Inter-paradigm leveling in Hebrew verbal system

Gila Zadok1 · Outi Bat-El1
Received: 31 July 2014 / Accepted: 24 April 2015 / Published online: 13 May 2015
© Springer Science+Business Media Dordrecht 2015
Abstract Paradigm leveling, whereby the number of surface allomorphs within a
paradigm is reduced, is often accompanied by the loss of contrast between paradigms
(analogy). Since these two are independent of each other, we distinguish between
intra- and inter-paradigm leveling. In this paper, we study inter-paradigm leveling
in the verb system of Hebrew, manifested by on-going change-oriented variation. In
this context, we respond to two questions often addressed in studies on paradigm
leveling: (i) Why do some paradigms interact in inter-paradigm leveling and others
do not? (ii) What determines the direction of leveling? With regard to the first question,
we argue that inter-paradigm leveling is triggered by similarity between whole
paradigms, and propose a model that quantifies similarity and predicts the relative
chance for two paradigms to undergo inter-paradigm leveling.With regard to the second
question, we identify two types of directionality, uni- and bidirectional leveling,
and show that the selection between these two is determined by the size of the inflectional
classes. Class size determines the direction in unidirectional leveling (the
larger is the winner) and class size ratio distinguishes between uni- and bidirectional
leveling (the higher the ratio the greater the chance for unidirectional leveling).
Keywords Paradigm leveling · Paradigm migration · Analogy · Similarity ·
Frequency · Variation · Change · Hebrew verbs
1 Introduction
Studies on ‘analogical leveling’ often concentrate on a few forms in the paradigm,
those that change due to leveling. In this paper we emphasize that leveling captures
whole paradigms, regardless of the number of forms within the paradigms. To avoid
B O. Bat-El
obatel@post.tau.ac.il
1 Department of Linguistics, Tel-Aviv University, Tel-Aviv 69978, Israel
272 G. Zadok, O. Bat-El
confusion, we use the term ‘inter-paradigm leveling’, which stands for loss of contrast
between whole paradigms.
To highlight this aspect of leveling, we first introduce our terminology (Sect. 1.1),
which accentuates the relevant distinctions and relations introduced in the literature.
In particular, the terminology distinguishes between inter- and intra-paradigm leveling
(leveling between and within paradigms respectively) and between paradigm
and inflectional class. Since the whole paradigm is involved in leveling, we also define
the process of inter-paradigm leveling as migration of a whole paradigm from
one inflectional class to another (Sect. 1.2). This perspective on leveling allows us to
answer questions on cause and directionality in inter-paradigm leveling (Sect. 1.3).
1.1 Inter- and intra-paradigm leveling
The change from <strive–strove–striven> to <strive–strived–strived> can be viewed
as a case of the traditional paradigm leveling, defined as “the complete or partial
elimination of morphophonemic alternations within a paradigm” (Hock 1991:168).
Since paradigm leveling “reduces or completely eliminates allomorphy” (Jeffers and
Lehiste 1986:55), when it comes to stems, it must be limited to within a paradigm.
However, paradigm leveling may also have an inter-paradigm effect, known as
analogical leveling, namely, a loss of contrast between two paradigms. Since <strive–
strove–striven> is changing to <strive–strived–strived>, it is possible that it is assuming
the model of <smile–smiled–smiled>, and consequently eliminating the contrast
between these two inflectional classes.
Albright (2005) inquires into the familiar case of leveling in Latin, asking whether
analogy (in its broad sense) is internal to the paradigm or external, internal being due
to paradigm uniformity (1a) and external being analogy (1b).
(1) Possible triggers for paradigm leveling
a. Paradigm uniformity (Steriade 2000:313)—the cause of paradigm leveling
All surface realizations of μ, where μ is the morpheme shared by the
members of paradigm x, must have identical values for property P.
b. Analogy (Lehmann 1992:227)
A process by which morphs, combinations of morphs, or linguistic patterns
are modified, . . . , on the pattern of those present in a language.
The Latin example presented in (2) below illustrates the ambiguity of causes addressed
by Albright. Does the change hono:s → honor follow a model word within
the paradigm (hono:ris), thus due to paradigm uniformity? Or does the change assume
the model of another paradigm (soro:ris – soror), thus due to analogy (known
as proportional or four-part analogy)?
(2) Latin leveling
Inter-paradigm leveling in Hebrew verbal system 273
The traditional terms ‘paradigm leveling’ and ‘analogy’ seem to differ mainly in their
domain; in both cases there are leveling and analogy, i.e. loss of contrast on the basis
of similarity, but the domain is within and across paradigms respectively. Thus, in
order to maintain uniformity and specificity of terminology we use the terms intraand
inter-paradigm leveling (roughly corresponding to stem- and pattern-analogy in
Kraska-Szlenk 2007).1
(3) Two types of paradigm leveling
a. Intra-paradigm leveling involves reduction or elimination of contrast between
allomorphs within a paradigm.
b. Inter-paradigm leveling involves reduction or elimination of contrast between
paradigms.
In the English and Latin examples given above, inter- and intra-paradigm leveling are
tied together. However, these two types of leveling need not co-occur. Hebrew provides
evidence for the independence of inter-paradigm leveling; the paradigm <gerá–
. . . –gerí-ti> ‘to tease’ is changing to <girá–. . . –girí-ti>, adopting the model of <nisá–
. . . –nisí-ti> ‘to try’.2 Paradigm uniformity is not involved in this case because (i) the
old paradigm (<gerá–. . . –gerí-ti>) does not have a form with i that could serve as
the model word for paradigm uniformity; and (ii) both the old and the new paradigms
have the same number of stem allomorphs. In addition, there is no vowel harmony
or e > i sound change that can motivate the change in the paradigm. Therefore, this
change must be due to inter-paradigm leveling alone.
Garrett (2008:130) claims that “in 900 years of Middle and Modern English
linguistic history, there was never any case of pure leveling. The vast majority of
preterite stem changes yielded paradigm uniformity, to be sure, but only given a preexisting
uniform paradigm of the same type.” The reason for this tie is that intraparadigm
leveling without inter-paradigm leveling would increase the number of
distinct paradigms for a particular morpho-syntactic category. Since this distinction
overloads the grammar without serving any purpose, such change is quite implausible.
Hebrew supports Garret’s claim. There are many cases of inter-paradigm leveling,
where paradigm contrast is reduced, but there is only one case of pure intra-paradigm
leveling, where a new paradigm is created; the paradigm <n>itséax–. . . –n>itsáxti> is
changing to <n>itsáx–. . . –n>itsáxti> ‘to win’, where the diphthong (historically occurring
before a final guttural) is simplified, resulting in a leveled paradigm, but also in
a new one. This is probably a combining force of intra-paradigm leveling and diphthong
simplification.
Having established the independence of the two types of leveling, we can now
announce that the present paper studies inter-paradigm leveling (although some
paradigms, as in the English and Latin examples, may exhibit also intra-paradigm
1We refrain from using the term ‘analogy’ because it is not specific enough for our purpose, or as Bybee
(1980:45) phrased this term “encompasses both too much and too little”. See Kraska-Szlenk (2007) and
Blevins and Blevins (2009) for recent reviews of analogy in linguistics, and Itkonen (2005) for the wide
spread use of analogy in linguistics and cognitive science.
