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QUANTIFICATIONAL
REPRESENTATION OF MEANING
By: R. Yohanes Radjaban
The
quantificational approach to meaning has been applied to broad sections of the
English vocabulary. This approach resembles the componential approach in
several ways. It is concerned with word sense. It assumes that word sense
consists of components called ‘factors’ or ‘dimensions’. It assumes that the
more components two words have in common, the more similar they are in meaning.
The major difference between the two approaches is in the role of the
investigator’s own semantic judgments. In the componential approach, it is
typically the investigator who judges which analogies are well formed and which
are not. In the quantificational approach, other people make the judgements and
the investigator merely extracts the component latent in their judgments. The
quantificational methods were developed for three reasons. First, it was felt
that these methods would be more ‘objective’ and less open to the
investigator’s own biases. Second, it was possible to investigate semantic
field about which the investigator had no clear intuitions. And third, these
methods were able to handle components of meaning that were continuous, like
age, where the componential approach could handle only components that were
discrete, like adult versus non-adult.
Semantic Factors
In an early quantificational approach to meaning, Osgood,
Suci, and Tannenbaun (1957) tried to measure ‘affective’ meaning by a test they
called the semantic differential.
(See Clark & Clark, pp. 433) People
were asked to rate certain words based on twenty bi-polar adjective scales. The
word mother, for example, might be
rated impressionistically as quite happy,
very soft, and neither fast nor slow. These ratings were than analyzed by a
method called factor analysis. A word
was given similar ratings on each scale within a group, but different ratings
on scales not in the same group. Each group of bi-polar scales seemed to
reflect a different ‘factor’ or aspect of affective meaning. The three factors
were :
Evaluation
(reflected in good/bad, happy/sad, and beautiful/ugly)
Potency
(reflected in strong/weak, brave/coward,
and hard/soft)
Activity
(reflected in fast/slow, tense/relaxed, and
active/passive)
As a complete representation of word senses, the semantic
differential has limitation. The most serious is that it measures the affective
reactions a word elicits, but not the concept it denotes. Although the semantic
differential has been useful in studying attitudes and emotional reactions, it
has had little success in explaining how word sense is involved in
comprehension, production, and acquisition.
Semantic Space
In more recent quantificational methods, word meanings are
often represented by means of a semantic
space. The meaning of a word is taken
to be a location in physical space in which each dimension represents one of
the word’s semantic components. (See Clark & Clark, pp. 434) The closer two
words in semantic space are, the more similar they are in meaning.
Multidimensional Scaling
Multidimensional
scaling developed by Shepard (1962) and Kruskal (1964) work backward from
people’s judgements of similarity to the semantic space. In applying this
method, one typically shows people all possible pairings of words within a
semantic domain. For each pair they rate how similar the two words are on a
scale of 1 to 10. The average ratings for the twenty-eight pairs are then
submitted to a special computer program. It is designed to find a semantic
space in which the more similar two words are rated on the average, the closer
they are in the space. (See Clark & Clark, pp. 436).
Semantic Clusters
Word domains that do not fit into neat semantic spaces may
instead divide into two word clusters. For these S. Johnson (1967) has devised
a method called hierarchical cluster
analysis. People are asked to rate all word pairs within a domain for their
similarity in meaning, but what is produced is a hierarchical arrangement of
clusters. The words within a cluster are all closely related, and the clusters
themselves are related to each other in a hierarchy. For illustration consider
the clusters of English pronouns in Table 11-5 on page 437 as analyzed by
Fillenbaum and Repoport (1971).
Cluster analysis, however, can miss certain relationships and
be misleading on others. Note that English pronouns are nominative (I, we, he, she, they), accusative (me, us, him, her, them), or possessive
(my, our, his, her, their, your).
Cluster analysis cannot represent this fact because it does not extract
cross-classifications from clusters. Cluster analysis is limited to discovering
only certain types of relationships.
