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.