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On CategorizationOn Categorization
INF5020 INF5020 –– Philosophy of InformationPhilosophy of Information
L5, slide set #2L5, slide set #2
From
George Lakoff, “Women, Fire, and Dangerous
Things: What Categories Reveal About the Mind”
University of Chicago Press, 1990
Prepared by:
Erek Göktürk, Fall 2004
Edited by:
M. Naci Akkøk, Fall 2004
Importance of Categorization #1Importance of Categorization #1
Categorization is basic to
thought, perception, action,
and speech.
Every time we see
something as a kind of a
thing, we are categorizing.
Not only things, we also
categorize actions (motor
activities).
Tree
Running
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Importance of Categorization #2Importance of Categorization #2
Categorization is automatic and unconscious, except
for problematic cases.
This leads to the impression that every thing in the
world (spoon, cup, monitor, glasses, etc.) comes in
natural kinds, and our categories of mind naturally fit
this categorization inherent in the world.
The problem is that we also categorize abstract
entities, and an accurate theory should account for all
of our categories.
Importance of Categorization #3Importance of Categorization #3
Almost everything we do involves categories. Think of
any utterance: categories of speech sounds, of words,
of phrases and clauses, as well as conceptual
categories.
Reasoning is also closely tied to categorization.
Thus understanding of how we categorize is central to
any understanding of how we think, reason and how
we function.
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Classical Categorization Theory
“Things are in the same category if and only if they have
certain properties in common. These properties define the
category.”
The classical view is not an empirically grounded theory, but
it was taken for granted, from Aristotle to late Wittgenstein.
Until recently, it wasn’t even considered a theory, it was
taken to be a definitional truth.
It is not entirely wrong. We often do categorize things on
the basis of shared apparent properties, but it is only part of
the story.
And the other side of the story will come shortly…
Disembodied Reasoning and Disembodied Reasoning and
Classical Categorization TheoryClassical Categorization Theory
The view of reason as disembodied symbol-
manipulation implicitly assumes classical
categorization theory. (Mind-as-Computer
Metaphor)
“Symbols get their meaning through their capacity
to correspond to things in the world”
- implies -
“Category symbols get their meaning through a
capacity to correspond to categories in the world
(real or some possible one).”
Thus classical theory fits in, since disembodied
reasoning calls for categories existing in the world
independent of human capabilities, i.e., the
capabilities of the categorizer.
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Last DecadesLast Decades’’ DevelopmentsDevelopments
Collecting previous studies that suggest problems
related to classical view of categorization under one
perspective, Eleanor Rosch’s pioneering work made
categorization theory a major field of study.
Some of studies that lead Rosch to formulate
prototype theory follow, then we’ll talk about Rosch’s
work.
WittgensteinWittgenstein
Wittgenstein is generally acknowledged to be the
first to become aware of the cracks in classical
view.
His famous example is the category of “games”,
and he makes the observation that there are no
common properties shared by all games.
Wittgenstein explains the category of games by
what he calls family resemblances: the members of
a family resemble to one another in various ways,
such as hair color, facial features, eye color, but
usually not all of them!
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WittgensteinWittgenstein’’ss
Family ResemblancesFamily Resemblances
• There are no
properties shared by
all members!
• The boundaries are
extendable (video
games recently
introduced).
• Some games are
better examples of
the category: there
are central and non-
central members.
(Dice is not very
representative of a
game)
J.L. AustinJ.L. Austin’’s Work ons Work on
Meaning of WordsMeaning of Words
Various senses of a word can be seen as forming a category.
The senses of a word usually do not share a fixed set of properties, whereas
they are related to one another in various ways. (Similar to Wittgenstein’s family
resemblances)
Austin: “The adjective ‘healthy’: when I talk of a healthy body, and again of a
healthy complexion, of health exercise: the word is not just being used
equivocally . . . There is what we may call a primary nuclear sense of ‘healthy’:
the sense in which ‘healthy’ is used of a healthy body: I call this nuclear because
it is ‘contained as a part’ in the other two senses which may be set out as
‘productive of healthy bodies’ and ‘resulting from a healthy body’. . . . Now are
we content to say that the exercise, the complexion, and the body are all called
‘healthy’ because they are similar?” (metonymy)
Austin: “When A:B::X:Y then A and X are often called by the same name, e.g.,
the foot of a mountain and the foot of a list. Here there is good reason for calling
the things both “feet” but are we say they are “similar”? Not in any ordinary
sense. We may say that the relations in which they stand to B and Y are similar
relations. Well and good: but A and X are not the relations in which they stand.”
