Morphological characteristics of numerals

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Morphological characteristics of numerals

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1THE MINISTRY OF HIGHER EDUCATION, SCIENCE AND
INNOVATIONS OF THE REPUBLIC OF UZBEKISTAN
SAMARKAND STATE INSTITUTE OF FOREIGN LANGUAGES
COURSE WORK
THEME: MORPHOLOGICAL CHARACTERISTICS OF NUMERALS
SAMARKAND-2024

2CONTENT
INTRODUCTION ................................................................................................... 3
CHAPTER I. BACKGROUND INFORMATION ABOUT FOUNDATIONS
OF NUMERICAL MORPHOLOGY
1.1 Overview of categorization of numerals morphological representation and
grammatical functions .............................................................................................. 5
1.2 Types and Forms of Numerical Constructs ..................................................... 10
Conclusion on chapter I ........................................................................................ 14
CHAPTER II. MORPHOLOGICAL CHARACTERISTICS OF NUMERALS
2.1 Numerals and their Position in Universal Grammar ....................................... 15
2.2 Derivational processes of numerical forms ....................................................... 27
Conclusion on chapter II ....................................................................................... 30
CONCLUSION ...................................................................................................... 31
THE LIST OF USED LITERATURE ................................................................. 33

3INTRODUCTION
Learning a language is a broad and varied endeavor that offers benefits for
one's career, culture, mind, and personal life. When individuals embark on the
journey of language acquisition, they open themselves up to new insights, fulfilling
experiences, and a deeper understanding of the world around them. Acquiring
proficiency in a language goes beyond mere language acquisition; it presents a
chance for individual growth, global engagement, and profound intercultural
understanding. Acknowledging the process of acquiring a language is more than
just learning vocabulary and syntax; it's a transformative experience that opens
doors and alters viewpoints in significant and enduring ways.
So, President of Uzbekistan is paying his much attention to education and
foreign languages and signing rules and decisions. For instance, one of them is
signed in May 19, 2021 “On measures to bring quality to a new level of promotion
of foreign language learning activities in the republic of Uzbekistan”. The main
purpose from this document is to develop the sphere of education, especially
language learning. In this way, almost all educational institutions have mentioned
their aims, goals and responsibilities, and doing them one by one.
Topicality of the course work. the study of numerical morphology provides
valuable insights into how languages encode and convey numerical information,
offering a window into the intricate ways in which numbers are structured,
inflected, and used within linguistic frameworks. By exploring the foundations of
numerical morphology, we uncover the rich interplay between language, culture,
cognition, and mathematics within the realm of linguistic expression.
The aim of the course paper is to clarify the topic of morphological
characteristics of numerals and giving the main information according to the
theme.

4The object of the course paper is methodology, effective and modern
methods and materials in education.
The subject of the course paper morphological characteristics of numerals.
Innovative and traditional approaches to learn syntactic analysis of English
complex sentences and giving specific information about the given topic.
The main material of the course paper is used myriad of foreign and local
authors’ researches, articles and statistics which are listed in the list of used
literature.
The structure of the course paper includes introduction, two chapters,
conclusion and list of used literature. The first chapter is devoted to analyze
background information about foundations of numerical morphology and its
features in language acquisition; the second chapter discusses morphological
characteristics of numerals. Writer’s opinions and whole summary is given in
conclusion. The list of used literature is given in the end of the course paper.
The practical and theoretical value of the course work : is large material
which can be included into the lectures on methods of teaching foreign languages,
using effective approaches and techniques in the process.

5CHAPTER I. BACKGROUND INFORMATION ABOUT
FOUNDATIONS OF NUMERICAL MORPHOLOGY
1.1 Overview of categorization of numerals morphological representation and
grammatical functions
Number is the category through which languages express information about
the individuality, numerosity, and part structure of what we speak about. As a
linguistic category it has a morphological, a morphosyntactic, and a semantic
dimension, which are variously interrelated across language systems. Number
marking can apply to a more or less restricted part of the lexicon of a language,
being most likely on personal pronouns and human/animate nouns, and least on
inanimate nouns.
In the core contrast, number allows languages to refer to ‘many’ through
the description of ‘one’; the sets referred to consist of tokens of the same type, but
also of similar types, or of elements pragmatically associated with one named
individual. In other cases, number opposes a reading of ‘one’ to a reading as “not
one” which includes masses; when the ‘one’ reading is morphologically derived
from the ‘not one,’ it is called a singulative. It is rare for a language to have no
linguistic number at all, since a ‘one – many’ opposition is typically implied at
least in pronouns, where the category of person discriminates the speaker as ‘one.’
Beyond pronouns, number is typically a property of nouns and/or determiners,
although it can appear on other word classes by agreement.
Verbs can also express part-structural properties of events, but this ‘verbal
number’ is not isomorphic to nominal number marking. Many languages allow a
variable proportion of their nominals to appear in a ‘general’ form, which
expresses no number information. The main values of number-marked elements
are singular and plural; dual and a much rarer trial also exist. Many languages also
distinguish forms interpreted as paucals or as greater plurals, respectively, for

