Morphological Productivity of Yorùbá Numerals

 This article is published by the Zamfara International Journal of Humanities.

Abdullahi Bashir
Department of Languages & Cultures
Federal University Gusau, Zamfara State
abdulbakori2@gmail.com 08036481158

Abstract: This paper discusses the morphological productivity of Yorùbá numerals where some morphological processes such as clipping, blending, compounding and reduplication were analyzed. It is aim at displaying the arithmetic operation of Yorùbá numerals from complex to simple and or from long to short words. Observation technique was used in the process of data collection and based on word-based morphology theory. The result of the analysis shows that numerals in the Yorùbá language require some arithmetic exercise in a way that stimulates intelligence. It also found out that, the Yorùbá numeral has many structures of counting, unlike other languages. However, it observed that, the numerical system in general has lexical items that represent the base numbers which are characterized by various possible combinations to the cardinal numerical resources in order to build up an increasing system of counting by means of productive mechanism. Furthermore, the word-formation rules here perform a unique operation on the word base to produce a new word where both the new word and the base share a morphological and semantic relationship.

 

 Introduction

_Linguistic  analysis  reveals  that  words  have  an  internal morphological structure with bases and affixes recurring in different degrees, which may be associated with a common core of meaning. Affixes may also convey a meaning or sub-serve to a particular grammatical function or else according to the  cross  linguistic  variation  in  morphology.  The  study of morphology  offers  an  important  insight  on  how  language works, revealing the need for different categories of words, the presence of word-internal structure, and existence of operations that create and modify words in various ways (O’Grady and Guzman,  2011).  Similarly,  words  are  more  important  in language as they carry meanings that are fundamental building blocks of communication. In this paper, the morphological productivity in numeral formation has been discussed according to some processes that occur during the arithmetic operations in Yorùbá numerals. The concept of morphological productivity here, can be considered through some morphological processes, such as; clipping, blending, compounding and reduplication in accordance with the rules of word formation.

 

Background of the Study

 

Yoruba speakers have made a various contacts with the speakers of other languages through many factors, such as colonization, religion and trade due to their geographical location where the Yoruba people can be said to be self-supported, there are some highly valued commodities produced in one area and their demand is in other area.

 

Similarly, the trade in kola-nuts, grains, cattle or horses as well as other raw-materials helped to cause the migration of Yoruba people while the kola transportations to northern Nigeria from the Yoruba land for the need of elders and women. The counting system (i.e. addition, subtraction, multiplication etc) must be occurred between buyers and sellers during that transaction where the simple arithmetic of a language has been used. Moreover, the interpreters come for the interactions in order to simplify the complex numerals during the manipulations. The productivity of the numerals helps to learn the calculation in a simple way that this research focuses on.

 

Statement of the Problem

 

There are several morphological studies on Yoruba language. It is observed that the numerical system of our indigenous languages have been ignored and neglected and that most of them are becoming lexicalized or unproductive. This research intends to unravel the various features of numerals in Yoruba.

 

The Morphological Productivity

 

Productivity as a morphological phenomenon can be defined as a possibility where language users can form uncountable number of new words unintentionally by means of a morphological process which is the basis of the form-meaning and the correspondence of some words they know (Booij, 1977:4) cited in (Bauer, 2001:13). It deals with the number of new words that can be coined by using a particular morphological process and is ambiguous between the sense of ‘availability’ and ‘profitability’ (Bauer, 2001:211). He also pointed out that, “The availability here relates to a morphological process that is potential for repetitive rule-governed morphological coining, either in general or in a particular well-defined environment or domain. It is determined by the system of a language while the profitability of a morphological process reflects the extent to which its availability is exploited in language use, and may be subjected to extra-systemic factors. In this case, a single morphological process has easily distinguishable meanings or sub-uses which may be assessed independently for both availability and profitability” (Bauer, 2001:211). This means that the bases are useful to create another words as well, the existing word can also be modified to create another word through one of the word formation processes. So, in any language, morphological rules must be considered to form a new word. The interaction of availability and profitability in morphological productivity is to constrain the number of words in the lexicon of the individual speaker which are coined according to the pattern provided by any particular morphological process.

