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Word and Paradigm Morphology

November 2015

Authors:

Farrell Ackerman

University of California, San Diego

Oxford Handbook of Morphological Theory J. Audring and F. Masini eds.

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Word and Paradigm Morphology

James P. Blevins

University of Cambridge

Farrell Ackerman

UC San Diego

Robert Malouf

San Diego State University

To appear in Oxford Handbook of Morphological Theory,

J. Audring & F. Masini (eds.)

Abstract

The 44 years since the publication of Matthews’ (1972) Inectional

Morphology have seen a resurgence of interest in word-based approaches.

One line of research has rehabilitated classical ‘word and paradigm’

(WP) approaches as general models of analysis. WP models have

shown themselves well adapted to the description and analysis of in-

ectional patterns, particularly those involving inection class mor-

phology. Contemporary WP approaches have also claried the formal

structure of classical models and isolated assumptions that reected

their longstanding use in pedagogical or reference materials. The con-

ception of morphological analysis in WP models is fundamentally im-

plicational: the central role of words (and paradigms) reects their

predictive value in a morphological system. To understand the nature

of (cross-linguistic) morphological organization one must explore the

fundamental elements of implicational relations. From a descriptive

perspective this means appropriately identifying the internal structure

of words and the ways that this structure facilitates their external or-

ganization into patterns of relatedness. From a theoretical perspective,

it is crucial to identify the appropriate analytic tools for quantifying

and specifying the nature of word internal and external organization.

Finally, it is important nd the types of learning theories that may

motivate the types of organization that occur and that may explain

their learnability.

1 Introduction

The common use of the terms ‘word’ and ‘structure’ often obscures, rather

than elucidates, what appear to be two distinct approaches to the study

of morphology. While both examine the ”structure” of words, they do so

from very dierent perspectives, assuming very dierent objects of analysis

and arriving at very dierent results. The ‘word-based’ tradition regards

morphology as the “branch of linguistics which is concerned with the ‘forms

of words’ in dierent uses and constructions” (Matthews 1991:3): the em-

phasis is on the ways that the internal structures provide whole words with

distinctive shapes and how these permit faciliate the development of pat-

terns of relations between them. The ‘sub-word’ tradition treats morphology

in terms of the morphemic internal structure of words and the nature of the

processes responsible for their composition. The two basic approaches fall

within parallel lineages that derive from dierent branches of ancient Indo-

European grammatical traditions, as schematized in Figure 1.

…

Sanskrit Grammarians

Altindische

Grammatik

‘American

Structuralism’

Morphemic analysis

Greco-Roman Tradition

Neoclassical WP

Realizational WP

Negrammarians

‘European

Structuralism’

Information-theoretic

Figure 1: Morphological lineages

Morphology from a Greco-Roman, Word and Pattern, perspective can be

construed as the study of part-whole organizations with respect to the inter-

nal and external organization of words. What are the elements constitutive

of words viewed as wholes and how are words themselves organized as con-

stitutive parts of patterns in morphological systems. Syntagmatics explores

the systematic internal organization of (classes of) words, while Paradig-

matics explores the external organization of relations between words. This

insight about the classical Graeco-Roman view of morphology is cogently

expressed in Matthews (1991: 204):

In the ancient model the primary insight is not that words can be

split into roots and formatives, but that they can be located in

paradigms. They are not wholes composed of simple parts, but

are themselves the parts within a complex whole. In that way,

we discover dierent kinds of relation, and, perhaps, a dierent

kind of simplicity.

Careful cross-linguistic description and analyses of inectional and deriva-

tional systems in typologically diverse languages reveal that internal organi-

zation involves considerably more than linear (or hierarchical) arrangements

of (minimal) meaningful elements (i.e., the ‘morphemes’ associated with the

Post-Bloomeldian structuralist and generative lineages). It also involves

the recognition of words as basic objects of morphological inquiry, either

synthetically or periphrastically expressed, and this permits exploration into

the principles informing the patterns of relatedness among (classes of) words.

The general applicability of part-whole approach to morphological organiza-

tion, i.e., one in which words are wholes with respect to their internal pieces

and words are pieces with respect to the patterns they participate in, raises

the question as to why a structuralist morphemic perspective that dispenses

with paradigmatic organization has persisted in the modern context and

what features of languages may have encouraged the appeal of this perspec-

tive.1After enumerating many of the problems that arise in decomposing

words into meaningful parts and summarizing the theoretical assumptions

guiding this enterprise, Matthews (1991: 204) comments on the nature of

the challenges presented by classical Greek and Latin to the foundational

idealizations of modern structuralist morphology:

Many linguists tend to boggle at such systems. They seem com-

plicated, while agglutinating systems seem so simple. They may

even seem perverse. Why should a language have rules which

obscure the identity and functions of its minimal elements?

From the perspective of WP models it is the examination of the part-whole

relations evident in these “perverse” systems that is most instructive to

1The rst part of this question is addressed in Blevins (to appear) and the second is

discussed briey below.

the development of viable and psychologically supportable morphological

theories. As illustrated below, the identication of the basic principles in-

forming morphological organization suggests, perhaps paradoxically, that

what seems to “obscure” relations from a morphemic perspective actually

permits the creation of coherence in the morphological system from a WP

perspective.

Although it is customary to regard models as ‘word-based’ or ‘morpheme-

based’, this classication is somewhat misleading: it is really the role and

status of words within competing types of analysis that is of criterial impor-

tance.2For present purposes, it is important to distinguish two dimensions

of wordhood: the morphosyntactic dimension concerns the meaning asso-

ciated with words, while the morphotactic dimension concerns the formal

internal constitution of words, inclusive of all varieties of exponence. Ac-

cording to the former, words, rather than morphemes, are commonly con-

struable as the most useful units of meaning for analysis, while according to

the latter, roots, stems as well as diverse and interacting types of exponents

are interpreted as abstracted patterns that serve to discriminate distinctive

shapes and patterns of related word types. This latter discriminative func-

tion of forms associated with words represents a central dierence between

”morpheme-based” versus word-based approaches. Both the recognition of

words as theoretical objects and their participation in paradigmatic orga-

nization are considered epiphemomenal in ”morpheme-based” approaches,

but they are focal elements of analysis in word-based approaches.

Given that morphological models vary along a number of dimensions,

a word-based/morpheme-based split oversimplies the more intricate iden-

tication of similarities and dierences that cuts across this divide. As a

rst approximation, it is useful to contrast a class of word-based approaches

with accounts that only recognize morphemes morphological units of anal-

ysis. The most consistently word-based approaches are traditional ‘word

and paradigm’ (WP) models of the type familiar from the description of

classical languages. In these models, the word is the smallest grammati-

cally meaningful unit and surface words are also the basic elements of form,

2The importance of dierences concerning the selection of basic theoretical units be-

comes clear when it is recognized that in e.g. Distibuted Morphology (DM) the morpheme

construct, based on Beard’s Lexeme/Morpheme distinction, is broadly construed to com-

prehend all internal structure of morphologically complex words: the morpheme construct

ceases to be an empirical hypothesis about word internal structure, but rather has be-

come a theoretical stipulation concerning universal internal morphological structure. In

this tradition all cross-linguistic strategies of exponence, i.e., segmental, suprasegmental,

morphomic distinctions, convey morphemic, i.e.,morphosytactic distinctions, while the

word as a totality is regarded as an epiphenomenal eect of morphemic composition.

since they are not conceived of as being composed of morphemes, However,

the modern WP tradition that grew out of the work of Matthews (1965,

1972) is less uniformly word-based. This tradition includes, among other

approaches, the Extended WP model (Anderson 1982)/A-Morphous Mor-

phology (Anderson 1992), Paradigm Function Morphology (Stump 2001),

and the family of realization-based and lexeme-based approaches (Zwicky

1985; Arono 1994; Beard 1995). These approaches all preserve the mor-

phosyntactic assumption that (grammatical) words are the primary locus

of grammatical meaning. But their morphotactic assumptions align more

with those of morphemic models, in which surface word forms are assembled

from more basic elements. Hence, they can be classied as morphosyntac-

tically word-based but morphotactically constructive (Blevins 2006), in

that they assume a model of the lexicon in which open-class items are repre-

sented by roots and/or stems, and surface word forms are constructed from

these units though the application of ‘spell-out’ or “realization” rules. In

these models, the paradigm cells or morphosyntactic representations that

represent the properties of word are basic, but the word forms that real-

ize those properties are derived. Such models focus on building individual

words, rather than identifying patterns that distinguish and relate words to

one another. In modern realizational approaches, analysis is an interpre-

tive process, in which ‘bundles’ of distinctive features are ‘spelled out’ by

realization rules that map features onto forms. The organization of modern

approaches has been elaborated in considerable detail, in the works cited

above and in chapters elsewhere in this volume.

