Transcript Concepts and Categorization

Psychological models
of concepts
James A. Hampton
City University London
What are concepts?
“Without concepts, mental life would be
chaotic.” Smith & Medin 1981
“Concepts are the glue that holds are
mental world together .. They tie our past
experiences to our present interactions
with the world” Murphy 2002
What are concepts?
“The elements from which propositional
thought is constructed, thus providing a
means of understanding the world,
concepts are used to interpret our current
experience by classifying it as being of a
particular kind, and hence relating it to
prior knowledge.”
(Hampton, MITECS 1999)
Why do concepts matter?
How concepts are defined may have
serious consequences, and can be at the
basis of political and legal debate:
Examples:
- abortion and euthanasia - how to define
“human” and “murder”
- marriage - should it include gay relationships
- drugs - cannabis legislation
Lecture synopsis:
We will look more closely at the notion of a
Concept largely from a Psychological point
of view, based on empirical evidence:
 how do we represent concepts in our minds?
how do we use them in our thinking?
We will consider two models in particular
Classical model (Aristotle)
Prototype model (Rosch; Hampton)
Two models of concepts
 Classical concepts - with explicit definitions and
logical taxonomies
 Prototype concepts - based on similarity to an
"average" or idealized exemplar
SOME TERMINOLOGY
Concept: a mental representation of a class of
things – a type
Category: the set of things that are included in the
concept class
Exemplar (= instance) one of the set of things in
the category
Attribute (= property = feature) a predicate which
can be true or false of a thing (exemplar) or
class of things (category or concept)
Frege (1848 – 1925)
Intension / Sense
(logically) the criterion by which membership
of a class is determined
 (psychologically) the set of attributes that you
associate with a particular class
Extension / Reference
the set of members of a class
what the term refers to
What defines the concept –
intension or extension?
 Intensions – for many terms are culturally relative,
individually variable, subject to revision
 Extensions – insufficient to individuate concepts since
two concepts can have the same extension, or a concept
may have no extension at all
 Logically - triangle and trilateral
 Contingently - Hollywood actor presidents and
Husbands of Nancy Davis
 Empty – unicorns, highest prime number
KNOWLEDGE and CONCEPTS
 The problem of knowledge: the dictionary and the
encyclopaedia
 Failure to distinguish them leads to “holism”
 Any new fact changes the meaning of the terms used
 Different people hold different beliefs so their conceptual
systems are never commensurate
“if a lion could talk, we could not understand him”
Ludwig Wittgenstein
Circularity
 As with dictionary definitions, some models
define concepts in terms of each other
 Must assume there is a level of “primitives”, from
which more complex terms are defined
 e.g. physics has fundamental undefined
concepts of mass, length, time and current
 complex thoughts are derived from their
elements and their means of combination –
principle of “compositionality”
Model 1
The Classical Model:
attributed to Aristotle
 A concept is a class of things which all have
certain attributes in common
 Everything which is in the class must possess all
these attributes
 Everything which possesses all these attributes
must be in the class
 Attributes are individually necessary and jointly
sufficient for category membership.
Classical Model
 What is a bachelor (scapolo)?
 Classical concepts are defined by a conjunction
of necessary features which are together
sufficient to pick out all bachelors and just
bachelors
Examples of classical concepts?
Biology
Law
Mathematics
Kinship
Carl Linnaeus 1707-1778
Classical taxonomy
Genus and differentia
Classical hierarchical taxonomy
Vertebrate
Mammal
Reptile
Canine
Dog
Rottweiler
Fox
Chihuahua
Advantages of classical model:
 Taxonomic Structure. Subsets in the tree are
mutually exclusive and jointly exhaustive of the
next class up. A “clean” way to divide up the
world
 Efficient Storage – each concept needs only its