7understanding the intricacies of cardinal numerals, we unveil the essential role they
play in structuring numerical information, quantifying the world around us, and
facilitating mathematical operations and reasoning in both language and
mathematics.
Morphological Representation: Cardinal numerals represent the basic
counting numbers (e.g., one, two, three) and are usually morphologically distinct
words or symbols.
Grammatical Functions: Cardinal numerals can function as determiners
(e.g., "three books"), adjectives (e.g., "three red apples"), or nouns (e.g., "the
three").
Ordinal Numerals: Ordinal numerals are a type of numeral that indicate the
position or order of an item in a sequence. They are used to show the rank, order,
or position of elements in a series. Ordinal numerals often have specific
morphological forms, distinct from cardinal numerals (which represent basic
counting numbers).
Morphological Representation: Ordinal numerals indicate the position or
order in a sequence (e.g., first, second, third) and often have distinct morphological
forms.
Grammatical Functions: Ordinal numerals can function as adjectives (e.g.,
"the second chapter") or nouns (e.g., "he finished in third place").
Multiplicative Numerals: Multiplicative numerals are a type of numeral
that indicates the number of times an action is performed or the degree of
multiplication. These numerals are used to express multiples or repetitions of a
quantity. Multiplicative numerals are often derived from cardinal or ordinal
numerals with specific morphological changes.

8Morphological Representation: Multiplicative numerals express
multiplication and are formed from cardinal or ordinal numerals with specific
morphological changes (e.g., single, double, triple).
“Grammatical Functions: They can function as adjectives or adverbs,
indicating the number of times something is repeated (e.g., "double the amount,"
"triple the speed").
Collective Numerals: Collective numerals refer to a type of numeral that
represents a group or collection of items as a single entity. These numerals are
used to quantify a set of items or objects as a whole. Collective numerals are often
distinct morphologically and are employed to convey a sense of unity or totality.
Collective numerals are useful for simplifying expressions of quantity, especially
when dealing with larger numbers. They are employed in various contexts such as
commerce, measurements, and general counting. While the examples provided are
common in English, other languages may have different collective numerals, and
the morphological representation can vary accordingly.
Morphological Representation: Collective numerals represent a group or
collection of items (e.g., dozen, score, hundred) and are often distinct
morphologically.
Grammatical Functions: They can function as determiners or nouns (e.g.,
"a dozen eggs," "two hundred people").” [5; 23-25]
Distributive Numerals: Distributive numerals are a type of numeral used to
indicate the distribution of an action or quantity among individual items within a
group. These numerals convey the idea of considering each element separately or
individually. Distributive numerals are often employed as determiners or adverbs,
emphasizing the individualized nature of the distribution. Distributive numerals are
particularly useful when precision is required in expressing the distribution of

$9actions or quantities among members of a group. The choice of distributive numeral depends on the context and the specific emphasis the speaker or writer wants to convey. Different languages may have their own ways of expressing distributive meanings. Morphological Representation: Distributive numerals indicate distribution among individual items (e.g., each, every) and are usually distinct morphologically. Grammatical Functions: They typically function as determiners (e.g., "each student") or adverbs (e.g., "they come every week"). Fractional Numerals: Fractional numerals are a type of numeral used to express a part or portion of a whole. They represent a division of an object, quantity, or unit into equal parts. Fractional numerals are typically used as nouns or adjectives, indicating a specific fraction of the whole. Fractional numerals are crucial for expressing precise proportions and dividing objects or quantities into equal parts. They are commonly used in various contexts, such as cooking recipes, measurements, financial calculations, and other situations where the division of a whole is relevant. The morphological representation of fractional numerals is generally straightforward, with the term derived from the corresponding cardinal numeral. Different languages may have their own terms for fractional numerals. Morphological Representation: Fractional numerals express a part of a whole (e.g., half, quarter) and are distinct morphologically. Grammatical Functions: They can function as nouns or adjectives (e.g., "half of the pizza," "a quarter cup"). “Roman Numerals: Roman numerals are a numeral system that originated in ancient Rome and were widely used throughout the Roman Empire. They are still used today in various contexts, such as numbering chapters or sections in$

10books, indicating the copyright dates of works of literature and film, and in certain
formal settings. Roman numerals use a combination of letters from the Latin
alphabet to represent numbers. Roman numerals are usually written largest to
smallest from left to right, and the numeral values are added together. However,
when a smaller numeral appears before a larger numeral, it is subtracted. It's
essential to note that there is no zero in the Roman numeral system, and it is not a
positional system like the Arabic numeral system (0-9).
Morphological Representation: Roman numerals use specific symbols (I,
V, X, L, C, D, M) to represent numbers and follow specific morphological rules.
Grammatical Functions: They are often used in a variety of contexts,
including representing numbers in outlines, chapters, sections, or in certain formal
contexts.
The specific categorization and usage of numerals can vary widely among
languages, and some languages may have unique numeral systems or categories
that differ from those outlined here. Additionally, the morphological and
grammatical features of numerals may change depending on the syntactic context
within a sentence.” [6; 82-86]
1.2 Types and Forms of Numerical Constructs
Word learning is a hard problem. Number word learning may seem to be an
exception. Indeed, unlike all other words, number words are part of a structure, namely
verbal counting, which, when understood, directly reveals their meaning. In other
words, it may seem that the problem of number word learning reduces to learning to
count, which English learning middle class children do shortly after their second
birthday. However, a large body of evidence shows that it is not so; number word
meanings do not come for free upon learning to count. Rather, children learn the
meanings of the number words for the first four numbers (“one” through “four” in