2The notation <X–. . . –Y>, where X and Y are forms in a paradigm, indicate a whole paradigm.
274 G. Zadok, O. Bat-El
leveling). If we go back to the literature on inter-paradigm leveling (analogical leveling),
we often see reference to proportional analogy as in (1), where only a pair from
each paradigm is taken. In this paper we emphasize that inter-paradigm leveling is
between whole paradigms, where one whole paradigm assumes the model of another.
Here, again, we must be precise with the use of the term ‘paradigm’, which is used
in various contexts in linguistics (and elsewhere), and it is often difficult (though not
always necessary) to distinguish between a paradigm of a particular verb/noun (4a)
and a paradigm shared by a group of verbs/nouns, i.e. the inflectional class (4b).
(4) Paradigm vs. inflectional class
a. A paradigm is a set of word forms sharing a lexeme within a particular
morpho-syntactic dimension.
b. An inflectional class is a paradigm of paradigms, i.e. the phonological
pattern shared by a set of paradigms.
For example, <strive–strove–striven> is a paradigm that shares an inflectional class
with <WRITE, STRIKE, ARISE, etc.>, where small caps stand for a whole paradigm.3
It is common for a language to have more than one inflectional class for a specific
morpho-syntactic dimension, where every class hosts a different number of
paradigms.4 The structural properties distinguishing among the inflectional classes
are language-specific, defined in morphological and/or phonological terms (e.g. affixes,
prosodic structure, segmental contrast, etc.). For example, Bybee and Moder
(1983) define the class of swim come begin etc. as . . . æ nasal (k)]Verb Past, and the
class of spin, win, cling as . . . 2 nasal/velar]Verb Past.
1.2 Paradigm migration
With these terms at hand, we can now introduce the process involved in interparadigm
leveling. Studies on analogy often refer to four-part analogy, as in the familiar
Latin case in (1), soro:ris : soror :: hono:ris : x; x = honor. With such a notation,
only one pair from each paradigm is presented and only one form undergoes change.
However, as Bloomfield (1933:406) points out, the sets at either side of the double
colon can consist of more than two members, as in scream : screams : screaming :
screamer : screamed :: dream : dreams : dreaming : dreamer : x; x = dreamed. That
is, whole paradigms can be involved in analogy, although the change can be realized
only in one form since all other forms are initially identical.
By introducing in (3) the term inter-paradigm leveling we secure reference to the
whole paradigm. That is, inter-paradigm leveling must (not just can) involve whole
paradigms, and therefore each form in the paradigm must adopt its parallel in the new
inflectional class, sometimes vacuously.
3The term ‘paradigm’ partially overlaps with the term ‘lexeme’ (see definition in Aronoff and Fudeman
2011).
4The ‘morpho-syntactic dimension’ is the combination of the morpho-syntactic features relevant to the
paradigm. The features relevant for the present study are tense (past and future), number (singular and
plural), gender (masculine and feminine), and person (1st, 2nd, and 3rd).
Inter-paradigm leveling in Hebrew verbal system 275
We refer to the process involved in inter-paradigm leveling as paradigm migration,
whereby a whole paradigm (in our case a verb paradigm) migrates from one inflectional
class to another. Migration of a whole paradigm is oblivious to the number of
forms that are changing, because at the moment a paradigm migrates from class A to
B, all the forms in the paradigm adopt the structure of the new class.
(5) Paradigm migration
Migration of a whole paradigm is more restrictive than four-part analogy, since the
latter allows for changes only in some forms in the paradigm, thus has the potential
of creating a new inflectional class. When the difference between inflectional classes
has no function in grammar, as in English tense paradigms (Bybee and Moder 1983)
and the Hebrew ones studied here, the addition of a new inflectional class leads to a
redundant increase in complexity. Other things being equal, languages tend to change
towards simpler systems, and therefore the null hypothesis is that a paradigm migrates
as a whole unless there is evidence for the contrary.
The notion of migration necessarily involves directionality. Our study of interparadigm
leveling in the verb system of spoken Israeli Hebrew (hereafter Hebrew)
reveals two major types of migration (see Zadok 2012 for a third, marginal type):
a. Unidirectional migration, whereby paradigms from class A migrate to class B,
but not vice versa. For example, the paradigm <jeesóf–. . . –teesóf > ‘to collect’ is
migrating from its original class to that hosting <jaavód–. . . –taavód> ‘to work’,
thus changing to <jaasóf–. . . –taasóf >.
b. Bidirectional migration, whereby paradigms from class A migrate to class B, and
other paradigms from class B migrate to class A. For example, the paradigm
<milé–. . . –miléti> ‘to fill’ is migrating from its original class to the one hosting
<nisá–. . . –nisí
¯
ti> ‘to attempt’, thus changing to <milá–. . . –milíti>. At the same
time, the paradigm <nisá–. . . –nisí
¯
ti> is migrating to the class hosting <milé–. . . –
miléti>, thus changing to <nisé–. . . –niséti>.
Unidirectional migration leads to reduction in the number of inflectional class, and
thus to a simpler system (other things being equal of course). As in the abovementioned
English case, there is no grammatical function to the distinction among
the various inflectional classes, and thus their migration has no further effect. Bidirectional
migration does not have such a positive effect on the system since it maintains
the same number of paradigms and preserves variation.
Migration, like analogy, is contingent upon similarity, where the more similar the
inflectional classes are the more likely they are to interact in inter-paradigm leveling.
Consequently, the more similar the classes are the less changes a paradigm undergoes
when migrating to a new class, where less changes can be fewer forms in the
paradigm and/or a minimal change in each form.
276 G. Zadok, O. Bat-El
1.3 Questions addressed
We respond in this paper to two questions (a and b) often addressed in the context
of paradigm leveling, and to one (c) that arises given the two types of directionality
specified above:
a. Why do paradigms from class A migrate to class B and not to class C; i.e. why do
some classes interact and others do not?
b. Why do paradigms from class A migrate to class B and not vice versa; i.e. what
determines directionality in unidirectional paradigm migration?
c. What determines whether migration is unidirectional or bidirectional?
In response to question (a), we show that inter-paradigm migration is dependent on
the degree of similarity between classes, where the greater the similarity the higher
the chance for variation and then change via migration. We propose a model for
quantifying similarity among whole paradigms and show that the model is able to
predict which two classes will interact in the migration process.
As for question (c), we argue that the type of direction in paradigm migration (i.e.
uni- vs. bidirectional) is regulated by the size ratio of similar inflectional classes,
where low ratio correlates with bidirectional and high ratio with unidirectional migration.
Within the unidirectional migration (b), verbs tend to migrate to the larger class,
i.e. the one that hosts more paradigms.
To conclude this section, we provide a roadmap for the rest of this article:We start
in Sect. 2 with the relevant background on the Hebrew verb system, distinguishing
between verb classes (binyanim) and sub-classes (gzarot), where each sub-class is
a unique inflectional class (Sect. 2.1). We then introduce the state of affairs at the
current stage of the language regarding the change-oriented variation (Sect. 2.2).
Following earlier studies, we adhere here to the notion of similarity, which has
always been addressed in studies on analogy (e.g. “analogy is a relation of similarity”;
Anttila 1972:88). We start the discussion on similarity in Sect. 3 by introducing the
objects and properties relevant for evaluating similarity in Hebrew (Sect. 3.1). We
then propose a model for quantifying similarity, which relies on the core tenet of our
proposal in this paper, and thus evaluates whole paradigms (Sect. 3.2). This section
thus answers our first question: Why do some inflectional classes interact and others
do not?