link to a superordinate plus its distinctive
attributes
 Inferences – many deductions can be made
from the taxonomy (all rottweilers have hearts)
Advantages of the Classical Model
Defining features provide accounts of
Analytic vs Contingent Truth
Dictionary vs Encyclopaedia
The classical model - evidence
 Collins and Quillian (1969) evaluated a
hierarchical taxonomic model of concepts by
measuring response times to verify or falsify
sentences
Category statements “A canary is a bird”
Property statements “A canary can fly”
Collins & Quillian 1969
A network representation of memory
Results
The classical model - evidence
the greater the number of links in the
hierarchy between the subject noun and
the predicate, the slower people were to
say the statement was true.
But….
 for false sentences, Collins & Quillian found the time to
say they were false was faster the further apart the two
concepts were
A canary is a fish
vs. A canary is a flower
 Smith, Shoben & Rips (1974) showed that there are
hierarchies where more distant categories can be faster to
categorize than closer ones
A chicken is a bird
was slower to verify than
A chicken is an animal
Animal
Bird
Chicken
General problems for the model
 People find it very difficult to give explicit definitions of
most concepts. Either they don’t know the defining
features, or those defining features do not exist.
(Hampton, 1979, McNamara & Sternberg, 1983)
 There is vagueness and uncertainty in many concept
classes – what exactly is a bug or a fish, what
differentiates a spaniel from a terrier?
 Many domains do not have any obvious taxonomy
 The model doesn’t explain why we have the concepts
that we do, and not others
Model 2: Prototypes
Eleanor Rosch
Carolyn Mervis
Second Model - The Prototype Model
 Concepts are represented in the mind by
“prototypes” which are summary representations
of the average or ideal members of a class
 Membership in the conceptual category is
determined by similarity to the prototype
Four prototype phenomena
1.
2.
3.
4.
people cannot give explicit definitions of the concepts
(Hampton, 1979; Wittgenstein, 1953)
when asked to list attributes that are relevant to the
definition, they include attributes which are not true of
all category exemplars (Hampton, 1979)
people cannot agree on whether some cases fall in the
concept class or not, and change their minds from one
occasion to the next (McCloskey & Glucksberg, 1978)
people reliably judge that some exemplars are better,
more representative examples of the concept than
others - "typicality" (Rosch, 1975)
Prototype model of concepts
 A prototype consists of a set of attributes (an
intension)
 These are attributes which are mutually
predictive within a particular general domain
 Items belong to the concept class if they
possess enough of these attributes
Example - creatures
creatures differ in their number of legs,
mode of locomotion, skin covering etc.
having two legs, flying and being covered
in feathers are strongly correlated - if a
creature has one, then the likelihood of it
having the others is increased.
Concepts reflect this pattern of correlation
Example: BIRD
An object is a bird if it has a sufficient
similarity to the prototype of the class, as
defined in terms of the following attributes:
flies
has feathers
has wings
has two legs
has a beak
lays eggs
The Prototype Model - Evidence
 Rosch and Mervis (1975) "Family resemblances”
 Typical category members have more features in
common with the other members, and fewer in
common with contrasting categories
 Rosch (1975)
 Typical category members are faster to categorize,
and more similar to the general notion of the category
 Hampton (1979)
Hampton (1979)
1.
Interviewed people about the meaning of concepts like “fruit”
“furniture” “vehicle”, and produced a feature list
Fruit
1. Contains seeds
2. Has an outer layer of skin or peel
3. Is edible, is eaten
4. Is juicy, thirst quenching
5. Is sweet
6. Is eaten as a dessert, snack or on its own
7. Grows Is a plant, organic, vegetation
8. Grows above ground, on bushes or trees
9. Is brightly coloured
10. Is round
11. Is a protection for seeds
Hampton 1979
2. People judged a list of words according to how confident they
were that the word was a kind of fruit or not

