Concepts and Categorization

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					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                         Fox



 Rottweiler                 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
                                                 Animal
   A chicken is a bird
      was slower to verify than                   Bird

   A chicken is an animal                      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.   people cannot give explicit definitions of the concepts
     (Hampton, 1979; Wittgenstein, 1953)
2.   when asked to list attributes that are relevant to the
     definition, they include attributes which are not true of
     all category exemplars (Hampton, 1979)
3.   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)
4.   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   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)
             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.

				
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