Frequency vs. iconicity in explaining grammatical asymmetries

Abstract

This paper argues that three widely accepted motivating factors subsumed under the broad heading of iconicity, namely iconicity of quantity, iconicity of complexity and iconicity of cohesion in fact have no role in explaining grammatical asymmetries and should be discarded. The iconicity accounts of the relevant phenomena have been proposed by authorities like Jakobson, Haiman and Giv贸n, but I argue that these linguists did not sufficiently consider alternative usage-based explanations in terms of frequency of use. A closer look shows that the well-known Zipfian effects of frequency of use (leading to shortness and fusion) can be made responsible for all of the alleged iconicity effects, and initial corpus data for a range of phenomena confirm the correctness of the approach.

Full text

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13. April 2005, F.-S.-Universität Jena
Iconicity versus frequency
in explaining grammatical asymmetries
MARTIN HASPELMATH
Max-Planck-Institut für evolutionäre Anthropologie
1. Introduction
"the intuition behind iconicity is that the structure of language reflects in
some way the structure of experience" Croft's (2003:102)
(1) Iconicity of quantity
Greater quantities in meaning are expressed by greater quantities of form.
Example: In Latin adjective inflection, the comparative and superlative
denote increasingly higher degrees and are coded by increasingly longer
suffixes (long(-us) 'long', long-ior 'longer', long-issim(-us) 'longest').
(2) Iconicity of complexity
More complex meanings are expressed by more complex forms.
Example: Causatives are more complex semantically than the
corresponding non-causatives, so they are coded by more complex forms,
e.g. Turkish düş(-mek) 'fall', causative düş-ür(-mek) 'make fall, drop'.
(3) Iconicity of cohesion
Meanings that belong together more closely are expressed by
more cohesive forms.
Example: In possessive noun phrases with body-part terms, the possessum
and the possessor are conceptually inseparable. This is mirrored in
greater cohesion of coding in many languages, e.g. Maltese id 'hand', id-i
'my hand', siġġu 'chair', is-siġġu tiegħ-i [the-chair of-me] 'my chair'
(*siġġ(u)-i).
• these three types of iconicity play no role in explaining grammatical
asymmetries of the type long(-us)/long-ior, düş(-mek)/düş-ür(-mek), id-i/is-siġġu
tiegħ-i.
• such formal asymmetries can be explained by frequency asymmetries:
In all these cases, the shorter and more cohesive expression types occur
significantly more frequently than the longer and less cohesive expression
types, and this suffices to explain their formal properties.
• Iconicity is not only not necessary, but also makes wrong predictions.
• I make no claims about other types of iconicity, such as
– iconicity of paradigmatic isomorphism (one form, one meaning, i.e.
synonymy and homonymy are avoided; Haiman 1980, Croft 1990a)
– iconicity of syntagmatic isomorphism (each form has a meaning, each
meaning has a form, i.e. empty and zero morphs are avoided; Croft 1990a)
– iconicity of sequence (sequence of forms matches sequence of
experiences; e.g. Greenberg 1963:103)
– iconicity of contiguity (forms that belong together semantically occur
next to each other)