Orange 100%

Raisin

Tomato 71%

Rhubarb 54%

Gourd

Marrow 23%

Garlic

Mushroom 5%
87%
43%
12%
3. People judged whether each word (e.g. garlic) had each feature
(e.g. contains seeds)
Hampton 1979
 For most categories, there was no classical
definition
 There are many borderline cases
 Degree of category membership reflects the
number of features that an exemplar possesses
Rosch 1975 – substitutability
test.
 Ss generated a sentence using the category
name “Birds fly past my window in the morning”.
Then replace “BIRD” with either a typical or an
atypical exemplar, and see if the sentence is still
meaningful – more likely to be meaningful for a
typical member.
Examples of prototypes:
Evidence has been found for prototype
structure in:
 Biological kind categories (fish, insects etc)
 Food categories (fruit, vegetables, flavours)
 Artifacts (tools, furniture, weapons, vehicles)
 Diagnostic categories (in psychiatry)
 Personality trait concepts (extrovert, shy)
 Activity concepts (sport, game, science, lying, art)
Advantages of the Prototype
Model
The model captures all four phenomena:
 the lack of explicit definitions
 the relevance of attributes which are not
common to all exemplars
 the existence of borderline cases
 the existence of differences in typicality
among exemplars
Learning
 Unlike classical concepts, prototypes can be
learned from the environment provided that a
starting set of attributes is selected as likely to
be relevant
 It explains why have have these concepts and
not others
 Prototypes can be easily learned by simple
neural mechanisms that learn the statistical
properties of the environment
PDP Model for concept learning
 McClelland & Rumelhart (1985)
 Neural network linking feature nodes
to category nodes
 Start with random weights on links
and change links by error feedback
 Rogers & McClelland (2003)
 models concept learning in children –
global distinctions first
Jay McClelland
Conceptual
structure becomes
represented here
Used the taxonomy from Collins & Quillian 1969
SIMILARITY CLUSTERS
Rosch Simpson and Miller 1976
 Experiments on learning categories of artificial
stimuli. Similarity to the prototype and distance
from a contrasting prototype dictated
 Speed of learning
 Speed of verification
 Accuracy of verification
 Recall of category exemplars
Evidence for prototypes in
reasoning
 The classical model provides a firm basis for
logical reasoning, and is preferred by some
philosophers for this reason
 The prototype model provides an explanation for
non-logical reasoning, as demonstrated in many
psychology experiments
Hampton (1982):
Intransitivity in categorical reasoning
 Subjects agreed that
 "Car-seats are a kind of chair"
 and that
 "Chairs are a kind of furniture"
 but not that
 "Car-seats are a kind of furniture"
Tversky & Kahneman (1985): Conjunction fallacy
 Subjects were told a story about a woman, Linda, who
had been involved in liberal politics at college. Later
they had to judge which was more probable about Linda
now:
 1.
Linda is a bank teller
 2.
Linda is a feminist
 3.
Linda is a feminist bank teller
 They preferred (3) to (1), although (1) includes (3).
 They were influenced by the similarity between the
description of Linda and their prototype of a feminist
The Prototype model - evaluation
 The main criticisms of the model relate to its
failings to provide a rich enough representation
of conceptual knowledge
 how can we think logically if our concepts are so vague?
 Why do we have concepts which incorporate objects which are
clearly dissimilar, and exclude others which are apparently
similar (e.g. mammals)?
 how do our concepts manage to be flexible and adaptive, if they
are fixed to the similarity structure of the world?
 if each of us represents the prototype differently, how can we
identify when we have the same concept, as opposed to two
different concepts with the same label?
Concepts as theories
 A development of the prototype idea to include more
structure in the prototype
 Concepts provide us with the means to understand our
world
 They are not just the labels for clusters of similar things
 They contain causal/explanatory structure, explaining
why things are the way they are
 They help us to predict and explain the world
What information do our concepts
include?
Attributes
Birds:
 Two wings
 Two legs
 Flies
 Eats insects or worms or grain…etc
Relational Information
Relations between attributes
Relations between concepts
Sloman, Love & Ahn, 1998
Has wings
Has feathers
Light weight
Flies
Lays eggs
Hops
Has two legs
Builds nests
Centrality of a feature is based on its links to other features
Concepts need to help us explain things
Choosing a concept for its
explanatory value
What do correct concepts have that more
naïve ones lack? EG VOLUME
Concepts like volume are embedded in a
web of inter-related concepts
Each is part of the whole, and is defined at
least partly by the role it plays in the theory
which the whole structure represents.
Defining a concept of physical
volume:
Different naive definitions of volume
are possible
how high up a glass the liquid comes
the height in the glass times the width
of the glass

postal regulation
(e.g. length plus circumference)
Naive concepts of "size" and
"amount"
Example of measurements of parcel size:
USA = a + 2(b+c), where a is the longest side
France = a.(b+c)
Correct definition = a.b.c
c
b
a
What makes a concept “correct”?
 What does the correct concept of volume have
that more naive ones lack?
 stability under transformation
e.g. conservation tasks (Piaget)
 link with underlying theory of matter
e.g. atomic theory
 internal consistency
e.g. thought experiments - breaking a cube into
smaller cubes
 relation to other concepts
e.g. area, displacement volume (Archimedes)
Conclusions
 Classical model provides the basis for logic
and reasoning – but people are not very good
at logic and reasoning
 Prototypes capture the way that our minds
adapt to the similarity of things in the world
 Deeper structure is needed to allow us to use
concepts to explain the world, to go beyond
surface appearance of things and discover
underlying principles.