path: root/linguistics/syntax.md

---
layout: linguistics
title: linguistics/syntax
---

# morphology and syntax

Morphology is the study of word formation. Syntax is the study of sentence formation.<br>
Specifically, both morphology and syntax focus on **structure**.

The distinction between syntax and morphology varies cross-linguistically.<br>
They can be considered to form an overarching **morphosyntactic** theory.

These notes are ordered in a way that I feel builds upon itself the best. This is not the order in which topics were covered in my syntax class, nor in my textbook. My syntax class covered Agree before Move, and my textbook deeply intertwined Merge with X'-theory and Move with Agree: and I think the both of them suffered a little bit pedagogically for that.

Certainly, all of syntax cannot be taught at once. Yet the desire to generalize and apply what one has learned to real-world examples is strong, and it is extraordinarily difficult to teach syntax in a way that builds upon itself naturally. This is my best attempt, but it will fall flat in places: when it does, I do recommend either skipping ahead or being content with temporarily (hopefully temporarily) not knowing what's going on.

<details markdown="block">
<summary>Table of Contents</summary>

- History of Syntax
  - A wrong approach: Phrase Structure Rules
- Morphology [SKS 2]
  - Syntactic Categories [SKS 2.1]
  - Compositionality [SKS 2.3]
  - Headedness [SKS 2.4]
- Merge, Part I
  - Constituency [SKS 3]
    - Constituency Tests [SKS 3]
  - Heads, Specifiers and Complements
  - Silent Heads
- Notation
  - X'-theory [SKS 6]
  - Bare Phrase Structure [n/a]
  - Lexical Entries [SKS 6.8]
- Minimalism [n/a]
- Merge, Part II
  - Projection [SKS 5]
  - Selection
    - Small Clauses
- Move [SKS 8]
  - Head Movement (affix hopping) [SKS 8.3]
  - Questions
  - vP Shells [SKS 12.4]
- Agree
  - Theta Roles (assigned by verbs)
  - Locality (c-command)
  - Binding (Principles A, B, C) [SKS 7]
    - Small Clauses [SKS 7.4]
  - Raising & Control [SKS 9]
- Advanced Syntax
- References

</details>

> Be warned! These notes are incomplete and almost certainly somewhat inaccurate. Proceed at your own risk.

## history

### a wrong approach: phrase structure rules

## morphology

### syntactic categories

### compositionality

### headedness

## Merge, Part I

We concluded the following from our excursion into morphology:
- words are composed of morphemes
- morphemes come in categories
- morphemes combine in a regular fashion
- morphemes can be silent

Surprisingly (or unsurprisingly), we shall see that these ideas generalize to sentence structure as a whole.

### constituency

### heads, specifiers, and complements

### silent heads

Why are proper names Ds? Why is it possible to say either *I moved the couches* and *I moved couches*, but only possible to say *I moved the couch* and not *I moved couch*? Why is the infinitive form of a verb identical to the present, in some cases?

These inconsistencies can be all addressed by one (controversial) concept: the idea of *silent morphemes*, invisible in writing and unpronounceable in speech. We represent such morphemes as ∅, and so may write the earlier strange sentence as *I moved ∅-couches*.

...

p-features | f-features
-----------|-----------
the | $D_{N}$
a | $D_{N (-plural)}$
∅ | $D_{N (+plural)}$

p-features | f-features | s-features
-----------|------------|-----------
will | $T_{D,V}$ | future
-ed | $T_{D,V}$ | past
∅ | $T_{D,V}$ | present
to | $T_{D,V} (-tense)$ | infinitive

These tables are using notation and language formally introduced at the end of the next section. Ignore them for now.

## notation

So far, we've been discussing syntax and giving examples using somewhat informal notation. We now formalize this notation.

### X'-theory

**X'-theory** (x-bar theory) is a notation originally put forth by Chomsky...

...