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– iconicity of repetition (repeated forms signal repetition in experience, as
when reduplication expresses plurality or distribution).
• explanation vs. observation:
"The traditional view of language is that most relationships between linguistic units and
the corresponding meanings are arbitrary... But the cognitive claim is that the degree of
iconicity in language is much higher than has traditionally been thought to be the case."
(Lee 2001:...)
• What I am denying is that iconicity is playing a motivating role and
should be invoked in explaining why the patterns are the way they are.
• some authors (e.g. Givón 1985, 1991) seem to use the term "iconicity" as a
kind of antonym of "arbitrariness", so that almost anything about language
structure that is not arbitrary fals under iconicity.
2. Iconicity of quantity
2.1. Advocates and examples
(4) Greater quantities in meaning are expressed by greater quantities of form.
Jakobson (1965[1971:352]) and (1971), three examples:
(i) In many languages, "the positive, comparative and superlative degrees
of adjectives show a gradual increase in the number of phonemes, e.g. high-
higher-highest, [Latin] altus, altior, altissimus. In this way, the signantia reflect
the gradation gamut of the signata" (1965[1971:352]). The higher the degree,
the longer the adjective.
(ii) "The signans of the plural tends to echo the meaning of a numeral
increment by an increased length of the form" (1965[1971:352]). The more
referents, the more phonemes (e.g. singular book, plural books, French singular
je finis 'I finish', plural nous finissons 'we finish').
(iii) In Russian, the perfective aspect expresses "a limitation in the extent
of the narrated event", and it is expressed by a more limited (i.e. a smaller)
number of phonemes (e.g. perfective zamoroz-it', imperfective zamoraž-ivat'
'freeze') (Jakobson 1971).
(see also Plank (1979:123), Haiman (1980:528-9), Anttila (1989:17), and
Taylor's (2002:46) Cognitive Grammar textbook).
2.2. Frequency-based explanation
Any efficient sign system in which costs correlate with signal length will
follow the following economy principle:
(5) The more predictable a sign, the shorter it is.
Since frequency implies predictability, we also get the folloiwng prediction
for efficient sign systems:
(6) The more frequent a sign is, the shorter it is.
(well known at least since Horn's (1921) and Zipf's (1935) work)

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• universally comparative and superlative forms are significantly rarer
than positive forms of adjectives, and singular forms are significantly rarer
than plural forms (see Greenberg 1966:34-37, 40-41)
• for Russian, Fenk-Oczlon (1990) has shown that there is a strong
correlation between length and frequency of a verb form: in general, the more
frequent member of an aspectual pair is also shorter.
• the principle of iconicity of quantity makes many wrong predictions (as
was also observed by Haiman 2000:287):
– that plurals should generally be longer than duals,
– that augmentatives should generally be longer than diminutives,
– that words for 'ten' should be longer than words for 'seven', or even
– that words for 'long' should be longer than words for 'short', or
– that words for 'elephant' should be longer than words for 'mouse'
3. Iconicity of complexity
3.1. Advocates and examples
(7) More complex meanings are expressed by more complex forms.
some quotations from the literature that describe this principle and refer to it as "isomorphic"
or "iconic":
• Lehmann (1974:111): "Je komplexer die semantische Repräsentation eines
Zeichens, desto komplexer seine phonologische Repräsentation."
• Mayerthaler (1981:25): "Was semantisch "mehr" ist, sollte auch
konstruktionell "mehr" sein."
• Givón (1991:§2.2): "A larger chunk of information will be given a larger
chunk of code."
• Haiman (2000:283): "The more abstract the concept, the more reduced its
morphological expression will tend to be. Morphological bulk corresponds
directly and iconically to conceptual intension."
• Langacker (2000:77): "[I]t is worth noting an iconicity between of's
phonological value and the meaning ascribed to it (cf. Haiman 1983). Of all
the English prepositions, of is phonologically the weakest by any
reasonable criterion.... Now as one facet of its iconicity, of is arguably the
most tenuous of the English prepositions from the semantic standpoint as
well..."
often iconicity of complexity is described as a kind of "iconicity of markedness matching":
(8) Marked meanings are expressed by marked forms.
• Jakobson (1963[1966:270]): "language tends to avoid any chiasmus between
pairs of unmarked/marked categories, on the one hand, and pairs of
zero/nonzero affixes...on the other hand"
• Plank (1979:139): "Die formale Markiertheitsopposition bildet die
konzeptuell-semantische Markiertheitsopposition d[iagrammatisch]-
ikonisch ab."
• Haiman (1980:528): "Categories that are marked morphologically and
syntactically are also marked semantically."