The dierent morphotactic assumptions adopted in traditional and mod-

ern word-based models yield alternative strategies for expressing content-

form relations. Traditional models represent these relations by sets of exem-

plary patterns, together with (proportional) analogies that extend patterns

to new items. Internal structure is important not because it provides in-

ventories of pieces useful for deriving words, but because (congurations

of) pieces provide resources for patterns that (classes of) words participate

in and which cohere into the ensembles of patterns that dene the organi-

zation of morphological systems. Since these models are less familiar, the

remainder of this chapter focuses primarily on traditional WP models, in

their classical and pedagogical formulations as well as in their more recent

formal versions.

2 Words

As elaborated in more detail in section 3 below, the role of words and

paradigms in traditional models is pre-eminent not as a rst principle but

as a result of empirical study that reveals their reliable informativeness and

implicational value. As units of form and as exponents of grammatical prop-

erties, it turns of that whole words are ordinarily more stable than the sub-

word units, i.e., morphemes that often serve as fundamental constructs in

morphological theory. The closed and often intersective feature space of the

words in inectional paradigms likewise sanctions highly reliable deductions

about the existence and shape of other words in the same paradigms. Al-

ternatively formulated, the stable grammatical information associated with

a whole word not only serves to identify its own meaning and function but

also locates it within an inectional paradigm or derivational ‘morphologi-

cal family’ as well as within the larger morphological system. In this way,

the information associated with a word form facilitates deductions about

other forms, based on systematic and systemic interdependencies within a

language. All aspects of form that sanction implications express a type of

information that can be modelled by notions developed within Information

Theory (Shannon 1948). In the case of an inectional paradigm, the infor-

mativeness of a form correlates with the degree to which knowledge of that

form reduces uncertainty about the specic shape of other related words

within the same paradigm. The notion of uncertainty reduction is implicit

in the traditional use of ‘diagnostic’ principal parts, where the utility of

principle parts can be construed as ensuring the predictability of specic

forms related to it, i.e., reducing uncertainty to zero. On the other hand,

the possibility of calculating the predictability of unknown forms of words

from known forms of words, renders nearly all forms of words as informative

to some degree about other forms of words. The ability to distinguish de-

grees of interpredictability among forms of words is a dimension that sharply

distinguishes morpheme-based from word-based models, especially in terms

of their potential for explaining the learnability of (complex) morphological

systems (see below for some discussion).

2.1 Form-meaning associations

In what, following Hockett (1954), has been come to be known as Item

and Arrangement (IA) models, the task of morphological analysis involves

identifying the constitutive pieces of complex words and the nature of the

reassembly processes that reconstitute the whole from its parts. In Hockett’s

terms “morphology includes the stock of segmental morphemes, and the

ways in which words are built out of them” (Hockett 1958: 172). For e.g.,

smirked this task is straightforward: the concatenation of disassembled parts

produces a word that appears to ‘sum’ the form and the meaning of the

verbal stem and the past tense sux.

Words, accordingly, are concatenations of morphemes and meaning re-

sides in sub-word units, whose distribution is regulated by rules specifying

their linear and hierarchical arrangement (with phonological readjustments

diverse strategies of exponence posited as necessary).3Yet as observed

in Jackendo (1975) and Bochner (1993), the expected gains in descrip-

tive economy achieved by morphological decomposition are undermined by,

among other factors, the redundancy between the rules proposed to build

words and the existence of complex words only opaquely, if at all, derivable

via these rules.4

In a second variant of morphemic analysis, termed the ‘Item and Process’

(IP) model by Hockett (1954), the meanings of words do not reside in pieces,

but are associated instead with the processes that apply to build complex

words. As with IA approaches, IP approaches are centrally concerned with

building words from simpler components – in this case stems and processes

– guided by the goal of reducing or avoiding redundancy in linguistic rep-

resentations. The words themselves and their organization into paradigms

once again plays no direct role in morphology and questions concerning their

potential relevance do not even naturally arise.

Both models are exclusively concerned with the assembly and disassem-

bly of individual word forms in isolation, so relations between words fall

outside their descriptive scope. The word is not regarded as a primary

object of morphological analysis but functions instead as the ‘output’ of

processes that assemble forms from their constitutive pieces or as the ‘in-

put’ to processes which disassemble forms into their ultimate constituents:

words are only useful to the extent that they provide clues for identifying

the minimal elements and operations that produce them. The practice an-

alyzing words in isolation precludes the search for strategies that represent

3In the typology of Stump (2001), this qualies as lexical-incremental. Morphosyntactic

information associated with exponents of morphemes, i.e., entities of the lexicon, are

gradually combined to produce wholly inected (and derived) words. i.e., composition is

piece-driven.

4See Arono (1976), Jackendo (1975) and especially Bochner (1993) for the develop-

ment of cost metrics that measure the cost of ‘patterns’ in a morphological system rather

than the degree of (presumed) segmental redundancy in representations. This perspec-

tive will be briey explored below in relation to discriminative Information-Theoretic WP

models.

relations between words or organizing words into networks of related forms.

Given these familiar, limitations, words and paradigms can only occupy an

‘epiphenomenal’ status within models of morphemic analysis.

A ‘morpheme-based’ conception of morphological analysis, thus, leads or-

ganically to certain research questions, while excluding others. In particular,

it leads to eorts to identify small meaningful pieces (morphemes) as well as

the rules (morphotactic, phonological, morphophonemic, etc.) that deter-

mine the licit combinations of these entities evident in surface wordforms.

This enterprise has been guided by a priori notions of parsimony concerning

the minimal elements and operations required to construct wordforms. From

this perspective, neither surface wordforms nor the systematic patterns of

surface alternations that words participate in are fundamental to the or-

ganization of a grammatical system.5Hockett (1954, 1987) provides the

clearest chronology of the origin and development of these strategies within

the Americanist tradition established by Bloomeld’s successors. Although

Hockett was familiar with the classical morphological tradition (and respon-

sible for the moniker ‘Word and Paradigm’) it was left to Robins (1959) to

develop the idea that “WP deserves the same consideration … given to IP

and IA” (Hockett 1954: 386). The tradition reviewed in Robin’s ‘Defense of

WP’ is cogently summarized in Matthews (1972):6

The word is its central unit, and the grammatical word (the

Vocative Singular of brutus, for example) are minimal elements

in the study of syntax. At the same time, the intersecting cate-

gories form the framework or matrix within which the paradigm

of a lexeme can be set out. If a schoolboy is asked to recite

the paradigm of mensa or the paradigm of amo he will deliver

the sets of word-forms (mensa, mensa, mensam …; amo, amas,

amat …) in an order which explicitly or implicitly addresses their

assignment to the individual Cases, Persons, and so on.

5See Bochner (1993) for a systematic comparison of morpheme- and word-based models

with a particular focus on issues relating to morphemes and redundancy in grammatical

representations.

6A contemporary perspective on the learners task is reected in claims about the

psycholinguistic status of paradigmatic relations. This issue is explicitly raised by Hockett

(1967) when he contrasts the trade-o between the descriptive economy and psychological

plausibility of ‘word and paradigm’ and ‘morpheme-based’ descriptions of Yawelmani.

Hockett acknowledges that a description of “the complex alternations of Yawelmani by

principal-parts-and-paradigms would take much more space” than a “morphophoneme-

and-rewrite-rule presentation” (p. 221). “But” he continues, “there would be a net gain in

realism, for the student of the language would now be required to produce new forms in

exactly the way the native user of the language produces or recognizes them – by analogy”.

Indef Sg Indef Pl Def Sg Def Pl

Nominative kal kal-t kal-os kal-t-ne

Elative kal-sto kal-sto-ń kal-t-ne-ste

Table 1: Partial paradigm of Mordvin kal ‘sh’ (Rueter 2010)

The motivation for a classical approach as well as it value was also ap-

parent to some outside the WP community. Chomsky (1965: 173) provides a

notably concise summary, particularly relevant for modern theoretical mor-

phemic approaches:

I know of no compensating advantage for the modern descrip-

tive reanalysis of traditional paradigmatic formulations in terms

of morpheme sequences. This [= morphemic analysis ‚FA/JB]

seems, therefore to be an ill-advised theoretical innovation.

Two salient problems that Chomsky identies with morpheme-based

models concern (i) the reliance on unrealized (‘null’) morphological expres-

sions and (ii) the need to impose some kind of xed order on ‘sequences’ of

realized and unrealized elements. These issues are illustrated by the con-

trasts involving zero expression and morphotactics exhibited by the forms

of the Mordvin noun kal ‘sh‚in Table 1.

