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Phi Theory

OXFORD STUDIES IN THEORETICAL LINGUISTICS
general editors: David Adger, Queen Mary, University of London; Hagit
Borer, University of Southern California.
advisory editors: Stephen Anderson, Yale University; Daniel Büring, University of California, Los Angeles; Nomi Erteschik-Shir, Ben-Gurion University;
Donka Farkas, University of California, Santa Cruz; Angelika Kratzer, University of
Massachusetts, Amherst; Andrew Nevins, Harvard University; Christopher Potts,
University of Massachusetts, Amherst; Barry Schein, University of Southern California; Peter Svenonius, University of Tromsø; Moira Yip, University College London.
recent titles
10 The Syntax of Aspect: Deriving Thematic and Aspectual Interpretation
edited by Nomi Erteschik-Shir and Tova Rapoport
11 Aspects of the Theory of Clitics
by Stephen Anderson
12 Canonical Forms in Prosodic Morphology
by Laura J. Downing
13 Aspect and Reference Time
by Olga Borik
14 Direct Compositionality
edited by Chris Barker and Pauline Jacobson
15 A Natural History of Infixation
by Alan C. L. Yu
16 Phi Theory: Phi-Features across Modules and Interfaces
edited by Daniel Harbour, David Adger, and Susana Béjar
17 French Dislocation: Interpretation, Syntax, Acquisition
by Cécile De Cat
18 Inflectional Identity
edited by Asaf Bachrach and Andrew Nevins
19 Lexical Plurals
by Paolo Acquaviva
20 Adjectives and Adverbs: Syntax, Semantics, and Discourse
edited by Louise McNally and Christopher Kennedy
published in association with the series
The Oxford Handbook of Linguistic Interfaces
edited by Gillian Ramchand and Charles Reiss
For a complete list of titles published and in preparation for the series, see
p. 377.

Phi Theory
Phi-Features across Modules and Interfaces

Edited by
DANIEL H A RB OUR, DAVID AD GE R ,
A N D S U S A NA B É JA R

1

3

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Contents
General Preface
Notes on Contributors
Abbreviations
1 Why Phi?
David Adger and Daniel Harbour

vii
viii
x
1

2 Features on Bound Pronouns
Irene Heim

35

3 On the Semantic Markedness of Phi-Features
Uli Sauerland

57

4 Phi-Agree and Theta-Related Case
Milan Řezáč

83

5 Conditions on Phi-Agree
Susana Béjar

130

6 Phi-Feature Competition in Morphology and Syntax
Martha McGinnis

155

7 Discontinuous Agreement and the Syntax–Morphology Interface
Daniel Harbour

185

8 Third Person Marking in Menominee
Jochen Trommer

221

9 When is a Syncretism more than a Syncretism?
Heidi Harley

251

10 Where’s Phi? Agreement as a Postsyntactic Operation
Jonathan David Bobaljik

295

11 Cross-Modular Parallels in the Study of Phon and Phi
Andrew Nevins

329

Feature Index
Grammatical Topic Index
Language Index

369
371
375

This page intentionally left blank

General Preface
The theoretical focus of this series is on the interfaces between subcomponents
of the human grammatical system and the closely related area of the interfaces
between the different subdisciplines of linguistics. The notion of ‘interface’ has
become central in grammatical theory (for instance, in Chomsky’s recent Minimalist Program) and in linguistic practice: work on the interfaces between
syntax and semantics, syntax and morphology, phonology and phonetics, etc.
has led to a deeper understanding of particular linguistic phenomena and of
the architecture of the linguistic component of the mind/brain.
The series covers interfaces between core components of grammar, including syntax/morphology, syntax/semantics, syntax/phonology,
syntax/pragmatics, morphology/phonology, phonology/phonetics, phonetics/speech processing, semantics/pragmatics, intonation/discourse structure,
as well as issues in the way that the systems of grammar involving these interface areas are acquired and deployed in use (including language acquisition,
language dysfunction, and language processing). It demonstrates, we hope,
that proper understandings of particular linguistic phenomena, languages,
language groups, or inter-language variations all require reference to interfaces.
The series is open to work by linguists of all theoretical persuasions and
schools of thought. A main requirement is that authors should write so as to
be understood by colleagues in related subfields of linguistics and by scholars
in cognate disciplines.
The current volume seeks to bring together disparate strands of research
on ê-features across the modules of morphology, syntax, and semantics. It
also attempts to begin to delineate a programme of research that focuses on
the formal properties of these features and what they have to tell us about the
nature of the interfaces between grammatical modules.
David Adger
Hagit Borer

Notes on Contributors
David Adger is Professor of Linguistics at Queen Mary, University of London.
He is author of Core Syntax (OUP 2003) and co-editor of the journal Syntax.
He has published in various journals including Language, Linguistic Inquiry,
and Natural Language and Linguistic Theory on syntax and its interfaces with
other components of the grammar.
Susana Béjar is a lecturer at the University of Toronto. Her research investigates complexity in morphosyntactic systems. She has published in Syntax
and Revue québecoise de linguistique and has a forthcoming book on ê-features
with OUP.
Jonathan David Bobaljik is a professor of linguistics at the University of
Connecticut. He has written widely on aspects of syntax, morphology, and the
relationship between them. His publications have appeared in the journals
Linguistic Inquiry, Natural Language and Linguistic Theory, and Journal of
Linguistics.
Daniel Harbour is a lecturer at Queen Mary, University of London. His primary research interest is features, from interpretation to pronunciation. His
book publications include Morphosemantic Number (Springer 2007) and his
articles have appeared in Syntax and Natural Language and Linguistic Theory.
Heidi Harley is an associate professor of linguistics at the University of
Arizona. She has interests in morphology and the syntactic representation
of event and argument structure. Her publications include English Words: A
Linguistic Introduction (Blackwell 2006) and papers in the journals Language,
Linguistic Inquiry and Studia Linguistica.
Irene Heim is Professor of Linguistics at MIT and is co-editor of the journal
Natural Language Semantics. She has published widely in semantics and is coauthor of Semantics in Generative Grammar (Blackwells 1998).
Martha McGinnis is an assistant professor in the Department of Linguistics
at the University of Calgary. Her research deals with the architecture of grammar with an empirical focus on argument structure and ê-features. She has
published in the journals Linguistic Inquiry and Language.

Notes on Contributors

ix

Andrew Nevins is an assistant professor of linguistics at Harvard University.
His research spans topics in phonology, morphophonology, morphology, and
syntax, and his publications have appeared in Linguistic Inquiry, Natural Language and Linguistic Theory, and Euskalingua.
Milan Řezáč is a postdoctoral researcher at the University of Nantes. He is
interested in the syntax of agreement and non-thematic positions. His publications on cyclicity, expletives, and agreement interactions have appeared in
such journals as Linguistic Inquiry, Syntax, and Lingua.
Uli Sauerland leads a research group at the Center for General Linguistics
(ZAS) in Berlin. His publications span syntax, semantics, and pragmatics
and have appeared in such journals as Linguistic Inquiry, Natural Language
Semantics, and Linguistics and Philosophy.
Jochen Trommer is a lecturer at the Institute of Linguistics at the University of Leipzig. His main research areas are theoretical morphology and
phonology, especially in Distributed Morphology and Optimality Theory. His
publications have appeared in the Yearbook of Morphology and Linguistische
Berichte.

Abbreviations

˘

Person

1

First person

2

Second person

3

Third person

I, II, . . .

Class labels (Latin, Tsez)

A

Transitive agent

abs

Absolutive

acc

Accusative

act

Active

addr

Addressee

agr

Agreement

aor

Aorist

appl

Applicative particle

asp

Aspect (particle)

ATR

Advanced tongue root

aux

Auxiliary

ax

Accessory

ben

Benefactive

comit

Comitative

conj

Conjunct

cpl

Completive

D

Dative argument

dat

Dative

decl

Declarative

dem

Demonstrative

dflt

Default

dir

Direction marker (direct/inverse)

Number

Abbreviations
DL

Dative displacement

dl

Dual

dyn

Dynamic

emph

Emphatic

erg

Ergative

evid

Evidential

ex

Exclusive

expl

Expletive

fem

Feminine

FS

Functional Sequence

fut

Future

GB

Government and Binding

gen

Genitive

GF

Grammatical Function

GPSG

Generalized Phrase Structure Grammar

hab

Habitual

hon

Honorific

HPSG

Head-Driven Phrase Structure Grammar

i

Irrational/inanimate

imprs

Impersonal

impf

Imperfect, imperfective

in

Inclusive

inch

Inchoative

ind

Indicative

inf

Infinitive

instr

Instrumental

intr

Intransitive

kase

Structural case

LDA

Long-Distance Agreement

LFG

Lexical Functional Grammar

loc

Locative

lrs

Low referential status

xi

xii

Abbreviations

masc

Masculine

mood

Mood

MP

Minimalist Program

ms

Marked scenario (particle)

nact

Nonactive

neut

Neuter

nmlz

Nominalization

nom

Nominative

npst

Nonpast

nr

Near

O

Transitive object

obl

Oblique

obv

Obviative

OT

Optimality Theory

part

Participant

pc

Paucal

PCC

Person–Case Constraint

pf

Perfect, perfective

pl

Plural

pot

Potential

ppl

Participle

pres

Present

pret

Preterit

prev

Preverb

prog

Progressive

pron

Pronominal base

prox

Proximate

prt

Particle

pst

Past

quot

Quotative

refl

Reflexive

RG

Relational Grammar

Abbreviations
S

Intransitive subject (structural)