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• Mayerthaler (1987: 48-9): If (and only if) a semantically more marked
category Cj is encoded as "more" featured [=formally complex] than a less
marked category Ci, the encoding of Cj is said to be iconic."
• Givón 1991: "The meta-iconic markedness principle: Categories that are
cognitively marked—i.e. complex—tend to also to structurally marked."
• Aissen 2003:§3: "Iconicity favors the morphological marking of syntactically
marked configurations."
see also Matthews (1991:236), Newmeyer (1992:763), Helmbrecht (2004:226)
"formally marked" = "expressed overtly"; typical examples of such
markedness matching:
(9) less marked/unmarked (more) marked
number SINGULAR (tree-Ø) PLURAL (tree-s)
case SUBJECT (Latin homo-Ø) OBJECT (homin-em)
tense PRESENT (play-Ø) PAST (play-ed)
person THIRD (Spanish canta-Ø) SECOND (canta-s)
gender MASCULINE (petit-Ø) FEMININE (petit-e)
causation NON-CAUSATIVE CAUSATIVE
(Turkish düş-Ø-mek 'fall') (düş-ür-mek 'fell, drop')
object INANIMATE ANIMATE
(Spanish Veo la casa Veo a la niña.
'I see the house' 'I see the girl.')
These universal formal asymmetries have been known since Greenberg (1966)
(who did not invoke iconicty to explain them!)
3.2. Iconicity of complexity: frequency-based explanation
Greenberg (1966): frequency asymmetries explain formal asymmetries:
– "less marked" forms are more frequent, and "more marked" forms are less
frequent across languages
• the English preposition of is not only the most "semantically tenuous", but
also the most frequent of all the English prepositions.
• not only sufficient to account for the relevant phenomena, but also
necessary, because iconicity of complexity makes wrong predictions:
(10) less marked/unmarked (more) marked
number PLURAL SINGULAR
Welsh plu 'feathers' plu 'feather'
case OBJECT CASE SUBJECT CASE
Godoberi mak'i 'child' mak'i-di (ergative)
person SECOND P. IMPERATIVE THIRD P. IMPERATIVE
Latin canta-Ø 'sing!' canta-to 'let her sing'
gender FEMALE MALE
English widow-Ø widow-er
causation CAUSATIVE NONCAUSATIVE
German öffnen sich öffnen
• in all these cases, frequency makes the right predictions!
• often: "markedness reversal"
• "unmarkedness" = 'frequency': "Marked" means "rare", and "unmarked"
means "frequent". Cf. Haiman (2000:287):

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"...what is fundamentally at issue is markedness. Where plurality is the norm, it is
the plural which is unmarked, and a derived marked singulative is employed to
signal oneness: thus, essentially, wheat vs. grain of wheat."
• what is fundamentally at issue is frequency, not markedness!
(see Haspelmath 2005 for further arguments why a notion of markedness is
superfluous in linguistics)
• Lehmann (1974) and Haiman (2000): grammatical morphemes are
universally shorter than lexical morphemes, and this iconically mirrors their
more abstract or less complex meaning.
• But again frequency and economy account for the same facts!
• Iconicity makes the wrong prediction that lexical items with highly abstract
or simple meanings should be consistently shorter than items with more
concrete or complex meanings (as noted by Ronneberger-Sibold 1980:239).
• It predicts, e.g., that entity should be shorter than thing or action, that animal
should be shorter than cat, that perceive should be shorter than see, etc.
3.3. The causative-inchoative alternation: Economy instead of iconicity
(Haspelmath 1993)
puzzle: the apparent counter-iconicity of anticausatives:
Russian otkryvat' otkryvat'-sja
'cause to open' 'open (intr.)'
Observation in Haspelmath 1993 (cf. also Croft 1990b):
different verb meanings behave differently across languages:
preferably coded as causatives: 'freeze', 'dry', 'sink', 'go out', 'melt', etc.
(spontaneous)
preferably coded as anticausatives: 'split', 'break', close', 'open', 'gather', etc.
(agent-caused)
Saving the iconicity hypothesis:
"Iconicity in language is based [not on objective meaning but] on conceptual
meaning... Events that are more likely to occur spontaneously will be associated
with a conceptual stereotype (or prototype) of a spontaneous event, and this will
be expressed in a structurally unmarked way." (Haspelmath 1993:106-7)
Simpler explanation:
Spontaneous verb meanings tend to occur more frequently as inchoatives;
agent-caused verb meanings occur more frequently as causatives. Due to
economic motivation, the rarer elements tend to be overtly coded.
cf. Wright (2001: 127-8):
% transitive
freeze 62% more causatives
dry 61%
melt 72%
burn 76%
open 80%
break 90% more anticausatives

