1 the Compositionality Principle at the Syntax-Semantics Interface

PLIN0009 Semantic Theory Spring 2020 Lecture Notes 2

1 The Compositionality Principle at the Syntax-Semantics Interface

We assume the Compositionality Principle in order to account for the fact that native speak- ers know the truth-conditions of all grammatical declarative sentences.

(1) The Compositionality Principle: The meaning of a syntactically complex expression is determined solely by the meanings of its parts and how they are arranged.

It should be stressed that how the words are arranged—that is, the syntactic structure of the expression—is relevant for its truth-conditional meaning. It is easy to see why. Com- pare, for example, A man saw Mary and Mary saw a man, which evidently have different truth-conditions, despite the fact that they are (at least seemingly) made up of the same words.

One way to account for the relevance of syntax in semantics is by understanding the Com- positionality Principle in a very particular way, that is, the meaning of a complex phrase is determined by the meanings of its immediate daughter constituents.

(2) The Compositionality Principle (strict ver.): The meaning of a syntactically complex expression is determined solely by the meanings of its immediate daughter constituents.

This will be the working hypothesis throughout this module, so it’s worth remembering.

In order to how (2) works, let’s assume that the sentence A man saw Mary has the syntactic structure in (3) (The details of the structure could be wrong, but are not so important for the current purpose of demonstrating the idea).

(3) S

DP VP

a man saw Mary

According to the principle in (2) above, the meaning of (3) should be determined by the meaning of the DP a man and the meaning of the VP saw Mary, and nothing else. It furthermore tells us that the meaning of the DP a man, in turn, should be determined by the meaning of a and the meaning of man, and nothing else. Likewise, the meaning of the VP saw Mary should be determined by the meaning of saw and the meaning of Mary, and nothing else.

Let’s now consider the other sentence, Mary saw a man, which we assume has the structure in (4).

1 (4) S

Mary VP

saw DP

a man

The meaning of this sentence is determined by the meaning of Mary and the meaning of the VP saw a man. And, just as in the previous example, the meaning of the VP is determined by its immediate daughter constituents, saw and the DP a man, and so on.

According to these analyses, then, it’s not at all surprising that the two sentences have different meanings. Although the ingredients are the same, the way they are combined is different, which has immediate consequences on how the component meanings are combined.

We will make this idea more concrete in the next couple of lectures, but it should be em- phasized at this point that this entails that the semantics is dependent on the syntax. That is, at least part of how we analyze the meaning will depend on the syntactic analysis of the expression in question. So if our syntactic analysis turns out to be wrong, we often have to make changes in our semantic analysis as well. But for the same reason, semantics some- times has implications on how syntax should operate.

2 Model Theory

To construct a concrete semantic theory that embodies (the strict version of) the Compo- sitionality Principle, we will adopt the so-called model-theoretic approach to meaning. Let us start with analyses of declarative sentences and proper names in model-theoretic terms.

2.1 Sentences Denote Truth-Values

The truth-conditions of a declarative sentence tell us in what kind of situations the sentence is true and in what kind of situations the sentence is false. If you are given the truth- conditions and a particular situation, you should be able to tell whether the sentence is true or false in that situation.

Let us look at a concrete example. As we know English, we know the truth-conditions of Paul vapes, namely, it is true iff Paul vapes. In order to determine whether this sentence is true or false in a given situation, we have to know certain things about the situation. In particular, we have to know who the proper name Paul refers to, and whether that person vapes or not. If they do, the sentence is true in this situation, and if not, the sentence is false in this situation.

We represent information about situations that is relevant for determining the truth or falsity of sentences in certain mathematical constructions called models. You don’t need to know the details of what models are at this point (we will come back to them next week). All you have to know for now is that a model is a mathematical representation of some par-

2 ticular state of affairs that contains enough information to decide the truth or falsity of a given sentence. A semantic theory that uses models is called model theoretic semantics.

We often give (boring) names to models, most typically, M, M1, M2, etc. If a model M is given, you can, by assumption, tell any declarative sentence S is true or false in the situation represented by M. Or equivalently, we say S denotes truth or falsity in (the situation represented by) M. Other ways of saying the same thing include: the denotation of S is truth or falsity in M; the extension of S is truth or falsity in M.

Truth and falsity are standardly denoted by 1 and 0, respectively, and are called truth- values. We follow this tradition here, and use 1 and 0 for truth and falsity from now on. So, we will say things like ‘This sentence denotes 0 in M’ and ‘The denotation of that sentence is 0 in M2’, etc. Furthermore, semanticists often use a more compact notation for this. The denotation (or equivalently, referent, or extension) of any expression X with respect to a model M M is written vXw . Therefore, for any declarative sentence S and for any model M, either M vSw = 1 (which means that S is true with respect to the situation represented by M) or M vSw = 0 (which means that S is with respect to the situation represented by M). This is just notational convention, but we will adopt it for the rest of this module.