SAP

Speech Act Participant

sg

Singular

sjnct

Subjunctive

spkr

Speaker

subj

Subject (syntactic)

thm

Theme

tns

Tense

top

Topic

tr

Transitive

u

uninterpretable

UG

Universal Grammar

VI

Vocabulary item

xiii

This page intentionally left blank

1
Why Phi?
DAVID AD GER AND DANIEL HARB OUR

1.1 Introduction
Phi-features present a rare opportunity for syntacticians, morphologists, and
semanticists to collaborate on a research enterprise in which all have an equal
stake and which all approach with proprietary data and insights: syntacticians
with intervention effects and the theory of Agree, morphologists with patterns
of syncretism and hierarchies of person, definiteness, and so on, and semanticists with theories of binding and anaphora and theoretical approaches to the
presuppositions and entailments that ê-features engender.
Given ê-features’ transmodular relevance, it is inappropriate for syntacticians, semanticists, and morphologists to devise three monomodular accounts
of ê-features in their own domains. Rather, the study of Universal Grammar
must meet the concerns of all three fields with a single unified account and
only an account of transmodular generality can be aptly called Phi Theory.
Hence this volume’s subtitle: Phi-features across Modules and Interfaces.
These research concerns were guiding questions at the 2004 workshop on
ê-features held at McGill University, Montreal. The purpose of the conference
was to bring together established and upcoming researchers in the syntax,
semantics, and morphology of ê-features and to have them present recent
advances of intra- and intermodular interest. The current volume derives from
the presentations and discussion of the workshop.
In this opening chapter, we situate Phi Theory in Generative Grammar,
focusing on the history of ê-features and how recent theoretical developments
have given them greater prominence.

We are grateful to Jonathan Bobaljik, Paul Elbourne, Andrew Nevins, Jochen Trommer, and two
anonymous OUP referees for comments on earlier drafts of this introduction. This volume grew
out of a conference funded by the Canadian Social Sciences and Humanities Research Council, with
supplementary funding from the School of Modern Languages, Queen Mary, University of London.

2

David Adger and Daniel Harbour

Before doing so, a word on what we mean by ê-features. We take ê-features
to be those involved in predicate–argument agreement, typically person, number, and gender. Other features, such as those involved in honorification and
definiteness also fall within this definition, while case, for example, does not.
We will refer to the class of such features as ÷ and to the individual features
which make up this class as ê-features. As in any emerging theory, the limits
of the empirical domain are not given a priori, and we expect the precise
definition of ê-features to emerge only after much more work. This volume is
merely a preliminary step in what we hope is a promising direction.
In the next sections, we trace a necessarily brief and incomplete history of
attempts to tackle the development of a theory of ÷. Because the range of
relevant works is enormous, our approach will be to tease out what we see
as the major themes that have led to the current situation within transformational approaches to Generative Grammar. Because of the historical nature of
this overview, we have organized the discussion into three domains: syntax,
semantics, and morphology. However, the common themes that begin to
emerge challenge the necessity of treating these domains of enquiry separately,
a point taken up in the chapters of this volume.

1.2 Syntax
There are currently a number of areas of syntactic research in which ê-features
play key roles: the cartographic analysis of verb movement and clitic placement, displaced agreement phenomena, the theory of case and agreement,
to name a few (see references in the following subsections). However, the
prominence afforded to ê-features in current syntactic theory is a recent
phenomenon. Indeed, although agreement, as a general phenomenon, was
afforded a syntactic treatment very early in generative work, it took a long time
for attention to be paid to the properties of the linguistic items that entered
into agreement.
There were two major impediments to the development of a Phi Theory:
lack of appreciation of the relevance of ÷ for syntactic theory in general, and
lack of a robust theory of features. Syntactic concern tended to concentrate
on the extent to which agreement processes could be assimilated to general
syntactic mechanisms, while the substance of what did the agreeing, the internal nature of ÷, was largely ignored. Nevertheless, as we trace the history of
topics where properties of agreement were argued to be syntactically relevant,
we see that attempts to fine-tune the syntactic debate led naturally to efforts
to articulate what the inventory of ê-features is and how their organization
impacts on syntactic operations.

Why Phi?

3

It did not take long for generative research to reach the idea that ÷, the
substance of agreement, was composed of features and that these were manipulated by the syntax. Initially, in Syntactic Structures (Chomsky 1957),
agreement was treated as a context-sensitive transformation, converting one
category into another. For English subject agreement, this took the form:
(1)

Number Transformation—obligatory

(Chomsky 1957: 112)

Structural Analysis: X–C–Y⎧
⎫
⎨ S in the Context NPsing – ⎬
Structural Change: C → Ø in other contexts
⎩
⎭
past in any context
The idea is that the inflectional component of non-past sentences is rewritten
as the morpheme S in the context of a singular NP, but as zero elsewhere.
The notion of “singular NP” is technically dealt with via an atomic symbol,
although this is clearly unsatisfactory, a placeholder for further analysis. The S
morpheme undergoes morphophonological rules to surface as the appropriate
form: /s/, /z/, /-iz/. (Clearly, more irregular alternations, be∼is, have∼has,
will require special provision.) This structural change transformation is, in
essence, a rewrite rule, belonging primarily to the part of the grammar that
specifies how the pronunciation of syntactic structures is effected (cf. Bobaljik,
this volume).
By the time of Aspects of the Theory of Syntax (Chomsky 1965), however, the
approach to agreement had become both featural and syntactic. Two pieces of
work fed into this change of perspective. First, a fully transformational account
was offered by Postal (1966). Postal suggested that a Spanish noun phrase like
unos alumnos “some students” consisting of a determiner and a head noun
had the representation:
(2)

[NP [Article un]
[Noun [Stem alumn] [Affix [Gender M] [Number Pl]]]]

An obligatory transformation copies the nominal affix to the determiner:
(3)

[NP [Article un [Affix [Gender M] [Number Pl]]]
[Noun [Stem alumn][Affix [Gender M] [Number Pl]]]]

This receives the appropriate spellout after the morphophonological rules
have applied:
(4)

[NP [Article un[Affix [o]s]]
[Noun [Stem alumn][Affix [o]s]]] = unos alumnos

4

David Adger and Daniel Harbour

Second, Harman (1963) had begun to exploit in the syntax the descriptive
power afforded by symbols that were internally complex. Chomsky (1965)
combined these approaches by positing an N node that branches into a feature
matrix containing various features, such as gender, number, case:
(5)

⎤
⎡
+N
· gender
⎢· gender ⎥
⎥
Article →⎣‚ number⎦/__ · · ·⎢
⎣‚ number⎦, where [Article . . . N] is an NP
„ case
„ case
⎡

⎤

This rule assigns the features of the noun to the article, effectively restating
Postal’s analysis with features rather than morphemes. Such feature matrices
could then be matched with lexical items. The structure of these features was
modeled along the lines of the structure of phonological features, as motivated
by Halle in a number of publications following work by Jakobson (Halle 1962,
Jakobson, Fant, and Halle 1963).
This approach places ê-features squarely in the syntax: they undergo syntactic operations triggered by their positioning in syntactic structures. However, the goal in Aspects was to provide an account for the phenomenon of
agreement generally. There was no interest in developing a theory of the
individual components of agreement.
Following Aspects, little more attention was paid to the development of a
theory of ÷. In fact, as Gazdar, Klein, Pullum, and Sag (1985: 18) observe:
But [after Aspects of the Theory of Syntax], development in the theory of syntactic
features basically stopped. Although generative grammarians continued to assume
features in their descriptive apparatus, hardly any generative grammarians attempted
to give syntactic features the kind of well-defined formal underpinnings that, say,
the theory of phrase structure rewriting rules had. George Lakoff ’s 1965 dissertation
(published as Lakoff 1970) was an honorable exception, but it influenced the field
more toward the development of abstract deep structures and complex transformational derivations than toward appropriate exploitation of features in phrase structure
description, despite the rich proposals for feature analysis that it presented.

They conclude that “the theory of features fell gradually into a state of chaos.”
For their own part, during the 1980s, Gazdar, Klein, Pullum and Sag did
provide a theory of features in Generalized Phrase Structure Grammar in
the context of which a theory of ê-features could have been developed.
However, the ê-features that they themselves posited merely recapitulated
the traditional descriptive labels (e.g., PLU, +/− for plural∼non-plural,
PER, 1/2/3 for first∼second∼third person) and so did not provide any deep
insight into ÷ itself. The same tendency held sway in the Government and

Why Phi?