There are no overt markers for nominative or singular in the Mordvin

indenite declension. Consequently, one zero marker would be required for

nominative case and another for singular number. This yields a question

concerning their linear (and/or hierarchical) arrangement. In principle, the

two zero markers could occur in either order. Looking at the nominative

plural denite forms we see that plural and nominative are cumulatively

expressed, once again raising the issue, this time with an overt marker as to

what the relative order of number and case categories might be. Reviewing

the elative forms, which do not have distinct denite and indenite singular

forms, it turns out that the two possible orders of number and case exist,

depending on whether the inected nominal is singular or plural. The sin-

gular denite marker n’t’ appears after the case marker sto in the singular,

whereas both the basic plural marker tand denite plural marker ne, exem-

plifying multiple exponence, appear before the case marker ste in the plural

In other words, case and number in the singular and plural denite forms

display opposite orders. A compelling basis for establishing an invariant

ordering for covert markers remains elusive, even with reference to overt

markers. The problems cited for linear order, of course, only increase if the

analyst attempts to justify a particular hierachical structure.

Phenomena such as these clarify the basis for Chomsky’s concerns about

the reformulation of transparent paradigmatic patterns in terms of abstract

morpheme sequences. It should be observed that WP models do not oer

solutions to the questions of element order just posed, much less attempt

to locate e.g., Mordvin within some kind of universal schema governing the

arrangement of morphosyntactic markers. Instead, they identify the sys-

temic variation that obtains between morphosyntactic properties and their

surface forms: they identify the patterned associations between declensional

properties and the inected forms that realize them.

Irrespective of how the alternative orders for denite singular and def-

inite plural marking and case markers is resolved for Erzya Mordvin, the

alternation does not depend on specic case values.7In contrast, Udmurt

(Kel’makov and Hännikäinen 1999) partitions its case markers according

to the relative ordering of case markers and possessive markers. The basic

patterns are presented below in (1)–(3). In each pattern a stem precedes a

possessive marker and one of a specied set of case markers.8

(1) Pattern 1: Stem–pnm–cm, where cm ∈{Abes, Abl, Adv, App, Dat,

Gen}

pi-ed-lị

boy-2sg.px-dat

‘to your boy’

(2) Pattern 2: Stem–cm–pnm, where cm ∈{Egr, Ela, Ines, Illa, Inst,

Pro, Trans}

pi-en-id

boy-inst-2sg.px

‘with your boy’

(3) Pattern 3: Either Pattern 1 or Pattern 2, where cm =Term and

pnm =Sg

7As mentioned above, Table 1 contains only a partial paradigm for kal. The alternation

illustrated in these forms obtains for all 15 cases in Erzya Mordvin.

8The cases are Abes(sive/Caritive), Abl(ative), Adv(erbial), Appr(oximative),

Dat(ive), Egr(essive) Ela(tive), Gen(itive), Ines(ssive), Illa(tive), Inst(rumental),

Pro(lative), Term(inative), Trans(lative).

busi-jed-oź

eld-2sg.px-term

∼

busi-ioź-ad

eld-term-2sg.px

‘up to your eld’

This type of data, along with recent research on variable ax orders cast

substantial doubt on the status of principles that are taken to determine

basic (let alone universal) orderings of inectional markers. As with the

challenges that arise in imposing order on ‘zeros’, it appears that the most

desirable position for a morphological model is to avoid commitments about

xed or even ‘universal’ element orders.

Finally, in this connection it is important to observe another funda-

mental problem associated with a morphemic morphotactic perspective on

morphology: the operative denition of morphemes themselves as well as

the requirement specify denitive segementations of them within complex

words have both been subject to perennial criticism, as suggested previously.

Of course, this is not to suggest that the construct word is much more easily

denable. However, the psychological reality of whole words versus psycho-

logical claims about their necessarily morphemic structure is indicated by

native speakers’ easier access to the former and frequent perplexity in trying

to retrieve the latter.

We have been referring to words as single morphophonologically inte-

grated units, i.e., synthetic realizations: the main focus has been on the

internal structure of these units and how they realize morphosytactic prop-

erties. But, the word-based emphasis on patterns associated with mor-

phosyntactic information, rather than on the combinatorics of meaningful

pieces, encourages research about words that is less commonly asked in mor-

photactically oriented morphemic proposals: Can there be structure and

pattern to morphological objects that extend beyond the bounds of single

morphophonologically integrated units, encompassing dependencies between

individually co-occurring units in what appears to be phrasal structure? For

example, consider the case and number inected forms for nouns in Tundra

Nenets.

In Tundra Nenets, the three grammatical cases NOM, ACC, GEN are

ordinarily distinguished from the remaining four local cases. As can be seen,

all of the case distinctions for singular and plural are realized synthetically.

In contrast, in the dual, there is syncretic realization for the grammatical

cases and periphrastic realization for the local cases. In particular, the local

dual forms consist of the invariant dual lexeme and an appropriately case-

inected postposition. While it is commonplace to inquire about the nature

of the internal structure for the synthetic realizations of word, it seems

sg du pl

nom ti texəh tiq

acc tim texəh ti

gen tih texəh tiq

dat tenəh texəh n’ah texəq

loc texəna texəh n’ana texəqna

abl texəd texəh n’ad texət

prol tewna texəh n’amna teqm

Figure 2:

equally sensible to inquire into the structure of periphrastic realizations.

This becomes especially clear when generalizations that frequently obtain

for synthetic words extend to sets of synthetic and periphrastic expressions

As Ackerman and Stump 2004 observe, there is a cross-linguistically familiar

pattern to the synthetic versus periphrastic realizations in Tundra Nenets

that parallels the same sort of patterning observed in languages with only

synthetic realizations. In particular, the less morphosyntactically marked

convergences of case and number categories are reected in their less for-

mally marked synthetic encodings. This is evident in the Tundra Nenets

nominal paradigms where the convergence of the most marked categories in

Tundra Nenets, i.e., local case and dual number, are realized by the most

marked realization, i.e., periphrasis. On this view, the purview of most

transformational and non-transformational theories has been too narrow

with respect to the proper objects of morphological theory: morphological

theory encompass both synthetic and periphrastic forms of words. This is

a view advocated by P.H. Matthews in his 1970 state-of-the-art article on

morphology. He observes that

The history of morphology since the 1930’s has led to a progres-

sively complex and non-patent relationship between the elements

of grammar, on the one hand, and their phonological realization

on the other: Is there any reason why the domain in which an el-

ement may be realized should be kept within traditional limits.”

Matthew 1970:12.

What he has specically in mind is the question as to whether mor-

phosyntactic properties (“grammar”) can receive either synthetic (“tradi-

tional limits”) or periphrastic, i.e., multi-word expression, in clausal struc-

ture. He hypothesizes that, “ One can foresee a thorough re-examination of

the morphology-syntax division in the coming decade.” Within the context

of his article one way of formulating this sort of inquiry would be to explore

whether some periphrastic expressions are properly included within mor-

phology. This is a perspective facilitated by Word and Paradigm models:

these models do not require that words are encoded as synthetic expres-

sions, since multi-word morphological expressions can be analyzed in terms

of patterned organization as well as synthetic expressions.9This empirical

domain permits the articulation of two alternative hypotheses concerning

the morphological status of periphrastic constructions, an issue beyond the

scope of the present chapter:

Hypothesis 1: Periphrasis as morphology Dierent morphological

expression types, i.e., synthesis and multi-word exponence realize cross-

linguistically recurrent inectional/derivation distinctions. -

Consequence: Morphology contains both synthetic expressions and periphrases.

Hypothesis 2: Periphrasis as syntax Morphology competes with syn-

tax for the realization of cross linguistically recurrent inectional/derivational

distinctions. -

Consequence: Morphology contains only synthetic expressions.

At their core, arguments for periphrastic morphology presuppose the

utility of positing words as primary objects of morphological analysis: these

are entities that participate, single or jointly, in paradigmatic relations

within networks of forms serving to express morphological information.

The hypothesis that words are central morphological units raises ques-

tions concerning (cross-linguistic) criteria for identifying them. Haspelmath

(2011) presents a detailed survey of failed eorts to devise such criteria,

casting doubt on its theoretical value. In the course of his discussion he

identies several linguists who operate with a notion of wordhood based on

language particular criteria. Typifying this approach he cites:

9Particularly compelling evidence of the importance of paradigmatic relations for un-

derstanding periphrastic expressions as morphological can be found for Algonquian lan-

guages in Goddard (1990) and LeSourd (2009) and cross-linguistically in Bonami (2015).