The second question, regarding directionality, is addressed in Sect. 4, where we
introduce the various types of directionality (Sect. 4.1) and argue for the role of inflectional
class size in determining directionality (Sect. 4.2).
We wrap up in Sect. 5 with a brief summary and draw attention to some residual
issues, such as the pace of change.
2 Hebrew verb system
A lot has been said about the verb classes (binyanim) in Semitic languages in
general (McCarthy 1979, 1981; see a review in Bat-El 2011) and in Hebrew
Inter-paradigm leveling in Hebrew verbal system 277
in particular (Berman 1978; Goldenberg 1994; Lederman 1982; Aronoff 1994;
Bat-El 1989, 2003; Ussishkin 2000; Laks 2011). However, most studies refer to the
prototypical sub-class in each binyan, where all stems within a paradigm have three
or more surface consonants (e.g. sipér ‘to tell’, h-igdíl ‘to enlarge’, tilfén ‘to phone’,
hit-balbél ‘to be confused’). In this paper we attend to the so-called “weak” or “defective”
verbs (Gesenius 1910; Schwarzwald 2001), whose inflectional classes are
structurally different from those of the prototypical verbs. The weak verbs suffer
from a great degree of change-oriented variation, and thus serve as fruitful grounds
for the study of inter-paradigm leveling.
Change-oriented variation indicates an ongoing change, where a phenomenon in a
language is in the midst of a shift from grammar A to grammar B. At this stage, both
grammars are still active, i.e. grammar A has not vanished entirely and grammar B
has not yet taken over. The change-oriented variation discussed in this paper is identified
on the basis of (inter- and intra-speaker) variation between the normative and
colloquial forms (A and B respectively), which we consider here old and new respectively
(see Zadok 2012 for a discussion on the notions ‘normative’ and ‘colloquial’
and related terms). The pace of change also varies among inflectional classes, such
that among the classes that are in the process of vanishing some are still alive and
kicking while others are almost extinct.
2.1 Hebrew verb paradigms
Hebrew verbs are allocated into five verb classes (called binyanim; singular binyan),
where each verb class consists of several sub-classes (called gzarot; singular gizra),
and each sub-class, in turn, hosts one or more verb paradigms.5 Every sub-class is
structurally unique and thus a sub-class is an inflectional class. In this paper, when
we use the term “verb” we refer to its entire paradigm (finite forms), and to emphasize
this point, we often refer to verb paradigm.
(6) Organization of Hebrew verb system
2.1.1 Verb classes (binyanim)
The verb classes are structurally defined in terms of configurations (Bat-El 2003),
which include prosodic structure, vocalic pattern, and a derivational prefix (if any).
The configurations often found in the literature, as in (7) below, are of the prototypical
sub-class of each binyan. To illustrate the alternation within each binyan, we
provide here Past and Future forms with stems in three phonological environments:
final position (3rd person masculine singular), before a consonant-initial suffix (only
in Past), and before a vowel-initial suffix. All Future forms have an inflectional prefix
(here we provide the 3rd person prefix j-).
5Some studies refer to 7 binyanim, counting the passive forms of B3 and B4.
278 G. Zadok, O. Bat-El
(7) Hebrew verb classes (each represented by its prototypical sub-class)
Past Future
Stem Stem]-C (. . . ) Stem]-V (. . . ) Stem Stem]-V (. . . )
3rd ms.sg. 1st sg. 3rd fm.sg. 3rd ms.sg. 3rd pl.
B1 gadál gadál-ti gadl-á jigdál jigdel-ú ‘to grow’
CaCaC CaCaC- CaCC- -VCCaC -VCCeCB2
nixnás nixnás-ti nixnes-á jikanés jikans-ú ‘to enter’
niCCaC niCCaC- niCCeC- -iCaCeC -iCaCCB3
higdíl higdál-ti higdíl-a jagdíl jagdíl-u ‘to enlarge’
hiCCiC hiCCaC- hiCCiC- -aCCiC -aCCiCB4
tipés tipás-ti tips-á jetapés jetaps-ú ‘to climb’
CiCeC CiCaC- CiCC- -eCaCeC -eCaCCB5
hitkatév hitkatáv-ti hitkatv-á jitkatév jitkatv-ú ‘to
hitCaCeC hitCaCaC- hitCaCC- -itCaCeC -itCaCC- correspond’
The individual forms in the paradigm are different in terms of prosodic structure
and/or vocalic pattern across tenses, across environments, and across binyanim. The
structural difference among the binyanim is usually maintained throughout the inflectional
paradigm, such that every form in the inflectional paradigm of one binyan is
structurally different from its counterpart in another binyan. As argued in paragraph
“Blocking”, preservation of contrast among binyanim may block otherwise predicted
inter-paradigm leveling. The minimal difference between parallel forms from different
binyanim is in vowel quality, as in the Future configurations of B2 (-iCaCeC) and
B4 (-eCaCeC). The structural differences among the forms within each inflectional
class are maintained with the person-number-gender affixes. One consistent case of
syncretism is, however, found in all Future paradigms, where the 2nd person masculine
singular and the 3rd person feminine singular take the same form (e.g. tigdál
‘you/she will grow B1’, tikanés ‘you/she will enter B2’). Another, currently developing
case of syncretism, again in the Future paradigm, is the shared form of the 1st
person singular and 3rd person masculine singular (e.g. jigdál ‘I/he will grow B1’,
jikanés ‘I/he will enter B2’).6
Verbs distinguished by their configuration only (i.e. the residual stem consonants
are identical) are often semantically related, though to varying degrees; e.g. gadál ‘to
grow B1’ – higdíl ‘to enlarge B3’, zarák ‘to throw B1’ – hizrík ‘to inject B3’, masár
‘to hand over B1’ – hitmasér ‘to devote oneself B5’.7 That is, the binyan system has
grammatical and semantic functions (Berman 1978; Doron 2003; Laks 2011).
6Historically, the normative 1st person singular Future form (prefix PV-) has been replaced with the 3rd
person singular form (prefix jV-). Although the change is on-going, we are using here the syncretic form.
7Unless otherwise specified, the citation form is 3rd person masculine Past form with a gloss in the infinitive.
Inter-paradigm leveling in Hebrew verbal system 279
2.1.2 Sub-classes (gzarot)
Each verb class (binyan) consists of several sub-classes, which are structurally distinguished
from each other in at least one form in the paradigm. That is, the sub-class
defines the pattern of a group of paradigms and it is thus an inflectional class. The
difference between sub-classes can be prosodic (e.g. in the presence vs. absence of
a prosodic position) and/or segmental (vowel quality); the derivational prefixes of
the class (if any) are constant. Below are a few examples of B1 and B3 sub-classes.
There is no semantic contrast among the sub-classes in each binyan, and therefore
the sub-classes are inflectional classes.
(8) Sub-classes (inflectional classes)
Past Future
3rd ms.sg. 1st sg. 3rd fm.sg. 3rd ms.sg. 3rd pl.
