsequent roads. Because you are an English speaker, you understand what that metaphor is trying to say. That is an example of a bit of elasticity with this Principle of Compositionality, that we can play with this a little bit. This also includes idioms, and it includes something called collocations. A collocation is a combo: X and Y. They are understood as a unit, and they have a little bit of a metaphor quality to it. For example, if I was describing somebody in their late 40s through early 60s, and they are a dark haired individual but there's quite a bit of gray sprinkled throughout their hair. A term we might use in English is salt and pepper, that that person has salt and pepper hair. If I just said, salt hair or pepper hair, you wouldn't understand what I was trying to say. If I say, salt and pepper, together, that is understandable, as a chunk of meaning. It stretches that Principle of Compositionality just a little bit, but it's understood because of the context, because that phrase is part of the ontology of English. I'll give you another example. I used to have a neighbor who did not tell stories very well, and one of the things they used to do was not give very much in the way of detail. If you talked to them after a trip, they would say they went here and there, and did this and that. Here and there, this and that, those are two collocations. They are general phrases to explain that there was probably nothing important going on: they didn't go to anywhere that they felt was interesting, or they didn't want to tell us where they went. Either way, they used two different collocations to describe his vacation.

All of these expansions of the Principle of Compositionality and the Principle of the Arbitrary inform everything with respect to semantics. From this point going forward, both of those principles will have a role in every aspect of semantics and pragmatics.

## 6.1.2: From 10.1 Elements of Word Meaning: Intensions and Extensions, in Anderson's Essentials of Linguistics

### Video Script

We’re now starting to consider how our minds represent the meanings of words. If someone asked you, “What’s the meaning of the word pencil?” you’d probably be able to describe it — it’s something you write with, it has graphite in it, it makes a mark on paper that can be erased, it’s long and thin and doesn’t weigh much. Or you might just hold up a pencil and say, “This is a pencil”. Pointing to an example of something or describing the properties of something, are two pretty different ways of representing a word meaning, but both of them are useful.

One part of how our minds represent word meanings is by using words to refer to things in the world. The denotation of a word or a phrase is the set of things in the world that the word refers to. So one denotation for the word pencil is this pencil right here. All of these things are denotations for the word pencil. Another word for denotation is extension.

If we look at the phrase, the Prime Minister of Canada, the denotation or extension of that phrase right now in 2017 is Justin Trudeau. So does it make sense to say that Trudeau is the meaning of that phrase the Prime Minister of Canada? Well, only partly: in a couple of years, that phrase might refer to someone else, but that doesn’t mean that its entire meaning would have changed. And in fact, several other phrases, like, the eldest son of former Prime Minister Pierre Trudeau, and the husband of Sophie Grégoire Trudeau, and the curly-haired leader of the Liberal Party all have Justin Trudeau as their current extension, but that doesn’t mean that all those phrases mean the same thing, does it? Along the same lines, the phrase the President of Canada doesn’t refer to anything at all in the world, because Canada doesn’t have a president, so the phrase has no denotation, but it still has meaning. Clearly, denotation or extension is an important element of word meaning, but it’s not the entire meaning.

We could say that each of these images is one extension for the word bird, but in addition to these particular examples from the bird category, we also have in our minds some list of attributes that a thing needs to have for us to label it as a bird. That mental definition is called our intension. So think for a moment: what is your intension for the word bird? Probably something like a creature with feathers, wings, claws, a beak, it lays eggs, it can fly. If you see something in the world that you want to label, your mental grammar uses the intension to decide whether that thing in the word is an extension of the label, to decide if it’s a member of the category. The next unit will look more closely at how our intensions might be organized in our minds.

One other important element to the meaning of a word is its connotation: the mental associations we have with the word, some of which arise from the kinds of other words it tends to co-occur with. A word’s connotations will vary from person to person and across cultures, but when we share a mental grammar, we often share many connotations for words. Look at these example sentences:

Dennis is cheap and stingy.

Dennis is frugal and thrifty.

Both sentences are talking about someone who doesn’t like to spend much money, but they have quite different connotations. Calling Dennis cheap and stingy suggests that you think it’s kind of rude or unfriendly that he doesn’t spend much money. But calling him frugal and thrifty suggests that it’s honourable or virtuous not to spend very much. Try to think of some other pairs of words that have similar meanings but different connotations.