 

The notion of productivity must make reference to the speaker’s ability to form new words and to the conditions the language system imposes on new words. In other words, one morphological theory can make predictions in which words are possible in a language and which words are not. These assume that the existence of morphological rules according to which complex words are structured or formed can easily observe that some rules are often used to create new words. In another view, “the degree of productivity of a word formation rule can be seen as inversely proportional to the amount of competence that restricted to the word formation rule” (Booij, 1977:5) in (Bauer, 2001:12). In this position, we can find out that the word formation rule has its proper restrictions where the degree of productivity would naturally fall out. In view of this, the word formation rules have to be considered when forming a new word by any other process of morphology.

 

Theoretical Framework

 

Aronoff (1976) posits a theory which states that a new word is formed from another word through the operation of devices which he terms as “Word Formation Rules” (henceforth WFRs. The WFRs perform a unique operation on the base (which is a word) to produce a new word where both the new word and the base share morphological and semantic relationships while the meaning of the derived word is compositional, including part or all of the meanings of the existing word and the affix. For example, the WFR # ish can produce the adjective ‘foolish’ from the noun ‘fool’ therefore is the base of the operation of the WFRs while the morphological operation involves the suffixation of # ish to the base ‘fool’.

 

The theory of Word Formation by Aronoff (1976:82) is used to analyze the data of this research. Theory of word-based morphology also argues that productive processes of derivational morphology do not seem to operate over anything other than words, where some words cannot be morphologically productive unlike other numerals as in (èèwéwa*, èèjéjo*, èèrérin*, as opposed to èèjééji and èèréérin) as the case of full and partial reduplication of Yorùbá numerals. The most important feature of Aronoff’s theory is the assumption of word formation rules called word-based morphology that operates on words but not morphemes. However, among the forms and functions of these rules are bases (words). For instance, according to the WFR, the suffix – la can produce the higher denomination of the Yorùbá numeral mèjìlá ‘twelve’ from the base mèjì ‘two’. Therefore, the word-based is under the WFR while the morphological operation involves the suffixation of -la to the base. Examples:

 

[mèjì] numeral=  base  ‘two’

 

[(mèjì) numeral (-lá)] bound morpheme = mèjìlá ‘twelve’.

The Numerical System

 

Numerals are among the first steps of learning a new language. The acquisition of numeracy starts from the counting base of the language that depends on the structure of a language (Mbah and Uzoigwe, 2013:73). Numerals are uniform because in many natural languages they comprise simple and complex expressions. Simple numerals are the easily conceivable set of numerical expression in a language (e.g. one, two, three, four, etc.). However, the simple numbers are preferred for having a ‘cyclic’ pattern of atoms that cannot be separated and also morphologically derived to form the complex elements of numerals that have the highest potential to make a continuous counting in each language. These can be in the form of addition, subtraction and multiplication. All human languages count things because numeration is a universal phenomenon (Omachonu, 2013). Furthermore, numeral systems of human languages differ in organization, mode of reduplication of higher numbers based on ones that are more basic and the grammatical devices utilized in the realization of counting. At times, the differences in the numeral systems of languages are based on the significant needs basically motivated by demands on what needs to be counted and at other times, they are simply based on the nature of language, hence more philosophically explained beyond certain systematic reasons for variations that may be adduced (Ejeba, 2013). A numeral is a written sign or symbol that is used to represent a number while numeral system or numbering system is a set of symbols, identifying or expressing the quantity/quantities of something, determining order or position, comparing amounts, performing calculations, and representing value (Prezi, 2013:245). Generally, a numeral can be described as a sign, mark or symbol used to represent a number. Even though, numeral system is a written system for expressing numbers, in linguistics, numerals are specific words in a natural language that represent numbers (Obikudo, 2013:27).

 

The Hausa Numeral System

 

Amfani (2013:239) states that “The Hausa traditional numeral system uses base ten for counting. Thus, Hausa has basic numerals one to ten and subsequent numeration’’ i.e. eleven upward, is achieved through the manipulation of the basic numerals one to ten which are as follows:

 

1. ɗaya ‘one’, 2. biyu ‘two’, 3. ukù ‘three’, 4.