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3.4. Differential object marking: Economy instead of iconicity
(Aissen 2003)
Observation (Blansitt 1973, Comrie 1981, Bossong 1985, 1998, etc.):
The higher a direct-object is on the animacy scale, the more likely it is to be
overtly coded (i.e. accusative-marked).
Comrie 1989:128: "...the most natural kind of transitive construction is one where
the A[gent] is high in animacy and definiteness and the P[atient] is lower in
animacy and definiteness; and any deviation from this pattern leads to a more
marked construction."
Aissen 2003:§3 proposes a constraint subhierarchy involving local conjunction
of a "markedness hierarchy" of relation/animacy constraints with a constraint
against non-coding (*ØCASE):
"markedness subhierarchy":
*OBJ/HUM >> * OBJ/ANIM >> *OBJ/INAN
local conjunction with *ØCASE:
*OBJ/HUM & *ØCASE >> * OBJ/ANIM & *ØCASE >> *OBJ/INAN & *ØCASE
"The effect of local conjunction here is to link markedness of content (expressed
by the markedness subhierarchy) to markedness of expression (expressed by
*Ø). That content and expression are linked in this way is a fundamental idea of
markedness theory (Jakobson 1939; Greenberg 1966). In the domain of
Differential Object Marking, this is expressed formally through the constraints
[shown immediately above]. Thus they are ICONICITY CONSTRAINTS: they favor
morphological marks for marked configurations." (Aissen 2003)
Simpler explanation:
Inanimate NPs occur more frequently as objects; animate NPs occur more
frequently as subjects. Due to economic motivation, the rarer elements tend
to be overtly coded.
4. Iconicity of cohesion
4.1. Advocates and examples
(11) Meanings that belong together more closely are expressed by more
cohesive forms
Haiman (1983:782-3): "The linguistic distance between expressions
corresponds to the conceptual distance between them."
(12) Haiman's (1983:782) cohesion scale
a. X word Y (function-word expression)
b. X Y (juxtaposition)
c. X-Y (bound expression)
d. Z (portmanteau expression)

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• "cohesion" preferable to "distance" (cohesion ≠ contiguity!); Newmeyer
(1992:761-2) and Givón (1985:202, 1991:89) conflate cohesion and contiguity)
examples:
(i) Possessive constructions:
Inalienable possession shows at least the same degree of cohesion as alienable
possession, because in inealienable possession (i.e. possession of kinship and
body part terms) the possessor and the possessum belong together more
closely semantically (Haiman 1983:793-5), e.g.
(13) Abun (West Papuan; Berry & Berry 1999:77-82)
a. ji bi nggwe 'my garden'
I of garden
b. ji syim 'my arm'
I arm
(ii) Causative constructions:
Causative constructions showing a greater degree of cohesion tend to express
direct causation (where cause and result belong together more closely),
whereas causative constructions showing less cohesion tend to express
indirect causation (Haiman 1983:783-7; cf. also Comrie 1981:164-7, Dixon 2000:74-8).
(14) Buru (Austronesian; Indonesia; Grimes 1991:211, cit. after Dixon 2000:69)
a. Da puna ringe gosa.
3SG.A cause 3SG.O be.good
'He (did something which, indirectly,) made her well.'
b. Da pe-gosa ringe.
3SG.A CAUS-be.good 3SG.O
'He healed her (directly, with spiritual power
cf. also English cause to die vs. kill
(iii) Coordinating constructions:
Many languages distinguish between "loose coordination" and "tight
coordination" (i.e. less vs. more cohesive patterns), where the first expresses
greater conceptual distance and the latter expresses less conceptual distance
(Haiman 1983:788-90).
(15) Fe'fe' Bamileke (Hyman 1971:43)
a. à kà gén ntēe nī njwēn lwà'
he PAST go market and buy yams
'He went to the market and also (at some later date) bought yams.'
b. à kà gén ntēe njwēn lwà'
he PAST go market buy yams
'He went to the market and bought yams (there).'
Wälchli (2005): noun phrase coordination ("accidental coordination" vs.
"natural coordination")
(16) Georgian
a. gveli da k'ac'i 'the snake and the man'
snake and man
b. da-dzma 'brother and sister'
brother-sister