There is a considerable amount recent literature that focuses on identifying criteria for

the analysis of particular multi-word expressions as morphological and for distinguishing

them from syntactic phrases. See Ackerman (1987); Ackerman and LeSourd (1997); Bör-

jars et al. (1996); Ackerman and Webelhuth (1998); Ackerman and Stump (2004); Brown

et al. (2012); Bonami (2015), among others. The arguments for periphrastic inectional

morphology nd parallel arguments for periphrastic derivational morphology in Ackerman

(1987); Booij (2010); Masini (2009); Masini and Benigni (2012).

Wurzel (1984: 35): “Was in einer Sprache ein morphologisches

Wort ist, wird durch die einzelsprachlichen morphologischen Reg-

ularit.ten bestimmt.” [‘The language-specic morphological reg-

ularities determine what is a word in a language.’]

Spencer (2006: 129): “There may be clear criteria for wordhood in indi-

vidual languages, but we have no clear-cut set of criteria that can be applied

to the totality of the world’s languages. . .” Haspelmath (2011: 61)

From a Word and Paradigm perspective it is expected that dierent

languages can express morphosyntactic and derivational properties in ways

that defy universal contentive characterization. In contrast, the relational

nature of morphological systems and their language particular morphological

organization encourage cross-linguistically and typologically relevant ques-

tions such as: What are the (types of) patterns observed in a language

for the encoding of morphosyntactic and derivational information? The

units expressing such information as well as entering into systemic relations

can be operationalized as words. Are there principled ways to dierentiate

between morphological constructs such as words and syntactic constructs

such as phrases? In sum, it is almost universally acknowledged that words

are more useful than sub-word units for practical descriptions, including

teaching grammars, dictionaries and reference grammars. Even Bloomeld

(1933: 178) concedes that “[f]or the purposes of ordinary life, the word is the

smallest unit of speech”. But for proponents of traditional WP models, the

practical benets of word-based descriptions carry over directly to the use of

words for “the systematic study of language” (Bloomeld 1933: 178). This

reects the belief that the same properties that make words useful for practi-

cal descriptions, notably a stable relation between forms and morphological

classes and grammatical meaning, are of equal value to theoretical accounts.

The word is, as Robins (1959: 120) emphasizes, “a grammatical abstraction”

from the speech stream, but it is a maximally useful abstraction, whether

for abstract analysis or for more practical purposes.

The word is a more stable and solid focus of grammatical re-

lations than the component morpheme by itself. Put another

way, grammatical statements are abstractions, but they are more

protably abstracted from words as wholes than from individual

morphemes. (Robins 1959: 128)

From the perspective of the word-based WP model, nothing precludes

the possibility that simple units of grammatical meaning might stand in

correspondence to minimal units of form in some languages. In other words,

straightforward and simple morphemic concatenation is possible. However,

there was never motivation nor need within WP to regard this pattern as

canonical or normative, given that these approaches grew out of a tradition

that described languages in which “categories and formatives are in nothing

like a one-to-one relation” (Matthews 1972: 173). Matthews (1972, 1991)

outlines a typology of the non-biunique ‘exponence’ relations exhibited by

classical languages, though a pair of examples will suce to illustrate the

irreducibly many-to-many relations that arise when analyses attempt to as-

sociate individual properties with sub-word units. The Latin verb re:ksisti:

‘you had ruled’ (rēxistī in the standard pedagogical orthography) exhibits

the many-many feature-form relations displayed in gure 3. The ending -ti:

exhibits what is traditionally known as a ‘fusional’ pattern, as it is associated

with the features perfective aspect, 2nd person and singular number. At the

same time, the perfective feature exhibits a converse ‘ssional’ pattern, as

it is realized by the formatives -s-, -is-, and -ti:.

re:k s is ti:

(stem) 2nd sing

perfective

Figure 3: Morphological analysis of Latin re:ksisti: (Matthews 1972: 132)

This analysis exhibits the striking contrast between the interpretation of

re:ksisti: and those of its parts. There is a biunique correspondence between

the form re:ksisti: and the second person perfective cell of rego ‘rule’. Yet

none of the formatives that make up re:ksisti: can be brought into a biunique

correspondence with any individual properties. Nor is this a particularly

extreme or unrepresentative example. Classical Greek exhibits even more

tangled feature-form associations, as illustrated by the verb elelýkete ‘you

had unfastened’, in gure 4 below.

e le lý k e te

perf past ind 2nd plu

Past active

Figure 4: Morphological analysis of Greek elelýkete (Matthews 1991: 173)

As in the case of re:ksisti:, the word form elelýkete stands in a biunique

relation to the second person past perfective indicative active cell in the

paradigm of lyo ‘unfasten’. But as Matthews (1993: 173) observes, the

realization of aspect and voice confounds any attempt to establish biunique

property-formative relations.

2.2 Gestalt exponence

Even more acute diculties arise in associating properties with formatives in

cases of what has been termed ‘gestalt exponence’ in Ackerman et al. (2009).

The observations that the properties of words are not in general reducible to

the properties of their parts applies not only to the properties of individual

words but also to relations between words. Just as the grammatical mean-

ing of a word cannot always be broken down into discrete units of meaning

that are assigned to sub-word formatives, relations between the elements of

a paradigm cannot invariably be reconstructed from relations between their

parts. Irreducibly word-level properties bring out a basic asymmetry be-

tween wholes and parts. The formatives that make up a word may uniquely

identify the place that the word occupies in its inectional paradigm or,

more broadly, within the morphological system of a language. But if the

same formatives occur in dierent combinations in other forms, as is often

the case, it is not possible to associate discrete meanings with individual

formatives. Much the same is true of implicational relations. In most cases

where a stem or exponent is of predictive value, the value is preserved by

a word containing the stem or exponent. But in cases where the predic-

tive value of a word is keyed to the absence of an element or to distinctive

combinations of elements, the predictive value of the whole is lost when it

is disassembled into parts. This is because, as mentioned previously, it is

frequently not the parts as individually expressive of meanings that are in-

structive, but rather their coordination into distinctive patterns associated

with (classes of) words that is the proper level of morphological analysis.

In other words, familiar strategies that seek to build words from pieces ne-

glect a crucial dimension of morphological organization, namely, the uses

to which the pieces are put to produce discriminably dierent patterns of

arrangement: word meanings, by hypothesis, inhere in these arrangements,

but the dimension of arrangement is compromised when exclusive focus is

given to one or another of the constitutive pieces alone.

An example will help to clarify how particular combinations of elements

can have distinctive meanings and predictive values within a language. The

rst four columns in table 2 contain the singular grammatical case forms of

nouns that exhibit productive ‘weakening’ gradation in Estonian: weakening

is specied relative to the nominative forms of these nouns consisting of a

strong stem, identied by the double consonant -kk. Beyond the rst row,

the remaining forms in the columns consist of a strong stem, or a weak stem

in -k, followed by one of the ‘theme vowels’ a,e,iand u.10

Nominative sukk kukk pukk lukk lugu

Genitive suka kuke puki luku loo

Partitive sukka kukke pukki lukku lugu

Illative 2 sukka kukke pukki lukku lukku

‘stocking’ ‘rooster’ ‘trestle’ ‘lock’ ‘tale’

Table 2: Singular nouns in Estonian (Erelt et al. 2000; Blevins 2008)

Now consider a possible locus for the property ‘partitive singular’. This

property can be associated with a pattern of sub-word units in table 2 The

partitive singulars of this class contain two ‘recurrent partials’: a strong

stem and a theme vowel. Thus sukka can be analyzed as sukk +a,kukke as

kukk +e,pukki as pukk +iand lukku as lukk +u. But partitive case cannot

be associated either with strong stems or with theme vowels in isolation.

The strong stems sukk,kukk,pukk and lukk cannot be analyzed as partitive,

because these same stems realize the nominative singular when they occur

without a theme vowel, and also underlie the second ‘short’ illative singular

forms. Partitive case also cannot be associated with the theme vowels,

because the same vowels occur in the genitive and illative singular forms.