11English) in a drawn out process that takes over a year, and acquire the meanings of
these four number words before they figure out the numerical significance of counting.
These facts suggest that children do not deduce the meaning of the first three or four
number words from their understanding of counting.
“The acquisition of the meanings of the number words for the first four
numbers must be achieved simply by hearing the words used in contexts in which they
refer to cardinal values of sets. Thus, factors which contribute to learning non-
numerical words (e.g., nouns and verbs) could also contribute to number word
learning. Much evidence suggests that knowledge of syntax and/or morphology
scaffolds the acquisition of the meaning of non-numerical words such as proper names
and count nouns, adjectives and verbs. Bloom and Wynn suggested that something
similar could be true for the acquisition of number word meanings, proposing that
English-learning children infer that each number word denotes a unique, exact
numerosity from the fact that it is the only meaning that is consistent with the syntax
and semantics of the different types of phrases where number words occur. Similarly,
Barner and colleagues suggest that the distributional overlap between number words
and quantifiers contributes to helping children discover the relevant semantic space for
number word meanings.” [16; 65-68]
Even more simply, number word learning may be supported by children’s
knowledge of the meaning of numerical morphology. In many languages, number is
obligatorily marked on various parts of speech, most commonly on nouns and verbs.
For example, the distinction between singular and plural is marked on English count
nouns and on English verbs. Other languages with obligatory numerical morphology
make more extensive numerical distinctions. For example, Slovenian and the Najdi
dialect of Saudi Arabic make a tripartite distinction between singular, dual and plural.
“How could prior knowledge of the meaning of numerical morphology help
children learn number word meanings? Consider the case of singular/plural in English.

12Given their meaning, singular nouns do not have to be used only when there is a single
individual in the situation being talked about. For example, it is acceptable to say
“There is a dog walking down the street” when, actually, multiple dogs are walking
down the street. Also, when they fall within the scope of a quantifier (e.g., “A
few/some/most of the children are eating a (different) hot dog”), singular nouns can be
used in situations that involve more than one individual of the type designated by the
noun. As for plurals, it is unlikely that they literally mean more than one or else one
cannot explain why negated plurals (e.g., “No windows were broken”) do not mean
less than 2. Still, in many contexts, speakers do use singular nouns to refer to situations
where there is only one individual of the type designated by the noun and plural nouns
to refer to situations where there are more than one. Speakers use singular and plural
nouns this way as a result of scalar implicatures. Moreover, when we consider the
number of individuals introduced in discourse instead of the number present in a
situation, then there clearly is a numerical distinction between singular and plural
nouns. For example, in “There is a dog walking down the street,” the singular “a dog”
introduces a single dog in discourse. Thus, “It is big” is an acceptable continuation of
the discourse but “They are big” is not. Similarly, “They are big” is an acceptable
continuation of “Some dogs are walking down the street” but “It is big” is not.” [3; 69-
77]
There is thus a regular (although imperfect) relation between English singular
and plural nouns and the number of things being referred to, and to the number being
introduced in discourse. This regularity can provide information that is useful for
learning the meaning of the number word “one,” and for distinguishing it from the
meaning of number words that denote larger numbers. Indeed, in noun phrases in
which “one” is used with an overt noun to express the meaning one x, the noun is
always in singular form. Likewise, English number words that denote numerosities
greater than one always co-occur with a plural noun. Thus, children could use the

13numerical information provided by numerical morphology to learn that “one” means
one, and to learn that the other number words denote numbers greater than one.
Some evidence suggests that this hypothesis could be true. First, some studies
suggest that young learners are sensitive to the regular relation between noun
numerical morphology and numerosity, before they begin to learn number word
meanings. For example, American children learn the meaning of “one” sometime
between age 24 and 36 months By 24months, English-speaking American children
assume that nouns that are preceded by the singular indefinite determiner “a” and that
agree with a singular verb (as in “Look, there is a blicket!”) are more likely to refer to
one than to more than one individual, and that plural nouns that are preceded by
“some” and that agree with a plural verb (“Look, there are some blickets”) are more
likely to refer to a plurality of individuals. They also obtain suggestive evidence that,
by 24-months, a noun marked with the /-s/ allomorph of the plural is sufficient to
indicate reference to a plurality. Similarly, that children aged between 18 and 28
months refer to sets of a single object with singular nouns, and to sets of two objects
with plural nouns. This suggests that young English learners’ knowledge of the
numerical meaning of singular/plural morphology could help them learn the meaning
of the number word “one.”
“Cross-linguistic comparisons provide evidence that children actually use the
numerical information conveyed by numerical morphology to learn number word
meanings. Numerical morphology in some Slovenian dialects and in the Najdi dialect
of Saudi Arabic makes a tripartite distinction between singular, dual and plural
Children learning dual-marking Slovenian and Najdi Arabic learn the meaning of the
number word for two faster than do English learners, but are not faster at learning
number words that denote numbers greater than two. Thus, the cross-linguistic
difference in rate of number word learning matches precisely with the differences in
numerical morphology between English and Slovenian and Saudi Arabic. Furthermore,
knowledge of the meaning of the number word for two is related to knowledge of the