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According to Haiman (1983), "conceptual dependence" also correlates with
cohesion ("The linguistic separateness of an expression corresponds to the
conceptual independence of the object or event which it represents."):
(iv) Complement clause constructions:
"The more integrated the two events are, the more likely is the complement
verb to be co-lexicalized—i.e. appear contiguously—with the main verb. The
less integrated the two events are, the more likely it is that a subordinating
morpheme will separate the complement clause from the main clause."
(Givón 1991:95-6; cf. also Haiman 1983:799, Cristofaro 2003)
(17) a. She let go of the knife.
b. She made him shave.
c. She told him to leave.
4.2. Iconicity of cohesion: frequency-based explanation
The cohesion scale is also found elsewhere in language structure:
(18) X Y X-Y Z
comparatives more arid dri-er worse
past tense play-ed went
negation doesn't see has-n't won't
gender lady doctor actr-ess nun
diminutive young elephant pig-let puppy
Explanation:
• The items that show greater formal cohesion are simply more frequent.
• High frequency is known to be a favorable environment for
– phonological fusion (e.g. hasn't vs. *knowsn't)
– preservation of older patterns (e.g. actress vs. *protectress)
– preservation/creation of suppletion (see Osthoff 1899, Ronneberger-Sibold 1988)
(i) Possessive constructions:
With inalienable possessed nouns, possessive constructions are of course
much more frequent than with alienable possessed nouns (cf. Nichols 1988).
Preliminary figures (from IDS Goethe corpus):
unpossessed
possessed
Gärtner 'gardener'
24
0
Jäger 'hunter'
48
2
alienab
le
Pfarrer 'priest'
12
0
Schwester 'sister'
32
58
Tante 'aunt'
47
22
inalien
able
Tochter 'daughter'
46
53
Table 1
• What counts is relative frequencies, not absolute frequencies: The
percentage of possessed occurrences of inalienable nouns will always be
significantly higher than the corresponding percentage of alienable nouns.
• Different predictions of the frequency-based explanation:

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(A) Frequency predicts that the pronominal possessor should tend to be
shorter in inalienable possession, whereas this is not predicted by iconicity.
(19) alienable construction inalienable construction
a. Nakanai luma taku lima-gu
(Johnston 1981:217) house I hand-1SG
'my house' 'my hand'
b. Hua dgai
ʔ
fu d-za
ʔ
(Haiman 1983:793) I pig 1SG-arm
'my pig' 'my arm'
c. Ndjébbana budmánda ngáyabba nga-ngardabbámba
(McKay 1996:302-6) suitcase I 1SG-liver
'my suitcase' 'my liver'
d. Kpelle
ŋ
a p
ɛ
r
ɛ
i m-pôlu
(Welmers 1973:279) I house 1SG-back
'my house' 'my back'
(B) Iconicity (Distance matching) predicts that the additional element in
alienable constructions should occur in the middle between the possessor and
the possessum, as seen in the canonical examples: Maltese is-siġġu tiegħ-i [the-
chair of-me] 'my chair', Abun ji bi nggwe [I of garden] 'my garden'.
• But the extra element may also occur to the left or right of both the
possessor and the possessum:
(20) alienable construction inalienable construction
a. Puluwat nay-iy hamwol pay-iy
(Elbert 1974:55, 61) poss-1SG chief hand-1SG
'my chief' 'my hand'
b. 'O'odham ñ-mi:stol-ga ñ-je'e
(Zepeda 1983) 1SG-cat-POSSD 1SG-mother
'my cat' 'my mother'
c. Koyukon se-tel-e' se-tlee'
(Thompson 1SG-socks-POSSD 1SG-head
1996:654, 667) 'my socks' 'my head'
The frequency-based account makes no prediction about the ordering, so this
is expected.
(C) Some languages show overt coding of alienable nouns as well:
(21) Koyukon unpossessed possessed
alienable teł se-tel-e'
socks 1SG-socks-POSSD
'socks' 'my socks'
inalienable k'e-tlee' se-tlee'
UNSP-head 1SG-head
'head' 'my head'

