This is my honors Bachelor's thesis from the University of Illinois Urbana-Champaign which covers Semantic Numerosity.

1. Semantic Numerosity
Jeet Samarth Raut
Submitted in fulfillment of the
requirements for the honors degree of
Cognitive Psychology
at
University of Illinois Urbana-Champaign
2011

2. The brain is an amazing organ. It weighs a mere three pounds and astonishingly
contains as many as 100 billion brain cells(Magill's Medical Guide Revised Edition.
Salem Press, 1998: 221.) It is the most complex organ in the human, and controls major
functions of the body, such as: moving, reasoning, processing the five types of sensory
information, thinking, and speaking to name a few. Since ancient times, humans have
sought out to find what makes everything in the brain work and try to explain the
functions of the different areas of the brain. In the 1950’s there was a shift in interest
and researchers started trying to find models to describe the manner in which the brain
works. These models combined psychology, linguistics, philosophy, computer science,
artificial intelligence, and neuroscience, and the study of these models assimilated into a
new field, known as cognitive science.
60 years later, the field of cognitive science is as busy as ever. New discoveries
illicit more research as researchers delve into the intricacies of the mind. A great
example of this is the field of linguistics. Linguistics is used to examine grammar, but
this grammar is one which is unfamiliar to most people. Grammar is the set of rules
used to generate a language. When you think of grammar, what you probably think of is
what a student would learn in a elementary school English class. Perscriptive grammar
is how some educators believe people should talk and write, and insignificant to
cognitive science. Examples of perscriptive grammar include not starting a sentence
with a preposition(“Also I am thirsty.”) and using the word “whom”. What we seek out to
learn is the “natural” or descriptive grammar, which is the way to describe how people
actually talk and write. Descriptive grammar used in everyday language because the
entire concept of linguistics is based on communicating, and what we study is the

3. behavior of communication.(Carrol, 26)
Linguistics is divided into several sub-categories of study. These include the ways
in which we physically produce speech(phonetics), the manner in which we analyze an
individual word’s structure(morphology), the structure of sentences (syntax), the
meaning of words and sentences(semantics), and the how the linguistics is used to
communicate (pragmatics) . Psycholinguistics is a interdisciplinary study combining
linguistics and psychology. It is divided into 3 main categories, language acquisition,
language comprehension, and language production. This paper will primarily focus on a
specific question about language production, though there is much overlap from the
other two categories.
If you are reading this, you are presumably an English speaker, and as an English
speaker, when you attempt to pluralize words, you make sure that there is more than
one of whatever you are pluralizing so that there is agreement and the statement makes
sense. For example consider the following four statements:
1.That dog barked.
2.Those dogs barked.
3.*That dogs bark.
4.*Those dog.
(In linguistics, an * will precede grammatically incorrect sentences.) “That” can only be
used to refer to a singular object and “those” can only be used to refer to plural objects,
and this property of word agreement is known as grammatical number. (Bock and
Miller, 48)
Pluralization is dependent on the grammatical number, and every category of
linguistics is involved with the pluralization. How would you pluralize a word that you are
unfamiliar with? Jean Berko asked children that exact question in a 1958 paper entitled
The Child's Learning of English Morphology. She took group of pre-school students
ranging in age from five to seven, and had them participate in a sentence

4. completion test, an example of which is listed below.
This is a wug
Now there is another one. There are two of
them. There are two _________.
Just like you or I would complete the sentence, the overwhelming majority(91%)
of the pre-schoolers answered with “wugs”, by adding “-s” to the unknown word.
The same test was given with other made up words such as “gulch” and “heaf”,
and though the pre-schoolers weren’t quite as accurate( 36% came up with
“gulches” and 86% came up with “heaves”) some still knew how to pluralize the
unknown words. The aforementioned noun endings “-s”, “-es” and “-ves” are
known as morphemes and are the smallest unit of meaning, and they add a
pluralized meaning to nouns.(Berko, 159) The grammatical number is used
extensively in understanding and producing these morphemes, and therefore the
morphemes are an essential part of pluralization.
As you may have noticed by now, all the plural morphemes had a feature in
common, they all contain the letter “s”. The grammatical number is also important
on the way we physically produce the sounds to pluralize words. The “s” sound is
known as an alveolar fricative. The “alveolar” specifies that the sound is made at
the alveolar ridge, the bumpy area right behind your upper set of teeth. The