$14meaning of the dual marker. For example, Slovenian children who know the meaning of the number words for one and two use the dual marker correctly 65% of the time, whereas Slovenian children who have not yet learned the meaning of the number word for two use it correctly only some 30% of the time.” [19; 103-112] Conclusion on Chapter I. In conclusion, the foundations of numerical morphology provide a comprehensive understanding of how numerical concepts are represented, structured, and formed in language. Numerical morphology involves the study of the internal structure of words related to numbers, exploring the morphological rules and patterns that govern their formation. Key elements in numerical morphology include cardinal numerals, ordinal numerals, multiplicative numerals, collective numerals, distributive numerals, fractional numerals, Roman numerals, and other numeral systems like decimal, binary, and hexadecimal. These numerical constructs play a crucial role in expressing quantities, order, and relationships within a linguistic framework. The morphological representation of numerals varies across languages, reflecting the unique rules and structures inherent to each linguistic system. The study of numerical morphology is essential not only for linguistic analysis but also for understanding how numerical concepts are embedded in the fabric of human communication. The morphological forms of numerical constructs range from standalone words to symbols, and they often undergo specific morphological changes to convey different aspects such as order, multiplication, distribution, or collection. The various types and forms of numerical constructs contribute to the richness and flexibility of language, allowing speakers to convey precise information about quantities and relationships. As language is dynamic and ever-evolving, the foundations of numerical morphology continue to be a subject of exploration and research. Understanding the morphological intricacies of numerical constructs enhances our grasp of linguistic diversity, aiding in cross-cultural communication and contributing to the broader field of linguistics.$

15CHAPTER II. MORPHOLOGICAL CHARACTERISTICS OF
NUMERALS
2.1 Numerals and their Position in Universal Grammar
Numerals are linguistic elements that represent numbers, quantities, or order
in a sentence or phrase. They play a crucial role in conveying information about
quantity, measurement, and other numeric attributes in language. Numerals can be
broadly categorized into cardinal numerals, which indicate the quantity or number
of items, and ordinal numerals, which indicate the order or position of items. These
morphological characters are essential for understanding the role and relevance of
numerals in language.
Morphologically, numerals exhibit various inflections and modifications
based on grammatical and syntactic factors. In many languages, numerals can
change forms to reflect gender, case, and agreement with other elements in a
sentence. For example, in languages with grammatical gender, numerals may take
different forms depending on the gender of the noun they modify. Similarly, in
languages with case markings, numerals may inflect to match the case of the noun
they modify. These morphological variations are important for ensuring agreement
and coherence within a sentence.
Numerals often exhibit distinct morphological characteristics when used as
adjectives or adverbs. In many languages, numerals can function as attributive
adjectives, modifying nouns by indicating quantity or order (e.g., "three apples,"
"the first book"). When used as adverbs, numerals indicate the frequency, duration,
or sequence of an action (e.g., "He runs twice a week," "She arrived third in the
race"). Understanding the morphological properties of numerals in different
linguistic contexts is essential for accurate and effective communication.

16The relevance of numerals morphological characters extends beyond their
grammatical and syntactic functions. Numerals also play a crucial role in
conveying cultural and numerical information. Different languages and cultures
may have unique systems for expressing numerals, including variations in
numerical symbols, counting systems, and numerical conventions. Morphological
characteristics of numerals can provide insights into the historical, cultural, and
cognitive aspects of numerical representation within a specific language or
linguistic group.
Moreover, numerals are essential for various domains, including
mathematics, science, finance, and everyday communication. In mathematics,
numerals are fundamental for representing and manipulating mathematical
concepts, such as arithmetic operations, algebraic equations, and numerical
computations. In science, numerals are used to express measurements, quantities,
and numerical data in various disciplines, including physics, chemistry, and
biology. In finance, numerals are crucial for representing currency, financial
transactions, and numerical data for business and economic analyses. In everyday
communication, numerals are used for indicating time, dates, quantities, and other
essential numerical information.
The morphological characters of numerals are essential for understanding
their grammatical, syntactic, cultural, and functional relevance in language. By
analyzing the morphological properties of numerals, linguists, language learners,
and researchers can gain insights into the diverse ways in which languages express
numerical concepts and the role of numerals in conveying quantitative and
numerical information. Understanding the morphological properties of numerals is
critical for effective communication and comprehension in both written and spoken
language.