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(ii) Causative constructions:
Indirect/direct causative is difficult to study in corpora — verbs like kill, teach,
put, give, send, show are all direct causatives!
*make have: give
*make see: show
*make be: put
*make learn: teach
cf. *female brother: sister
*child woman: girl
*lower hand: foot
Morphological causatives must be more frequent than periphrastic causatives
(but no data available).
Frequency-based account makes a further prediction: markers of indirect
causation should not only be less cohesive, but should also tend to be longer
(cf. Dixon 2000:74-8)
(22) indirect causative direct causative
a. Amharic as-bälla a-bälla
(Haiman 1983:786, CAUS-eat CAUS-eat
Hetzron 1976:379) 'force to eat' 'feed'
b. Hindi ban-vaa- ban-aa-
(Dixon 2000:67, be.built-CAUS be.built-CAUS
Saksena 1982) 'have sth. built' 'build'
c. Jinghpaw -shangun sha-
(Dixon 2000, from Maran & Clifton 1976)
d. Creek -ipeyc -ic
(Martin 2000)
Dixon (2000): more semantic contrasts that are associated with longer/shorter
markers:
(23) longer marker shorter marker
action state
transitive intransitive
causee having control causee lacking control
causee unwilling causee willing
causee fully affected causee partially affected
accidental intentional
with effort naturally
Not all of these can be subsumed under "less conceptual distance", but they
can be plausibly related to frequency asymmetries.
(iii) Coordinating constrictions:
"Natural coordination" is presumably more frequent...
("natural" = "frequent")

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(iv) Complement-clause constructions:
[I discuss only same-subject vs. different-subject 'want' constructions here; cf.
Haspelmath 1999b]
Givón 1990: 560: “the degree of finiteness is an iconic expression of the degree
of integration of the main and complement events”
"Given a hierarchy of degree of finiteness (or its converse, degree of nominality) of verb forms found in
a language, the more integrated the two events are,
(i) the more noun-like is the complement verb likely to be, and
(ii) the less finite verbal morphology – such as tense-aspect-modality and pronominal agreement –
is the verb likely to display." (1990:561)
Cristofaro 2003: "At this stage, an iconic effect is obtained: states of affairs which are semantically
integrated, or conceptually close, are coded by morphosyntactically integrated structures."
• Different predictions of the frequency-based account:
(A) Complementizer may be shorter in same-subject constructions:
(24) Hopi (Uto-Aztecan) (Kalectaca 1978:170-71)
(SS) Pam as nös-ni-qe naawakna.
he PTCL eat-FUT-SS want
‘He wants to eat.’
(DS) Pam as nu-y nös-ni-qat naawakna.
he PTCL I-AKK eat-FUT-DS want
‘He wants me to eat.’
(B) the verb 'want' is sometimes shorter in same-subject constructions:
(25) Samoan (Oceanic) (Mosel & Hovdhaugen 1992:710, 714)
(SS) e fia si‘i e Leona Iosefa
GEN want carry ERG Leona Iosefa
‘Leona wants to carry Iosefa.’
(DS) e le mana‘o le teine e fasi ia le tama
GEN NEG want ART girl [GEN hit she ART boy
‘The girl doesn’t want the boy to hit her.’
5. Conclusion
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