B1 a. Prototypical katáf katáf-ti katf-á jiktóf jiktef-ú ‘to pick’
b. V-initial avár avár-ti avr-á jaavór jaavr-ú ‘to pass’
c. V-final A kará kará-ti kar-á jikrá jikre-ú ‘to read’
d. V-final B kaná kaní-ti kant-á jikné jikn-ú ‘to buy’
e. Monosyllabic sam sám-ti sám-a jasím jasím-u ‘to put’
B3 a. Prototypical higdíl higdál-ti higdíl-a jagdíl jagdíl-u ‘to enlarge’
b. V-initial heír heár-ti heír-a jaír jaír-u ‘to wake’
c. V-final A him>tsí him>tsé-ti him>tsí-a jam>tsí jam>tsí-u ‘to invent’
d. V-final B hifná hifné-ti hifnet-á jafné jafn-ú ‘to direct’
The prototypical sub-class, traditionally called gizrat hashlemim ‘the sub-class of
the wholes’, defines the structure of the entire class because it is prosodically intact,
i.e. it has no missing or additional syllables or sub-syllabic units. In addition, the
vocalic pattern in this sub-class is primal, i.e. free of the (mostly historical) effect of
neighboring consonants or empty prosodic positions.
Below is the number of sub-classes (a) and verb paradigms (b) in each verb class
(binyan), as well as the number of verbs in the proto-typical sub-class (c). The numbers
refer to normative forms, based on 3,600 fully conjugated verbs presented in
Tarmon and Uval (1998). In our database, we excluded the passive verbs derived by
replacing the stem vowels with the vocalic pattern {u a} (Bat-El 1994), as in hixnís
– huxnás ‘to put in Past Active–Passive’ and xibér – xubár ‘to connect Past Active–
Passive’. Therefore our database consists of 2,952 verbs.
(9) Distribution of classes and sub-classes (normative Hebrew)
B1 B2 B3 B4 B5 Total
a. Sub-classes–
Inflectional classes
45 22 25 10 7 109
b. Verb paradigms 719 328 527 861 515 2952
c. Verb paradigms in the
prototypical sub-class
226 120 237 654 369 1606
% (c/b) (31.4 %) 36.6 % (45.0 %) (76.0 %) (71.7 %) (54.4 %)
280 G. Zadok, O. Bat-El
The prototypical sub-class in each binyan is the largest one, hosting more verbs
than any other sub-class within the class. Consider B1 below, the richest binyan in
terms of sub-classes, with 719 verbs distributed among 45 sub-classes.8 The top five
sub-classes on the list, which constitute 11 % (5/45) of the sub-classes, host 68 %
(489/719) of the verbs. The distribution is provided below (the sub-classes are identified
by their 3rd person Past—Future templates).
(10) The top 5 most frequent sub-classes of B1
Sub-class Paradigm (#)%of verb paradigms
a. CaCaC – -iCCoC sagár – jisgór ‘to close’ (226) 31 %
b. CaCaC – -iCCaC gadál – jigdál ‘to grow’ (85) 12 %
c. CaaC – -iCaC Saál – jiSál ‘to ask’ (87) 12 %
d. CaCa – -iCCe kaná – jikné ‘to buy’ (47) 7 %
e. aCaC – -aaCoC avád – jaavód ‘to work’ (44) 6 %
Total (489) 68 %
The first two sub-classes, (10a) and (10b), are minimally distinct; they are prosodically
identical, differing only in the quality of the vowel in suffixless future forms. In
suffixed future forms the distinction is neutralized, since the vowel in the final stem
syllable, either o or a, is replaced with e (e.g. jisgór – jisgerú ‘he–they will close’,
jigdál – jigdelú ‘he–they will grow’). Other sub-classes diverge from the prototypical
one to a greater extent, both in the number of different properties and the number of
different forms in the paradigm.We attend to this divergence in detail, as we approach
the discussion on similarity between paradigms.
Unlike the division into verb classes (binyanim), the division into sub-classes
(gzarot) does not have grammatical or semantic function. Verbs are distributed among
sub-classes within a particular binyan only on the basis of the structural properties
of the forms in their paradigm. Therefore, inter-paradigm leveling, occurring only
among sub-classes of the same binyan, has no effect on the grammatical function
of the verbs. This restriction is independent of the model we propose in the ensuing
sections. Inter-paradigm leveling among paradigms of different binyanim is rare for
two reasons: (a) it affects the grammatical function of the verbs involved (see Laks
2011), and (b) the classes are not similar enough to be open to migration among
them.
It is important to emphasize that we do not study here how irregular verb
paradigms become regular, or more accurately (after all, what is ‘regular’?), how
verb paradigms migrate towards the prototypical sub-classes. In some cases, as in
(11a) below, we see migration towards the prototypical sub-classes, but in others, as
in (11b), inter-paradigm leveling occurs between two non-prototypical sub-classes.
However, since class size plays a role in directionality (Sect. 4.2) and since the prototypical
sub-classes are the most populated ones (see (9) above), it may turn out that all
8Tarmon and Uval (1998) list 64 distinct B1 sub-classes. However, since we consider here the past and
future tenses only (ignoring the present, imperative, and infinitive), we end up with 45 distinct sub-classes.
Inter-paradigm leveling in Hebrew verbal system 281
verb paradigms within a class will end up within the proto-typical sub-class. But this
may not be the only possible scenario. At any rate, other things being equal (which is
never the case), our model predicts an end-state with one sub-class per binyan.
(11) Regular and irregular verbs
Apparently, most of the migration is currently among the non-prototypical subclasses.
2.2 Variation and change in the Hebrew verb system
While the organization of Hebrew verbs into binyanim is relatively stable, the division
among sub-classes suffers from a great degree of change-oriented variation, i.e.
variation indicating an ongoing change in the verbal system. The variation has been
reported in various studies, such as Schwarzwald (1981) and Diskin-Ravid (1995),
and the quantitative data supporting it in the present study consists of 2964 tokens
obtained from natural speech (Zadok 2012).
As it is usually the case, the variation is due mostly to opacity, and the source of
the opacity can be found in the history of the language. Hebrew verb paradigms are
drawn from earlier stages of the language, where morpho-phonological alternations
were systematically conditioned by phonological properties (prosodic and segmental).
However, while adopting the paradigms, Hebrew failed to adopt many of the
phonological properties that conditioned the alternations. Consequently, quite a few
morpho-phonological alternations in Hebrew paradigms lack phonological environment,
and are thus opaque.
One of the major causes of opacity is segmental merger, as in the case of P and Q,
which merged into P and more often null.
(12) Segmental merger: Loss of P–Q contrast
Stage A B
-eeCoC
Future 3sg.
-aaCCFuture
3pl.
-aaCoC
Future 3sg.
-aaCCFuture
3pl.
I P Q jePesóf jaPasf-ú jaQavór jaQavr-ú
II P/Ø je(P)esóf ja(P)asf-ú ja(P)avór ja(P)avr-ú
III Ø jaasóf jaasf-ú jaavór jaavr-ú
‘to collect’ ‘to pass’
282 G. Zadok, O. Bat-El
In Biblical Hebrew (for the sake of argument, stage I), P and Q triggered different
morpho-phonological alternations. Normative Modern Hebrew (stage II) adopted
this morpho-phonology, but not its trigger, since the distinction between P and Q
has been lost.9 Consequently, the morpho-phonological alternations became opaque.
