Methods of Lexicological Analysis
Methods of Lexicological Analysis
МІНІСТЕРСТВО
ОСВІТИ І НАУКИ УКРАЇНИ
НАЦІОНАЛЬНИЙ
ТЕХНІЧНИЙ УНІВЕРСИТЕТ УКРАЇНИ
КИЇВСЬКИЙ
ПОЛІТЕХНІЧНИЙ ІНСТИТУТ
Факультет
лінгвістики
Кафедра
теорії, практики та перекладу
англійської мови
Реферат
з
порівняльної лексикології англійської та української мов
на
тему:
„Methods of Lexicological Analysis”
Виконала
студентка ІІІ
курсу ФЛ
Київ
2008
CONTENTS
INTRODUCTION
3
І. Methods of Lexicological Analysis
5
І.1. Contrastive
Analysis 5
І.2. Statistical
Methods of Analysis 7
І.3. Immediate
Constituents Analysis 9
І.4. Distributional
Analysis and Co-occurrence 10
І.5. Transformational
Analysis 13
І.6. Componential
Analysis 14
І.7. Method
of Semantic Differential
16
І.8. Contextual
Analysis 18
CONCLUSION
19
LITERATURE
20
APPENDIX І
APPENDIX ІІ
INTRODUCTION
Growing interest in
methods of study is one of the most symptomatic features of present-day
linguistics.
The research methods used
in lexicology have always been closely connected with the general trends in
linguistics. The principles of comparative linguistics have played an
important role in the development of a scientific approach to historical word
study. They have brought an enormous increase in ordered and classified
information about the English vocabulary in their proper perspective. The
methods applied consisted in observation of speech, mostly written, collection
and classification of data, hypotheses, and systematic statements. Particular
stress was put on the refinement of methods for collecting and classifying
facts. The study of vocabulary became scientific.
19th century scientific
language study having recognized variety and change in language, comparative
philology insisted on regarding the descriptive statements as subordinate, not
worth making for their own sake. Its aim was to reconstruct the fundamental
forms and meanings which have not come down to us. With the use of sets of
phonetic correspondence philologists explored and proved genetic relationships
between words in different languages. They rejected prescriptive trends
characteristic of the previous stage. It was realized that the only basis for
correctness is the usage of the native speakers of each language. They
destroyed the myth of a Golden Age when all the words had their primary
"correct" meaning and when the language was in a state of perfection
from which it has deteriorated. It became clear from intensive work on the
great historical dictionaries that multiple meaning for words is normal, not an
"exception". Comparative studies showed that, save for specific
technical terms, there are no two words in two languages that cover precisely
the same area.
The process of scientific
investigation may be subdivided into several stages:
·
Observation
·
Classification
·
Generalization
Due to these processes
the certain classification of the methods of lexicological analysis has
appeared.
Nowadays
scientists distinguish:
·
Contrastive
analysis
·
Statistical
methods of analysis
·
Immediate
Constituents analysis
·
Distributional
analysis and co-occurrence
·
Transformational
analysis
·
Componential
analysis
·
Method of
semantic differential
·
Contextual analysis
The detailed description
of these methods will be shown further.
I. METHODS
OF LEXICOLOGICAL ANALYSIS
I.1. Contrastive
Analysis
In fact contrastive
analysis grew as the result of the practical demands of language teaching
methodology where it was empirically shown that the errors which are made
recurrently by foreign language students can be often traced back to the
differences in structure between the target language and the language of the
learner. This naturally implies the necessity of a detailed comparison of the
structure of a native and a target language which has been named contrastive
analysis.
It should be borne in
mind that though objective reality exists outside human beings and irrespective
of the language they speak every language classifies reality in its own way by
means of vocabulary units. In English, the
word foot is used to denote the extremity of the leg. In Ukrainian there is no
exact equivalent for foot. The word denotes the whole leg including the foot.
Classification of the
real world around us provided by the vocabulary units of our mother tongue is
learned and assimilated together with our first language. Because we are used
to the way in which our own language structures experience we are often inclined
to think of this as the only natural way of handling things whereas in fact it
is highly-arbitary.
One example is provided
by the words watch and clock. It would seem natural for Ukrainian speakers to
have a single word to refer to all devices that tell us what time it is; yet in
English they are divided into two semantic
classes depending on whether or not they are customarily portable. We also find
it natural that kinship terms should reflect the difference between male and
female: brother or sister, father or mother, uncle or aunt, yet in English we
fail to make this distinction in the case of cousin (the Ukrainian — двоюрідний брат, двоюрідна сестра).