 

huɗu ‘four’, 5. bìyar ‘five’, 6. shidà ‘six’, 7. bakwài ‘seven’, 8. takwàs ‘eight’, 9. tarà ‘nine’, 10. góomà ‘ten’.

 

Counting from 11 to 19 is achieved in Hausa through the addition of each of the basic numerals 1-9 to the basic numeral 10 by using the morpheme shâa. Amfani (2013:240) cites the counting as follows:

11 = goomà shâa ɗaya, 12 = goomà shâa biyu,

 

13 = goomà shâa ukù, 14 = goomà shâa huɗu, 15 = goomà shâa bìyar, 16 = goomà shâa, shidà, 17 = goomà shâa bakwài, 18 = goomà shâa takwàs, 19 = goomà shâa tara.

(Amfani, 2013:241).

 

The Igala Numerals

Omachonu (2013:136) indicates that, the Igala numerals are

categorized into two broad groups: the basics numerals (1 to

 

10, 20, 50, 200, 400 and 800) and the derivatives or non-basic

whose derivational history is traceable to a combination of the

basic  numerals  through  some  addition,  multiplication  or  a

 

combination of both processes. The basic numerals in Igala are

in two forms as follows:

i. Basic numerals; 1 to 10:

 

1- okà ‘one’, 2- èjì ‘two’, 3- ètā ‘three’, 4- èlè ‘four’, 5- èlu ‘five’, 6- èfe ‘six’, 7- èbie ‘seven’, 8- èjo ‘eight’, 9- èla‘nine’ 10- ègwa ‘ten’.

ii. Other numerals; (20, 50, 200, 400 and 800):

 

20 - ogwu/ogbo ‘twenty’, 50 - ooje ‘fifty’ etc. Moreover, the higher denominations of arithmetic operations in Igala numerals are derived from these two sets of the base numerals. Examples:

 

12 - egweji ‘twelve’, 15 -         egwelu ‘fifteen’,

 

19 - egwela ‘ninteen’, 21 - ogwuɲokeka ‘twenty one’, 23 - ogwuɲokemeta ‘twenty

three’, 27 - ogwuɲokemebie ‘twenty seven’ etc.

 

It has also observed that there are simple and complex words in Igala numeral system where the complex ones are derived from the simple (base) 1 to ten while others are also derived from the second sets unlike in Hausa and Yoruba where the higher numerals are derived from the ten-base only.

 

The Nupe Numerals

 

Alkali (2010:20) defines Nupe numerals as simple and complex which consist of many morphological features. He further explains that the system starts from the two sets of their base numerals which include 1 to 5 as first set while the second set starts from 6 to 10. These show that the Nupe counting system consists two groups of basic numbers from where the higher numbers are extracted, unlike in Hausa and Yoruba numeral systems where they have only one set or group each (i.e. 1 to

10)as follows:

 

1 - 5

1 –inni ‘one’, 2 – guba ‘two’, 3 – guta ‘three’,

 

4 – gunni ‘four’, 5 – gutsun ‘five’

 

However, the other numerals here in the second group are derived from the first set as follows:

 

6–10

6 – gutswayin ‘six’, 7  – gutwaba  ‘seven’,

8  –  gutwota  ‘eight’,  9  –  gutwaani  ‘nine’,

10 – guwo ‘ten’.

 

In Nupe language, numerals are derived in different methods which are very complex but simple to understand as the manipulation goes on. Similarly, the system used the morpheme be as connected particle for addition while the morpheme din is used for the subtraction and such morphemes serve as an infix between the two given words (numbers) as the case of compounding in forming the higher numbers from the base. There is a situation where the e suffix occurs especially at the lower numbers which considered as phonological conditions. Examples:

 

11-14

 

11 - guwo be nini ‘eleven’, 12 - guwo be gubae ‘twelve’, 13 - guwo be gutae thirteen’, 14 - guwo be gunnie.