The next step, on-going in Spoken Israeli Hebrew (stage III), is inter-paradigm leveling
(as well as intra-paradigm leveling in this case), whereby the verb paradigm
of ‘to collect’ migrates from its original sub-class (A) to the sub-class hosting the
verb paradigm ‘to pass’ (B). There are 15 verb paradigms in the sub-class hosting
‘to collect’, and when all will eventually defect, this sub-class will be extinct and
the consequent reduction in the number of sub-classes will contribute to the simplification
of the verbs system. Since the two verb paradigms in (12) belong to the same
binyan (B1), the structural distinction between their sub-classes, as noted above, does
not have a grammatical or semantic function. Therefore, the reduction in the number
of sub-classes is a pure improvement in the grammar, without impinging on anything
else.
Another dominant source of opacity is the loss of contrast between geminates and
singletons (as well as short vs. long vowels). Given the important role of the prosodic
structure in Hebrew morphology, the prosodic change from geminates to singletons
had a great effect on morpho-phonology (see also Bat-El 2008).
(13) Prosodic merger: Loss of geminate–singleton contrast
Stage A B
CaCaC
Past
-iCaC
Future
CaCaC
Past
-iCCaC
Future
I /nC/→CiCi naSáx jiSSáx gadál jigdál
II CiCi » C naSáx jiSáx gadál jigdál
III C » nC naSáx jinSáx gadál jigdál
‘to bite’ ‘to grow’
The two paradigms A and B in (13) were prosodically identical during stage I, though
sub-class A had a geminate, due to a synchronic process of n-assimilation (/jinSáx/
→ jiSSáx). With the loss of geminate–singleton contrast during stage II, these two
paradigms became prosodically distinct, where B is the prototypical one (<gadál–
. . . –jigdál>) and A has a missing stem consonant in all Future forms (<naSáx–. . . –
jiSáx>). Change-oriented variation (jiSáx ∼ jinSáx) is observed at the current stage
III, signifying that (<naSáx–. . . –jiSáx> is migrating to the sub-class of <gadál–. . . –
jigdál>, thus changing to <naSáx–. . . –jinSáx>. Note that the missing stem consonant
is recovered in the future forms since it surfaces in the past forms. No such recovery
is possible otherwise, i.e. we do not expect to recover a third stem consonant in one
of the forms in <Sar–. . . –jaSír> ‘to sing’ since there is no form in the paradigm of
9Actually, Bolozky (2003) shows that the distinction between P and Q has been a bit fragile already in
Biblical Hebrew. This is evident by a few words, which are spelled with the letter corresponding to P in
some places and with the letter corresponding to Q in others.
Inter-paradigm leveling in Hebrew verbal system 283
this verb where a third consonant surfaces. A third consonant may appear if this
verb serves as the base for deriving a new verb, since three or four stem consonants
coincide with bisyllabicity, which is one of the constraints defining verb forms in
Hebrew (Bat-El 1994; Ussishkin 1999).
Unlike in (12), the migration in (13) is towards the prototypical sub-class, but as
we argue in subsequent sections, this is a consequence of similarity and class size,
rather than the cause. That is, verb paradigms do not migrate from sub-class A to
sub-class B because B is prototypical, but rather because B is more similar to A than
any other sub-class and the size of B is larger than that of A (size often correlates
with prototypicality).
All the variation cases discussed in this paper are change-oriented, where the variation
indicates an on-going migration. Of course, the various sub-classes are at different
places in the migration process, but we do not address this issue here. For the
purposes of the present study, all paradigms are still in the process of migration and
thus exhibiting change-oriented variation. The loss of phonological cues for sub-class
classification forces speakers to memorize and/or regularize. Memorization is partial
and not stable, and regularization comes in the form of inter-paradigm leveling. When
faced with a less frequent verb, speakers search for a similar, more familiar verb. They
may find one in the same sub-class or in a similar sub-class. In the latter case, they
essentially reassign the verb to a new sub-class, resulting in paradigm migration (see
also fn. 10).
3 Paradigm similarity
We concentrate in this study on the development from two similar verb paradigms
(stage II) to two identical ones (stage III), granting similarity a major role in the
process. We argue that a verb paradigm migrates from sub-class A to sub-class B
because the two sub-classes have similar patterns. Similarity is of course gradient,
and thus the greater the similarity between two sub-classes the greater their chance
to interact in inter-paradigm leveling.
Consider the examples below, where the two paradigms in each pair (sub-classes A
and B) are at least intuitively similar (differences are underlined). In (14a), corresponding
forms (having identical clusters of morphological features) in sub-class A
and B are structurally identical, with the exception of the suffixless stems, which
differ in the quality of the vowels ([. . . ee . . .] vs. [. . . aa . . .]). In (14b), the only difference
between the two paradigms is in the quality of the vowel in the first syllable
in each and every form ([. . . e . . .] vs. [. . . i . . .]). Inter-paradigm leveling, whereby
the whole paradigm migrates (}») from sub-class A to sub-class B, eliminates these
dissimilarities.10
10A reviewer noted that a whole paradigm migration entails that for a given speaker all forms change at
once. This is not entirely accurate since speakers may use the old paradigm in high-register contexts and
the new one in casual contexts. Hyper-correction in high-register contexts make the situation even more
complex. As long as there is variation, it is impossible to “prove” that the entire paradigm migrates; the
only proof is in the end-state. We predict that the end state will consist of fewer sub-classes, but we have
to wait several generations to prove it right.
284 G. Zadok, O. Bat-El
(14) Inter-paradigm leveling11
a. B1 Future paradigms (Past paradigms are identical)
b. B4 Past paradigms (Future paradigms are identical)
As in the English and Latin examples in Sect. 1, (14a) could be either inter- or intraparadigm
leveling. (14b), however, must be a case of inter-paradigm leveling since
there is no form with i within the paradigm that can serve as a model for a paradigm
internal change. As shown in the table below, since some verb paradigms, like (14a),
exhibit inter- and intra-paradigm leveling and others, like (14b), exhibit only interparadigm
leveling, we consider all cases as inter-paradigm leveling. There are no
cases of intra-paradigm leveling alone, as this would imply a creation of a new subclass.
(15) Migration distributed by leveling type
Inter only Inter & Intra Total migrating verbs Total verbs
B1 26 38 64 719
B2 26 22 48 328
B3 491 0 491 527
B4 141 65 206 861
B5 8 41 49 515
The highest degree of similarity, or null degree of dissimilarity between two
paradigms means identity, and identical paradigms belong to the same sub-class.
11For independent reasons, which are not relevant here, the normative 1st person singular Future form has
been replaced with the 3rd person singular. In order to avoid further complexity, we do not use the PVprefix
of the normative 1st person singular form.
Inter-paradigm leveling in Hebrew verbal system 285
When two paradigms are only “a bit” dissimilar, they must belong to two different
sub-classes. However, their high degree of similarity causes speakers to confuse
them, and the more speakers confuse them, the more likely they are to undergo interparadigm
leveling.
The notion of similarity has been addressed in various contexts, in particular with
reference to segmental similarity (Pierrehumbert 1993; Frisch 1996; Cohen 2009).
Here we study paradigm similarity, asking what makes two paradigms similar, or
more precisely, how do we quantify similarity between paradigms?
We respond to this question in the following subsections, where we specify the
objects and properties required to evaluate similarity (Sect. 3.1), introduce our model
of similarity quantification (Sect. 3.2), and provide evidence supporting our model
(Sect. 3.2).