Contrastive analysis also
brings to light what can be labelled problem pairs, the words that denote two
entities in one language and correspond to two different words in another
language.
Compare, for example годинник in Ukrainian and clock, watch in English, художник in
Ukrainian and
artist, painter in English.
Contrastive analysis on
the level of the grammatical meaning reveals that correlated words in different
languages may differ in the grammatical component of their meaning.
To take a simple instance
Ukrainians are liable to say the news are good, the money are on the table, her
hair are black, as the words новини, гроші, волосся have the grammatical meaning of plurality in the Ukrainian language.
Contrastive analysis
brings to light the essence of what is usually described as idiomatic English,
idiomatic Ukrainian the peculiar way in which every
language combines and structures in lexical units various concepts to denote
extra-linguistic reality.
For example, a typical Ukrainian
word-group used to describe the way somebody performs an action, or the state
in which a person finds himself, has the structure that may be represented by
the formula adverb followed by a finite form of a verb (or a verb + an adverb),
він кріпко спить, він швидко/повільно/ засвоює. In English we can also use structurally similar
word-groups and say he smokes a lot, he learns slowly (fast). The structure of
idiomatic English word-groups however is different. The formula of this
word-group can be represented as an adjective + deverbal noun, he is a heavy
smoker, a poor learner, “The Englishman is a slow starter but there is no
stronger finisher" (Galsworthy). Another English word-group used in
similar cases has the structure verb to be + adjective + the infinitive, (He)
is quick to realize, (He) is slow-to cool down,which is practically
non-existent in the Ukrainian language. Commonly used English words of the type
(he is) an early-riser, a music-lover, have no counterparts in the Ukrainian language
and as a rule correspond to phrases of the type (він) paнo встає, (він) дуже любить музику.
Last but not least
contrastive analysis deals with the meaning and use of situational verbal
units, words, word-groups, sentences which are commonly used by native
speakers in certain situations.
For instance when we
answer a telephone call and hear somebody asking for a person whose name we
have never heard the usual answer for the Ukrainian speaker would be Ви помилились (номером).
The Englishman in identical situation is likely to say Wrong number .
To sum up contrastive
analysis cannot be overestimated as an indispensable stage in preparation of
teaching material, in selecting lexical items to be extensively practiced and
in predicting typical errors. It is also of great value for an efficient teacher
who knows that to have a native like command of a foreign language, to be able
to speak what we call idiomatic English, words, word-groups and whole sentences
must be learned within the lexical, grammatical and situational restrictions of
the English language.
I.2.
Statistical Methods of Analysis
An important and
promising trend in modern linguistics which has been making progress during the
last few decades is the quantitative study of language phenomena and the
application of statistical methods in linguistic analysis.
The first requirement for
a successful statistical study is the representativeness of the objects counted
for the problem in question, its relevance from the linguistic point of view. Statistical
approach proved essential in the selection of vocabulary items of a foreign
language for teaching purposes.
It is common knowledge
that very few people know more than 10% of the words of their mother tongue. It
follows that if we do not wish to waste time on committing to memory vocabulary
items which are never likely to be useful to the learner, we have to select
only lexical units that are commonly used by native speakers.
It goes without saying
that to be useful in teaching statistics should deal with meanings as well as
sound-forms as not all word-meanings are equally frequent.
Besides, the number of
meanings exceeds by far the number of words. The total number of different
meanings recorded and illustrated in Oxford English Dictionary for the first
500 words of the Thorndike Word List is 14,070, for the first thousand it is
nearly 25,000. Naturally not all the meanings should be included in the list of
the first two thousand most commonly used words. Statistical analysis of
meaning frequencies resulted in the compilation of A General Service List of
English Words with Semantic Frequencies. The semantic count is a count of the
frequency of the occurrence of the various senses of 2,000 most frequent words
as found in a study of five million running words. The semantic count is based
on the differentiation of the meanings in the OED and the frequencies are
expressed as percentage, so that the teacher and textbook writer may find it
easier to understand and use the list. An example will make the procedure clear.
room (’space’)
takes less room, not
enough room to turn round (in)
make room for
(figurative)
room for improvement –
12%
|
|
come to my room,
bedroom, sitting room; drawing room, bathroom – 83%
|
|
(plural = suite,
lodgings)
my room in college
to let rooms – 2%
|
|
It can be easily observed
from the semantic count above that the meaning ‘part of a house’ (sitting room,
drawing room,) makes up 83% of all occurrences of the word room and should be
included in the list of meanings to be learned by the beginners, whereas the
meaning ’suite, lodgings’ is not essential and makes up only 2% of all
occurrences of this word.