5. “fricative” means that the person creates a narrow passage of air, and the friction
of the air and the narrow passage makes the sound. There are two different
types of alveolar fricatives, the voiced alveolar fricative, and the unvoiced
alveolar fricative. An example of a voiced alveolar fricative is the word “dogs”
which is pronounced more like the word “dogz”. If a sound is voiced, it means
that the vocal chords continue to vibrate if you hold the sound. If you say the
word “dogs” and continue to hold the “s” at the end, and then you place your
hand on your neck, you will feel your vocal chords vibrating. This is contrasted
with a unvoiced alveolar fricative, an example of which is the “s” at the end of the
word “cats”. If you place your hand on your throat while saying cats, you will feel
no vibrations. Since grammatical number effects the way we pluralize words, it
also then effects the movements that we make in our mouths to produce plural
morphemes.
Robert Manell, The Articulation of Fricatives,
2001 http://clas.mq.edu.au/
phonetics/phonetics/ consonants/fricatives.html
Figure 4

6. I’m sure by now the concept of the grammatical number might seem very
simple to you, as long as you have more than one object in a set its pluralized right?
While this is true for the model of the grammatical number, it conflicts with another
process known as enumeration. Let’s say that you are given two separate unique sets
of items. You are not allowed to explicitly count the number of objects in each of these
sets, but you wish to compare the number of items in each set. We can then deem this
specific characteristic of number which differentiates between the two sets as the
numerosity When figuring at the numerosity of an object, we can search with relative
numerosity( seeing if one set has a greater number or a fewer number of items in
comparison to another set), or we can search with the absolute numerosity (where we
examine the specific number of objects given as an integer value)(Kaufman, Lord,
Reese, and Volkman, 498). Forms of numerosity include estimation and subitization, but
before we define those terms, lets examine counting.
Counting is the process that everyone is accustomed to. It is a serial process
which allows a person to determine the numerosity of a set, In order to specify the
numerosity of any group we have to successively pair each object in the group with a
numeral from the numeral-series, beginning of course with the first number in the series.
This operation we call counting.(Kaufman, Lord, Reese, and Volkman 500). Counting is
usually done by increments of one, but it is also not uncommon to count in groups of
two, three or four.
Estimation is the first major form of enummeration. It is an educated guess
as to how many of an object is contained within a set. The more objects there are in a
set that a person is estimating, the less accurate the estimation will be, and the less
confidence the person estimating will have. If a subject is asked to state the numerosity
of a set containing greater than four objects, it is considered estimation.
Subitization is the second major form of enummeration that we’ll discuss. It’s

7. etymology stems from the latin verb subitare which means “to arrive suddenly”. It is
believed to be a parallel process dependent on the total number of objects in a set being
less or equal to three(though there is a dispute whether it incorporates four). First
proposed by Kaufman, Lord, Reese, and Volkman in the 1949 paper The Discrimination
of Visual Number, subitization deals with the rapid, confident, and accurate assessment
of enummeration on a set of objects containing three or less objects.
Counting, estimation, and subitization are used in conjunction with each other in
order to figure out the conceptual number. The conceptual number is what it sounds
like, it is the idea of an number, but is not dependent on language. To most people,
having two different mechanisms of numerosity may seem strange, but both are
necessary in order to pluralize speech. As an English speaker, it becomes obvious that
you would pluralize a word as long as there is more than one of an object in a set, but in
doing so, you you are ignoring information about numerosity that the brain is giving you.
It is hypothesized that English speakers ignore the process of subitization, because they
only need to know that there is more than one of an object, but there needs to be more
research done before we can come to a conclusion. This gap in the knowledge is what
we intend to fill.
There is further evidence of conceptual number usage that can be observed
throughout the developmental stages of childhood. Famed psychologist Jean Piaget
believed that a child’s mind was a blank slate, and that children learned enummeration
through sersory-motor interactions with objects around them. Piaget cited a child’s
likelihood to think that two sets of similar numbered objects could be thought to have
differing numerosities when one of the sets was spaced further apart than the other. For
example, if you had a set of four marbles, each spread three inches apart from each
other, compared to a set of four marbles each spread four inches away from each other,
the child would say that the set that contained the marbles that were each four inches
apart would have a higher numerosity. It is important to note that these children were at