3.1 Objects and properties of similarity
As described in Sect. 2, verb configurations in Hebrew are defined in terms of
prosodic structure (C and V slots would do for the present purpose), vocalic patterns,
and derivational prefixes. Out of these properties, the vocalic pattern and the
prosodic structure of the stem are most relevant for evaluating similarity.
(16) Elements relevant for quantifying similarity (irrelevant elements are grayed
out)
Elements that are always identical or always different do not contribute to evaluating
similarity. These include the derivational prefix of the binyan, which appears in all
its sub-classes, and the inflectional suffixes, which are identical for comparable forms
(i.e. forms sharing the cluster of morpho-syntactic features). The stem consonants are
always different, and thus do not contribute to evaluating similarity.
As for the objects of similarity, we have already emphasized that it is not sufficient
to refer only to the pairs of words involved in the leveling. Rather, similarity
is evaluated with reference to whole paradigms. Comparing verb paradigms should
be straightforward, as most paradigms, being inflectional, have the same number of
members and the same categories (tense, gender, number, person). Thus, when we
compare sub-classes A and B, we compare all the comparable pairs. As noted earlier,
we compare here only finite verbs, thus circumventing debates regarding the coherence
of non-finite forms in the verb paradigm.
3.2 Quantifying paradigm similarity
Membership in a specific verb class (binyan) necessarily means a certain degree of
similarity among its sub-classes. Nevertheless, the surface variation exhibited within
286 G. Zadok, O. Bat-El
each binyan, and more specifically the surface variation that is notably unattested
within the binyan, suggests that the interaction of sub-classes is not random. If surface
variation is attested between A and B, but not between A and C (where A, B, and C
are sub-classes within a particular binyan), this suggests that A&B are more similar
than A&C. Similarity, therefore, must be quantifiable.
In order to evaluate the degree of similarity of two paradigms, we sum up the
number of dissimilar properties found in each comparable pair. We take pairs of
forms, one from each paradigm, such that the members in each pair are from the same
paradigm cell, i.e. they match in tense, gender, number, and person. For each pair we
evaluate differences in the two relevant phonological properties: vowel quality and
the presence vs. absence of a prosodic slot. The quality of the stem consonants, as
noted above, is not relevant (thus grayed out below), and so are the prefixes and
suffixes.
The following is an example of how similarity between forms can be measured.
Each difference between comparable forms counts as a single unit of dissimilarity
(1).12 The dissimilarity units are summed up and the sum, marked by delta ( )
determines the degree of similarity (or difference). This sum is compared among
competing paradigm pairs (sub-classes within the same binyan), resulting in a scale
of similarity; the smaller the difference, the greater the similarity.
(17) Quantifying similarity (partial paradigms)
The evaluation of the three partial paradigms in (17) reveals that A&B are more
similar than A&C, which in turn are more similar than B&C. If these were whole
paradigms, we would predict that out of the three paradigms, A and B have a higher
chance of undergoing inter-paradigm leveling.
For evaluating the degree of similarity between inflectional paradigms in Hebrew,
we take into consideration finite verb forms (thus excluding infinitives and participles).
Every paradigm includes 16 members divided between two tenses, where each
tense has 8 members, 5 singular and 3 plural. For each bundle of morph-syntactic
features (tense, number, person, and gender), i.e. for each cell in the paradigm, we
take the two comparable members, one from each paradigm (placed one below the
other).
12The model would work equally well if we counted similarities rather than dissimilarities. It is, however,
easier to count dissimilarities because we measure distance from identity ( 0).
Inter-paradigm leveling in Hebrew verbal system 287
(18) Measuring paradigm similarity: Example of whole paradigms
The two properties of the stem, prosodic structure and vocalic pattern, are sufficient
for evaluating similarity in Hebrew verb paradigms. However, other languages, or
other paradigms within the same language, may employ different or additional properties.
Given what we know about the prominence of prosodic structure, stress could
be relevant, such that two segmentally identical syllables are more similar if they
have the same prominence. Likewise, syllabic position could be relevant, such that a
missing C slot weighs more in onset position than in coda position, or in a stressed
syllable than in an unstressed syllable. Such additional properties are not relevant to
our data, but the model we propose can be enriched with more or different properties.
To highlight this avenue of research, consider the notion of variegated similarity
introduced in Albright and Hayes (2003).
288 G. Zadok, O. Bat-El
(19) Variegated similarity
Words a-d in (19) are equally dissimilar from splIN in two dissimilarity units each,
one for a missing consonant and another for a different consonant (note that unlike
in Hebrew, the consonants in English are relevant for measuring similarity). For Albright
and Hayes (2003), who study English past tense, (19a–d) is a collection of
structured similarities that can be expressed with rules. It is however possible that for
some systems, similarity would need to be further tuned with weight for each similarity
rule. For example, a rule referring to word final consonant weighs less/more
than a rule referring to word initial consonant, due to the different degrees of positional
prominence. While this can be further elaborated in different directions, the
data studied in this paper requires a simple similarity measure.
3.3 Evidence supporting the model
Having established how to measure similarity between paradigms, we now lay down
the evidence supporting our claim that the more similar two paradigms are the greater
their chances to merge via migration.
In (20) below we provide examples of verb paradigms (represented by a single
member) from sub-classes A, B, and C within each class. For each triplet, we show
that a verb paradigm migrates from sub-class A to sub-class B, rather than sub-class
C, where migration correlates with similarity; the dissimilarity value of A&B is always
lower than that of A&C, i.e. A&B are more similar than A&C.
The current reality of paradigm migration is change-oriented variation, which indicates
inter-paradigm leveling. In B1, for example, the normative jinák varies with,
thus changing to jinók rather than to *janúk, because the sub-class of jinák (A) is
more similar to that of jipól (B) than to that of jakúm (C), 6 vs. 30 respectively.
(20) Whole paradigm similarity measurement ( ) and change-oriented variation
(»)
Sub-class A Sub-classes B & C Sim. Migration
B1: jinák ‘suck’ B. jipól ‘will fall’ 6 jinák » jinók
C. jakúm ‘will get up’ 30 *janúk
B2: nexsáf ‘be exposed’ B. nixnás ‘entered’ 15 nexsáf » nixsáf
C. nosád ‘was established’ 26 *noxsaf
B3: hisí ‘marry’ B. heví ‘brought’ 8 hisí » hesí
C. hiká ‘hit’ 12 *hisá
B4: gerá ‘tease’ B. nisá ‘attempted’ 8 gerá » girá
C. milé ‘filled’ 15 *giré
B5: hitmalé ‘be filled’ B. hitkasá ‘covered oneself’ 2 hitmalé » hitmalá
C. hitkoféf ‘bent’ 43 *hitmolé
Inter-paradigm leveling in Hebrew verbal system 289
It is important to emphasize that the model accounts for similarity being a relative
term. For example, 15 is sufficient for inter-paradigm leveling in the B2 nexsáf –
nixnás pair in (20), but not in the B4 gerá – milé pair, because in the latter case,
but not in the former, there is a more similar pair. The absolute number indicating
the distance between two paradigms is therefore not the most crucial indicator. What
determines whether or not inter-paradigm leveling will take place is whether or not
a more similar paradigm exists. This is what makes the notion of similarity relative.