It is important to keep in mind the difference between truth-values and truth-conditions. Both are in some sense ‘meanings’ of declarative sentences, but truth-conditions are more abstract than truth-values. Truth-values are denotations of declarative sentences in particular models, which represent particular states of affairs, and they are either 1 or 0. Truth-conditions are conditions that tell you in what kind of situation the sentence is true and in what kind of situations it is false. So two completely independent sentences, for instance, It is raining in London and Andy lost a laptop, can have the same denotation in some models, but their truth-conditions are always distinct, so there are models in which they have different truth-values.

Using the new notation we introduce above, we can state the truth-conditions of a given declarative sentence S as follows.

M (5) For any model M, vSw = 1 iff S in M.

For example, the truth-condition of ‘There is a circle in a square’ can be stated as (6). (We often omit ‘for any model M’, when it is obvious.)

M (6) For any model M, vThere is a circle in a squarew = 1 iff there is a circle in a square in M.

Please note that in this document, we will use a different font for the material between v and w. This is to emphasize that whatever occurs there is an expression in the object language, and everything that is not in this font belongs to the metalanguage.

2.2 Proper Names Denote Individuals

Let us now turn to the meanings of proper names. Proper names are linguistic devices that we can use to refer to particular people or things.

3 Since one and the same proper name, e.g. Daniel, refers to different people in different contexts, we cannot say that its referent is part of the inherent meaning of the expression. Nonetheless, every time we use this expression, we typically have some particular referent in mind. Since a model represents a particular situation, we could have the (intended) referent of the proper name as its model-theoretic denotation.

Importantly, who the referent is matters for the truth-condition of the sentence containing the proper name. If we refer to Daniel Kahneman by Daniel, the truth-conditions of Daniel is sleeping will be about Daniel Kahneman, but if we refer to somebody else by this proper name, what Daniel Kahneman is doing now will be irrelevant for the truth-conditions of the sentence.

How do we know who the referent of a given proper name is in a give model? We simply assume that a model M ixes it to a particular person, just as M ixes the denotation of a sentence to 1 or 0. For our limited purposes here, we need not know exactly how this is done (and there is a lot of ideas and debates in the literature), and just assume that the denotation of a proper name like Daniel is some particular person (as represented in M the model). Or using our notation above, for any model M, vDanielw is an entity (or individual) in the model. In formal semantics, it is common to use ‘entity’ or ‘individual’ to talk about concrete people as well as any other creatures and non-creatures, including cups, desks, cars, etc.

The semantics and pragmatics of proper names is a very good potential topic for your Long Essay. It has a long tradition in philosophy, which is nicely summarized in the following survey article:

Cumming, Sam (2016) Names. In Edward N. Zalta (ed.), The Stanford Ency- clopedia of Philosophy, Fall 2016 Edition. https://plato.stanford.edu/ archives/fall2016/entries/names/

The following paper by Ora Matushansky contains a lot of interesting linguistic observa- tions.

Matushansky, Ora (2008) On the linguistic complexity of proper names. Lin- guistics and Philosophy, 21: 573–627. https://link.springer.com/article/ 10.1007/s10988-008-9050-1

3 Summary

Let us summarize the discussion so far. To achieve the goal of constructing a inite semantic system capable of assigning meanings to ininitely many sentences, we assume the Compositionality Principle. In particular, we assume the strict version:

(2) The Compositionality Principle (strict ver.): The meaning of a syntactically complex expression is determined solely by the meanings of its immediate daughter constituents.

We have only discussed the denotations (alt.: referents, extensions) of sentences and proper names with respect to models, but in the end we will talk about those of any (grammatical)

4 M expression. We write vXw to mean the denotation of X with respect to model M, for any grammatical expression X (We don’t need to talk about the meanings of ungrammatical expressions; they are ungrammatical anyway).

M M If X is a declarative sentence, we have either vXw = 0 or vXw = 1. If X is a proper name, M vXw will be some particular entity (alt.: individual) as determined by the model.

With the material so far, we already have a partial analysis of sentences like John smokes. Let us assume that it has the following simple structure.

(7) S

John smokes

With respect to any model, (7) will be true or false, or equivalently, it will denote 1 or 0. Let’s say with respect to M9 it is false. Using the notation introduced above, we state this as in (8). 4 < M9 S (8) 5 = = 0 John smokes

According to the strict version of the Compositionality Principle, we want the meaning of the sentence to be determined by the meaning of John and the meaning of smokes. The kind of meaning we are interested in here is the denotations in this particular model. So we can state this as follows. 4 < M9 S 5 = M9 M9 (9) is determined by vJohnw and vsmokesw (and nothing John smokes else).

M We know that vJohnw 9 is some person, whoever it is. So the only thing we have to igure M out to complete our analysis of this sentence is vsmokesw 9 and how to combine these two meanings to get the truth-value 0. This is what we will do in the next lecture.