 

Similarly, the system has another two different bases that considered as unproductive as the normal circumstances found in the other numerals. They are as follows:

 

15 - gwegi ‘fifteen’ and 35 - rudin ‘thirty five’. However, the other bases found in Nupe numerals are as follows:

 

20 - eshi ‘twenty’, 30 - gbanwo ‘thirty’, 40 - shiba ‘fourty’, 50 - arata ‘fifty’, 60 - shita ‘sixty’, 70 - adwani ‘seventy’, 80 - shini ‘eighty’ and 100 - shitsun ‘one hundred’.

 

But in the case of 90 - shini be guwe ‘ninety’, there is an extraction from the base of 80 - shini ‘eighty’ plus 10 - guwo ‘ten’ (80+10) after which some phonological changes occur while the morpheme be was inserted at the middle of the two existing words i.e. shini be guwe, (80+10) as compounding process.

 

The Tiv Numerals

 

Orkar (2005) states that, Tiv numerals consist of simple and complex numerals, the simple (base) have been categorized into two main groups (1 - 5 and 6 - 10) as follows:

 

1 – 5

1 – môm ‘one’ 2 – har ‘two’ 3 – tar ‘three’

4 – nyin ‘four’ 5 – taan ‘five’

 

6–10

 

6 – teratar ‘six’ 7 – taankar-uhar ‘seven’ 8 – nieni ‘eight’ 9 – tankar-unyin ‘nine’ 10 – pue.

 

The Tiv language has complex numerals where the higher numbers are derived from the base. There are other sub-categories of base despite that 1 to 5 and 1 to 6 are used to manipulate for the higher denomination. In this case, the morpheme kar inserts in between the two words of the higher and the lower numbers. Examples are as follows:

 

11–19

11- puekar-môm ‘eleven’, 12- puekar-uhar

‘twelve’,  13-    puekar-utar     ‘thirteen’,

 

14- puekar-unyiin ‘fourteen’, 15- puekar-utaan ‘fifteen’, 16- puekar-ateratar ‘sixteen’,

17-     puekar-utaankar-uhar    ‘seventeen’,

 

18- puekar-anieni ‘eighteen’, 19- puekar-utaan-kar-unyiin ‘nineteen’.

 

The other numerals are derived from the following bases in Tiv counting system:

 

20- ikyundu ‘twenty’, 100- deri môm, ‘one hundred’, 200- deri uhar ‘two hundred’, 300, 400, 500, 600, 700, 800, 900 and 1000- dubu môm. All these are used to derive the other numbers by using the morpheme kar for joining the two or more numerals that give birth to other numerals. This also shows that morphology plays a vital role in most of the numerals i.e. compounding process as the case of Tiv language in which it relates to this research where the additional morpheme ‘da’ incerted at the middle of two words in the case of Hausa numerals, though the basic numerals of the Tiv are in two groups unlike the single set in Hausa, and Yoruba languages respectively.

 

The Yorùbá Numerals

 

Ajiboye (2013) says that; “Numerals whose forms cannot be broken down into identifiable meaningful morphemes are the first group which consists of numerals from one to ten as basic numerals” (Ajiboye, 2013:3).They are as follows:

 

1. ení ‘one’ 2. èjì ‘two’ 3.ẹ̀ta ‘three’ 4. ẹ̀rin ‘four’ 5. àrún ‘five’ 6. ẹ̀fà ‘six’ 7. èje ‘seven’

8. ẹ̀jọ ‘eight’ 9. ẹ̀sán ‘nine’ 10. ẹ̀wá ‘ten’.

 

It appears that the second basic numerals have nothing in common other than being among other numerals that are in multiples of ten. It is observed that ogún and igba can be used in multiplication whereas ọgbọ̀n cannot (cf. Oduyoye, 1969 in Ajiboye, 2013:3). Examples:

a.      20  ogún ‘twenty’

 

b.      30   ọgbọ̀n ‘thirty’

 

c.       200  igba  ‘two hundred’

 

Apart from the numerals that appear as base numerals in Yoruba, the remaining numerals were derived through some morphological processes where the higher denominations being produced. In fact, there are no other base numerals in Yoruba after ogún, ọgbọ̀n and any round figures above igba (200). (i.e. the long forms from eleven to ninety nine (11 to 99) are based on the occurrence within the Yoruba numerals; ọ̀kan ‘one’ to ẹ̀sán ‘nine’).