5

Binding tradition (e.g., Lumsden 1987) and in Lexical Functional Grammar
(Bresnan 1982).
However, if the field was in chaos with respect to its views of features, the
chaos was neither total, nor uncreative. Notably, Muysken and van Riemsdijk
(1986: vii) observed:
Syntactic features have played a somewhat marginal role in the development of the
theory of grammar over the past fifteen or twenty years. Even basic questions such
as “how many are there?”, “what are they?”, “how do they distribute over syntactic
structures?” were hardly addressed, let alone answered. Nevertheless, it is clear that
syntactic features do play an important role in syntax. Few, if any, grammarians today
hold, that syntactic categories are unanalyzable atomic primitives, and any additional
intrinsic properties of syntactic categories are expressed in the form of features. It
would appear to be high time, therefore, to examine the theory of syntactic features
in a more systematic way.

Moreover, Muysken and van Riemsdijk recognized ÷ as a potential source
of enlightenment in this domain. Indeed, of the several strands of research
that were eventually to place ê-features in a prominent position in syntactic
theory, they recognized two: the notion of rich agreement (Taraldsen 1980,
Rizzi 1982), and hierarchies of case marking (Silverstein 1976 [1986]). They
also drew attention to another work of this period, that was eventually to have
major influence (Hale 1973; see Section 1.4 below.)
In the twenty years since Muysken and van Riemsdijk’s volume, four major
strands of syntactic research have conspired to place ê-features in a position
of prominence. The first and second—work on the pro-drop parameter and
then, later, on height of verb movement—led to a concept of “rich agreement”, the eventual explication of which has naturally fed into questions about
the nature of ÷. Third, the role of case in argument licensing has inspired
research into the mechanisms of case and agreement. This, in turn, has led
to notions of ê-completeness versus ê-defectiveness, notions that can only be
fully justified in the context of an explicit Phi Theory. Fourth, the Person Case
Constraint—the impossibility of certain ê-feature combinations in multiple
agreement/clitic systems—has recently received much attention as attempts
are made to reduce it to other syntactic phenomena. In the subsections that
follow, we review these developments and highlight key contributions, conjectures, and results.
1.2.1 Rich agreement
The importance of rich agreement was first noted in regard to pro-drop
(Taraldsen 1980). Essentially, in languages, like Italian and Greek, where the

6

David Adger and Daniel Harbour

verb reveals the person and number of the subject, pro-drop is possible; in
languages where it only partially reveals it, such as German and English, it is
not. The descriptive generalization is that when agreement is “rich”, it licenses
a null subject.
The internal richness of Agr, that is, how much information is specified
in Agr, became crucial to later analyses of subject pro-drop (Rizzi 1982), and
of the generalized pro-drop found in polysynthetic languages (Jelinek 1984).
Curiously, however, little attention was paid to what the featural composition
of Agr actually was and how it related to the intuitive notion of rich agreement.
However, following Emonds (1978) and then, especially, Pollock (1989),
it was noted that rich agreement potentially correlated with height of verb
movement: for instance, Romance finite verbs, which show rich agreement,
move higher than both English finite verbs and Romance participles, which
agree less fully. The idea was thoroughly explored for a wide variety of
Germanic languages (beginning with a series of works by Platzack and Holmberg, e.g., 1989). This led to attempts to show two things: on the synchronic
side, that Germanic languages that had retained verb movement possessed
correspondingly richer subject agreement (see, especially, Rohrbacher 1994);
on the diachronic side, that the decline of subject agreement and verb movement proceeded in tandem (e.g., Roberts 1985). This work ultimately failed
to shed light on the nature of ê-features per se, though, for two reasons.
First, the biconditional correlation between rich agreement and verb movement proved to be too strong (see Bobaljik 2003 for thorough overview and
formulation of a weaker generalization). Second, it focused on the paradigm,
rather than the ê-features that generate paradigms, as the basic explanatory
unit in terms of which richness was to be explicated. Despite these failings,
the research program did succeed in placing ÷-related morphosyntax center
stage.
In addition, the research program stemming from Pollock’s work, which
used the different landing positions of verbs in French and English to argue
for a splitting of I(NFL) into separate tense and agreement projections, progressed to more fine-grained decompositions. For instance, Shlonsky (1989)
argued, on the basis of Modern Hebrew (morpho)syntax, for separate PersonP,
NumberP, and GenderP (see Linn and Rosen 2003 for similar arguments based
on Euchee); and Poletto (2000) argued, on the basis of the distribution of
subject clitics (SCL) in Northern Italian dialects, for a structure that splits the
person features into separate projections:
(6)

[NegP [NumP SCL [HearerP SCL [SpeakerP V [TP . . .]]]]]

(Poletto 2000: 31)

Why Phi?

7

Here we see the connection between syntactic position and richness of
agreement captured by projecting ê-features as parts of the basic clausal
backbone.
Another vein of research where ê-features are claimed to have a presence
in the extended projection of the clause involves the fine structure of the left
periphery (Rizzi 1997): like IP, CP has come to be decomposed into several different projections and some researchers have argued for relationships between
these and various ÷-categories. The general viewpoint taken is that personlike features are represented on high C-domain heads that encode whether
sources of knowledge, opinion or belief are shared between the speaker and
other discourse participants. This idea has been used to capture a wide range
of data, from evidentiality and logophors (Speas 2004, Tsoulas and Kural 1999)
to long-distance binding (Sigurðsson 2004) and person hierarchies (Bianchi
2006).
1.2.2 Agreement and case
We can see the general approach to the connection between ê-features and
case licensing emerge in Lectures on Government and Binding (Chomsky 1981),
which influenced much work afterwards. There, what was important once
again, however, was the feature bundle Agr, which was implicated in theories
of case and government. Agr was assumed to work as a single syntactic unit,
just as in the original approaches to the role of rich Agr in licensing null
subjects discussed directly above.
This approach to Case and syntactic licensing allowed a fairly successful implementation of an important generalization connecting Case and êfeatures: overt subjects with nominative case are restricted to clauses specified
with tense and agreement features (that is, finite clauses).
Within the Government and Binding framework, this idea was captured by
the following kind of specification (see Chomsky 1981):
(7)

I[+tense +Agr] assigns nominative case to its specifier

Note that Agr is itself taken to be a feature here. The plus value may be
taken as suggesting a specification of ê-features, though none in particular
are mentioned.
This proposal now extends naturally to a potential challenge for the original
generalization which is raised by languages like European Portuguese, where a
nominative subject is, in fact, possible in an infinitive just when the infinitive
is inflected for agreement (see Raposo 1987 for Portuguese, and George and
Kornfilt 1981 for similar data from Turkish inflected gerunds):

8

David Adger and Daniel Harbour

(8) É correto nós
ignor-ar-mos isto.
Is right us-nom ignore-inf-1pl this
“It is right for us to ignore this.”
We can capture the data by assuming that the following holds universally:
(9)

[+Agr] assigns nominative case to its specifier

Other analyses treating Agr itself as a feature are Haegeman’s (1986) treatment
of West Flemish subject licensing, and, later, Rizzi’s (1990) theory of whmovement, where it was used to explain the possibility of subject extraction
after certain complementizers. Throughout this period, no attempt was made
to explain the features that comprised Agr or to explicate the notion of rich
Agr, [+Agr], in terms of a given inventory of ê-features. As discussed in
Section 1.2.1, it was not until the work of Platzack and Holmberg (1989) and
Rohrbacher (1994), that there was an attempt to explicate the meaning of
[+Agr] in terms of properties of the agreeing verbs: essentially, in terms of
how many of a language’s pronominal categories corresponded to unique
agreement affixes (see also Vikner 1995).
As previously mentioned, Pollock (1989) argued that apparently atomic
syntactic categories should be split into their constituent features. Moreover,
these features themselves should project as heads which could act as landing
sites for verb movement, giving the following clause structure:
(10)

TP
Subject

T
T

AgrP
Subject

Agr
Agr

VP

V Object
Belletti (1990), on the basis of pursuing a transparent relationship between
the internal morphological structure of words, and the syntactic structure of

Why Phi?