Hence partitive case is an irreducibly word-level feature that is real-

ized by the combination of a strong stem and a theme vowel. This type

of gestalt exponence or ‘constructional’ exponence (Booij 2005) is dicult

to describe if stems and theme vowels are represented separately. Because

the grammatical meanings associated with strong stems and theme vowels

are context-dependent, these elements cannot be assigned discrete mean-

ings that ‘add up’ to partitive singular when they are combined. From a

traditional perspective, this context-dependence underscores the dierence

between ‘analyzability’ with respect to word internal structure and claims

about the morphemic status of word internal structure. An individual word

form is often analyzable into parts that recur elsewhere in its inectional

paradigm or in the morphological system at large. But these parts may

function solely to dierentiate larger forms, so that the minimal parts that

10The choice of theme vowel is a lexical property of an Estonian noun, and is not

conditioned by phonological properties of the stem or by morphosyntactic features of the

noun.

distinguish a pair of word forms cannot be associated with the dierence in

grammatical meaning between these word forms. To return to the patterns

in table 2, the theme vowel -udistinguishes the partitive singular lukku ‘lock’

from the nominative singular lukk. In isolation, however, the vowel -unei-

ther realizes a specic case value nor expresses ‘the grammatical dierence’

between nominative and partitive. Exactly the same is true of the grade

contrast between partitive singular lukku and genitive singular luku.

Furthermore, the implicational value of a form often depends essentially

on the paradigm cell – or, more generally, the grammatical properties – that

it realizes. A strong partitive singular such as lukku identies lukk ‘lock’

as a rst declension noun and permits the deduction of the other forms in

its paradigm (Blevins 2008). However, in isolation the strong vowel-nal

lukku provides limited information, because in the paradigm of a noun such

as lugu ‘tale’ in table 2 it may only realize the short illative singular and

thus be dissociated from the other forms of the noun. A strong form like

tekke may likewise realize the genitive singular of the ‘strengthening’ second

declension noun teke ‘origin’.

2.3 Stems

These examples illustrate some of the fundamental limitations of stems qua

forms. While it is often possible to identify stems from the word forms that

they realize or underlie, the separation of stems from exponents raises re-

calcitrant problems in many languages. This is a familiar issue in Romance

languages, where motivating a particular segmentation among several alter-

natives is a perennial problem.

The order of morphemes is xed [in Spanish JPB]: (derivational

prex(es)) + lexical stem + theme vowel + tense marker (some-

times including an empty morph) + person marker. Some forms,

however, have fused in the course of history and a neat segmen-

tation is not always possible. The preterit is the most dicult

paradigm to analyse, since the theme vowel is sometimes indis-

tinguishable, and segmenting the second and third person plural

markers in the regular way, /-is, -n/, leaves an awkward residue

that occurs nowhere else in the system. (Green 1997: 99)

WP models do not oer a general solution to this type of selection chal-

lenge; they can disregard it as an artifact of morphemic analysis, since there

is no theoretical need to make commitments to xed segmentations of word

forms. Determinate segmentations can, of course, arise and remain stable

within specic languages. However, from the implicational perspective of

a WP model, it is unsurprising that dierent, and possibly overlapping,

sequences may be of dierent predictive value, with several distinct segmen-

tations providing alternative entry points to analyzing a specic system. A

stem and theme vowel may be useful for identifying the lexical class of an

item, whereas the vowel and inection – or even a stem consonant, vowel

and inection – may predict patterns of inection.

This gestalt-based conception of word structure is implicit in the rules

of a classical grammar and more explicit in the (proportional) analogies

developed by Neogrammarians such as Paul (1920). As Morpurgo Davies

(1998: 258f.) remarks, much of the initial appeal of analogy derived precisely

from the fact that “it oered an algorithm for a structurally based form of

morphological segmentation, without making any claims about the segments

in question”.

Even in cases where no diculties arise in identifying or segmenting

stems, isolating stem forms loses information that is associated with the cor-

responding or larger word forms. For example, as suggested in the following

quote, in some descriptive traditions, it is customary to analyze paradigms

or morphological families in terms of abstract stems, believing that this

avoids unwanted semantic commitments of a word-based analysis.

Two dierent opinions can be found in the literature: (a) these

markers [in Archi, JPB/FA] are markers of the ergative case and

all oblique cases are formed from the ergative; (b) these mark-

ers are markers of the oblique stem (of the singular or plural)

and the ergative has no special marker and coincides with the

oblique stem of the appropriate number. The rst point of view

is unsatisfactory: it does not take account of the semantics of

the oblique cases (ergative meaning is not a component here),

nor of the data from other Daghestanian languages, where the

ergative frequently has a special morphological marker like other

oblique cases … (Kibrik 1998: 257)

Kibrik’s objection that a word-based analysis “does not take account

of the semantics of the oblique cases” highlights a common misinterpreta-

tion of WP models. Such models do not dene the entry associated with

the meaning of an oblique case form from the entry associated with the

meaning of the ergative case: particular obliques are not composites of the

meanings of the two relevant forms. Instead, they exploit the fact that the

form of an oblique case form is predictable from the form of the ergative

case. The features of these forms merely identify their place in the paradigm

of an item. The purely form-based nature of these relations is brought out

clearly by the layered system of ‘parasitic’ syncretism (Matthews 1972) in

the paradigm of lukk in table 3. There are countless candidates for ‘abstract

stems’ in these forms. The nominative singular lukk underlies the partitive

singular lukku, which is in turn identical to the short illative singular lukku

and underlies the partitive plural lukkusid and the genitive plural lukkude.

The genitive singular luku underlies the nominative lukud and the illative

through comitative singular, while the genitive plural lukkude underlies the

illative through the comitative plural.

Sing Plu

Nominative lukk lukud

Genitive luku lukkude

Partitive lukku lukkusid

Illa2/Part2 lukku lukke

Illative lukusse lukkudesse

Inessive lukus lukkudes

Elative lukust lukkudest

Allative lukule lukkudele

Adessive lukul lukkudel

Ablative lukult lukkudelt

Translative lukuks lukkudeks

Terminative lukuni lukkudeni

Essive lukuna lukkudena

Abessive lukuta lukkudeta

Comitative lukuga lukkudega

Table 3: Full paradigm of lukk ‘lock’ (Erelt et al. 2000)

Thus one could in principle avoid reference to word-based implication by

identifying a stem set including lukk,luku,lukku and lukkude. But none of

these stems can be assigned substantive properties in isolation that would

determine their distribution in the paradigm of lukk. This problem can,

of course, be handled by ‘indexing’ stems in ways that will dene their

distribution, as proposed in Brown (1998), Arono (1994) or Stump (2001).

But from a traditional perspective, this strategy gives rise to a descriptive

diacritic, since appropriate indexing is stipulated whenever it is required.

2.4 Cues and distribution

The abstraction of words is facilitated in most languages by cues that en-

hance the perceptual salience of words. Open-class items in many languages

are subject to a minimum word constraint, whether measured in terms of

moras, syllables or metrical feet, and there is experimental evidence that

speakers exploit these constraints in the segmentation of continuous speech

(Norris et al. 1997). Words often dene the units on which stress, pitch or

other suprasegmental features are realized, and word edges may be marked

by processes such as boundary lengthening (Bybee 2001). The perceptual

salience of words is further enhanced by the fact that words (unlike sub-

word units such as phonemes or morphemes) may often stand on their own

as independent utterances. In addition, if there is any basis to notions like

‘the one-word stage’ (Dromi 1987), it would appear that the word is the

canonical utterance during early stages of language acquisition.

As one would expect, the functional load of individual cues varies across

languages, reecting general dierences in their phonological systems, so

that no single cue identies words cross-linguistically. There may, as Robins

(1959) acknowledges, be discrepancies between ‘grammatical words’, which

provide the basis for the description of grammatical relations, and ‘phono-

logical words’, which are marked phonetically.11 It is nevertheless important

to appreciate that these discrepancies arise precisely because there are pho-

netic cues which, with varying degrees of reliability, mark word boundaries

or otherwise guide the segmentation of utterances into words. The existence

of mismatches should not obscure the fact that the two notions of ‘word’

overlap at least partially in many languages, and that this overlap permits

speakers to isolate grammatical words.

Although grammatical words may be imperfectly demarcated, stems are

even less clearly marked, and morphemes – including, signicantly, roots –

are rarely if ever cued at all by phonetic properties. There is no discrepancy

between the ‘grammatical morpheme’ and the ‘phonological morpheme’ for

the simple reason that there is no such thing as a ‘phonological morpheme’.

Hence the objection that grammatical words are not directly ‘given’ in the

speech stream might be taken as support for the primacy of the utterance

(Bloomeld 1914). But this observation provides no motivation for shifting

the focus of morphological analysis onto units even smaller than the word

(such as morphemes), since these units require an even greater degree of ab-

straction from the speech signal. The fact that words are abstractions falls

under the generalization that all linguistic units smaller than utterances

11See the papers in Dixon and Aikhenvald (2002) for further discussion of this issue.

are abstracted from larger sequences of connected speech. It is the useful-

ness of particular abstractions for the purposes of systematic description or

the psychological plausibility of abstractions within a model of the mental

lexicon that is of principal interest for a theory of morphology.