 

According to Olúbọde-Sàwẹ (2013:190), the complexity of numeral derivation in Yoruba is due to many factors, including but not limited to what follows. The higher numbers are compounded from the cardinal forms and the process of compounding involves series of mathematical operations. However, the products of these operations are then subjected to complex phonological processes which produce forms that differ, sometimes radically, from their constituent bases. Yoruba also has a multiplicity of number scales or bases (Olúbọde-Sàwẹ, 2013:190).

 

Accordingly, it was observed that the affixes (bound morphs) play some vital roles in the counting system of the Yoruba language. The prefixes and inter-fixes are signaling increase by or decrease by of a certain number. Examples:

 

Base Suffix	Computation	Numerals	Gloss
àádó+ òta=	(60-10 = 50)	àádó-òta	‘fifty’
ogó + èje	=  (20× 7 = 140)	ogóòje	‘one hundred and

forty’

 

One of the sources of complexity in the numeral system is that number derivation in Yoruba is by compounding of the cardinal numbers, involving several arithmetic operations; addition, subtraction or multiplication (Olubode, 2013:190). Examples:

(a) Addition:

moókànlá ‘one plus ten’            (1+10=11)

‘eleven’

igba       ólé             métàlàá        ‘two      hundred         plus    three-plus-ten’

(200+3+10=213)

(b) Subtraction:

 

meérìndínlógún                  ‘twenty less four’   (-4+20=16)     ‘sixteen’

aádórùn-ún                             ‘five twenties –less ten’ (-10+20x5=90)           ‘ninety’

(c)Multiplication:

ogójì ‘two twenties’               (20x2=40)            ‘forty’ etc.

 

Oyebade (2013:331) states that, ‘‘Yoruba speakers use the arithmetical computation operations of addition, subtraction and multiplication to compute more numbers’’. However, the decimal numbers i.e. one to ten (1 to 10), ten to twenty (10 to 20), twenty to thirty (20 to 30) etc which exploit addition and subtraction where one to four (1 to 4) applied in the decimal while the subtraction in five to nine (5 to 9) on the other hand. But from thirty five numerals (35 to 49), a combination of mathematical operations is introduced; multiplication and subtraction (35 to 39, 45 to 49, etc.), while multiplication and addition in (41 to 44 and 61 to 64 etc).

 

Table    1:     The   Basic  Set       of            Yorùbá         Numerals      (Simple

Cardinals):

 

Like other natural languages, Yorùbá derives the complex cardinal numerals from the simple cardinal numerals (base), where the higher number can be produced in accordance with the system used. So, the Yoruba arithmetic operations can be set to have productive and unproductive systems which depend on the sets of the basic numbers. In the examples from 1 to 4 of Yoruba numerals, the addition is used to produce the numerals at the hierarchy, where the remaining numbers from 5 to 9 are being manipulated through subtraction of the lower number from the lexical item ahead, e.g. 20, 30, 40, 50, 60, 70, etc as another base of counting operations that can be derived. 

Table2: The Word Formation Process in Addition of Yorùbá Numerals: 

The process of word formation that occurs in table 2 above is unproductive in the system of Yorùbá numerals-formation where deletion of bound morphemes (lèèwà) at the middle position of a numeral word occurred in order to shorten the long words unintentionally by the speakers. The Yorùbá numerals are also unproductive in the compounding process where the two or more words are joined together to produce a meaningful idea that can to solve some arithmetic operations. 

Table 3: The Word Formation Process in Multiplication of

Yorùbá Numerals:

Moreover, the operations in the table 6 above are not enough for solving the problem of calculation or manipulation in the Yorùbá language as the speakers combine the two arithmetic operations (i.e. subtraction and multiplication). In this case, the three lexical items are merged together. The long and complex words are no longer use in most of the languages of today. In this case, the clipping process plays a vital role in a situation where some parts of four syllable-words were deleted (front or back) to arrive at a short and simple lexical items as follows: 

Table 4: The Word Formation Process in Subtraction and

 

Multiplication of     Yoruba Numerals: 

The BODMAS ¹ logic used to be solved for the above computation. Meanwhile, blending has been identified as one of the word formation processes. It is described as a process usually arrived at by cutting parts of two different words to form another, a product of which does not show transparent resemblance to the originals (Mathews, 1993, Bauer, 1983 and Abubakar, 2001) in Shettima and Bulakarima (2012:32). Example of clipping are as follows: Euro (pe) and Asia = Eurasia etc.