9

clauses (the Mirror Principle of Baker 1988), suggested that AgrP selects TP
rather than the structure in (10), while Chomsky (1989) suggested that there
were two AgrPs, one below T, which is associated with object agreement, and
one above, associated with subject agreement:
(11)

AgrP

Subject

Agr

Agr

TP
Subject

T
T

AgrP
Agr

Object
Agr

VP

V Object
This enriched system allowed a more general approach to case assignment, and Chomsky (1993) proposed that structural Case in general is
checked in the specifier of Agr heads. Each Agr acted as a “mediator” for
the case features of the heads of the phrases they selected (TP and VP).
Structural Case checking can then be seen as arising from an agreement
relation.
However, there were a number of conceptual arguments against the projection of Agr heads in clause structure. In The Minimalist Program, Chomsky
(1995, chapter 4) argued that heads which project without semantic effects,
such as Agr, should be dispensed with. His alternative suggestion for maintaining the link between ê-features and Case comes from investigations into the
syntax of argument structure (especially Hale and Keyser 1993). He proposes
that subjects are introduced by a functional head, v (Chomsky 1995: 315 and
references therein; see also Kratzer 1996 among many others). This head can

10

David Adger and Daniel Harbour

be endowed with ê-features and hence accusative case checking capabilities.
Similarly, T is endowed with ê-features that Case license the subject, which
itself moves to T’s specifier:

TP

(12)

Subject

T
T− ê

vP

Subject

v
v− ê
V

v

VP

V Object

In more recent versions of the Minimalist Program, Chomsky (2001)
has maintained the intuitive link between agreement and structural Case
checking, however, he has made proposals for ê-features themselves. Specifically, person and number features play distinct roles in structural Case
checking: when one is absent from a head, the head is defective and Case
checking is impossible (this is how he analyses the non-finite T of raising
constructions).
The idea that the separate features that make up ÷ act independently in
the syntax has been developed in analyses of complex agreement phenomena.
These analyses differ from the work discussed above in that their focus is
not the connection between Case and agreement, but a general theory of the
syntactic dependencies established by the operation Agree (Chomsky 2000).
An example of such work is Béjar (2004), which investigates the classical problem of Georgian agreement, where the controller of agreement on the verb is
not determined by syntactic position or grammatical function, but rather by
ê-featural richness. Béjar concentrates on examples which show that person
agreement on a verb can arise from one argument whereas number agreement
comes from another. For example, in (13), the second person singular object

Why Phi?

11

triggers person agreement and the first person plural subject triggers number
agreement:
(13) g- k’lav-t
2sg-kill- pl
“We kill you (singular).”

(Hewitt 1995: 132)

This kind of agreement has been treated morphologically in the past (Anderson 1992, Halle and Marantz 1993). Béjar argues that a more satisfying explanation is available when one allows the features within one ÷-set to establish
disjoint Agree relations separately in the syntax, and she extends this basic idea
to a general analysis of what she terms “agreement displacement phenomena”
(see also Řezáč 2003, and for earlier ideas along the same lines Ritter 1995 and
Taraldsen 1995).
1.2.3 Person Case Constraint
The theories of Case and agreement come together in a single grammatical
phenomenon that has proved to be a very productive domain of application
and refinement of the theory of ê-features in recent years: the Person Case
Constraint.
Perlmutter (1971) observed an intriguing restriction on the combination
of dative and accusative clitics in Spanish: the accusative in such a situation
must be third person. This constraint is known in the literature as the *me lui
Constraint, or Person Case Constraint (PCC). We give here an example from
French (see Anagnostopoulou 2003 and Haspelmath 2004 for many other
cases):
(14)

a.

Agnès me la
présentera.
Agnès 1sg 3sg.fem present.fut.3sg
“Agnès will introduce her to me.”

b. *Agnès me lui
présentera.
Agnès 1sg 3sg.fem present.fut.3sg
“Agnès will introduce me to her.”
c.

Agnès me présentera
à elle.
Agnès 1sg present.fut.3sg to her
“Agnès will introduce me to her.”

Example (14a) shows that dative and accusative clitics may cooccur. However,
such combinations are only licit if the accusative is third person, hence the
contrast between (14a) and (14b). In French, such argument combinations can
only be expressed periphrastically, as in (14c).

12

David Adger and Daniel Harbour

Bonet (1991) gives a tentative approach to this phenomenon (developed
more fully in Bonet 1994) which uses a filter to block the morphological
realization of non-third person accusatives in the presence of dative clitics.
However, more recently, there have appeared a range of syntactic analyses of
the PCC, which crucially appeal to the various ê-features that make up agreement. These approaches have attempted to connect the PCC to various other
phenomena. For example, Boeckx (2000) and Anagnostopoulou (2003) have
proposed that it is connected to the restrictions on the appearance of first and
second person nominative objects in Icelandic; Richards (2005) connects it
with cross-clausal extraction in Tagalog; Bianchi (2006) connects it to inverse
agreement systems found in languages like Plains Cree and Bobaljik and
Branigan (2006), to the Spurious Anti-Passive construction found in Chukchi
in configurations that are reminiscent of inverse agreement; Ormazabal and
Romero (2002) draw a connection to animacy on the basis of leísta dialects
of Spanish, and Adger and Harbour (2007), in a somewhat related vein,
have connected it with patterns of case syncretism across different languages.
Finally, Nevins (2007), applying, in the syntax, ideas from phonological feature
formalisms, comes the closest of any researcher to tackling the full typological
variety of the PCC reviewed by Haspelmath in his (2004) crosslinguistic survey
of the phenomenon.
There is an interesting parallel here with the Georgian agreement effects
discussed above: what was once thought to be a paradigm case of a morphological phenomenon can be understood syntactically when we pay attention
to the behaviour of the components of ÷ (see especially Béjar and Řezáč 2004
for the impact of the PCC on the theory of Agree).
The research displays an exciting lack of consensus, even if some themes
are clear: feature structure—whether in terms of competition, or the behaviour of Agree, or the specification of arguments—lies at the heart of
these analyses. The sub-÷-structure is crucially implicated in all of these
analyses and so a well articulated theory of ê-features is crucial for such
work.

1.3 Semantics
Although Phi Theory may have taken a time to come into its own in syntax,
related issues have enjoyed long attention in semantics. These begin in the
philosophico-semantic tradition, in which philosophers aimed to supplement
the Fregean and Tarskian theories of formalized languages (Frege 1879, Tarski
1935) for the analysis of natural language (beginning with Frege 1892 and
Russell 1905 and leading to the important work of Davidson 1967, Montague

Why Phi?

13

1970, 1973, Lewis 1972, which attempted to connect contemporary philosophical semantics with grammatical theory). Key amongst the requisite additions
relevant here were notions of indexicality and presuppositionality, and mechanisms for the representation of quantities. We address each of these below.
1.3.1 Indexicality and presuppositionality
The category of person was an early focus of research in the philosophy
of language. It arose naturally in two regards: first, indexicals (Jespersen’s
“shifters”) were an obvious domain that was not embraced by semantic theories designed for the elucidation of mathematics; second, the interest in the
logical properties of proper names led naturally to attempts to deal with the
semantics of pronouns and deictics (e.g., Russell 1940). The most influential
work in the philosophical tradition is that of Kaplan. Kaplan (1977 [1989])
formulated the thesis that indexicals are directly referential, entailing that their
semantic value is fixed purely by the context of the speech act and cannot be
acted on by logical operators. Recently, a variety of evidence has called this
view into question. Schlenker (2003), for instance (see also von Stechow 2003,
Anand and Nevins 2004), has argued against the Kaplanian view on the basis
of Amharic sentences such as (15), which can be used to describe John’s saying
of himself “I am a hero”:
(15)

on @gna n@-ññ
y-il-all
John hero be.pf-1sgO 3masc.say-aux.3masc
“John says that he is a hero.”

(Schlenker 2003: 68)

Schlenker demonstrates that the embedded clause in Amharic is not a quotation. This shows, straightforwardly, that the semantic value of “I” is not fixed
by the context of utterance, as “I” refers to John, not to whoever utters (15).
Schlenker’s own treatment of the semantics of person pursues an idea first
developed by Cooper (1983) with respect to gender, namely, that it is presuppositional. To see the intuition, consider the following dialogue:
(16) “Tell me about Alex.”
“Evidently she’s married: you can see the wedding ring in this photo of
her hand.”
If the first speaker knows that Alex is a man, it would be impossible to attempt
to correct the second speaker by saying “No, she isn’t married”; this would
be taken as accepting that Alex is a woman and disagreeing about his/her
marital status. So, Alex’s gender does not form part of the assertion in “She’s
married”, but rather is a presupposition. This accords with the intuition that
“She’s married”, said of a husband, is not false, but infelicitous.

14

David Adger and Daniel Harbour

An influential implementation of this idea, which pursues Tarski’s intuition
that reference arises via an assignment of values to variables, is Heim and
Kratzer’s (1998). They propose that ê-features are syntactically adjoined to
pronominals and that their semantic contribution is a presupposition that
restricts the range of the assignment of values to variables. For instance, the
structure of the pronoun she, say, is:
(17)

DP

DP

[thirdperson]

[feminine]

DP
[singular]

DP
she1

(Heim and Kratzer 1998: 244)
The features are partial identity functions (indicated by the colon in (18)).
That is, [feminine] maps individuals to themselves (an identity function),
subject to the proviso that the individual is female; it is undefined otherwise
(hence, a partial function).
(18) [[feminine]] = Îx : x is female. x
Applying this to “She is married”, we have that the lower nodes of the DP are
assigned to Alex, however, when we move up the tree to [feminine], the partial
function fails to return a value as Alex is not female.
Schlenker applies this kind of approach to person features too. He proposes
a meaning for the first person feature so that it is only defined when the
pronoun bearing the feature refers to a group which includes the speaker who
utters the sentence in the context, and a similar meaning for the second person
feature. He then proposes that third person pronouns are essentially chosen as
semantic defaults (see also Sauerland, this volume).
However, an interesting semantic problem arises on the presuppositional
approach to person and gender features, with respect to bound variable readings of personal pronouns. Consider the following example, where gender

Why Phi?