The implicational structure of a WP model suggests another solution

to the apparent conundrum of demarcating words in the speech stream. In

parallel to theoretical and descriptive studies, there is a large and diverse

psycholinguistic and computational literature on word segmentation and

recognition. This literature includes the work on identifying ‘uniqueness

points’ in Marslen-Wilson and Welsh (1978) and Marslen-Wilson and Tyler

(1980), neural network-based predictive models (Elman 1990), and statis-

tical models of word segmentation (Goldwater et al. 2009). The models of

word segmentation developed in these studies are based on the observation

that entropy (roughly, uncertainty about the segments that follow) declines

as more of a word is processed, then peaks again at word boundaries. These

sorts of prediction-based approaches suggest that the search for invariant

cues may in fact be misconceived and that the observable phonetic proper-

ties that have been assumed to be dening are just secondary cues for what

is an essentially statistical notion.

Observations about predictability at word boundaries are con-

sistent with two dierent kinds of assumptions about what con-

stitutes a word: either a word is a unit that is statistically in-

dependent of other units, or it is a unit that helps to predict

other units (but to a lesser degree than the beginning of a word

predicts its end). (Goldwater et al. 2009: 22)

3 The ‘item and pattern’ model

As the moniker ‘word and paradigm’ suggests, WP approaches assign a

special status to words, and attach grammatical signicance to inectional

paradigms and other collections of words. However, this designation is some-

what misleading, reecting an inconsistency in the initial classication pro-

posed by Hockett (1954). It is important to correct this inconsistency, be-

cause in mistaking an instantiation of the WP model for the model itself,

Hockett creates the false impression that WP models are relevant only to

languages of the ‘ectional’ type.

Hockett’s rst use of the term ‘word and paradigm’ comes in a brief

and apologetic preface to his 1954 paper, which is mainly concerned with

articulating and addressing problems that arise for models of morphemic

analysis.

Quite apart from minor variants of IP [item and process] or IA

[item and arrangement], or models that might be invented to-

morrow, there is one model which is clearly distinct from either

IA or IP, and which is older and more respectable than either.

This is the word and paradigm (WP) model, the traditional

framework for the discussion of Latin, Greek, Sanskrit, and a

good many more modern familiar languages … It will not do to

shrug this frame of reference o with the comment that it is ob-

viously insuciently general, incapable of organizing eciently

the facts of a language like Chinese. As yet we have no com-

pletely adequate model: WP deserves the same consideration

here given to IP and IA. (Hockett 1954:386)

Hockett’s nomenclature proved remarkably resilient, usefully in the case

of IA and IP, less so in the case of WP. The term IA just provided a la-

bel for the Post-Bloomeldian accounts that had already begun to run up

against the limitations of analyzing words in terms of linear arrangements of

morphemes. The term IP was applied to a new variant of morphemic anal-

ysis, which Hockett proposed to overcome the challenges to IA analysis that

he had previously addressed by introducing various types of non-segmental

‘morphs’ (Hockett 1947). The name ‘item and process’ acknowledged an

intellectual debt to the process-based perspective of Sapir (1921), which

Hockett, like other Post-Bloomeldians, had previously regarded with sus-

picion. The central dierence between IA and IP analysis concerned the

nature and status of the operations that derived complex forms. In an IA

model, complex forms arose through the concatenation of morphemes, which

were then mapped onto morphs by morphophonemic rules. The IP model

departed from this picture by admitting a class of processes that directly

applied operations to a base form. Both of these terms classied a model

in terms of the strategies it employed (arrangements or processes) to dene

non-basic units from basic ‘items’ (morphemes or stems).

But ‘WP’ is at a completely dierent level of specicity, referring to a

particular unit (words) and to a specific network of units (inectional

paradigms). Hence, the third model should in fact have been ‘item and

pattern’, where comparison of the item against the pattern sanctions the

deduction of new forms. Reclassifying traditional WP approaches as spe-

cic instantiations of a general ‘item and pattern’ model is of more than

purely historical interest. This characterization highlights the fact that the

model is dened less by the units it recognizes than by the relations it

establishes between units. Instead of disassembling a language into inven-

tories of ‘atoms’ that can be combined to build larger units, WP analyses

focus on the implicational structure dened over networks of interrelated

elements. The privileged status of words in these models does not rest on

claims about their epistemological priority, or their place within procedures

of classication or methods of analysis. Instead, the status of words is due

to their relative informativeness, as reected in Robins’ claim above that

“the word is a more stable and solid focus of grammatical relations than the

component morpheme by itself” (Robins 1959: 128). A second dimension of

informativeness is expressed in “the general insight that one inection tends

to predict another” (Matthews 1991: 197). In this domain, the primary

locus of form-based implication is again “words as wholes, arranged accord-

ing to grammatical categories … distinguished by their endings” (Matthews

1991: 187). The role of paradigms likewise follows from the fact that impli-

cations are most reliable within the essentially closed and uniform feature

space of an inectional paradigm.

3.1 Morphological organization

The networks of interdependencies within an inectional system allows it

to be factored into exemplary paradigms and sets of principal parts. This

traditional factorization rests on a genuine insight about the structure of

morphological systems. In contrast, paradigms conceived as consisting of

fully independent forms cannot be factored in this way, because such a

‘paradigm’ cannot be identied by any subset of its forms. It is this essential

interdependency, rather than numerical bounds or extrinsic constraints on

paradigms, that accounts for the ‘paradigm economy’ eects discussed by

Carstairs (1983); Carstairs-McCarthy (1994); Ackerman and Malouf (2013).

Despite this insightful recognition concerning the fundamentally rela-

tional nature of morphological organization, traditional formulations of WP

models incorporate a range of assumptions that mainly reect the uses to

which these models have been put. While the prominence of words and

paradigms is one obvious assumption, there are various other less produc-

tive formal assumptions as well. Inectional systems are almost always

factored into a discrete number of inection classes, usually with provisions

for macroclasses or subclasses in cases where there is considerable overlap.

Principal part inventories are also normally ‘static’ in the sense of Finkel

and Stump (2007), in that the same forms or sets of forms, e.g., the nomina-

tive singular or rst person singular, are taken to represent non-exemplary

items. The deduction of new forms by matching principal parts against ex-

emplary paradigms is likewise attributed to a symbolic process of the kind

represented by (four-part) proportional analogies.

Each of these assumptions creates problems of the same kind raised

by the indeterminacy of stem segmentation. For example, the diculty of

motivating the choice of principal parts (or ‘leading forms’) is perhaps the

best known of these problems.

One objection to the Priscianic model … was that the choice

of leading form was inherently arbitrary: the theory creates a

problem which it is then unable, or only partly able, to resolve.

(Matthews 1972: 74)

The other assumptions are equally problematic. Although pedagogical gram-

mars often converge on a similar number of classes for a given language, this

consensus tends to reect practical considerations of utility. In the absence

of agreed criteria for class identication, the number of classes associated

with a language can vary enormously, as in the celebrated case of Estonian

declensions. This generates pseudo-problems and competing solutions to

them.

As with the problem of stem segmentation, the best solution involves de-

veloping models in which the artifactuality of these problems becomes plain.

For pedagogical purposes, it is useful to draw the most informative cells of a

paradigm to the attention of language learners. However, there is no reason

to assume that a single form will always suce to identify the inectional

pattern of an item. Conversely, there is no reason to ignore the partial in-

formation supplied by other forms. There is also no reason to assume that

a language can be organized into some xed set of classes. Instead, dierent

sets of interdependent forms will, like segments, be dened by their predic-

tive value. For pedagogical purposes, it will again be useful to bundle these

sets of interdependent forms into larger collections that specify the shape

of each form of an item, irrespective of how loosely the forms of dierent

sets are connected to each other. The number of such larger connections

will depend on the uses that they are meant to perform and, accordingly,

the level of detail at which they are dened and individuated. Finally, there

is no principled reason to assume that the analogical processes that deduce

new forms of an item should be representable symbolically, rather than sub-

symbolically by a reasoning system such as TiMBL (Daelemans and Van den

Bosch 2005).

3.2 Morphological information

Formulating WP models in terms of information theory avoids each of these

problematic commitments. Each paradigm cell can be associated with a

measure of variability or uncertainty that correlates with the number of

ways that the cell can be realized (and the frequency of those alternatives).

One cell is likewise of diagnostic value in identifying the realization of an-

other cell (or set of cells) if knowing the realization of the rst cell reduces

uncertainty about the realization of the second cell (or set). To formalize

these intuitions, it is useful to regard paradigm cells as random variables

that take realization ‘outcomes’ as their values. The uncertainty associated

with the realization of a cell Ccan then be dened in terms of the entropy

(Shannon 1948) of the cell, H(C).