(metonymy and metaphor)
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ZadehZadeh’’ss
Fuzzy Set TheoryFuzzy Set Theory
Fuzzy Set Theory: A form of set theory to model graded categories.
In a classical set, everything is either in the set (has membership
value 1) or not (has membership value 0).
In a fuzzy set, elements can have membership values between 0
and 1.
The operations in the original version of the fuzzy set theory are the
following. Suppose element x has membership value v in fuzzy set
A and membership value w in fuzzy set B.
{ Intersection: The value of x in A ∩ B is the minimum of v and w
{ Union: The value of x in A U B is the maximum of v and w
{ Complement: The value of x in the complement of A is 1 – v
Other definitions of intersection and union was suggest after these
originals.
LounsburyLounsbury’’s Work on s Work on
American Indian Kinship SystemsAmerican Indian Kinship Systems
The field he works in is called cognitive anthropology.
The rules of naming relatives shows that cognitive
categories can also be defined by some central
elements plus generation rules (Generative
categories: Generator plus “something else”)
For example, he found the following rules:
{ Skewing rule: Anyone’s father’s sister, as a linking
relative, is equivalent to that person’s sister.
{ Merging rule: Any person’s sibling of the same sex, as a
linking relative, is equivalent to that person himself.
{ Half-sibling rule: Any child of one of one’s parents is
one’s sibling.
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Berlin and KayBerlin and Kay’’ss
Basic Color TermsBasic Color Terms
They challenged the classical view that different languages could
carve up the color spectrum in arbitrary ways.
They found that some color terms appeared to be basic:
{ They had less number of morphemes
{ They are not contained in another color (Scarlet and red)
{ They are not restricted to a small number of objects (blonde)
{ They must be common and generally known
They found that the categories the basic color terms can attach to are
the equivalents of English color categories named by black, white,
yellow, green, blue, brown, purple, pink, orange, and gray.
Some languages have fewer basic color categories, and when a
basic color category covers more than one of the above, for example
say grue covering green and blue, the typical color (focal color) for
this category is not turquoise, but either focal blue or focal green.
Kay and McDanielKay and McDaniel’’s Work on Explaining Berlins Work on Explaining Berlin--
Kay FindingsKay Findings
They used DeValois et.al. work on neurophysiology of
color vision.
DeValois et.al. identified six types of cells:
{ One pair for the perception of blue and yellow
{ One pair for the perception of red and green
{ One pair for the perception of light intensity
Kay and McDaniel fitted a fuzzy set model to DeValois
results, with partial success.
Their finding suggest that the basic color categories
are a product of both neurophysiology and cognitively
real operations that can be partially modeled by fuzzy
set intersection and union.
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Brown and BerlinBrown and Berlin’’ss
Basic Level CategoriesBasic Level Categories
Brown: Objects have many names of different level of detail:
animate being, quadruped, dog, boxer, Fido ☺. Of all the possible
names in a category hierarchy, a particular name, at a particular
level of categorization, “has a superior status.” It feels the real
name of the thing.
Brown: This “first level” categorization has the following properties:
{ It is the level of distinctive actions (we think of playing with the
dog, not the quadruped)
{ It is the level which is learned earliest and at which things are
first named
{ It is the level at which names are shortest and used most
frequently
{ It is a natural level of categorization, as opposed to a level
created by “achievements of the imagination”
Berlin and his students and associates found evidences of such
basic level classification by studying folk classification of plants and
animals in speakers of Tzeltal (a Mexican local language).
Eleanor RoschEleanor Rosch
She’s the first to provide a general perspective on all these special
cases.
The theory has come to be called “the theory of prototypes and
basic-level categories” or “prototype theory”.
She focused on two implications of the classical view on
categorization:
{ “If the categories are defined only by properties that all
members share, then no members should be better examples
of the category than any other members.
{ If categories are defined only by properties inherent in the
members, then categories should be independent of the
peculiarities of any beings doing the categorizing; that is they
should not involve such matters as human neurophysiology,
human body movement, and specific human capacities to
perceive, to form mental images, to learn and remember, to
organize the things learned, and to communicate efficiently.
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ElanorElanor RoschRosch
Prototype EffectsPrototype Effects
Her early studies were on color categorization in speakers of
Dani (a New Guinea language).