15

is relevant: in a coed class, where the only person to have done the assigned
homework is Mary, one can say:
(19) Only Mary has done her homework.
The important fact about such uses of personal pronouns (first noted by
Partee 1989 with respect to the first person) is that they can break free of
their presuppositions: (19) means, informally, “Look at the set of people who
have done their homework: only Mary is in that set”. So, the pronoun “her”
does not constrain the statement to hold only of females, contrary to what
one would expect given (18). Elements of this debate have thrown light on
the complex interplay between semantic, syntactic, and morphological aspects
of ê-features (see, for instance, Déchaine and Wiltschko 2002 and Rullman
2004). Several aspects of the debate are discussed by Heim (this volume).
In addition to person and gender, another ê-category, number, has been
a productive area of philosophical investigation (e.g., Goodman and Quine
1947, Quine 1960). Given that philosophical semantics has its origins in the
foundations of mathematics, set theory is, unsurprisingly, frequently used to
represent notions of singularity and plurality. An influential version of this
is the lattice-theoretic treatment of plurals (Link 1983). The concepts this
work introduced have been deployed in the treatment of plurality, masshood,
distributivity, collectivity, and a wide range of aspectual phenomena (Krifka
1992, Verkuyl 1993, Schein 1993, Lasersohn 1995, Landman 1996, Doetjes 1997,
Chierchia 1998, Ojeda 1998, Winter 2001, amongst others). Interestingly, in
contrast to person and gender, no presuppositional account of number has, to
our knowledge, been offered (though Heim and Kratzer 1998: 245 suggest the
possibility). It may be (Nevins, p.c.) that, if definiteness were incorporated
more fully into the treatment of ÷, it would be possible to attribute all
presuppositionality effects to definiteness and to simplify the representation
of person and gender. The non-presuppositional treatment of number would
then be the norm for other ÷-categories. For steps in this direction, see
Kratzer (2006).
1.3.2 Agreement: syntactic or semantic?
We have seen that person, number, and gender can be treated as presupposition inducing features. However, gender is of two types: semantically
contentful and purely grammatical. An obvious issue for the presuppositional
approach is whether grammatical gender is amenable to a purely semantic
approach.
For example, in German, Mädchen “girl” is grammatically neuter, as can be
seen from the form of the relative pronoun that it controls:

16

David Adger and Daniel Harbour

(20) das
Mädchen, das/*die
das Buch ließt
the.neut girl
that.neut/that.fem the book read.pres
“the girl who reads the book”
The relative pronoun is obligatorily neuter, agreeing with the noun and article.
The feminine relative pronoun, required in an example with a grammatically
feminine noun such as (21) below, is impossible.
(21) die
Frau, die/*das
das Buch ließt
the.fem woman that.fem/that.neut the book read.pres
“the woman who reads the book”
However, if the girl is referenced by a pronoun, the feminine, rather than the
neuter, is used:
(22) Das
Mädchen sagt,
daß sie/*es
das Buch ließt.
the.neut girl
say.pres that she.fem/it.neut the book read.pres
“The girl says that she is reading the book.”
On the assumption that the pronoun’s function is the semantic one of picking
out a referent, these examples appear to show that the neuter agreement
that Mädchen “girl” triggers is sensitive to a syntactic rather than a semantic
feature.
Dowty and Jacobson (1988), however, argue against this idea, as part of a
general program to minimize the contribution of syntax, and suggest instead
that agreement should be treated as an essentially semantic phenomenon.
Pollard and Sag (1994) provide evidence for this approach on the basis of a
range of phenomena where simple feature matching in the syntax would give
the wrong results. A striking case of this is reference transfer of the following
sort (a modification of Nunberg’s 1979 ham sandwich example):
(23) The hash browns at table six is/*are getting angry.
“The person at table six, who ordered the hash browns, is getting angry.”
Here the agreement on the verb seems to be with the referent of the subject, the
person who ordered the hash browns, rather than with the syntactic specification of the hash browns. Collective nouns in British English provide further
evidence that differences in number agreement correlate with differences in
interpretation:
(24) The committee has/have voted today.
For such dialects, the agreement on the auxiliary correlates with interpretational effects on the subject, independent of singular number marking on

Why Phi?

17

the noun. Sauerland and Elbourne (2002) note a number of other semantic
phenomena affected by this kind of agreement.
The theoretical point made by Dowty and Jacobson is that verbal agreement
features can contribute to semantic interpretation. This constitutes a prima
facie difficulty for the syntactic approach to agreement outlined above, where
agreement on the verb is supposed to lack semantic content.

1.4 Morphology
1.4.1 Precursors
Morphology is a natural place to look for a theory of the internal featural
constitution of ê-structures. To see why, consider the Tok Pisin pronoun
paradigm (Foley 1986: 67):
(25) Person
1in
1ex
2

Singular

Dual

Plural

—
mi
yu

yumitupela
mitupela
yutupela

yumi
mipela
yupela

Observe that the meaning/pronunciation of the first person inclusive is the
sum of the meaning and pronunciation of its parts: yumi . . . means yu and
mi. This suggests that first person inclusive, first person exclusive, and second person are not sui generis, but are composed of more fundamental
features. The same conclusion—that traditional categories of description
are composites of features—is underlined by number in (25). Observe that
the dual, tupela, is the plural, pela, plus something else. Thus, these numbers share part of their meaning, non-singularity, and part of their sound,
pela.
The phenomenon of syncretism, as discussed by Hale (1973, see also Halle
1997), reveals the same fact about duals and plurals. In Warlpiri, in certain
contexts, plural agreement occurs where, on purely semantic grounds, we
would expect dual; call these *dl-contexts. Hale accounts for this by supposing
that dual is a composite [a b], where [a] means simply non-singular (cf., Tok
Pisin pela) and [b] restricts the non-singularity to duality (cf., Tok Pisin tu).
What is special about *dl-contexts is that [b] is deleted, making dual [a b]
identical with plural [a].
Thus, we see that core morphological phenomena lead quickly to a set of
research questions for which the development of a theory of ê-features is

18

David Adger and Daniel Harbour

necessary. It is, therefore, surprising to discover that ê-features are all but
wholly absent from such volumes as Theoretical Morphology (Hammond and
Noonan 1988) and The Handbook of Morphology (Spencer and Zwicky 1998).
However, on closer inspection, there are legitimate reasons for this absence. As
Spencer and Zwicky observe, morphology was neglected in deference to syntax
and phonology in early developments of generative grammar (as we have
indicated above, agreement was treated as the result of a rewrite rule or syntactic transformation); only with Halle’s (1973) programmatic statement for a
generative theory of morphology did interest begin to center on morphology
as research domain in its own right. The Lexicalist interpretation of Chomsky
(1970) gave this extra life as the debate about morphology could be cast in
terms of the division of labor between the lexicon and syntax (see Borer 1998
for overview). To the extent that the nature of inflection was studied at this
time, it was as a means of examining how labor was shared between modules
of the grammar. For instance, Anderson (1982) uses agreement in Breton verbs
and prepositions to argue that agreement is syntactically autonomous and
subject to syntactic processes; it is only due to such processes that the agreement comes to be incorporated into the word of which it ultimately forms
part. As such, agreement phenomena were counterexamples to the generalized
Lexicalist hypothesis. However, in this context, the internal constituency of êstructures was not overly of interest.
Nonetheless, two major precursors to a theory of ê-features did emerge
at this time, namely, the above-mentioned Hale (1973) and Silverstein (1986).
Both of these works present articulated inventories of ê-features which
go beyond the mere “featurization” of traditional grammatical categories,
and give thought to what minimal set of features will generate all of the
attested categories. In particular, both authors stress the idea that person
categories, like the first person inclusive, and number categories, like the
dual, are not features in their own right (e.g., [+inclusive] or [+dual]), but
are composites of features (in Silverstein’s system, [+ego +tu] and [+plural
+restricted]).
Hale’s work has been particularly influential for several reasons. He presented analyses of data types that have since become mainstays for the field.
For instance, the 1973 paper treats syncretism between morphological categories in a way that prefigures the impoverishment analysis of Bonet (1991)
and later authors. Similarly, Hale (1997), versions of which had been in circulation several years earlier, introduced the notion of composed number and
emphasized its relevance as an alternative demonstration of the fact that the
dual is not a feature in its own right, but an overlap of the feature specification
of singular and plural.

Why Phi?
(26)

19

a. Pam wari.
that run.pf
“He/she ran.”
b. Puma wari.
those run.pf
“They (two) ran.”
c. Puma yùutu.
those run.pf
“They (plural) ran.”