That is, a paradigm migrates from sub-class A to sub-class B, rather than to sub-class
C because A and B are more similar than A and C.Without external intervention (e.g.
borrowing, sound change, etc.), the model predicts an end stage of a single sub-class
per class. However, the chances of this happening in reality are quite low because
language does not exist in a vacuum.
4 Directionality
So far, we have established the role of similarity in inter-paradigm leveling. In the
ensuing discussion we take the interaction between sub-classes A and B as a given,
and concentrate on the factors determining the direction of migration. We present
each paradigm with a pair of forms, where one of the forms exhibits the changeoriented
variation.
4.1 Types of directionality
Within the context of change, directionality refers to the migration path of verb
paradigms. Do paradigms migrate from sub-class A to B or from B to A? Furthermore,
since a sub-class can host several verb paradigms, directionality may be mixed.
Indeed, we identify two major types of directionality in inter-paradigm leveling (see
Zadok 2012 for a third marginal type, called multi-path).
(21) Directions of migration
a. Unidirectional migration (A ⇒ B)
Given sub-classes A and B, paradigms migrate from A to B and not
vice versa.
b. Bidirectional migration (A B)
Given sub-classes A and B, some paradigms migrate from A to B and
other paradigms migrate from B to A.
In unidirectional migration, there are paradigms migrating from A to B, but there
are no paradigms migrating from B to A. From the perspective of each of the two
sub-classes, members either defect or are admitted, but not both. For example, all
the 7 paradigms in sub-class A, represented in (22) below by <janák–. . . –jinák>,
are migrating to sub-class B (originally consisting of 17 paradigms), represented by
<nafál–. . . –jipól>, and there is no paradigm in sub-class B that migrates to A.13
13The 7 verb paradigms are: javáS ‘to dry (intr.), jasád ‘to establish’, jaáts ‘to advise’, jakád ‘to blaze’,
jarák ‘to spit’, jaráS ‘to inherit’.
290 G. Zadok, O. Bat-El
(22) Unidirectional migration (B1 past-future)
Unidirectional migration may lead to the extinction of a sub-class, and thus to a reduction
in the number of sub-classes in the system. This happens when the following
two conditions are met:
(23) Conditions for the extinction of a sub-class (gizra)
Given sub-classes A, B and X, sub-class A will be extinct when
a. all paradigms hosted by A migrate to B, and
b. there is no paradigm hosted by X that migrates to A.
However, the second condition does not always hold, since a sub-class suffering from
defection may welcome other paradigms. This leads to a daisy chain migration, where
members from sub-class A migrate to sub-class B and members of sub-class B migrate
to sub-class C. That is, although verbs from B migrate to C, B survives since it
hosts verbs migrating from A. Sub-class A, however, will eventually disappear since
it does not receive new members.
(24) Daisy chain migration (B1 past-future)
Bidirectional migration is characterized by mutual migration, and therefore the two
sub-classes are preserved and variation is maintained. From the perspective of each
sub-class, members defect and new members are admitted such that both sub-classes
survive.
(25) Bidirectional migration (B4 and B5 past–future)
Inter-paradigm leveling in Hebrew verbal system 291
Since daisy chain migration is a multipart unidirectional migration, we are thus left
with two major types of directions. The question we address in the following section
is what determines whether migration is uni- or bidirectional. The answer to this
question involves class size.
4.2 Class size
Two questions are addressed in the context of directionality:
a. A ⇒ B or A B?
Given inter-paradigm leveling, what determines whether migration is unidirectional
(A ⇒ B) or bidirectional (A B)?
b. A ⇒ B or B ⇒ A?
Given unidirectional migration, what determines which paradigm wins, i.e.
whether paradigms migrate from A to B (A ⇒ B) or from B to A (B ⇒ A)?
For both questions the answer is class size (or type frequency of a class), i.e. the
number of verbs in the class. For question (a) it is the size ratio, while for question
(b) it the relative size. We start with (b).
4.2.1 Relative class size in unidirectional migration
In unidirectional migration, as shown below, the sub-class hosting more verb
paradigms wins. That is, paradigms migrate from sub-class A to B, and not vice
versa, because B hosts more paradigms than A.
(26) Class size in unidirectional paradigm migration14
Migration: A » B Sub-class A Size Sub-class B Size
B1: jinák » jinók jinák 7 jipól 17
‘to suckle’ ‘to fall’
B1: jeesóf » jaasóf jeesóf 15 jaavód 44
‘to collect’ ‘to work’
B2: nexkár » nixkár nexkár 26 nixnás 120
‘to be investigated’ ‘to enter’
B4: exér » ixér exér 38 gidél 654
‘to be late’ ‘to grow’
B4: gerá » girá gerá 1 nisá 51
‘to tease’ ‘to attempt’
14Differences are significant in all cases except B1, where the number of members in the paradigms is
probably too small to yield significance.
292 G. Zadok, O. Bat-El
It must be emphasized that paradigm uniformity does not play a role in determining
directionality, i.e. it is not the case that paradigms tend to desert the least uniformed
sub-class. Actually, in many cases the two paradigms interacting in inter-paradigm
leveling are uniformed to the same degree. For example, the two paradigms in (14b)
above have the same number of stem allomorphs (7 each).15 The fact that <gerá–
. . . –jegaré> ‘to tease’ is migrating to the sub-class hosting <nisá–. . . –jenasé> ‘to
try’ and not vice versa has thus nothing to do with paradigm uniformity but rather
with the size of the classes: the sub-class of <nisá–. . . –jenasé> hosts 51 paradigms
and that of <gerá–. . . –jegaré> hosts only one. In this respect we support Garrett’s
(2008) claim that inter-paradigm leveling (extension in his terms) is not driven by
paradigm uniformity, i.e. it is not necessarily the case that the uniformed paradigm
serves as the host for the changing paradigm.
The claim that the relative class size determines which sub-class wins in unidirectional
migration is consistent with earlier claims on four-part analogy. Hock
(1991:175) notes that four-part analogy “commonly draws words from one, often less
productive paradigm into another, often more productive one”. As Hock emphasizes,
“productivity is not an absolute, but a gradient phenomenon” (p. 174).
The literature refers to words migrating from one paradigm to another, rather than
paradigms migrating from one sub-class to another. If this were the only possibility,
then the role of class size could only be addressed with reference to unidirectional
migration. And yet, in the next sub-section we address class size in relation to bidirectional
migration.
4.2.2 Class size ratio determines the type of directionality
Given that migration can be uni- or bidirectional, the question addressed in this section
is what determines the type of directionality. Recall that in bidirectional migration
there is indeed migration towards the larger sub-class, as in unidirectional
migration, but there is also migration towards the smaller sub-class.
We argue that what determines whether migration is uni- or bidirectional is the
ratio of the sizes of the two sub-classes; large ratio leads to unidirectional migration
and small ratio to bidirectional migration. A small ratio means that the size of the two
sub-classes is not different enough to allow selecting an obvious winner. When the
ratio is high, the highly populated sub-class is easily identified and thus serves as the
sole host of migration.
The following table provides the size ratio of some comparable paradigms as well
as their actual directionality of change. In (27a) the size ratio of the hosting classes
is rather low and migration is bidirectional, while in (27b) the size ratio is high and
migration is unidirectional.
15The 7 allomorphs consist of 4 in Past (geri-, gera, gert-, ger- / nisi-, nisa, nist-, nis-) and 3 in Future
(agare, -egare, egar- / anase, -enase, enas-).
