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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
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 particularClassical 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 / Referencethe 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 1The 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 taxonomyGenus 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 ofAnalytic 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 1969A 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. 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: BIRDAn 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
Fruit1. Contains seeds2. Has an outer layer of skin or peel3. Is edible, is eaten4. Is juicy, thirst quenching5. Is sweet6. Is eaten as a dessert, snack or on its own7. Grows Is a plant, organic, vegetation8. Grows above ground, on bushes or trees9. Is brightly coloured10. Is round11. Is a protection for seeds
Hampton 19792. 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 dictatedSpeed 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?
AttributesBirds:
Two wings Two legs Flies Eats insects or worms or grain…etc
Relational InformationRelations between attributes
Relations between concepts
Sloman, Love & Ahn, 1998
Has wings Has feathers
Light weightFlies
Has two legs
Lays eggs
Hops
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 possiblehow 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
ab
c
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.