(Hale 1997: 74)

Hale’s work has been incorporated into key studies of ÷-structure, especially,
Bonet (1991) and Noyer (1992), and into work on morphology in general, most
notably, Halle and Marantz (1993) and Halle (1997).
1.4.2 The composition of ÷
In morphology, the onset of Phi Theory proper must be attributed to the two
works by Bonet and Noyer just cited. In these, the authors were concerned
with issues of what ê-features there are, how they are structured, what operations the morphology can perform on them, and how such operations are
constrained.
Bonet’s investigation (see also Bonet 1995) was motivated, in large part, by
an attempt to account for non-transparent surface outputs in clitic combinations, a topic that (pace Hale 1973) had “hardly received any attention” (Bonet
1991: 10). A classic case of this phenomenon concerns the combination, in
Spanish, of the third person masculine singular clitics for indirect and direct
objects, respectively, le and lo. When the context demands that the clitics
cooccur, they surface, not as le lo, but as se lo. Perlmutter (1971), who first
drew attention to the phenomenon in the Generative context, posited what
was, essentially, a phonological rewrite rule:
⎡
⎤⎡
⎤
(27)
PRO
PRO
⎣ III ⎦ ⎣ III ⎦
Dat.
Acc.
1
2
→ se, 2
As Bonet observes, an equally legitimate rule, on this approach, would introduce the syllable ba instead of se; it is coincidental that what emerges when le
is prevented from surfacing is another clitic, the reflexive se, rather than any
other phonological string. The issue, then, that Bonet investigates is how the
ê-structure of le is transformed into that of se.

20

David Adger and Daniel Harbour

Bonet’s theory involves several notions that have been key to later developments of morphological Phi Theory. First, she adopts (p. 58) a hierarchical
organization of ê-features:
(28) First/Second
CLITIC

ARGUMENT

PERSON

Third Person Dative
CLITIC

ARGUMENT

OBLIQUE

Third Person Accusative
CLITIC

ARGUMENT

Agreement

Agreement

([fem]) ([pl])

([fem]) ([pl])

[±1]

Agreement

([pl])

Here, the “defining properties of the clitics” are in small capitals, the agreement features themselves in lowercase. (Bonet is ambivalent as to whether the
geometrical feature structure, an idea she attributes to Marantz, constitutes
morphological structure in its own right—whether syntax deals in feature
bundles that are mapped onto geometrical structures in the morphology—or
whether the geometries are simply syntactic structures “pruned” of extraneous
information.)
The feature structures in (28) serve to constrain morphological operations
and to define metrics of markedness and defaulthood. Basically, the more
structure, and so features, a ê-set contains, the more marked it is. Bonet
accounted for the le lo → se lo neutralization by supposing that morphology
can delink lower parts of the structure. In particular, given that the structure
for se is a substructure of that for le, delinking the lower part of the le structure
reveals the se structure, explaining why le becomes se, rather than any other
syllable of the language.
Noyer (1992), like Bonet, was concerned with the organization of ê-features
and operations on them (see also Noyer 1998). In particular, he proposed
the process of Fission, whereby a single syntactic terminal node is split
into separate positions for multiple phonological strings (see Harbour, this

Why Phi?

21

volume, for an overview of the account). However, he also resumed another
theme of research, from Hale (1973) and Silverstein (1976 [1986]), namely, the
inventory of ê-features. Investigating a wide variety of languages, some of
them in great depth and with great insight, he arrived at two number features [+
_ singular] and [+
_ augmented], and three person features, [+
_ author],
[+
_ hearer], and [+
_ participant]. Moreover, Noyer showed that languages do
not all use every one of the features in their person/number inventories.
For instance, a language with singular, dual, and plural, such as Kiowa
(Harbour 2007), uses both number features; a language with just singular and plural, such as Mam (England 1983), uses only [+
_ singular]; and
a language with a dual–plural distinction in first person inclusive, and a
singular–plural distinction in all other persons, such as Ilocano, uses just
[+
_ augmented].
Since Noyer’s work, more extensive typological research has been undertaken with regard both to person and to number (Corbett 2000, Cysouw 2003,
Siewierska 2004). And so, it remains to be seen whether Noyer’s inventory of
features naturally extends to the cases that he did not directly consider.
Not only did Noyer present detailed arguments for the quantity and definitions of his features, but he even argued for the necessity of their bivalence. He did this primarily by appeal to ·-rules, that is, to rules that
switch the values of particular features, or that are triggered when pairs of
features have opposing values. Most notably, he argued for the bivalence
by motivating ·-rules in the treatment of person in Mam and number in
Kiowa-Tanoan. This issue has been taken up since by Harley (1994), McGinnis (2005), Harbour (2005), amongst others. The significance of ê-feature
valence extends beyond morphology: Béjar’s syntactic treatment of Georgian agreement discussed above crucially relies on the absence of a feature
rather than its negative specification; bivalence permits a three-way distinction
between assertion, negation, and absence of a property, that is not replicable
with privativity, consequently, the two feature notations can be semantically
distinguished.
So long as number features were assumed to be [singular], [dual], [trial],
and so on, that is, mere “featuralization” of traditional descriptive labels,
their definition attracted little attention from, and paid little heed to, semantics. A plausible reason for this is that both morphologists and semanticists
may have taken semantic methods to be overly complex for the treatment
of such apparently simple notions as “one”, “two”, “three”. Such overlap in
interest as there was came in the domains of collectives and distributives (e.g.,
Ojeda 1998 and Corbett 2000) and in pluralities of events (e.g., Mithun 1988
and Lasersohn 1995). However, as work like Noyer’s moves morphological

22

David Adger and Daniel Harbour

definitions of number away from the obvious and into the abstract, questions
begin to arise concerning the semantic nature of these definitions: are they
exclusive to morphology, or are they shared with other semantic systems?
Developing Noyer’s system, Harbour (2007) has demonstrated that the
primitives that morphologists require in the treatment of complex agreement
syncretisms are the same as those semanticists require in the representation
of collectivity, distributivity, and basic cardinality (singular, dual, plural).
Subsequent investigation (Harbour 2006a, 2006b), building also on semantic
work by Krifka (1992), has shown that the formal notions developed in the
treatment of aspect are almost exactly the feature definitions required to
generate the number systems attested across the world, including even the
rarest, incorporating, for instance, unit augmented, or trial, or greater and
lesser paucal.

1.5 Markedness
Markedness has been a major theme in ê-theory; not only was it addressed
by many of the authors mentioned already above (Bonet, Harley, Noyer, Ritter, Silverstein), but it goes back to the earliest work on features by Jakobson and Trubetskoy (Haspelmath 2006 for an overview), and has become a
focus of some debate since (e.g., Cowper 2005, Nevins 2007, Sauerland, this
volume).
Morphologically, one can distinguish “formal” and “functional” markedness (Dixon 1994). Formal markedness concerns, quite simply, whether a
form is overtly marked. For instance, for English nouns, the singular is
unmarked, the plural marked: compare singular book with plural books. Functional markedness concerns which of a group of grammatical categories is
distinguished from the others. For example, within the English pronominal
system, nominative and genitive appear only in specialized contexts, while
accusative is unmarked, being used for, amongst other things, direct objects,
indirect objects, predicates (It’s me), subjects of gerunds, and Jespersen’s (1924)
“nexus of deprecation” (Me dance?).
There is frequent coincidence between formal and functional markedness.
The third person is a well known instance. Silverstein (1976 [1986]: 173)
observes a number of pronominalization phenomena in which, although no
person is intended, third person forms are used. He concludes that third
person is functionally unmarked, whereas first and second are marked. Benveniste, on the other hand, in an often alluded to passage, observes that third
person is often formally unmarked:

Why Phi?

23

Certain languages show that “third person” is indeed literally a “non-person”. To
take just one example among many, here is how the possessive pronominal prefixes
are presented in two series (something like inalienable and alienable) in Yuma
(California): first person ?-, ?an y -; second person, m-, man y -; third person, zero, n y -.
The personal reference is a zero reference outside the I/you relationship.
(Benveniste 1971: 221; last ‘-’ added—dah/dja)

However, this is far from a perfect correlation, as the English present tense -s
for third person singular attests.
Given the imperfect correlation between formal and functional markedness, there is debate about what the precise criterion of functional markedness
consists of, and, indeed, whether there can be a single criterion of functional
markedness, or whether, in fact, it is a cluster of notions (see Haspelmath 2006
for discussion).
There are a number of means of representing markedness. At the level of
the ê-set, one can regard size of structure (whether a geometry or a feature
bundle), as a metric of markedness. Additionally or alternatively, markedness
can be attributed to features themselves, rather than to the feature structure.
For instance, Harley and Ritter (2002) posit two number features and suppose
that one feature is unmarked in the sense that, if a language uses only one
feature in its grammar, it will be that feature. Furthermore, if features are
bi- or multivalent (Harley and Ritter’s are privative), then markedness can
be attributed to feature values, additionally or alternatively to the concept of a
feature’s being marked itself.
In systems where the feature values are + and −, there is sometimes the
assumption made that plus is the marked value and minus the unmarked.
Silverstein (1976 [1986]) made an early attempt to maintain this position. Yet,
his own analysis shows it to be empirically untenable in its simplest form (see
Silverstein, p. 188, on “markedness polarity” and his footnote 9, pp. 227–8).
One way to capture context-dependent markedness is by directly encoding
it as a feature’s value (Chomsky and Halle 1968). So, a feature, [ÏF], would be
specified as marked (m) or unmarked (u), with the eventual +/− value being
determined by a rewrite rule which is sensitive to context:
(29)

m → + in the context [__F] [ÏG]
m → − in the context [__F] [ÏH]
u → + in the context [__F] [ÏI]
u → − in the context [__F] [ÏJ]

Lakoff (1970) provides specific arguments, attributed to Postal, in this direction. See also Bierwisch (1967), and more recently Wiese (1999).