Limitations of the
Quantificational Approach
Quantificational
methods were taken up because they were felt to be more ‘objective’. They used
simply judgments from naïve people and relied on mechanical procedures for
extracting the semantic spaces and clusters latent in the judgments. But this
objectivity was bought at the cost of certain limitations. Some were in the
methods themselves, and others were in the notions of semantic space and
semantic clusters.
Are the Methods Adequate?
Ironically,
the objectivity in the methods constitutes one of their chief weaknesses. When
people distill their knowledge of two words into a 1-to-10 rating of how
similar the words are, they gloss over the subtleties of word meaning. And
averaging over many such ratings only obscures any subtleties that may be
there. Even more troubling is the unavoidable tendency for people to change
their criterion for ‘semantic similarity’ as they go from one word pair to the
next.
For many investigators, another drawback is that these
methods tacitly take the encyclopedic view of meaning. When people make a
1-to-10 judgment of word similarity, they are not asked to distinguish what
they know about dogs from what they
know about the word dogs. They do
not distinguish their mental encyclopedia from their mental lexicon.
Is a Semantic Space Enough?
Even in the ideal, the notion of semantic space has inherent
limitations. One problem is that its dimensions have incomplete
interpretations. In the kinship terms, for example, one dimension space would
be ‘parent-child’, a dimension that distinguishes parent from child, father from
son, and mother from daughter.
What the semantic space does not tell us is that parent and child are
rational, specifying the relation between two people x and y as in x is
the parent of y. Nor does it tell us that parent and child are
converses, that if x is the parent of y,
then y is the child of x.
A related problem is that while this approach may reveal the
meaning of single words or simple phrases, it cannot deal with sentences. It
cannot in principle tell how word meanings fit together to form sentence
meanings. For many investigators, this is the central goal in studying meaning—to
explain how man is just a compressed
version of male adult human and how man, bite, and dog go together to form man
bites dog.
The word dog
accomplishes what it does via the concept dog. Recall that in the nominal view
of meaning, dog is merely the name
for the category dog, which is defined by one’s concept of dog.
Within the
functional approach, concepts are defined by rules, but the rules correspond to
mental operations by which people actually decide whether or not an object
belongs to a category. This assumption has been made concrete in the approach
called procedural semantics.
Procedural Semantics
The basic idea behind the procedural semantics is that the sense of
a word is a procedure—a set of mental operation—for deciding when a word
applies to a thing. (See Table 11-6, pp. 440)
Components as Procedures
No one will have missed the obvious resemblance of the procedure for
man to the semantic components of man, namely Male(x) & Human(x). The procedure is just the three components
of man strung out in a serial order.
Each procedure itself relies on other procedures in its operation.
In the procedure for Man(x), Step 1
is really another procedure called Human(x)
in turn makes use of other more elementary procedures, and so on. The procedure
Male(x) itself may be used as part
of other procedures, like that for King(x)
and Bachelor(x). The advantage of
this system is that the sense of a word like man calls on the same mental operations that are required for the
senses of many other words. Elementary procedures can be combined in various
ways to form the procedures for complex words.
Procedures as Mental
Operations
In the functional approach, semantic components have a natural
explanation. They are those basic mental operations in the human cognitive
system that are used for classifying encyclopedic knowledge—for categorizing
immediate perceptions and past recollections.
Limitations of Procedural
Semantics
Because procedural semantics is in its infancy, its strengths and
weaknesses are not easy to judge. Most procedures proposed so far have been
taken directly from componential analysis, and where that is successful, so is
procedural semantics. Yet procedural semantics has made some progress beyond
componential analysis.
Are
Procedures Flexible Enough?
Because the procedures designed so far are fairly inflexible, they
run into difficulties where flexibility is called for—as in contextual
variation, received knowledge, conversational adjustments, and fuzzy
boundaries.
Semantic procedures must also be flexible enough to deal with
received knowledge. Another problem is how to adjust procedures to speakers and
listener. An adult speaking to a child may refer to a wolf as a doggie to accommodate to the child’s
conception of wolves. And a scientist talking to a layman might use science to include astrology and
numerology to accommodate to the layman’s understanding of science, Semantic procedures do not yet allow for such
conversational adjustments.