Inter-paradigm leveling in Hebrew verbal system 293
(27) Size ratio in uni- and bidirectional migration
a. Bidirectional migration (A B)
Size Ratio A Migration B
i. A ikír ‘to recognize’ (26)
1.65
ikír » ekír
B ekím ‘to found’ (43) ikím « ekím
ii. A heví ‘to bring’ (1)
3.00
heví » hiví
B hisí ‘to marry trans.’ (3) hesí « hisí
iii. A milé ‘to fill’ (12)
4.25
milé » milá
B gilá ‘to reveal’ (51) gilé » « gilá
iv. A hitmalé ‘to be filled’ (8)
5.12
hitmalé » hitmalá
B hitkasá ‘to be covered’ (41) hitkasá « hitkasé
b. Unidirectional migration (A ⇒ B)
Size Ratio A Migration B
i. A exér ‘to be late’ (38)
17.21
exér » ixér
B gidél ‘to raise’ (654) *gedél « gidél
ii. A sovév ‘to turn’ (38)
17.21
sovév » sivév
B ximém ‘to heat’ (654) *xomém « ximém
iii. A gerá ‘to tease’ (1)
51.00
gerá » girá
B nisá ‘to attempt’ (51) *nesá « nisá
iv. A jinzál ‘to drip’ (3)
75.33
jinzál » jinzól
B jisgór ‘to close’ (226) *jisgár « jisgór
Here we can provide additional evidence against the role of paradigm uniformity in
directionality (see also Sect. 4.2.1). Consider the two similar sub-classes, the one
including <itpaná–. . . –jitpané> ‘to clear intr.’ and the other including <itpalé–. . . –
jitpalé> ‘to be surprised’. These two sub-classes are very similar ( 2) and thus interact
in inter-paradigm leveling. Given the low size ratio of these two paradigms (5.12),
migration is bidirectional, although in terms of paradigm uniformity, one sub-class is
more uniformed than the other; the sub-class of <itpaná–. . . –jitpané> has four stem
allomorphs while that of <itpalé–. . . –jitpalé> has only two.16 If paradigm uniformity
played a role, we would expect unidirectional migration towards the sub-class hosting
<itpalé–. . . –jitpalé>.
4.2.3 Beyond size ratio
In light of the above argument, we consider in this sub-section two cases where the
prediction of size ratio is not born out.
16Stem allomorphs: pane-, pana, pant-, pan- / pale-, palP-.
294 G. Zadok, O. Bat-El
Cumulative size ratio We have argued above that bidirectional migration is limited
to cases of low size ratio. However, contrary to our prediction, one type of migration
in B3 is bidirectional regardless of frequency ratio. Examples of different frequency
ratios are given below.
(28) Bidirectional migration in B3 (regardless of size ratio)
Frequency Ratio A Migration B
i. igdíl ‘to enlarge’ (237)
13.94
igdíl » egdíl
exlít ‘to decide’ (17) ixlít « exlít
ii. im>tsí ‘to invent’ (10)
10.00
im>tsí » em>tsí
exbí ‘to hide’ (1) ixbí « exbí
iii. isí ‘to marry’ (1)
3.00
isí » esí
eví ‘to bring’ (3) iví « eví
iv. ikír ‘to recognize’ (26)
1.65
ikír » ekír
ekím ‘to found’ (43) ikím « ekím
In each of the pairs above, the first member begins with i and the second with e. For
both members we witness change-oriented variation; normative i varies with e (e.g.
hitxíl » hetxíl), and normative e with i (e.g. hexlít » hixlít). The general impression
might be that i » e is more common than e » i, but this is because 69 % (364/527) of
the normative B3 verbs have i in the first syllable.
One might argue that this is not a case of inter-paradigm leveling, but rather an
independent phonological variation. However, B4 and B5, like B3, have i in the first
syllable of Past forms, but this i does not vary with e; e.g. sipér ‘to tell B4’ (*sepér),
itkabél ‘to be received B5’ (*etkabél). The reason there is no migration in B4 and
B5 is because there are no sub-classes within B4 and B5 that have an e in the first
syllable.
We solve this problem by applying a cumulative ratio. Since the i − e distinction
divides most of the B3 sub-classes into two groups, it is possible that the size ratio is
calculated with reference to all sub-classes with i (364) and all the sub-classes with
e (139). In this case, the size ratio is relatively low (2.62), and thus, as expected,
migration is bidirectional.
Blocking The i − e distinction is found also in B2, where size ratio is also low
(3.84). With such a low ratio we would expect migration to be bi-directional; however,
it is unidirectional. For example, the paradigm <nexkár–. . . –jexakér> ‘to be
investigated’ is migrating into the sub-class hosting <nixnás–. . . –jikanés> ‘to enter’,
thus varying with the paradigm <nixkár–. . . –jixakér>. This migration is unidirectional,
as there is no new paradigms in the sub-class of <nexkár–. . . –jexakér>.
The unexpected unidirectional migration in this case is due to blocking, which
overrides the low size ratio predicting bidirectionality. The missing directionality
(i » e) would neutralize the contrast between the future paradigms of B2 and B4,
which minimally contrast in the vowel of the first syllable, i in B2 (jikanés ‘will enter’)
and e in B4 (jekanés ‘will gather’). This distinction is consistent in the entire
Inter-paradigm leveling in Hebrew verbal system 295
future paradigm. As the distinction among the binyanim has semantic and syntactic
functions, merger between them, even a partial one, is costly.
5 Final remarks
The role of similarity and class size in variation and change has been studied in numerous
works. Our paper further contributes to this field of research by addressing
paradigm similarity and providing a formal model with explanatory and predictive
power.
a. The similarity calculator explains why some sub-classes interact and others do
not. Within a stochastic approach, where variation is probabilistic, it could be argued
that the difference in similarity between comparable pairs denotes the probability
of their interaction (see Zadok 2012). Thus, a pair of sub-classes with similarity
value 10 is more likely to interact than a pair with similarity 21.
b. The class size calculator explains why some migration paths are bidirectional and
others are unidirectional. And within unidirectional migration, it predicts which
sub-class will survive and which will eventually become extinct.
Measuring similarity becomes more elaborate when the sub-classes are not tightly
defined as in Hebrew. This is demonstrated in Albright and Hayes (2003) for English
and Becker and Gouskova (2012) for Russian. Further phonological structure may
be taken into consideration and the phonological elements relevant for evaluating
similarity could be weighted. For example, do identical non-final stressed syllables
have less weight on the similarity scale than identical final unstressed syllables? Do
two syllables differing in onset have less weight on the similarity scale than syllables
differing in coda?
An independent issue that has not been addressed in this study is the pace of
migration, i.e. the pace of change. It has be argued that token frequency plays a role
in determining the pace of change (Bybee and Hopper 2001; Bybee 2001; Clark and
Trousdale 2009), such that high token frequency paradigms are expected to undergo
a change much slower. This would probably explain the advance stage of change
in the verb <navál–. . . –jiból> ‘to wilt’, which has change to <navál–. . . –jinból>,
as opposed to <nafál–. . . -jipól> ‘to fall’, which does not yet appear as <nafál–. . . -
jinpól>.
Acknowledgements This paper benefited from comments and suggestions contributed by the participants
of OCP 11, two anonymous reviewers, and the editor of Morphology. The usual disclaimers apply.
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