8. least five years old because they all implicitly had knowledge of the grammatical
number. (Dehaene, 42)
Piaget ideas were proven incorrect by Mehler and Bever in their 1967 paper
Cognitive Capacity of Very Young Children. They hypothesized that part of the reason
that children fell prey to picking longer or bigger sets was that the children could not
understand exactly what the experimenters were asking them to do. They also thought
that another major problem was that there was no motivation for the children to try to
know the numerosity of sets. Mehler and Bever then set up an experiment where the
told children aged from two to four to decide which set of clay pellets had more
members. The results were the same as Piaget’s experiments. They then replaced the
clay pellets with similar looking M&M’s and told to the children to pick one of the rows
and eat as many pieces of candy from that row as they wanted. The rows consisted of a
spread out row of four M&M’s and a close row of six M&M’s. What they discovered was
that the children would consistently take the shorter rows which contained more M&M’s.
Mehler and Bever then concluded that motivation was necessary and that Piaget’s test
could not correctly measure a child’s numeric aptitude. What was also amazing was the
fact that the subjects for the study included children who were as young as two years
old, but still managed to pick the shorter rows which contained more M&M’s. This study
shows that children who have not mastered speech have a knowledge of the conceptual
number, which strongly suggests that conceptual number and grammatical number are
two independent mechanisms.
Conceptual number can also be seen in the youngest of children. In 1983, Sue
Eleen Antell and Daniel Keating set up an experiment where they had 21 to 144 hour
old babies look at a card with two dots on it. The subsequent cards either had less area
between the two dots, or had three dots occupy the space. The experiment measured
the amount of time that the babies would look at the cards. This measure is significant
becaue babies tend to spend a longer time looking at objects they don’t expect to be

9. there. What they found is that even though the length of the row of dots was similar, the
babies could still differentiate the numerosity of the dots. This study is extremely
important because it shows that infants have knowledge of the conceptual number
before they they even acquire and produce language!
If you examine the years of publication of the journal articles cited in this paper,
you way notice that the some are quite old, but none of the papers discuss both
grammatical number and conceptual number. This is notable because while
grammatical number and conceptual number may be two separate mechanisms, they
could influence each other. This leaves room for many new and exciting discoveries in
the field. The only published paper regarding both grammatical number and conceptual
number is entitled Computation of Semantic Number from Morphological Information by
Iris Berent, Steven Pinker, Joeseph Tzelgov, Uri Bibi, Liat Goldfarb in 2005. They
discovered that people gather the grammatical number from words the same way that
people gather the conceptual number from visual cues, and that while they are
separate, they are both essential for speech. It is important to note that the
aforementioned study was in Hebrew and no comparable study has ever been
conducted in English. We cannot assume that the results of the study would be
applicable to English because Hebrew pluralizes in a different way than English does.
In the 1930’s, linguist Benjamin Whorf and his mentor Edward Sapir proposed a
new theory in linguistics, linguistic relativity. Linguistic relativity states that language
dictates the way in which we perceive the world. This is why we must conduct language
experiments in English to understand the grammatical number and conceptual number
in English speakers. Since each language is different, we cannot look at the results of
experiments conducted in other languages( for example, Hebrew in the previous
experiment) and assume that they apply to English in the same manner. There are
however similarities between all the languages in the world and Whorf and Sapir Whorf
had been studying various Native American tribes and a famous example of linguistic