In Dani, there are only two basic color terms: mili (for dark-
cool, incl. black, green, and blue) and mola (for light-warm,
incl. white, red, yellow).
Her hypothesis was if language alone determined color
categorization, then the Dani should have equal difficulty
learning new words for colors, no matter whether the color
ranges had primary color at the center or a nonprimary
color.
Her studies provided empirical evidence that primary color
categories were psychologically real for speakers of Dani,
and focal colors had a “special cognitive status”, which
would correspond to what she will call cognitive reference
points or prototypes in her later research.
Eleanor RoschEleanor Rosch
Prototype Effects (continued)Prototype Effects (continued)
Among the experimental paradigms she used are:
{ Direct rating: how good an example of a category (e.g.
bird) various members are (e.g. a robin, a chicken, etc.)
{ Reaction time: Subjects asked to press a button to
answer true/false questions of the form “An [example] is
a [category name]” (e.g., “A chicken is a bird.”)
{ Production of examples: Subjects were asked to list
or draw examples of category members. It was more
likely that more representative examples were drawn.
{ Asymmetry in similarity ratings: Less representative
examples are often considered to be more similar to
more representative examples than the converse. In one
study (involving Americans), subjects considered Mexico
to be more similar to the US than the US is to Mexico.
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Eleanor RoschEleanor Rosch
Prototype Effects (continued)Prototype Effects (continued)
Continuing the experimental paradigms she used:
{ …
{ Asymmetry in generalization: Information about a
representative member is more likely to be generalized
to non-representative members than the reverse. In one
study (Rips 1975) the subjects believed that a disease
was more likely to spread from robins to ducks than
ducks to robins.
{ Family resemblances: Rosch showed that there was a
correlation between the family resemblances, which
were a priori philosophical speculation, and the
numerical ratings of best examples in various studies.
Eleanor RoschEleanor Rosch
Prototype Effects (continued)Prototype Effects (continued)
BEWARE!
As Rosch herself had put it in her later works, the prototype
effects do not constitute a theory of cognitive
categorization. There is nothing called a prototype, what
exists is our observation of degree of prototypicality.
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Eleanor RoschEleanor Rosch
BasicBasic--Level EffectsLevel Effects
Extending Berlin’s work on Tzeltal plant and animal
taxonomies, Rosch and her associates found that the
psychologically most basic level is in the middle of the
taxonomic hierarchies.
They found that basic level is:
{ The highest level at which category members have
similarly perceived overall shapes
{ The highest level at which a single mental image can
reflect the entire category (try imagining a
representative image for “a furniture”, and then “a
chair”)
{ The highest level at which a person uses similar motor
actions for interacting with the category members
{ The level at which subjects are fastest at identifying
category members
Eleanor RoschEleanor Rosch
BasicBasic--Level Effects (continued)Level Effects (continued)
They found that basic level is:
{ …
{ The level with the most commonly used labels for
category members
{ The first level named and understood by children
{ The first level to enter the lexicon of a language
{ The level with the shortest primary lexemes
{ The level at which terms are used in neutral contexts
(“There’s a mammal on the porch.” needs special
context, whereas using dog would not)
{ The level at which most of our knowledge is organized.
Most attributes of category members are stored at this
level. Most of this knowledge is organized as part-whole
relations, and interactions with those parts (affordances)
(Tversky and Hemenway 1984)
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Eleanor RoschEleanor Rosch
Priority of CategorizationPriority of Categorization
At the outset, Rosch believed that the attributes of things were
inherent in the real world, “given an organism that had sensory
equipment capable of perceiving the attributes” (Rosch 1978). Thus
they grounded their system in reality using attributes listed by their
subjects as perceived attributes. But
{ Some attributes, such as “seat” for the “chair” appear to have names not
meaningful prior to the knowledge of object as “chair”
{ Some attributes such as “large” for object “piano” seems to have
meaning only with respect to a superordinate category: it is large for
furniture but small compared to another object such as building.
{ Some attributes such as “you eat on it” for the object “table” are
functional attributes that suggest possession of knowledge about
humans, their activities, and the real world in order to be understood.
Thus the analysis of objects into attributes is rather a sophisticated
activity that the subjects of Rosch’s study might have been
considered to be able to impose only after the development of a
system of categories.
Thus the notion of a “property” is not something objectively out
there in the world independent of any being.
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