17In linguistics, Universal Grammar refers to the theory that the ability to
acquire language is innate to humans and that there is a common set of
grammatical principles underlying the world's languages. While the concept of
Universal Grammar primarily focuses on syntactic structures and principles,
numerals, being a linguistic element, also fit into this framework. Here's a brief
exploration of numerals and their position in Universal Grammar:
“Numerals as a Universal Concept: The concept of counting and expressing
quantity is nearly universal across all languages and cultures. Numerals, in various
forms, are found in every human language. Numerals represent a universal concept
of conveying numerical information across different cultures and languages. While
the specific symbols and notations used to represent numbers may vary, the
underlying concept of numerals as a way to express quantities and values is
consistent across many diverse societies. Whether it's Arabic numerals, Roman
numerals, or other numerical systems, the fundamental idea of using symbols to
represent numbers is a universal concept that transcends language and cultural
barriers. This universal nature of numerals has been crucial in facilitating
communication and commerce across different societies throughout history.
Syntactic Structures of Numerals: Numerals are linguistic elements used to
express numbers or quantities. They play an important role in the syntactic
structure of a language, as they are used to convey information about quantity,
order, or measurement. In English, numerals can be classified into cardinal
numerals, which represent quantity (e.g., one, two, three), and ordinal numerals,
which represent order or position (e.g., first, second, third). In terms of syntax,
numerals can function in various grammatical roles within a sentence. They can act
as determiners, modifying a noun or noun phrase (e.g., "three dogs," "five books").
They can also function as adjectives, describing a noun (e.g., "the first place," "the
fifth chapter"). In addition, numerals can serve as pronouns, replacing a noun
phrase and standing alone to represent a specific quantity or position (e.g., "He

18took three, and she took five"). Numerals can also be combined with other
elements to form complex numerical expressions. For example, they can be
grouped with prepositions to indicate relationships such as "two of" or "a dozen
of." They can be linked with conjunctions to show addition ("three and four") or
subtraction ("seven minus two"). Numerals can also be modified by adverbs to
express frequency or repetition (e.g., "twice," "several times").” [9; 43-61]
Numerals can exhibit inflectional and derivational morphology in some
languages. They may change form to reflect grammatical categories such as case,
gender, or definiteness. In addition, some languages have special numeral
classifiers or measure words that must accompany numerals when quantifying
nouns. The syntactic structure of numerals is complex and varies across languages,
reflecting the diverse ways in which different linguistic systems encode numerical
information. Understanding the syntactic properties of numerals is crucial for
effective communication and comprehension in any language. The position of
numerals within a sentence or phrase varies across languages.
Numerals and Agreement: Universal Grammar suggests that languages share
certain principles of agreement. In the case of numerals, there might be agreement
with the nouns they modify in terms of grammatical features like gender, case, or
number. In linguistics, numerals and agreement are important concepts that occur
in the context of language structure and grammar. Numerals are words or phrases
that express the concept of quantity, and they are used to count or quantify things
in a language. There are different types of numerals, such as cardinal numerals
(e.g., one, two, three), ordinal numerals (e.g., first, second, third), and others.
Numerals can play a crucial role in the agreement system of a given
language. Agreement refers to the phenomenon in which various elements of a
sentence are made to "agree" with one another in terms of features such as number,
gender, and person. In many languages, numerals trigger agreement on nouns

19and/or verbs, based on the quantity they express. This agreement can manifest in
different ways, such as the inflection of the numeral itself, the inflection of the
noun it quantifies, or the agreement of a verb with a quantified noun.
The agreement often involves number (singular vs. plural) and, in some
languages, gender (masculine vs. feminine vs. neuter) and person (first vs. second
vs. third). For example, in English, singular cardinal numerals take singular
agreement with the noun they quantify, while plural numerals trigger plural
agreement. This is evident in phrases such as "one book is on the table" (singular
agreement) and "two books are on the table" (plural agreement).
In some languages, numerals may exhibit complex agreement patterns, and
they may interact with other elements of the sentence to trigger agreement
throughout the entire phrase or clause. This phenomenon illustrates the intricate
nature of linguistic agreement and the role that numerals play in shaping the
structure of a sentence. The study of numerals and agreement in linguistics
provides valuable insights into the ways in which languages encode quantity and
related features, and it sheds light on the intricate interplay between different
elements within a sentence. Understanding these phenomena is crucial for gaining
a comprehensive understanding of the grammar and structure of individual
languages, as well as for comparative linguistic analysis.
Numeral Classifiers: Many languages use classifiers or measure words with
numerals to indicate the type or shape of the counted objects. Universal Grammar
allows for the existence of such structures, although the specific classifiers used
can vary widely. Numeral classifiers, also known as measure words or counters,
are a feature of many languages, especially those in East and Southeast Asia. These
classifiers are used in combination with numerals to quantify or enumerate nouns,
and they often carry additional semantic or pragmatic information about the noun
being counted. In Mandarin Chinese, for example, classifiers are used to specify