10. relativity is the language of Eskimos. Whorf stated that since Eskimos had a couple of
hundred words for the English word “snow”, that the Eskimos could perceive
differentiations in snow that English speakers could not. This was later proven false
when it turned out that the Eskimos simply had compound words for strings of English
words( for example, “heavy, wet, snow” would be a compound word different from
“heavy snow”). Another example is with color terms. Paul Kay and Brent Berlin
published a book in 1969 entitled Basic Color Terms: Their Universality and Evolution.
The book outlined their theory that there is a sequential order of color term acquisition
Each row signifies one color. The arrows indicate the progression of language if you
have another color term in a language. For example, the 2nd box has 3 colors because
the color white/red/yellow differentiates into white and red/yellow
A Typological and Evolutionary Scheme Covering Most World Color Survey Languages
(Source: Kay and Maffi 1999, Figure 3.)
This graph shows how languages differentiate color. In the first box, we see that
all languages have at least two colors groups, and if a language were to have three
color terms, the first stand-alone color is white. Not all languages have all the colors
however. The Berinmo tribe is located in Papua New Guinea who only have five color
terms, but we know that they do not see in just five colors, they just do not differentiate
names for colors like English speakers do. In Russian, there a completely separate term
for light blue (sinij) then there is for a dark blue (goluboj). The same can be said about
number terms in regards to plurality. For example the Togan tribe has “duals” which can
be contrasted with singular and plurals that are found in English. Duals are nouns that
have different endings than the same word in its singular form. We don’t have any in

11. English, but imagine that the word “dogen” appeared in English and its definition was “2
dogs” This would be different than it’s singular form “dog” and it’s plural of 3 or more,
“dogs”. We know that the speakers of Tongan subitize in order to create duals but we
know that their perception of two objects is the same as ours, even though we don’t
have duals. If the theory of linguistic relativity is true, it is essential that we conduct
research attempting to figure out if the grammatical number and the conceptual number
share the same mental resources in English speakers
At this point, you might be wondering what the point of studying plurality is and
why we spend government money researching it. It is estimated that we use
grammatical number and conceptual number once every five seconds or once every 16
words in active speech! This cognitive system is used thousands of times daily, yet we
do not understand this commonly used process. By researching this topic, we are
hoping to understand this particular cognitive model, and hopefully it will help us to
understand other models of the brain, which is the goal of cognitive science.

12. Works Cited
Antel, Sue Ellen; Keating, Daniel P. (1983) Perception of Numerical Invariance in
Neonates Child Development, 54, 695-701
Berent, I; Pinker, S; Tzelgov, J; Bibi, U; & Goldfarb, (2005) Computation of Semantic
Number from Morphological Information Journal of Learning and Memory, 53,
342-358
Berko, J. (1958) The Child's Learning of English Morphology. Word, 14, 150-177.
Berlin, Brent & Kay, Paul (1969) Basic Color Terms: Their Universality and Evolution
University of California press, Berkeley
Bock, J. K., & Miller, C. A. (1991). Broken Agreement. Cognitive Psychology, 23, 45-93.
Carroll, D. W. (2008). Psychology of Language. (5th ed.). Superior: University of
Wisconsin.
Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The
Discrimination of Visual Number. American Journal of Psychology, 62, 498-525.
Mehler, Jacques & Bever, Thomas (1967)Cognitive Capacity of Very Young Children
Science 158, 141 - 142
Magill's Medical Guide Revised Edition. Salem Press, 1998: 221
Pinker, S. (1994). The Language Instinct: How the Mind Creates Language. New York,

13. : William Morrow and Company, Inc.