The categories, words name typically, have fuzzy boundaries,
putting an even greater strain on semantic procedures. Because tomatoes lie on
the boundary between fruit and vegetables, they may sometimes be called fruit and other times vegetable.
The limitations of inflexibility procedures are not necessarily
limitations of semantic procedures in general, nor are they limitations on the
broader functional approach to meaning. It could be argued that one strength of
the functional approach is that it draws out these issues and tries to address
them.
COMPLICATIONS IN THE REPRESENTATION OF MEANING
So far, each word has been treated as if it had one and only
one sense. This is incorrect for three reasons. First, almost all words are polysemous—they have more than one
sense. Second, there are expressions called idioms,
like kick the bucket meaning ‘die’,
which do not get their meaning directly from the words they contain. And third,
some words can be used for conveying senses never before associated with them.
This phenomenon will be called lexical
creativity.
Polysemy
Although words almost always have more than one sense, these
multiple senses are of two kinds: homonymy
and polysemy. Consider these
three senses for the phonological sequence ear:
Sense 1: the
visible organ of hearing, as in floppy
ears.
Sense 2: the
sense of hearing, as in good ear for
jazz.
Sense 3: the
spike that bears corn, as in three ears
of corn.
The American Heritage
Dictionary classify the first two senses together under a dictionary entry
labeled ear1, and the
third sense under another labeled ear2.
In this way, it claims that ear1
and ear2 are two
different words. By historical accident they happen to be pronounced (and
spelled) alike, but are otherwise as different as nose and stalk. Ear1 and Ear2 are therefore called homonyms. Sense 1 and 2 are claimed
to be different senses of the same word. Hey are historically related, with
sense 2 thought to be an ‘extension’ of sense 1. Ear1 is therefore said to be polysemous, to show the
property of polysemy.
Are Some Senses Built on the Spot?
In a study of line,
Camarazza and Grober (1976) demonstrated that people at least see some senses
as more central than others. Line has five relatively distinct senses:
Sense 1:
A physical mark, as in Two parallel
lines never meet.
Sense 2:
A demarcation, as in His bags checked at
the state line.
Sense 3:
A Continuous arrangement, as in Line up
the blocks.
Sense 4:
A Continuous sequence of words, as in Actors
learn lines.
Sense 5:
A sequence of constructs, as in What is
your line of work?
Through a variety of quantificational techniques, it was
shown that people view sense 1 as most central, sense 2 as next most central,
and so on. Caramazza and Grober argued that line had a core meaning, approximately ‘an extension’, and the five
senses were all realizations of this core meaning. Sense 1 was the most
concrete, and sense 5 the most abstract, and this led to people’s judgments of
centrality. However, they do not say whether all five senses are built on the
spot from a core meaning or come from ready-made for use when they are needed.
Idioms
Idioms are
phrases with special meanings. Most idioms are the petrified remains of dead
metaphors. New metaphors are created every day. At any moment some metaphors
have just been born, some are old and familiar, some are dying, and some are
dead and petrified.
Lexical Creativity
People are not content to leave language alone. When it
leaves them too little room to maneuver efficiently, they invent new uses for
old words and sometimes invent new words altogether. Some innovations are so natural
that they go unnoticed: The mountain is
jeepable. Others hit us as innovations: This music is very Beethoveny. The mental lexicon does not contain
them ready-made in this form. They must be created on the spot as a normal part
of speaking and listening.
The functional approach suggests a natural way of handling
innovations, for it allows semantic procedures to be built on the spot. Take Margaret 747’d to San Fransisco. On
hearing 747’d, listeners realize
they must come up with a procedure for an action. The action the speaker must
be suggesting with 747 is the one
associated with the normal function of 747’s,
namely flying with a 747 as an instrument. They would then build a procedure
for ‘fly by means of a 747’ just as the speaker intended. What makes the
functional approach especially suitable is that it views word senses as
dynamic, not static.