20the type, shape, or size of an object being counted. For instance, the classifier "ge"
is used for general, round, or small objects, whereas "zhi" is used for animals,
"ben" for books, and "zhang" for flat objects. Each classifier conveys specific
information about the noun it precedes, adding precision to the description of the
quantity.
“Languages such as Thai and Vietnamese also employ classifiers, which
serve a similar purpose in providing more detailed information about the objects
being counted. In Thai, classifiers are commonly used with numerals to specify the
shape, form, or type of the noun, while in Vietnamese, classifiers are used to
express specific characteristics of the nouns being counted. In Japanese, classifiers
are called "counters" and play a crucial role in quantifying nouns. There are
numerous counters for different types of objects, representing various shapes,
sizes, or categories. For instance, the counter "mai" is used for flat objects, "hon"
for long, cylindrical objects, and "hiki" for small animals. The use of numeral
classifiers is not restricted to East and Southeast Asian languages. Some
indigenous languages of the Americas, such as Cherokee and Quechua, also
employ classifiers to quantify nouns. Additionally, some European languages, such
as Romanian and Lithuanian, have remnants of classifiers in their grammar. The
presence of numeral classifiers in various languages reflects the significance of
categorization and specificity in expressing quantity. They enhance the precision
and richness of expression by allowing speakers to convey nuances about the
objects being counted. Moreover, the use of numeral classifiers can be seen as a
reflection of cultural values and cognitive categorization systems within different
linguistic communities.” [10; 54-61]
Numeral classifiers are an important linguistic feature found in many
languages, particularly in East and Southeast Asia. They play a crucial role in
quantifying and categorizing nouns, adding specificity and detail to the expression
of quantity. The use of numeral classifiers provides insight into the cognitive and

21cultural aspects of language and reflects the diversity of linguistic structures
around the world.
Derivational Processes: Universal Grammar permits the existence of
derivational processes applied to numerals, such as the formation of ordinal
numerals or multiplicative numerals through specific morphological rules.
Cultural and Cognitive Influences: Universal Grammar acknowledges the
role of both cultural and cognitive factors in shaping linguistic structures. The
specific ways in which numerals are expressed and used can reflect cultural
practices and cognitive predispositions. The study of numeral morphology explores
how numbers are expressed linguistically and the cultural and cognitive influences
on these expressions. Cultural influences can shape the way numbers are
constructed and used in language, while cognitive influences can affect how
individuals perceive and understand numerical expressions. For example, some
languages may have different numeral systems or ways of expressing numbers
based on cultural practices or historical developments. Additionally, cognitive
factors such as numerical cognition and perception may influence how individuals
process and interpret numerical information. Overall, the interaction between
culture and cognition plays a significant role in shaping numeral morphology.
Numerals and Recursive Structures: Universal Grammar posits the existence
of recursive structures in language. While this is often associated with syntactic
recursion, numerals and counting systems can also exhibit recursive properties,
especially in languages with complex numeral systems. Numerals and recursive
structures are two fundamental concepts in mathematics and computer science that
have wide-ranging applications and significance. Numerals are symbols used to
represent numbers and are an essential component of mathematics. The most
common system of numerals is the decimal system, which uses ten symbols (0, 1,
2, 3, 4, 5, 6, 7, 8, 9) to represent all numbers. The position of a numeral in a

$22number determines its value, and the base of the numeral system determines the number of symbols used. In addition to the decimal system, there are other numeral systems such as binary (base 2), octal (base 8), and hexadecimal (base 16) that are commonly used in computer science and digital systems. Each numeral system has its own set of rules for representing and manipulating numbers. Recursive structures are a fundamental concept in computer science and mathematics that involves defining a complex structure in terms of simpler versions of itself. In mathematics, recursive sequences and series are commonly used to generate patterns and solve problems. In computer science, recursive functions and data structures are widely used to solve problems that exhibit repetitive structures. “One of the most famous examples of recursive structures is the Fibonacci sequence, where each number is the sum of the two preceding numbers. This sequence can be defined recursively as F(0) = 0, F(1) = 1, and F(n) = F(n-1) + F(n- 2) for n > 1. Recursive structures can also be represented visually, such as in fractals, which are complex geometric patterns that exhibit self-similarity at different scales. Numerals and recursive structures are closely related in computer science, particularly in the context of programming and algorithm design. For example, recursive functions are commonly used to manipulate numerical data and solve mathematical problems. Additionally, recursive data structures, such as linked lists and trees, are fundamental in organizing and accessing numerical data in computer programs. Numerals and recursive structures are closely linked in the study of formal languages and automata theory. Numerals play a critical role in representing and manipulating data in formal languages, while recursive structures are used to define and process complex grammars and languages. Numerals and recursive structures are fundamental concepts that have far-reaching applications in mathematics, computer science, and beyond. Understanding these concepts is$ $23critical for solving complex problems, designing efficient algorithms, and developing sophisticated software systems.” [14; 65-68] Numerical Systems and Cognitive Universals: The cognitive universals that underlie numerical cognition, such as the ability to understand the concept of quantity and perform basic arithmetic operations, are considered part of the broader cognitive foundations supporting language acquisition. Numerical systems and cognitive universals in grammar involve the study of how languages around the world express numerical concepts and how these expressions may reflect universal cognitive patterns. This topic encompasses a range of linguistic and cognitive principles, including the ways in which languages form and express numerals, the cultural and cognitive factors that influence numerical systems, and the potential universality of certain numerical concepts and structures. Numerical systems vary greatly across languages, with different languages employing diverse strategies for counting, ordering, and expressing quantities. Some languages may have elaborate numerical systems that include specific words for individual numbers, while others may use more simplified or analytical systems. Some languages may also exhibit distinct numerical features, such as dual or trial number forms, or specific linguistic structures for expressing fractions or numerical quantities in certain contexts. The study of numerical systems in language can shed light on the cultural and cognitive factors that shape these systems. Cultural practices and norms, as well as the needs of a society, can influence the development of numerical expressions in language. Moreover, cognitive processes underlying numerical reasoning and understanding may influence the structure and organization of numerical systems in language. For example, the inherent properties of human cognition, such as the ability to perceive numerical quantities and understand$