(4)

H(C) = −∑

x∈RC

p(x)log2p(x)

In this denition, RCrepresents the set of realization outcomes for C,x

represents outcomes in RC, and p(x)represents the probability that Cis

realized by x. As in Shannon’s original denition, entropy is measured in

bits.12

The entropy of a cell is determined both by the number of outcomes

and by the uniformity of their distribution. The greatest uncertainty arises

in a system with a large number of equiprobable outcomes. Uncertainty is

reduced in a system that has fewer ‘choices’, either few outcomes in total or

else outcomes with highly skewed distributions. The cumulative uncertainty

associated with a paradigm Pdepends in turn on the uncertainty of its cells

C1, C2. . . , Cn. On a traditional model, cells are generally assumed to be

interdependent, so that the entropy of a paradigm, H(P), will correspond to

the joint entropy of its cells, H(C1, C2, . . . , Cn). Given a general measure

of uncertainty, the diagnostic value of an individual cell can be dened in

terms of uncertainty reduction.

The relevant notion can be based on conditional entropy,H(C2|C1),

which measures the amount of uncertainty that remains about C2given

knowledge of C1. The more information that C1provides about C2, the lower

H(C2|C1)will be. If C1is fully diagnostic, then H(C2|C1)will approach 1.

12The formal issues raised by the use of entropy to measure uncertainty are discussed

in the detailed treatment of information-theoretic notions in Moscoso del Prado Martín

et al. (2004) and Milin et al. (2009). These include the use of a logarithmic scale, the

choice of a binary base, the applicable notion of probability, and related issues.

If C1is completely uninformative about C2, then H(C2|C1)will preserve

the uncertainty of H(C2). Yet the more uncertain C2is to start with,

the higher H(C2|C1)will also tend to be. Hence in order to determine

relative informativeness, the original entropy values as well as the conditional

entropy values must be known. Both values are incorporated into the general

measure in (5), which denes morphological information M(C2|C1)as

a value between 0 and 1 that is obtained by subtracting from 1 the proportion

of the original uncertainty in C2.

(5)

M(C2|C1) = 1 −H(C2|C1)

H(C2)

The basic notion of uncertainty reduction expressed in (5) generalizes

directly to collections of cells. Given that the uncertainty of a paradigm,

H(P), can be dened in terms of joint entropy, the morphological informa-

tion that a cell Cexpresses about a paradigm Pis expressed in (6).

(6)

M(P|C) = 1 −H(P|C)

H(P)

To take a concrete example, consider the partial Estonian paradigms

shown in table 2. There are ve realizations for the partitive (str+a, str+e,

str+i, str+u, wk+u) and each is equally likely. The entropy of the partitive

realization therefore is:

(7)

H(part) = −(5×1

5log2

5)= 2.32 bits

However, there are only four distinct realizations of the illative 2 (str+a,

str+e, str+i, str+u), so its entropy is slightly lower:

(8)

H(ill2) = −(3×1

5log2

5+2

5log2

5)= 1.92 bits

There are also ve equally likely possible pairs of partitive and illative 2

realizations (both str+a; both str+e; both str+i; both str+u; one wk+u

and the other str+a), so the joint entropy H(part,ill2)is also 2.32 bits.

This means the conditional entropy H(part|ill2)of the partitive given the

illative 2 is:

(9)

H(part|ill2) = H(part,ill2)−H(ill2) = 0.4bits

It should be intuitively clear at this point how the traditional selection of

principal parts is implicitly guided by entropy reduction. A fully diagnostic

cell, such as the partitive singular in the Estonian paradigms in table 2, has a

morphological information value approaching 1 because it all but eliminates

uncertainty. Fully non-diagnostic cells, such as the dative, locative and

instrumental plurals in Russian, have a value approaching 0 because they

preserve uncertainty. If diagnostic value were an all or nothing aair, then

principal parts could be dened as cells that eliminated the uncertainty

associated with the paradigms to which they belong. A cell Cwould be a

principal part for a paradigm Pwhenever the value of M(P|C)approached

1. However, nothing guarantees that every class system will contain such

fully diagnostic forms. In contrast, any system that can be decomposed into

exemplary paradigms and principal parts will contain multiple, partially

informative, forms which, in various combinations, eliminate the uncertainty

associated with a paradigm.

The diagnosticity of a set of cells cannot be determined by summing

their individual morphological information values, since multiple forms may

reduce the uncertainty of the same (or overlapping) cells in a paradigm.

Instead, the diagnostic value of a set of forms is measured by their collective

morphological information value. Since conditional entropy is also dened

for sets of given forms, the diagnostic value of cells C1, C2, . . . , Cncan be

determined by generalizing the single cell Cin (6) to the set C1, C2, . . . , Cn.

The availability of a range of dierent diagnostic combinations clearly

enhances the robustness of class identication and form deduction, since

speakers are not dependent on encountering one uniquely informative form

of a paradigm. A classication based on morphological information thus of-

fers a principled solution to the traditional problem of identifying principal

parts (or ‘leading forms’). The informal idea that diagnosticity correlates

with variability across inection classes can be expressed more precisely in

terms of the uncertainty reduction that is measured by the morphological

information of a cell or set of cells. From the present perspective, one can see

that the choice of leading forms is to a large degree arbitrary. A pedagogical

or reference grammar might use seemingly arbitrary criteria to select a par-

ticular cell or cell set. A description might select the smallest set of cells, the

set with the most highly frequent members, or, more capriciously, the cell

or cell set with the morphologically simplest members, etc. Since any fully

diagnostic set of cells will do, all are equally suitable and the arbitrariness

involved in selecting one is harmless.13

Moreover, given that cells are informative about the realization of other

individual cells or sets of cells, there is no need to mediate the deduction of

new forms via a reied class structure. Instead of being part of the linguistic

system, classes can be regarded as being imposed within a description of the

system. Much the same is true of proportional analogies, which merely pro-

vide a symbolic representation of the deductions sanctioned by the morpho-

logical information that cells express about other cells. In this connection,

the present appeal to information-theory develops the advantages identied

by Hockett (1967:221) for WP approaches:

One of the most dangerous traps in any of the more complex

branches of science (by no means absent even in the simplest

branch, physics) is that of confusing one’s machinery of anal-

ysis with one’s object of analysis. One version of this is pan-

demic in linguistic theory today: almost all theorists take mor-

phophonemes (by one or another name) to be things IN a lan-

guage rather than merely part of our equipment for the analy-

sis and description OF the language… A correct principal-parts-

and-paradigms statement and a correct morphophoneme-and-

rule statement subsume the same actual facts of alternation, the

former more directly, the latter more succinctly.

Although formalized in information-theoretic terms, the notion of mor-

phological information invoked here captures the traditional intuition that

Matthews (1991: 197) expresses as “the general insight that one inection

tends to predict another”. It is this notion that is largely absent from most

contemporary morphological traditions, which represent only grammatical

information, such as case, number and gender. Part of the problem lies in

the fact that predictive value is not a property of a form in the same way

that, say, case is and hence cannot readily be expressed as a ‘feature’, even

if one accepts the use of diacritic features for expressing notions like class

aliation.

13There is also a trade-o between the number of cells required to identify class in a

system and whether one uses the same cells to identify class, as Finkel and Stump (2007,

2009); Stump and Finkel (2013) show. Recent information-theoretic research based on

large data bases with frequency information have been achieving important results using

joint entropy measures as in Bonami and Luís (2015) and Bonami and Beniamine (2015).

4 Concluding observations

The usefulness of information theory for formalizing traditional WP mod-

els provides further conrmation of the linguistic relevance of information

theory, as initially suggested by Descriptivists such as Hockett (1953, 1955)

and Harris (1951, 1991).14 Moreover, there is also a number of more general

consequences of recognizing implicational relations as the cornerstone of WP

models. Most obviously, this avoids the need to impose a uniform analysis

on all languages at the level of units. From the outset of the rejuvenated

WP tradition, it was clear that many languages do not conform to the ‘ag-

glutinative ideal’ of a morpheme-based model and that at least some depart

quite radically from that ideal.