24

David Adger and Daniel Harbour

The limiting case of markedness is that of the default. Intuitively, if an
element has multiple uses, it is relatively unmarked. Default items constitute
the most extreme cases of multiplicity of use within a natural class of items.
They are negatively defined, informally, as the form used where no other is
appropriate. Following on from work by Kiparsky (1973), defaults, or “elsewhere” forms, have been formally accommodated within some theories (e.g.,
Distributed Morphology, Halle and Marantz 1993).
The markedness metrics above, namely size of structure and number of
marked values, do not induce a complete ordering on all possible ê-sets:
different ê-sets can contain the same number of features and/or marked
values. For instance, if ê1 is marked with respect to person and unmarked with
respect to number, and ê2 , conversely, by whatever criterion of markedness,
then neither exceeds the other in total markedness. One way past this impasse,
if one takes total ordering with respect to markedness as a desideratum, is
to claim that person and number, for example, are not equally marked, but
rather that person is extrinsically more marked than number (in which case,
ê1 is more marked than ê2 ).
There are some intriguing generalizations in this domain. Both number and
gender distinctions are frequently lost with respect to person, but in opposite fashions. Simplifying Corbett (1991, 2000) slightly, if a language makes
number distinctions only for some persons, then it will be only for first, or
only for first and second (see Siewierska 2004 for some dissent); and if a
language makes gender distinctions only for some persons, then it will be
only for third, or only for second and third. In other words, in the domain
of person, where one tends to find gender, number is rarer, and where one
tends to find number, gender is rarer. As for number and gender themselves,
Greenberg (1966) observes that no language has more gender distinctions in
the plural than in the singular (e.g., German has masculine, feminine, neuter
in the singular, but only a common gender in the plural). If we take singular to
be the unmarked number, then Greenberg’s discovery is that gender distinctions decrease where number markedness increases. This ties in conceptually
with the person facts: where language is most likely to make number distinctions (in first, or first and second person), it is least likely to make gender
distinctions.
Even if these generalizations do form a conceptually sound cluster,
they are tendencies, not universals. A striking example is person/number
neutralization in Kuman: person distinctions are lost for some numbers in the (subject) agreement system, but number distinctions are lost
for some persons in the pronominal system (Foley 1986: 70, citing Piau
1985):

25

Why Phi?
Kuman subject agreement

Kuman pronouns

Person

Singular

Dual

Plural

Person

Singular

Plural

1
2
3

-i
-n
-uw

-bugl
-bit
-bit

-mun
-iw
-iw

1
2
3

na
ene
ye

no
ene
ye

Observe that the pattern of subject agreement left, is reminiscent of
Greenberg’s generalization concerning gender: fewer person distinctions in
the non-singular than in the singular (see Cysouw 2003 for other such
cases).
Despite the inherent interest of such generalizations, it must be admitted
that their precise formulation and how, or whether, they should be captured
by a theory of markedness currently evades us.

1.6 Themes in Phi Theory
Our focus so far has been on the history of ê-features in the three domains
of grammar where they are of primary relevance: syntax, semantics and morphology. However, if this volume is to fulfill its aim of motivating a transmodular Phi Theory, then we require a characterization of the research questions
that transcends and unites different modules. Above, we have, of course, noted
several places where research themes from different domains of the grammar
have converged (the end of Section 1.3 touches on this for syntax and semantics, and the end of Section 1.4 for semantics and morphology, and syntax and
morphology). To conclude, we now tie together the emergent issues in Phi
Theory in a way that, we hope, will excite further interest whilst serving to
emphasize areas where research into modules can be mutually informative,
insightful, and stimulating.
Questions of science often reduce to three broad issues: substance, structure, and interaction. In Phi Theory, these lead to the following broad themes.
Substance What are the different categories of ê-features? Above, we
addressed primarily person and number, and secondarily gender (reflecting the foci of the papers in this volume). However, recall that, in syntax,
ê-features were simply those that were affected by agreement transformations. Corbett (2006: 133–41) draws attention to a number of other categories
that are agreement-like in their behavior: case, definiteness, honorificity, and
even, in some languages, some tense/mood/aspect categories (on this last,

26

David Adger and Daniel Harbour

see especially, Nordlinger and Sadler 2004). Honorificity, in particular, has
received recent attention (Boeckx and Niinuma 2004, Potts and Kawahara
2004, Bobaljik and Yatsushiro 2006).
Within each category, what is the inventory of features? That is, what is
the inventory of person features, of number features, and so on, and are
they universal? Can the same be maintained for gender and honorificity? It
is important to emphasize that asking what the inventory of features is is
not the same as asking what values of a category are. Consider, for instance,
number. A possible value for this category is dual. However, we reviewed above
a variety of morphological evidence that suggests that dual is not a primitive
feature, but is featurally complex. Moreover, we showed how these number
features can be naturally defined given semantic research in the domain
of number, aspect, and Aktionsart. Are other familiar ê-categories likewise
complex?
Structure Within a given ê-category, how are the features structured? Pursuing further the example of number, why can languages have a paucal only
if they have a more basic distinction too (Corbett 2000); why can there not
be a language with paucal∼non-paucal as its only number distinction? Like
questions arise within person (see McGinnis, this volume). Do they arise also
within gender? One avenue, mentioned above, is to adopt a geometry, or a
filter system. These serve to constrain combinations of features, designating
some semantically possible ones as geometrically illicit. However, are geometries and filters themselves submissible to analysis, and, if so, what explains
them? Could more careful examination of the syntax or semantics of the features that compose these categories reduce geometries or filters to syntactically
or semantically natural conditions?
Like questions arise inter- as well as intracategorially. There are a number of well known, if well disputed, correlations between person, number,
and gender. For instance, if a language has two different verb forms which
move to two different heights, then, if only one has person, that is the
verb form that moves higher (Section 1.2.1). Or, no language makes more
gender distinctions in the singular than in the non-singular (Section 1.5).
Where such constraints concern cooccurrence restrictions, they can clearly
be captured by a geometry or filter system. However, these raise again the
questions just outlined: what is the origin of the geometry, can it be derived
by syntactic or semantic means? The need for syntactic exploration is particularly pressing, given the impact that some of these generalizations have
on the syntax (e.g., height of verb movement and clitic placement, or hierarchies and ergative splits). And, if geometric effects can be reduced to

Why Phi?

27

questions of syntactic structure, can these, in turn, be derived on semantic
grounds?
Interaction The questions just outlined begin to touch on issues of interaction between modules: how do module-specific operations interact with the
substance and structure of ê-features? On the semantic side, do geometric
generalizations stem from demands of the semantic interface, or are they
separately stipulated, syntactically or morphologically? How do ê-features
interact with the different modes of semantic composition; for instance, do
binding and predication treat ê-features on a par (Adger 2005, Kratzer 2006)?
On the syntactic side, the core operations are Merge, Move, and Agree. How do
ê-features trigger and constrain their application? Can one deduce the nature
of feature organization from any such constraints? On the morphological side,
do the operations that induce syncretism and allomorphy reveal any hierarchy
of ê-features, either organizational or markedness-based?
Doubtless, this list of topics and questions is incomplete. However, at this
early stage, where Phi Theory is merely emergent, not fully fledged, incompleteness is inevitable. If we are successful in stimulating research into the
issues raised, then the future will reveal just how incomplete a picture we have
painted. Hopefully, we are not too far off.

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2
Features on Bound Pronouns
IRENE HEIM

Are person, number, and gender features on bound-variable pronouns semantically interpreted, or are they just a superficial reflex of agreement between the
pronoun and its antecedent? Some have argued that at least some pronouns
have the semantics of featureless, unrestricted, variables. Others have pointed
out good predictions from the assumption that features on bound pronouns
restrict the range of the relevant variable. It has also been suggested in recent
work that simple deletion or copying rules such as those proposed in the
literature do not quite succeed in predicting the distribution of features on
bound pronouns. I will review the case for uninterpreted features and explore
some of the challenges involved in improving on existing accounts. Data about
plural pronouns with split antecedents will play an important role.