In Ukrainian:
Кімната (окреме приміщення перев. для
проживання в квартирі, будинку) – 41%
Хата розм. – 17%
Покій, палата заст. (перев. розкішне,
багате приміщення) – 3%
Світлиця, горниця розм. (перев. чисте, парадне
приміщення) – 7%
Вітальня (приміщення, обладнане для
приймання гостей)
- 29%
Ванькир (бічне
приміщення, відокремлене від великої кімнати, яке є спальнею і дитячою
кімнатою) –3%
One more specific feature
must, however, be stressed here. All modern methods aim at being impersonal and
objective in the sense that they must lead to generalizations verifiable by all
competent persons. In this effort to find verifiable relationships concerning
typical contrastive shapes and arrangements of linguistic elements, functioning
in a system, the study of vocabulary has turned away from chance observation
and made considerable scientific progress.
Thus, statistical
analysis is applied in different branches of linguistics including lexicology
as a means of verification and as a reliable criterion for the selection of the
language data provided qualitative description of lexical items is available.
I.3. Immediate
Constituents Analysis
The theory of Immediate
Constituents (IC) was originally elaborated as an attempt to determine the ways
in which lexical units are relevantly related to one another. It was discovered
that combinations of such units are usually structured into hierarchically
arranged sets of binary constructions. For example in the word-group a black
dress in severe style we do not relate a to black, black to dress, dress to in.
but set up a structure which may be represented as a black dress / in severe
style. Thus the fundamental aim of IC analysis is to segment a set of lexical
units into two maximally independent sequences or ICs thus revealing the
hierarchical structure of this set. Successive segmentation results in Ultimate
Constituents (UC), two-facet units that cannot be
segmented into smaller units having both sound-form and meaning. The Ultimate
Constituents of the word-group analysed above are: a | black | dress | in |
severe | style.
It is mainly to discover
the derivational structure of words that IC analysis is used in lexicological
investigations. For example, the verb denationalise has both a prefix de- and a
suffix -ise (-ize). To decide whether this word is a prefixal or a suffixal
derivative we must apply IC analysis. The binary segmentation of the string of
morphemes making up the word shows that *denation or *denational cannot be
considered independent sequences as there is no direct link between the prefix
de- and nation or national. In fact no such sound-forms function as independent
units in modern English. The only possible binary segmentation is de |
nationalise, therefore we may conclude that the word is a prefixal derivative.
There are also numerous cases when identical morphemic structure of different
words is insufficient proof of the identical pattern of their derivative
structure which can be revealed only by IC analysis. Thus, comparing,
snow-covered and blue-eyed we observe that both words contain two
root-morphemes and one derivational morpheme. IC analysis, however, shows that
whereas snow-covered may be treated as a compound consisting of two stems snow
+ covered, blue-eyed is a suffixal derivative as the underlying structure as
shown by IC analysis is different, (blue+eye)+-ed. In Ukrainian: без/совіс/ний, за/турк/ан/ий,
ні/куди/ш/ній, без/пом/іч/н/ий, зрад/н/ик, за/прод/ан/ець, не/роз/суд/л/ив/ий,
роз/важ/л/ив/ий, без/перспектив/ний, не/гід/н/ик, с/пад/ко/єм/ець.
It may be inferred from
the examples discussed above that ICs represent the word-formation structure
while the UCs show the morphemic structure of polymorphic words.
I.4.
Distributional Analysis and Co-occurrence
Distributional analysis
in its various forms is commonly used nowadays by lexicologists of different
schools of thought. By the term distribution we understand the occurrence of a
lexical unit relative to other lexical units of the same level (words relative
to words / morphemes relative to morphemes). In other words by this term we
understand the position which lexical units occupy or may occupy in the text or
in the flow of speech. It is readily observed that a certain component of the
word-meaning is described when the word is identified distributionally. For
example, in the sentence The boy — home the missing word is easily identified
as a verb — The boy went, came, ran, home. Thus, we see that the component of
meaning that is distributionally identified is actually the part-of-speech
meaning but not the individual lexical meaning of the word under analysis. It
is assumed that sameness / difference in distribution is indicative of sameness
/ difference in part-of-speech meaning.