### Bare Phrase Structure

**Bare Phrase Structure** (BPS) is a more modern notation that does away with much of the notational cruft of X'-theory. Instead of bar levels and distinctions between bar levels and "phrases", we simply put the *formal features* of our lexicon in the chart itself and only indicate the *types* of phrases. Whether a phrase has yet to close yet or not (previously indicated by a 'bar) is now indicated by whether there are any unsatisfied selectional requirements on the phrase label.

**Head-Initial Phrases**

![`[X [X_Y (head)] [Y (complement)]]`](head-initial.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$X$
  [$X_Y$ [(head)]]
  [$Y$ [(complement)]]]
\end{forest}
```

</details>

**Head-Final Phrases**

![`[X [Y (complement)] [X_Y (head)]]`](head-final.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$X$
  [$Y$ [(complement)]]
  [$X_Y$ [(head)]]]
\end{forest}
```

</details>

Recall that adjuncts are able to appear on either side of their head. Also recall that adjuncts *select* for their head. We indicate this in our labeling: adjuncts, like heads, have their selectional requirements marked, but do not propagate their type. While certain constructions may lead to notational ambiguity - an adjunct and a head of the same type, specifically - this is rare enough (only really occurring with adverbs) that we take the convenience of BPS notation regardless.

**Left Adjuncts**

![`[X [Y_X (left adjunct)] [X (head)]]`](left-adjunct.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$X$
  [$Y_X$ [(left adjunct)]]
  [$X$ [(head)]]]
\end{forest}
```

</details>

**Right Adjuncts**

![`[X [X (head)] [Y_X (right adjunct)]]`](right-adjunct.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$X$
  [$X$ [(head)]]
  [$Y_X$ [(right adjunct)]]]
\end{forest}
```

</details>

As a reminder, English is not consistently head-initial. Subjects ("specifiers") in English appear before the verb, breaking this convention. This common structure is represented as the following:

![`[X [Y (specifier)] [X_Y [X_{Y,Z} (head)] [Z (complement)]]]`](english-specifier.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$X$
  [$Y$ [(specifier)]]
  [$X_Y$
    [$X_{Y,Z}$ [(head)]]
    [$Z$ [(complement)]]]]
\end{forest}
```

</details>

The lexicon and structure are blended in bare phrase structure. This is useful, and allows us to indicate more specific selectional requirements on the tree itself.

...

It cannot be emphasized enough that notational conventions are *just that*: notational conventions. There's nothing stopping us from exclusively using X'-notation or exclusively using BPS, and syntactic concepts are *not* tied to any specific notation. I will pretty much exclusively use BPS going forth as I like it a whole lot more.

### lexical entries

We have stated that Bare Phrase Structure pulls aspects of the lexicon directly into the syntax tree. But what is a lexicon?

A **lexicon** is a language speaker's internal collection of lexical entries. But what is a lexical entry?

What exactly a lexical entry contains is up to some debate. The English language consists of (significantly) upwards of 400,000 words. How humans can hold that much information in our mind, and retrieve it so quickly? This is biologically interesting, and there are arguments for what such entries should and should not contain that come from such fields. For our purposes, we will focus entirely on syntactic analysis, and ignore biological motivations. We treat a **lexical entry** as containing the following information about an associated morpheme:
- phonetic features (**p-features**): how the word is pronounced
  - With our focus on syntax, we shall simply consider this the standard written representation of the morpheme. But it should really be written in IPA.
- formal features (**f-features**): the type of the morpheme and what types it selects, if any
  - These are often written directly on our tree in BPS. While most often they are simply the types of the arguments - heads can select for much more granular features, i.e. -tense, +animacy, etc.
- semantic features (**s-features**): the role of the entry and its arguments in the sentence
  - Not all lexical entries have s-features. For tense/aspect/etc, these are their appropriate tense/aspect/etc. For verbs, these are typically *theta roles* (which we shall address later).

## Minimalism

[Minimalism](https://en.wikipedia.org/wiki/Minimalist_program) is a *program* that aims to reduce much of the complexity surrounding syntactic analysis. While our theories may end up providing for adequate analyses of natural languages, this is not enough. Phrase structure rules, too, were *adequate*: yet we rejected them for their sheer complexity. If we can explain what we observe in a simpler framework, *we should adopt that framework*. Much of modern advancements in syntactic analysis have come out of Minimalism: bare phrase structure, in particular.

As with most Chomskyan theories: Minimalism has a *strong* focus on natural language facilities. A core thesis is that *"language is an optimal solution to legibility conditions"*. I don't find this interesting, so I won't get into it, and instead will focus on the definitions and usage of the basic operations rather than the motivation for them.

Modern Minimalism considers into three *basic operations*: <span style="font-variant: small-caps;">Merge</span>, <span style="font-variant: small-caps;">Move</span>, and <span style="font-variant: small-caps;">Agree</span>. All that we will discuss can fall into one of these basic camps.

## Merge, Part II

<span style="font-variant: small-caps;">Merge</span>(α, β) is a function that takes in two arguments of type α and β and outputs a single node of either type α or β.

Merge is *the* fundamental underlying aspect of syntax and arguably language as a whole. Compositionality, headedness, movement (in some camps), and a whole lot more can be considered to be rolled into it.

### projection

### selection

## Move

### head movement

![will](tense-no-tense.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$V$
  [$D$ [I, roof]]
    [$V_D$
      [$V_{D,P}$ [walk]]
      [$P$
        [$P_D$ [to]]
        [$D$
          [$D_N$ [the]]
          [$N$ [school]]]]]]]
\end{forest}
```