24mathematical relations, can have a significant impact on how numerical concepts
are expressed in language.
Another important aspect of this topic is the investigation of potential
cognitive universals in numerical grammar. Researchers in this field seek to
identify common patterns or principles that underlie numerical expressions across
different languages, with the aim of uncovering potential universal cognitive
mechanisms that shape the way humans understand and represent numerical
concepts. This research may involve cross-linguistic studies, experimental
investigations into numerical cognition, and analyses of the ways in which
different languages encode numerical information. The study of numerical systems
and cognitive universals in grammar provides valuable insights into the diverse
ways in which languages express numerical concepts and the underlying cognitive
processes that shape these expressions. By examining these phenomena, linguists
and cognitive scientists can gain a deeper understanding of the interplay between
language, culture, and cognition in the domain of numerical systems.
Numerical Syntax and Semantics: Universal Grammar allows for variation in
how languages express numerical syntax and semantics. Some languages may have
intricate numerical systems, while others may rely on simpler structures.
Numerical syntax and semantics refer to the grammar and meaning of numerical
expressions in mathematics and related fields. This branch of study is concerned
with understanding how numbers are represented, combined, and operated on in
various mathematical systems and how these operations produce meaningful
results. It also involves examining the rules and structures that govern numerical
expressions and their interpretations.
“Numerical syntax deals with the formal rules for constructing numerical
expressions, including the use of digits, symbols, and operations such as addition,
subtraction, multiplication, and division. It also encompasses the conventions for

25writing numbers in different bases, scientific notation, and other specialized
formats. The syntax of numerical expressions varies across different mathematical
systems, such as decimal, binary, hexadecimal, and others, and understanding these
differences is crucial for interpreting numerical information accurately. On the
other hand, numerical semantics focuses on the meaning and interpretation of
numerical expressions. This involves understanding the relationships between
numbers and the operations performed on them. For example, in arithmetic, adding
two numbers leads to a result that is larger than either of the original numbers,
while subtracting a smaller number from a larger number produces a result that is
smaller than the original number. These relationships are fundamental to the
interpretation of numerical expressions and play a crucial role in mathematical
reasoning and problem-solving.” [18; 101-108]
In more advanced mathematical contexts, numerical semantics also
encompasses concepts related to number theory, algebra, calculus, and other
branches of mathematics. For instance, in algebra, the interpretation of numerical
expressions often involves solving equations and inequalities, manipulating
algebraic expressions, and understanding the properties of different number
systems. In calculus, numerical semantics plays a key role in understanding the
behavior of functions, finding numerical approximations of solutions, and
evaluating limits and integrals.
Beyond mathematics, numerical syntax and semantics have important
applications in computer science, engineering, finance, and other fields where
numerical calculations and representations are essential. Understanding the rules
and meanings of numerical expressions is critical for developing accurate
algorithms, designing efficient numerical methods, and interpreting the results of
numerical simulations and analyses. The study of numerical syntax and semantics
is essential for developing a deep understanding of the language of mathematics
and its practical applications. By examining the rules, structures, and meanings of

26numerical expressions, researchers and practitioners in various fields can enhance
their ability to work with numbers effectively and accurately, leading to
advancements in technology, science, and commerce.
Challenges and Cross-Linguistic Variation: Challenges and cross-linguistic
variation in number morphology refers to the ways in which languages express
grammatical number (such as singular and plural) and the difficulties and
differences that arise in this area across different languages. Number morphology
is a key component of grammar that denotes the quantity or multiplicity of
referents in a given context.
One major challenge in the study of number morphology is the vast diversity
of systems found in the world's languages. While many languages use a simple
singular-plural system, others may have additional categories such as dual (for
referring to pairs) or paucal (for small, nonspecific quantities). Some languages
may even lack overt marking for number, relying instead on context or other
linguistic features to convey this information. Cross-linguistic variation in number
morphology also relates to the ways in which different languages mark number on
nouns, pronouns, and verbs. For example, in some languages, nouns will change
their form (i.e., undergo inflection) to indicate singular or plural, while in others,
number may be indicated through the use of specific words or particles.
Additionally, the correlation between number and other grammatical categories
(such as case, gender, or definiteness) can vary significantly from language to
language.
The challenges of number morphology extend to how it is acquired and
processed by language learners and users. Studies have shown that the acquisition
of number marking can be complex, particularly when learners are exposed to
languages with different number systems. Additionally, the processing of number
morphology in real-time language use has been a topic of interest in