According to Z. Harris,
"The distribution of an element is the total of all environments in which
it occurs, the sum of all the (different) positions (or occurrences) of an
element relative to the occurrence of other elements". In Soviet
linguistics this definition has been improved, applied on different levels and
found fruitful in semasiology. The "total" mentioned by Z. Harris is
replaced by configurations, combining generalized formulas of occurrence with
valency. Defining word classes for distributional analysis depends on the
structural use of the word in the sentence.
Observation is
facilitated by coding. In this, words are replaced by conventional word-class
symbols. Each analyst suggests some variant suitable to his particular purpose.
A possible version of notation is N for nouns and words that can occupy in the
sentence the same position, such as personal pronouns. To indicate the class to
which nouns belong subscripts are used; so that Np means a personal noun, Nm —
a material noun, Ncoll — a collective noun, etc. V stands for verbs. A — for
adjectives and their equivalents, D — for adverbs and their equivalents.
Prepositions and conjunctions are not coded.
Observation is further
facilitated by simplifying the examples so that only words in direct syntactic
connection with the head-word remain.
Thus, when studying the verb make, for example: The
old man made Henry laugh aloud may be reduced to The man made Henry laugh.
Until recently the
standard context was taken to be the sentence, now it is often reduced to a phrase,
so that this last example may be rewritten as to make somebody laugh.
When everything but the
head-word of the phrase is coded we obtain the distributional formula: make+ Np
+ V
The examples collected
are arranged according to their distributional formulas, and the analyst
receives a complete idea of the environments the language shows for the word in
question. The list of structures characteristic of the word's distribution is
accompanied by examples:
Make + a + N - make a
coat, a machine, a decision
Make + (the) + N + V -
make the machine go, make somebody work
Make + A - make sure
Make + a + A+N - make a
good wife.
In each of these examples
the meaning of make is different. Some of these patterns, however, may be used
for several meanings of the word make, so that the differentiation of meanings
is not complete. Compare, for instance, the following sentences, where the
pattern make + N remains unchanged, although our intuition tells us that the
meaning of make is not the same:
60 minutes make an hour.
60 people make a
decision.
A phrase, all elements of
which, including the head-word, are coded, is called a distributional pattern,
for instance to make somebody laugh to V1 Np V2
Another example:
Get + N (receive) – get
letter
Get + Adj (become) – get
angry
Get + Vinf (start) – get
to think
In Ukrainian:
йде дощ - іти +
N явище природи rainfalls
йде поїзд - іти +
N неістота train runs
йде чоловік -іти +
N істота man goes (walks)
йде дим - іти +
N неістота it smokes
йде зима - іти +
N неістота winter approaches
or;
іде заміж marries
іде на пенсію retires
іде конем (у шахи) moves the knight
To conclude, distribution
defined as the occurrence of a lexical unit relative to other lexical units can
be interpreted as co-occurrence of lexical items and the two terms can be
viewed as synonyms.
It follows that by the
term distribution we understand the aptness of a word in one of its meanings to
collocate or to co-occur with a certain group, or certain groups of words
having some common semantic component.
I.5.
Transformational Analysis
Transformational analysis
in lexicological investigations may be defined as re-patterning of various
distributional structures in order to discover difference or sameness of
meaning of practically identical distributional patterns.
Word-groups of identical
distributional structure when re-patterned also show that the semantic
relationship between words and consequently the meaning of word-groups may be
different. For example, in the word-groups consisting of a possessive pronoun
followed by a noun, his car, his failure, his arrest, his goodness, etc., the
relationship between his and the following nouns is in each instant different
which can be demonstrated by means of transformational procedures.
·
his car (pen,
table) may be re-patterned into he has a car (a pen, a table) or in a more
generalised form may be represented as A possesses B.
·
his failure
(mistake, attempt) may be represented as he failed (was mistaken, attempted) or
A performs В which is impossible in the case of
his car (pen, table).
·
his arrest (imprisonment,
embarrassment) may be re-patterned into he was arrested (imprisoned and
embarrassed) or A is the goal of the action B.