To sum up, our mental definition of a word is an intension, and the particular things in the world that a word can refer to are the extension or denotation of a word. Most words also have connotations as part of their meaning; these are the feelings or associations that arise from how and where we use the word.

### Check Yourself

##### Exercise $$\PageIndex{1}$$

Think about the compound word hockey player. What kind of meaning do Wayne Gretzky, Sidney Crosby, and Alex Ovechkin have in relation to hockey player?

• Extensions.
• Intensions.
• Denotations
• Connotations.

"Extensions" and "Connocations"

The reason: They denote hockey player because they are all names of famous hockey players. Another word for 'denotation' is 'extension'.

##### Exercise $$\PageIndex{2}$$

Think about the word champagne. Which of the following words represents a connotation of the word champagne?

• sparkling wine
• Veuve Clicquot
• celebration

"Celebration"

The reason: We associate champagne with any celebration.

##### Exercise $$\PageIndex{3}$$

Think about the compound word chocolate cake. Which of the following words represents an intension of the word chocolate cake?

• too many carbs
• made with flour, eggs, cocoa, sugar
• birthday party

The reason: When we think of chocolate cake, and we think about what it is made of, its ingredients, that is the intension.

## 6.1.3: From 9.1 Ambiguity, in Anderson's Essentials of Linguistics

In Chapter 8, as we learned to draw tree diagrams to illustrate how sentences are represented in the human mind, we thought about Deep Structure as the place where meaning is assigned and calculated. For example, in a question sentence like, “What are the kids eating for lunch?”, we claim that the word what is related to the verb eating in the same way that eggs and eating are related in the declarative sentence, “The kids are eating eggs for lunch.” The relationship between eating/eggs and between eating/what arises at Deep Structure, where eggs and what are both in the complement of the verb. In our theory, a sentence’s meaning is correlated directly with the sentence’s syntax.

This idea is a core one in linguistics: the meaning of some combination or words (that is, of a compound, a phrase or a sentence) arises not just from the meanings of the words themselves, but also from the way those words are combined. This idea is known as compositionality: meaning is composed from word meanings plus morphosyntactic structures.

If structure gives rise to meaning, then it follows that different ways of combining words will lead to different meanings. When a word, phrase, or sentence has more than one meaning, it is ambiguous. The word ambiguous is another of those words that has a specific meaning in linguistics: it doesn’t just mean that a sentence’s meaning is vague or unclear. Ambiguous means that there are two or more distinct meanings available.

In some sentences, ambiguity arises from the possibility of more than one grammatical syntactic representation for the sentence. Think about this example:

Hilary saw the pirate with the telescope.

There are at least two potential locations that the PP with the telescope could be adjoined. If the PP is adjoined to the N-bar headed by pirate, then it’s part of the DP. (Notice that the whole DP the pirate with the telescope could be replaced by the pronoun her or him.) In this scenario, the pirate is holding a telescope, and Hilary sees that pirate.

But if the PP is adjoined to the V-bar headed by saw, then the DP the pirate is its own constituent, and with the telescope gives information about how the pirate-seeing event happened. In this scenario, Hilary is using the telescope to see the pirate.

This single string of words has two distinct meanings, which arise from two different grammatical ways of combining the words in the sentence. This is known as structural ambiguity or syntactic ambiguity.

Structural ambiguity can sometimes lead to some funny interpretations. This often happens in news headlines, where function words get omitted. For example, in December 2017, several news outlets reported, “Lindsay Lohan bitten by snake on holiday in Thailand”, which led a few commentators to express surprise that snakes take holidays.

Another source of ambiguity in English comes not from the syntactic possibilities for combining words, but from the words themselves. If a word has more than one distinct meaning, then using that word in a sentence can lead to lexical ambiguity. In this sentence:

Heike recognized it by its unusual bark.

It’s not clear whether Heike recognizes a tree by the look of the bark on its trunk, or if she recognizes a dog by the sound of its barking. In many cases, the word bark would be disambiguated by the surrounding context, but in the absence of contextual information, the sentence is ambiguous.

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