27psycholinguistics, as it involves rapid recognition and interpretation of
morphological cues. In sum, the study of challenges and cross-linguistic variation
in number morphology encompasses a wide range of topics, including the
typological diversity of number systems, the morphosyntactic strategies for
expressing number, and the cognitive processes involved in number marking.
Understanding these challenges and variations is crucial for linguists, educators,
and language learners seeking to comprehend and navigate the complexities of
number morphology across different languages. While there are commonalities in
the expression of numerals, Universal Grammar also accounts for the variation
observed across languages. This variation can include differences in numeral
morphology, syntactic structures, and semantic nuances. The diversity in numeral
systems across languages is accommodated within the broader framework of
Universal Grammar, emphasizing both commonalities and variations in how
numerals are syntactically and semantically structured.
2.2 Derivational processes of numerical forms
Derivational processes in linguistics involve forming new words or word
forms by adding prefixes, suffixes, or other morphemes to a base word. In the
context of numerical forms, derivational processes often result in creating ordinal
numerals, multiplicative numerals, and other related forms. Let's explore some
common derivational processes applied to numerical forms:
“Ordinal Numerals:
Derivation: Ordinal numerals indicate the order or position of elements in a
sequence. They are often derived from cardinal numerals through specific
morphological processes.
Examples:
One →
First

28Two → Second
Three → Third
Morphological Process: Adding suffixes like -th, -eth, or others depending on
the language.” [17; 84-87]
Multiplicative Numerals:
Derivation: Multiplicative numerals express the idea of multiplication or
repetition. They are created through specific morphological processes.
Examples:
Two → Double
Three → Triple
Four → Quadruple
Morphological Process: Adding suffixes like -le, -ple, or using specific
derivational morphemes.
Collective Numerals:
Derivation: Collective numerals represent a collection or group of a specific
quantity.
Examples:
Two → Couple
Three → Trio
Four → Quartet
Morphological Process: Employing specific derivational morphemes or
adopting words from other languages.

$29Fractional Numerals: Derivation: Fractional numerals represent a part or division of a whole. Examples: One → Half (1/2) Three → Third (1/3) Four → Quarter (1/4) Morphological Process: Using specific morphemes or adopting words from other languages to indicate fractional values. Augmentative and Diminutive Numerals: Derivation: Creating numerals to indicate an increase or decrease in quantity or size. Examples: Two → Double (Augmentative) Two → Duo (Diminutive) Morphological Process: Adding specific derivational morphemes or adopting words from other languages. “Composite Numerals: Derivation: Forming numerals by combining multiple numerical elements. Examples: Twenty + Three → Twenty-Three Fifty + Five → Fifty-Five$

30Morphological Process: Compounding or combining morphemes to create
complex numerical forms.
Suffixation and Prefixation :
Derivation: Adding prefixes or suffixes to numerals for various linguistic
and semantic effects.
Examples:
Deci- (1/10, e.g., Decimeter)
Centi- (1/100, e.g.,
Centigram)
Morphological Process: Applying specific affixes to numerals to indicate a
particular meaning or context. Understanding these derivational processes
enhances our grasp of how numerical forms evolve in language, allowing for the
expression of various numerical relationships and concepts. Keep in mind that the
specific morphological rules and derivational processes can vary across
languages.” [6; 209]
Conclusion on Chapter II. In more advanced mathematical contexts,
numerical semantics also encompasses concepts related to number theory, algebra,
calculus, and other branches of mathematics. The interpretation of numerical
expressions often involves solving equations and inequalities, manipulating
algebraic expressions, and understanding the properties of different number
systems. In calculus, numerical semantics plays a key role in understanding the
behavior of functions, finding numerical approximations of solutions, and
evaluating limits and integrals.

31CONCLUSION
The study of numerals in linguistic morphology is an important area of
research that provides valuable insights into the structure and form of number
words in different languages. Numerals can be categorized based on their
morphological characteristics, which include their form, composition, and
inflectional patterns. Understanding these morphological characteristics is crucial
for gaining a deeper understanding of the underlying principles governing the
expression of numbers in language.
One key aspect of morphological characteristics of numerals is their form.
Numerals can take various forms, including cardinal, ordinal, distributive, and
multiplicative forms. Each form serves a specific function in expressing numerical
concepts, such as counting, ordering, or quantifying. Moreover, numerals exhibit
different morphological properties based on their form, such as the presence of
prefixes, suffixes, or stem modifications that distinguish them from other types of
words.
The composition of numerals is another important morphological
characteristic. In many languages, numerals are composed of smaller elements,
such as roots, affixes, or combining forms, which combine to create complex
number words. Understanding the morphological composition of numerals is
essential for identifying patterns and regularities in the formation of number words,
as well as for elucidating the historical development of numeral systems in
different languages.
Furthermore, numerals often display inflectional patterns that denote
grammatical categories such as case, gender, and plurality. The inflectional
morphology of numerals can vary significantly across languages, reflecting the
diverse ways in which number words are integrated into the grammatical and
syntactic systems of different language families. Analyzing the inflectional

32characteristics of numerals provides valuable insights into the morphosyntactic
properties of number words and their role in sentence structure and discourse.
In conclusion, the study of the morphological characteristics of numerals
sheds light on the intricate ways in which languages encode numerical concepts.
By examining the form, composition, and inflectional patterns of numerals,
linguists can uncover the underlying principles governing the expression of
numbers in language and gain a deeper understanding of the universal and
language-specific properties of numeral systems. This research is crucial for
advancing our knowledge of language structure and cognition and for enriching
our understanding of the diversity and complexity of human language.

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3412. Torruella, J. Challenges and limitations of syntactic analysis in real-
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