·
his goodness
(kindness, modesty) may be represented as he is good (kind, modest) or В is the quality of A.
In Ukrainian:
Болільник - той, хто уболіває
Зрадник - той,
хто зрадив
Чайник - те, що
призначено (посуд) для заварювання чаю
Спільник - той,
хто діє спільно з кимсь у незаконній справі
Здирник - той,
хто здирає, вимагає шляхом примусу і погроз
Супутник - той,
хто йде, їде разом
Могильник -
сховище чогось шкідливого, непотрібного, відпрацьованого
Намордник - те,
що надівають па морду
Полярник- той,
хто досліджує полярні райони
Ливарник - той,
хто відливає металеві вироби
Хабарник - той, хто бере хабарі
Types of transformation
differ according to purposes for which transformations are used.
There are:
·
permutation
·
replacement
·
additiоn
(or expansion)
·
deletion
Transformational
procedures are also used as will be shown below in componental analysis of
lexical units.
I.6.
Componential Analysis
Componential analysis is
thus an attempt to describe the meaning of words in terms of a universal
inventory of semantic components and their possible combinations.
Componential approach to
meaning has a long history in linguistics.
L. Hjelmslev's
commutation deals with similar relationships and may be illustrated by
proportions from which the distinctive features d1, d2, d3 are obtained by
means of the following procedure:
d1 = 'boy' = 'man' =
'bull'
'girl' 'woman' 'cow'
hence
d2 = 'boy' = 'girl'
'man' 'woman'
d3 = 'boy' = 'girl'
'bull' 'cow'
As the first relationship
is that of male to female, the second, of young to adult, and the third, human
to animal, the meaning 'boy' may be characterized with respect to the
distinctive features d1, d2, d3 as containing the semantic elements 'male',
'young' and 'human'. The existence of correlated oppositions proves that these
elements are recognized by the vocabulary.
In criticizing this
approach, the English linguist Prof. W. Haas argues that the commutation test
looks very plausible if one has carefully selected examples from words entering
into clear-cut semantic groups, such as terms of kinship or words denoting
colours. It is less satisfactory in other cases, as there is no linguistic
framework by which the semantic contrasts can be limited. The commutation test
borrows its restrictions from philosophy.
A very close resemblance
to componential analysis is the method of logical definition by dividing a
genus into species and species into subspecies indispensable to dictionary
definitions. It is therefore but natural that lexicographic definitions lend
themselves as suitable material for the analysis of lexical groups in terms of
a finite set of semantic components. Consider the following definitions given
in Hornby's
dictionary:
Cow— a full grown female
of any animal of the ox family.
Calf — the young of the
cow.
The first definition
contains all the elements we have previously obtained from proportional
oppositions. The second is incomplete but we can substitute the missing
elements from the previous definiton. It is possible to describe parts of the
vocabulary by formalising these definitions and reducing them to some standard
form according to a set of rules.
Componential analysis may
be also arrived at through transformational procedures. It is assumed that
sameness / difference of transforms is indicative of sameness / difference in
the componental structure of the lexical unit. The example commonly analysed is
the difference in the transforms of the structurally identical lexical units,
puppydog, bulldog, lapdog. The difference in the semantic relationship between
the stems of the compounds and hence the difference in the component of the
word-meaning is demonstrated by the impossibility of the same type of
transforms for all these words. Thus, a puppydog may be transformed into ‘a dog
(which) is a puppy’, bull-dog, however, is not ‘a dog which is a bull’, neither
is a lapdog ‘a dog which is a lap’. A bulldog may be transformed into ‘a
bulllike dog’, or ‘a dog which looks like a bull’, but a lapdog is not ‘a dog
like a lap’.
In Ukrainian:
свекор -
(фізичний об'єкт) (живий) (людина) (чоловік) (той, хто має одруженого сина) (по
відношенню до дружини сина)
холостяк - (фізичний об'єкт) (живий)
(людина) (чоловік) (дорослий)
(той, що ніколи не одружувався)
рухатися (щодо живої істоти) (по землі) (пересуваючи
ноги)
плентатися (щодо живої істоти) (по землі)
(пересуваючи ноги) (повільно, через силу).
I.7.
Method of Semantic Differential
All the methods of
semantic analysis discussed above are aimed mainly or exclusively at the
investigation of the denotational component of the lexical meaning.