2.1 Phi-features as presupposition triggers
Before we debate whether features on bound pronouns are semantically interpreted, we must agree on how they would be interpreted if they were. Uncontroversially, some occurrences of pronoun features are interpreted, notably
those on deictic pronouns. Let us make precise what their interpretation in
these uncontroversial cases is, so we know what the facts would be like if
features on bound pronouns were interpreted likewise.
2.1.1 Features on deictic pronouns
The features we are concerned with are the so-called “ê-features”: person,
number, and gender. Semanticists that have attended to them have generally
given them a presuppositional semantics, as pioneered by Cooper (1983) for
English gender. In the implementation of Heim and Kratzer (1998), this looks
as follows. In the syntax (LF), each pronoun has a numerical index. Indices are
variables and mapped to semantic values by an assignment. For free pronouns,

36

Irene Heim

the relevant assignment is given by the utterance context and represents the
speaker’s referential intentions. When ê-features are disregarded, the index
is the only semantically interpreted part of the pronoun, and the pronoun is
simply a variable, as reflected in rules like (1).
(1) If ‚ is a pronoun and i an index, then for any assignment g, [[‚i ]]g = g(i)
(or undefined, if i is not in the domain of g).
If one or more ê-features are present, these are adjoined to the indexed node
(in an arbitrary hierarchical order).
(2)

[3rd [singular [masculine [he7 ]]]]

Each feature denotes a partial identity function of type e,e. For gender, these
are:
(3) [[masculine]] = Îxe : x is male. x
[[feminine]] = Îxe : x is female. x
The constituent consisting of the feature and its complement is interpreted by
Functional Application. It denotes an individual only if the denotation of the
complement happens to have the relevant property (maleness or femaleness).
When it does denote, it denotes the same individual. The partiality of the
interpretation function is inherited up the tree and ultimately induces truthvalue gaps for the containing sentence. In a simplified example (omitting
person and number), we compute the following result.
(4) For any g: [[masc-he7 is married]]g is defined if 7 ∈ dom(g) and g(7) is
male.
Where defined, [[masc-he7 is married]]g = 1 if g(7) is married, and = 0
otherwise.
If we are dealing with an unembedded occurrence of this sentence, uttered by
a speaker who intends the 7th variable to refer to John, this means that the
speaker is presupposing John to be male and asserting him to be married.
This is Cooper’s treatment of gender features, and it can be extended
straightforwardly to person and number 1 (notwithstanding the prevailing
tradition in philosophy to analyze first person pronouns as indexicals rather
than variables). We can treat all pronouns, regardless of person and number,
as variables, hence subscripted by a numerical index and interpreted by rule
(1). The various features attached to this index all denote partial identity
functions. For number features, we need an ontology that has pluralities as
well as simple objects among its individuals and supports appropriate notions
1

See, e.g., Dowty and Jacobson (1989), Schlenker (2002), Sauerland (2003).

Features on Bound Pronouns

37

of atomicity and inclusion. Person features happen to be indexicals, 2 that
is, they denote functions defined with reference to an utterance context that
determines participant roles such as speaker and addressee. 3 I use “sc ”, “hc ” as
abbreviations for “the speaker (addressee) of c.”
number: [[singular]] = Îxe : x is an atom. x
[[plural]] = Îxe : x is a plurality. x

(5)

person: [[1st]]c = Îxe : x includes sc . x
[[2nd]]c = Îxe : x includes hc and excludes sc . x
[[3rd]]c = Îxe : x excludes sc and hc . x
For a first person singular pronoun, we compute the following presupposition
and assertion.
LF: I7 am married, spoken in a context c,
asserts that gc (7) is married, and
presupposes that gc (7) is an atom including sc .

(6)

Given the background ontology, an atom that includes the speaker can only be
the speaker himself. So if the speaker of (6) manifestly intends to refer with I to
himself, the presupposition in (6) is (trivially) true. If he manifestly intended
to refer to someone else, it would be obviously false. Since it is impossible to
presuppose an obvious falsehood, this cannot happen. Thus I always refers to
the speaker, despite being technically a variable.
2.1.2 Features on bound-variable pronouns
We have seen how ê-features on deictic pronouns, via their presuppositions,
constrain the range of possible referents. Turning now to anaphoric, and
specifically bound-variable, pronouns, it is not immediately obvious that the
role of ê-features is the same. Reference, after all, is beside the point here, and
the most salient job that ê-features appear to be performing is to constrain the
range of possible antecedents. This is reflected in the grammaticality contrasts
we obtain by varying ê-features of an obligatorily anaphoric pronoun such as
the English self -reflexive.
(7)

Mary invited herself/*himself/*myself/*themselves.

From a theoretical point of view, it would be disappointing to have different
analyses of the same features depending on whether they are on deictic or
anaphoric pronouns. And as we are about to see, there is good reason to
2
3

Notice that this is not the same thing as treating the pronoun itself as an indexical.
See, e.g., Zwicky (1977) and Noyer (1992) for analyses of the morphosemantics of person.

38

Irene Heim

believe that this undesirable maneuver is also unnecessary. The antecedentconstraining role of ê-features on anaphoric pronouns will be seen as a sideeffect of their basic reference-constraining semantics. 4
The LF of one of the ungrammatical versions of (7) must display the coindexing in (8) to satisfy Binding Theory.
(8)

Mary 5[t5 invited MASC5 ]

What happens in the semantics? We first derive that the open sentence t 5
invited MASC5 denotes a truth value only under those assignments that map 5
to a male. Next we apply Predicate Abstraction, which in a system with truthvalue gaps is naturally formulated as follows. 5
(9) [[i ·]]g = Îxe : · ∈ dom([[ ]]gx/i ). [[·]]gx/i
The predicate 5[t5 invited masc5 ] in (8) then denotes the partial function
whose domain is males and which maps those who invited themselves to 1
and the others to 0 (in symbols, [Îxe : x is male. x invited x]). In the final step,
we apply this function to Mary, which is only possible if Mary is male. So we
predict that (8) presupposes that Mary is male. The asterisk in (7) reflects the
judgment that “Mary invited himself ” is deviant under normal assumptions,
namely when (the relevant) Mary is assumed to be a female. To the extent that
the possibility of “Mary” naming a man is considered, the deviance judgment
is qualified—as we predict.
We saw already in this simple example that when we apply our presuppositional treatment of ê-features to bound-variable pronouns, we must complement it with a suitable theory of “presupposition projection”. In our setting,
this amounts to formulating composition rules and lexical entries so they
handle partiality in their inputs and pass it up appropriately to their outputs.
Specifically, we need the formulation of Predicate Abstraction in (9), and—
as we will see next—the right lexical entries for quantifying determiners.
Consider a quantified variant of (7).
(10) a. *Every girl invited himself.
b.

LF: every girl 5[t5 invited masc5 ]

To interpret this, we must know how the generalized quantifier every girl
applies to the partial function denoted by its sister. An appropriate entry is
(11), predicting for (10a) the presupposition that every girl is male.
4 This is the main point of Cooper’s chapter on “Gender agreement” (ch. 7 of Cooper 1983).
Dowty & Jacobson (1989) push Cooper’s approach further by considering number and person and
by applying it also to the agreement between subjects and verbs.
5 See Heim and Kratzer (1998), where this formulation is motivated by examples of definite descriptions inside relative clauses.

Features on Bound Pronouns

39

(11) [[every]] = Îfe,t . Îge,t : {x: f(x) = 1} ⊆ dom(g). {x: f(x) = 1} ⊆
{x: g(x) = 1}
Again, this corresponds to the relevant judgment about (10): a deviant utterance under normal assumptions about the world.
A consequence of this approach (highlighted by Cooper) is that common
nouns need not be marked for gender. For example, the explanation just given
for the deviance of (10) did not rely on the assumption that the noun girl was
feminine—only on the assumption that girls are female. 6 This helps account
for nouns that can antecede pronouns of either gender. Both (12) and (13) are
non-deviant, but one is appropriate if the class is all male and the other if it is
all female.
(12) Every student in my class voted for himself.
(13) Every student in my class voted for herself.
We derive this from the assumptions we used in the analysis of (10). Example
(12) presupposes that every student in my class is male, and (13) that every one
is female.
Cooper’s way of capturing gender mismatches between a bound pronoun
and its binder as presupposition failures can also be applied to person and
number mismatches. We derive impossible presuppositions also for (14) and
(15).
(14)

*Every girl voted for themselves.
LF: every girl 5[t5 voted for 3rd-pl5 ]
predicted presupposition: “every girl is a plurality”

(15)

*Every girl voted for myself.
LF: every girl 5[t5 voted for 1st-sg5 ]
predicted presupposition: “every girl is identical to sc ” 7

A worry may arise of how the account applies to the non-quantified version
of (15), which is no better.
(16)

*Mary invited myself.
LF: Mary 5[t5 invited sg-1st