 

Accordingly, it is observed that blending can be seen as another process of word formation, more especially in Yoruba numerals where some morphemes are deleted from the two existing words.

 

Table 5: The Word Formation Process in Subtraction of

Yorùbá Numerals:

 

2It is the formula for arithmetic logics as Bracket of Division, Multiplication, and Subtraction (BODMAS). ‘lo’ morpheme is missing as a result of the presence of clipping after compounding in the process to form mẹ́ẹdógún ‘fifteen’ which is unproductive. In this compounding process, the clipping occurs only on numeral ‘15’ as others take the insertion of the allomorph (l) instead of deletion which shows that the unproductive system in subtraction operation of Yorùbá counting that applied in 16 to 19 numerals. But it has observed that the multiplication pattern of arithmetical operations in Yoruba numerals affects the structure of a numeral word-formation where the process made the system productive by joining two lexical items, after which one or more morphemes can be removed or deleted as clipping.

 Meanwhile, another process of Yorùbá reduplication can occur in the Yorùbá numeral systems where the first syllable can easily be repeated completely according to the word-formation rules. 

The following are examples of numerals in Yoruba Reduplication: 

 

Discussion of Findings

 

The productivity of Yoruba numerical system occurs in some of the arithmetical operations such as addition, subtraction and multiplication. The morphology also plays a vital role in order to form other numerals in which the operation exists and expands to the higher numbers. However, the system shows that Yoruba numbers are counted in different manipulations which in most cases make the system unproductive or not standard as it can change from one system to another.

 

It has proved that some morphological patterns are more productive than others. This is because the morphological patterns make no differences to that of productive in terms of rules guiding their formations; they are unproductive based on the language traditions by the native speakers.

 

Furthermore, it is realized that the numerical system of Yorùbá has a distinctive lexicalization process in its numeracy. This lexicalization occurs in the process of forming a new word from the existing one as it appears in the analysis above. In relation to morphological processes of the language, the analysis shows that Yoruba language has different morphological processes in numerical formation; these are compounding, clipping, blending and reduplication processes. With regard to production of lexical numerals, this analysis shows that Yorùbá speakers have formed their numerals from the ten-base system like in Hausa and Igala numerals while other languages such as Nupe and Tiv differ in ten-base where they formed their higher numbers through five-base systems (1-5), it can also be found that, some bound morphemes are attached in between the two numeral words from those languages (i.e. da, sha, din, be, kar etc).

 Moreover, the issue of reduplication versus productivity can be realized from the analysis that some numerical reduplication is more productive than the unproductive as in Yoruba counting system. Numerals in full reduplication are more lexicalized than that of partial reduplication which indicates why some numerals are more productive than others. They are also more productive because the analysis shows that they are fitted to the language rules and are more acceptable by the native speakers. In addition, the partial reduplication turns out to be unproductive though the meaning remains the same base on the presence of productivity for full reduplication. (i.e *èwèwa instead of èwa-èwa, *òkókan instead of ókan-ókan which is productive morphologically).

 

Conclusion

 

Word-formation processes are not restricted, and the most productive affixes seem to be subjected to certain structural constraints. Meaning, they have their own rules that govern their structural formation. Some affixes may only be attached to the bases of a certain syntactic category, a specific phonological or morphological make-up. Semantic factors can also play a restrictive role, and the fashionableness of an affix is also dependent on extra-linguistic influences. However, the numeral system of this language is morphologically different to other languages with head-initial where Yoruba operates as head-final in which the higher denominations are derived from the base numbers according to the arithmetic operations that make the system productive or unproductive. It is also observed that the most interesting point here is how the speakers of the Yoruba language use clipping to process and shorten the long or complex to simple words in Yoruba numerals.

 

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