The analysis of the
differences of the connotational meaning is very hard since the nuances are often
slight, difficult to grasp and do not yield themselves to objective
investigation and verification.
An attempt to establish
and display these differences was developed by a group of American
psycholinguists. They set up a technique known as the semantic differential by
means of which, as they claim, meaning can be measured. It is perfectly clear,
however, that what semantic differential measures is not word-meaning in any of
accepted senses of the term but the connotational component of meaning or to be
more exact the emotive charge.
Their technique requires
the subjects to judge a series of concepts with respect to a set of bipolar
(antonymic) adjective scales. For example, a concept like horse is to be rated
as to the degree to which it is good or bad, fast or slow, strong or weak, etc.
Horse
+
good………………………………………………..bad
_
fast………………………………………………………………slow
strong……………………………………………………………week
+
hard……………………………………………………………...soft
+
happy…………………………………………………………….sad
The meaning of the seven
divisions is, taking as an example the first of the scales represented above,
from left to right: extremely good, quite good, slightly good, neither good nor
bad (or equally good and bad) slightly bad, quite bad, extremely bad.
In the
diagram above horse is described as neither good nor bad, extremely fast, quite
strong, slightly hard, equally happy and sad. The responses of the subjects produce a semantic profile representing the
emotive charge of the word.
In Ukrainian:
Людина
+
добра..................................................................................................зла
_
+
молода...............................................................................................стара
+
гарна.................................................................................................погана
+
засмучена.........................................................................................щаслива
+
висока..............................................................................................низька
I.8. Contextual
Analysis
Contextual analysis
concentrates its attention on determining the minimal stretch of speech and the
conditions necessary to reveal in which of its individual meanings the word in
question is used. In studying this interaction of the polysemantic word with
the syntactic configuration and lexical environment contextual analysis is more
concerned with specific features of every particular language than with
language universals.
Roughly, context may be
subdivided into lexical, syntactical and mixed. Lexical context, for instance,
determines the meaning of the word black in the following examples. Black
denotes colour when used with a key-word naming some material or thing, black velvet, black gloves. When used with keywords denoting
feeling or thought, it means 'sad', 'dismal': black thoughts, black despair.
With nouns denoting time, the meaning is 'unhappy', 'full of hardships': black
days, black period.
In Ukrainian: чорне діло; чорна справа - підступні вчинки, які викликають огиду, осуд, чорне слово - лайливий вираз із згадуванням чорта, чорний ворон - машина, в якій перевозять заарештованого. чорні дні - дуже важкий час, сповнений неприємних
клопотів, страждань, нужди, чорна хмара (туча) - Дуже сумний, похмурий, невеселий, невдоволений.
If, on the other hand,
the indicative power belongs to the syntactic pattern and not to the words
which make it up, the context is called syntactic. Make means 'to cause' when
followed by a complex object: I couldn't make him understand a word 1 said.
A purely syntactic
context is rare. As a rule the indication comes from syntactic, lexical and
sometimes morphological factors combined. Thus late, when ussd predicatively,
means 'after the right, expected or-fixed time', as to be late for school. When
used attributively with words denoting periods of time, it means 'towards the
end of the period', in late summer. Used attributively with proper personal
nouns and preceded with a definite article, late means 'recently dead'.
To sum up, the study of
details may be more exact with the contextual method.
CONCLUSION
Acquaintance with the
currently used procedures of linguistic investigation shows that contrastive
analysis and statistical analysis are widely used in the preparation of
teaching material and are of primary importance for teachers of English.
The special interest of
contemporary science in methods of linguistics research extends over a period
of about twenty five years. The present status of principles and techniques in
lexicology, although still far from satisfactory, shows considerable progress.
The structural synchronic approach may be said to have grown into a whole
system of procedures which can be used either successively or alternately.
The main procedures
belonging to this system are the analysis into immediate constituents;
distributional analysis with substitution test as part of it; transformational
analysis; componential analysis, and statistical analysis.
Bach of these techniques
viewed separately has its limitations but taken together they complete one
another, so that each successive procedure may prove helpful where the previous
one has failed. We have considered these devices time and again in discussing
separate aspects of the vocabulary system. All these are formalized methods in
the sense that they replace the original words in the linguistic material
sampled, for analysis by symbols that can be discussed without reference to the
particular elements they stand for, and then state precise rules for the
combination and transformation of formulas thus obtained.
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