Psychological models of concepts

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Psychological models of concepts

• James A. Hampton
• City University London

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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

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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)

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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

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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)

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Two models of concepts

• Classical concepts - with explicit definitions
  and logical taxonomies
  
• Prototype concepts - based on similarity to an
  "average" or idealized exemplar

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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)
  

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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

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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

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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

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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

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Model 1The Classical Modelattributed 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.

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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

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Examples of classical concepts?

• Biology
• Law
• Mathematics
• Kinship

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Carl Linnaeus 1707-1778

• Classical taxonomy
• Genus and differentia

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Classical hierarchical taxonomy
Vertebrate
Mammal
Reptile
Canine
Dog
Fox
Rottweiler
Chihuahua
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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)
  

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Advantages of the Classical Model

• Defining features provide accounts of
• Analytic vs Contingent Truth
• Dictionary vs Encyclopaedia

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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

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Collins Quillian 1969A network representation
of memory
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Results
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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.

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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
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General problems for the model

• People find it very difficult to give explicit
  definitions of most concepts. Either they dont
  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 doesnt explain why we have the
  concepts that we do, and not others
  

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Model 2 Prototypes
Carolyn Mervis
Eleanor Rosch
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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

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Four prototype phenomena

• 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)

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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
  

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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

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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

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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)

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Hampton (1979)

• Interviewed people about the meaning of concepts
  like fruit furniture vehicle, and produced
  a feature list
  
• Fruit
• Contains seeds
• Has an outer layer of skin or peel
• Is edible, is eaten
• Is juicy, thirst quenching
• Is sweet
• Is eaten as a dessert, snack or on its own
• Grows Is a plant, organic, vegetation
• Grows above ground, on bushes or trees
• Is brightly coloured
• Is round
• Is a protection for seeds

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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 87
• Tomato 71
• Rhubarb 54
• Gourd 43
• Marrow 23
• Garlic 12
• Mushroom 5
• 3. People judged whether each word (e.g. garlic)
  had each feature (e.g. contains seeds)

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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

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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.

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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)
  

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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

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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

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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
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Conceptual structure becomes represented here
Used the taxonomy from Collins Quillian 1969
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SIMILARITY CLUSTERS
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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

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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

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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"

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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

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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?

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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

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What information do our concepts include?

• Attributes
• Birds
• Two wings
• Two legs
• Flies
• Eats insects or worms or grainetc
• Relational Information
• Relations between attributes
• Relations between concepts

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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
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• Concepts need to help us explain things

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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.
  

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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)

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Naive concepts of "size" and "amount"

• Example of measurements of parcel size
• USA a 2(bc), where a is the longest side
• France a.(bc)
• Correct definition a.b.c

c
b
a
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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)

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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.