</details>

So far, we have not dealt with tense. We have diagrammed sentences with verbs in present and past forms by entirely ignoring their *-s* and *-ed* affixes. But tense is an aspect of grammar just like anything else, and writing it off as purely semantic does no good to anyone. Indeed, the English future having its tense marker *will* as a free-standing morpheme strongly suggests that we have to treat tense as a category in its own right, and not just as an inflectional property of verbs.

A tense needs a *subject*. This is evident in our tree structure below, but is motivated by...
For now, we'll consider the verb to no longer be in charge of selecting the subject. This is not in fact accurate - as we will see at the end of this section - but it is a simplification we shall make for the time being.

![will](tense-will.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$T$
  [$D$ [I, roof]]
  [$T_D$
    [$T_{D,V}$ [will]]
    [$V$
      [$V_P$ [walk]]
      [$P$
        [$P_D$ [to]]
        [$D$
          [$D_N$ [the]]
          [$N$ [school]]]]]]]
\end{forest}
```

</details>

...

![(-ed)](tense-ed.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$T$
  [$D$ [I, roof]]
  [$T_D$
    [$T_{D,V}$ [(-ed), name=tense]]
    [$V$
      [$V_P$ [walked, name=walk]]
      [$P$
        [$P_D$ [to]]
        [$D$
          [$D_N$ [the]]
          [$N$ [school]]]]]]]
  \draw[->,dotted] (tense) to[out=south,in=west] (walk);
\end{forest}
```

</details>

![()](tense-null.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$T$
  [$D$ [I, roof]]
  [$T_D$
    [$T_{D,V}$ [∅, name=tense]]
    [$V$
      [$V_P$ [walk, name=walk]]
      [$P$
        [$P_D$ [to]]
        [$D$
          [$D_N$ [the]]
          [$N$ [school]]]]]]]
  \draw[->,dotted] (tense) to[out=south,in=west] (walk);
\end{forest}
```

</details>

...

![(-s)](tense-s.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
[$T$
  [$D$ [Alice, roof]]
  [$T_D$
    [$T_{D,V}$ [(-s), name=tense]]
    [$V$
      [$V_P$ [walk, name=walk]]
      [$P$
        [$P_D$ [to]]
        [$D$
          [$D_N$ [the]]
          [$N$ [school]]]]]]]
  \draw[->,dotted] (tense) to[out=south,in=west] (walk);
\end{forest}
```

</details>

### wh-movement

### vP shells

Consider the following sentence: *Alice will speak to the assembly*. With our current knowledge of syntax, we would diagram it as so:

![`[T [D Alice] [T_D [T_{D,V} will] [V [V_P speak] [P [P_D to] [D [D_N the] [N assembly]]]]]]`](no-subject-movement.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
  [$T$
    [$D$ [Alice, roof]]
    [$T_D$
      [$T_{D,V}$ [will, roof]]
      [$V$
        [$V_P$ [speak]]
        [$P$
          [$P_D$ [to]]
          [$D$
            [$D_N$ [the]]
            [$N$ [assembly]]]]]]]
\end{forest}
```

</details>

The $D$ *Alice* here is the subject. While replacing it with some $D$s produces grammatical sentences ex. *The prime minister will speak to the assembly*: this is not true of all $D$s. Slotting in inanimate $D$s like *Time will speak to the assembly* and *Knowledge will speak to the assembly* produces grammatically unacceptable sentences. So there is some *selection* occurring somewhere in the sentence that wants a particular *feature set* (f-features) from the subject $D$.

Observe, however, that our tree structure suggests that $T$ - and only $T$ - is involved in the selection of $Alice$ as the subject, given locality of selection. But this can't be quite right. Plenty of other sentences involving the $T$ *will* are just fine with inanimate subjects: *Time will pass*, *Knowledge will be passed on*, etc. (Notice that *Alice will pass* and *Alice will be passed on* are similarly ungrammatical). How do we reconcile this?

We now introduce the idea of $vP$ shells and V-to-T movement. Our observations above point towards the $V$ of the sentence rather than the $T$ selecting for the subject $D$ - somehow. This selection would break our guiding principle of locality of selection. But this behavior *does* occur. Can we extend our model to explain this, *without* modifying the locality of selection that has been so useful thus far? We can, indeed, with movement, and illustrate so in the following tree.

![`[T [D Alice] [T_D [T_{D,V} will] [V [D (subj)] [V_D [V_{D,P} speak] [P [P_D to] [D [D_N the] [N assembly]]]]]]]`](subject-movement.png)
<details markdown="block">
<summary>LaTeX</summary>

```forest
\begin{forest}
  [$T$
    [$D$ [Alice, roof, name=Alice]]
    [$T_D$
      [$T_{D,V}$ [will]]
      [$V$
        [$D$ [(subj), roof, name=subj]]
        [$V_D$
          [$V_{D,P}$ [speak]]
          [$P$
            [$P_D$ [to]]
            [$D$
              [$D_N$ [the]]
              [$N$ [assembly]]]]]]]]
    \draw[->,draw opacity=0.5] (subj) to[out=west,in=south] (Alice);
\end{forest}
```

</details>

So we say that *Alice* is originally selected by the $V$ and *moves* to its surface position in the $T$. Our head movement principles allow for this. This does mean that every tree diagram we have drawn up until now is inaccurate, and that almost every tree we draw going forward will have to have this V-to-T movement. This is a fine tradeoff to make in exchange for accurately describing previously-unclear syntactic behavior.

> Note: this is not called V-to-T movement. What *is* it called?

### small clauses

## Agree

### theta roles

### locality

### binding

How do pronouns work?

...

The theory of binding operates under three fundamental principles.
- **Principle A**: an anaphor must be bound in its domain.
- **Principle B**: a pronoun must be free in its domain.
- **Principle C**: an r-expression may never be bound.

Our principles imply various things. Principle A implies that:
- a reflexive must be coreferential with its antecedent
- the antecedent of a reflexive must c-command the reflexive
- the reflexive and its antecedent must be in all the same nodes that have a subject


### raising and control

## Advanced Syntax

## References

- ✨ [An Introduction to Syntactic Analysis and Theory](https://annas-archive.org/md5/11bbf70ff9259025bc6985ba3fa4083b)
- MIT 24.902: [2017](https://web.mit.edu/norvin/www/24.902/24902.html), [2015](https://ocw.mit.edu/courses/24-902-language-and-its-structure-ii-syntax-fall-2015/), [2003](https://ocw.mit.edu/courses/24-902-language-and-its-structure-ii-syntax-fall-2003/)