One motive for the post-Bloomeldian model consisted, that is to

say, in a genuinely factual assertion about language: namely, that

there is some sort of matching between minimal ‘sames’ of ‘form’

(morphs) and ‘meaning’ (morphemes). Qua factual assertion

this has subsequently proved false: for certain languages, such

as Latin, the correspondence which was envisaged apparently

does not exist … One is bound to suspect, in the light of such a

conclusion, that the model is in some sense wrong. (Matthews

1972: 124)

Yet there is no reason in principle why some languages could not ap-

proach this ideal. It is apparently the belief that word-based models must

deny this possibility that leads some accounts to dispute the existence of

word-internal structure, in general (Singh and Starosta 2003) or in specic

domains, such as words formed by axation (Anderson 1992:§10). But

shifting the emphasis of a WP model from units to relations claries how

the model would apply to even a perfectly morphemic language. In such a

language, grammatical properties would reliably predict the formatives that

realize them (modulo any regular phonological processes), and formatives

would reliably signal the properties that they realize. Implicational rela-

tions would retain a central role, but they would hold between formatives

and properties rather than between words.

An implicational model likewise provides a framework for incorporating

morphemes alongside the patterns that Arono (1994) terms ‘morphomic’.

In the general case, a morphome is simply a unit of predictive value. The

14Harris’ perspective has had a more direct inuence on works such as Goldsmith (2001)

and Pereira (2002) and on statistical approaches to segmentation.

morphomes that Matthews (1972) terms ‘Priscianic’ or ‘parasitic’ sanction

predictions about the shape of one form based on the shape of another.

For any Verb, however irregular it may be in other respects, the

Present Innitive always predicts the Imperfect Subjunctive. For

the Verb ‘to ower’, orere →orerem; for the irregular Verb ‘to

be’, esse →essem, and so forth without exception. (Matthews

1991: 195)

The general patterns of stem syncretism in the Estonian declension in table 3

are similar in character. For example, the genitive of each number predicts

the stem of the corresponding semantic case forms. From an implicational

perspective, morphemes can be regarded as special cases of morphomes, ones

that encapsulate a biunique implication between properties and forms.

Finally, an implicational interpretation of traditional models oers a

novel perspective on morphological variation. One of the most striking

things about morphology is how much it appears to vary across languages.

Languages may have many, few or even no inection classes, paradigms

may have many cells or few, the forms that realize individual cells may

vary widely or be relatively invariant, and so on. Languages may even lack

morphology altogether, which has encouraged a view which, in its most

provocative form, holds that morphology is somehow “unnatural” or even a

“pathology of language” (Arono 1994: 413). However, much of the prob-

lematic variation involves aspects of morphological systems that are largely

irrelevant to the acquisition or use of language by human speakers. A speaker

doesn’t need to determine the exact number of inection classes in a lan-

guage, provided that the patterns within inectional paradigms provide a

reasonably secure analogical base for deducing new forms. The fact that

certain formatives may be unambiguous while others have a wider range of

functions and meanings also poses no great diculties if these occur in larger

word forms or constructions with stable grammatical properties. Hence

there is no reason why the pressures imposed by language acquisition and

use should mould languages in ways that produce clear answers to questions

concerning the number of inection classes in a language, the meaning of

specic formatives, determine an unambiguous segmentation of forms into

roots or stems and exponents, etc.

From a traditional perspective, these questions, and many of the other

kinds of questions that tend to vex theoretical studies, are either of mainly

pedagogical interest (numbers of classes or sizes of principal part invento-

ries) or else are artifacts of methods of analysis or schemes of classication

(meanings of formatives or ‘correct’ segmentations). Consequently, these

issues can be seen to fall within what one might call ‘theoretical lexicog-

raphy’ rather than within the study of linguistic morphology per se. Since

languages do not develop in response to the demands imposed by lexicog-

raphy, there is no reason to expect that these properties will be broadly

similar across languages. However, speakers of all languages do face what

Ackerman et al. (2009) call the ‘Paradigm Cell Filling Problem’, the task of

deducing or interpreting new forms of an item, based on exposure to other

forms of the item. Hence, a traditional model would lead one to expect

that the diculty of this task would fall within a fairly circumscribed range.

Information-theoretic notions provide the tools to measure the diculty of

predicting paradigms from subsets of their forms, and a research question

that is being actively pursued in the current literature explores what Ack-

erman and Malouf (2013) term ‘the low entropy conjecture’, namely that

the diculty of this task is in fact relatively low and largely independent of

the properties that give rise to apparently extreme morphological variation.

In eect, this dierent perspective on the organization and learnability of

morphological systems has begun to explore what Hockett (1967: 221) an-

ticipated would be a benet of developing WP approaches, namely, that

..there would be a net gain in realism, for the student of the

language would now be required to produce new forms in exactly

the way the native user of the language produces or recognizes

them- by analogy…

In line with this, the revival of old ideas and insights associated with

earlier less formal WP approaches to morphology are animating and al-

tering the modern perspective on “realism” with respect to morphological

systems and their organization. This arises from the use of quantitative, e.g.,

information-theoretic measures as well as Bayesian and discriminative learn-

ing models (see Chater and Perfors (2015); Seyfarth et al. (2014); Blevins

and Ramscar (2015); Ramscar (2015); Sims (2015), among others) which

reveal phenomena and patterns that were inaccessible without them. The

adoption of this perspective and these methodologies enfolds the study of

linguistic morphology within the fertile research regimen in the developmen-

tal sciences that explores and explains phenomena in terms of the dynamics

of interdependencies within complex adaptive systems.

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On the Analytic Expression of Predicates in Meskwaki

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Dec 2009

Philip S. LeSourd

Essays reflecting the influence of the versatile linguist David M. Perlmutter, covering topics from theoretical morphology to sign language phonology. Anyone who has studied linguistics in the last half-century has been affected by the work of David Perlmutter. One of the era's most versatile linguists, he is perhaps best known as the founder (with Paul Postal) of Relational Grammar, but he has also made contributions to areas ranging from theoretical morphology to sign language phonology. Hypothesis A/Hypothesis B (the title evokes Perlmutter's characteristic style of linguistic argumentation) offers twenty-three essays by Perlmutter's colleagues and former students. Many of the contributions deal with the study of the world's languages (including Indo-European languages, sign language, and languages of the Americas), reflecting the influence of Perlmutter's cross-linguistic research and meticulous analysis of empirical data. Other topics include grammatical relations and their mapping; unaccusatives, impersonals, and the like; complex verbs, complex clauses, and Wh-constructions; and the nature of sign language. Perlmutter, currently Professor Emeritus at the University of California, San Diego, and still actively engaged in the field, opens the volume with the illuminating and entertaining essay, “My Path in Linguistics.” ContributorsJudith Aissen, Mark Aronoff, Leonard H. Babby, Nicoleta Bateman, J. Albert Bickford, Sandra Chung, William D. Davies, Stanley Dubinsky, Katarzyna Dziwirek, Patrick Farrell, Donald G. Frantz, Donna B. Gerdts, Alice C. Harris, Brian D. Joseph, Géraldine Legendre, Philip S. LeSourd, Joan Maling, Stephen A. Marlett, Diane Lillo-Martin, James McCloskey, Richard P. Meier, Irit Meir, John C. Moore, Carol A. Padden, Maria Polinsky, Eduardo P. Raposo, Richard A. Rhodes, Wendy Sandler, Paul Smolensky, Annie Zaenen

Stem Indexing and Morphonological Selection in the Russian Verb: a Network Morphology Account

Chapter

Dec 1998

Dunstan Brown

Morphological Typology: From Word to Paradigm

Book

Nov 2019

In this radically new approach to morphological typology, the authors set out new and explicit methods for the typological classification of languages. Drawing on evidence from a diverse range of languages including Chinantec, Dakota, French, Fur, Icelandic, Ngiti and Sanskrit, the authors propose innovative ways of measuring inflectional complexity. Designed to engage graduate students and academic researchers, the book presents opportunities for further investigation. The authors' data sets and the computational tool that they constructed for their analysis are available online, allowing readers to employ them in their own research. Readers can access the online computational tool through www.cambridge.org/stump_finkel.

Inflectional Defectiveness

Book

Nov 2015

Andrea Sims

Paradigmatic gaps ('missing' inflected forms) have traditionally been considered to be the random detritus of a language's history and marginal exceptions to the normal functioning of its inflectional system. Arguing that this is a misperception, Inflectional Defectiveness demonstrates that paradigmatic gaps are in fact normal and expected products of inflectional structure. Sims offers an accessible exploration of how and why inflectional defectiveness arises, why it persists, and how it is learned. The book presents a theory of morphology which is rooted in the implicative structure of the paradigm. This systematic exploration of the topic also addresses questions of inflection class organization, the morphology-syntax interface, the structure of the lexicon, and the nature of productivity. Presenting a novel synthesis of established research and new empirical data, this work is significant for researchers and graduate students in all fields of linguistics.

The State of the Art

Article