1. Concepts Part 2

2. Outline Recap from Thursday Prototype Theories Problems for the Prototype Theory Problems for Feature Theories Generally Concepts as Theories –Theory-Theory and the Core Knowledge Hypothesis The Development of Concepts –Evidence for abstract theory driven concepts

3. The Classical Theory a.k.a. Definitional Theory Word meanings are a set of properties that are necessary and sufficient for membership in the category Triangle: a closed, three sided figure, whose angles add up to 180 degrees

4. Graded Concepts Classical theory: a word is defined by small set of necessary and sufficient features Category membership is ALL OR NONE 3 kinds of evidence for graded concepts (Rosch & Mervis)

5. SMITH beard1.0 brown hair.75 big nose.75 big ears.75 mustache.625 Representation of Concept in Prototype Theory

6. Advantages of Prototype Theory... Explains sentence verification results: –more typical instances quickly identified b/c they have more of the category features. Explains category membership ratings –membership is graded not absolute Consistent with feature listing results –more typical instances have more features in common with other members

7. Problems with Prototypes

8. Armstrong, Gleitman & Gleitman Structure of the Argument Prototype Claim: If a category shows typicality effects, then it must have a prototype structure Contrapositive: Whenever “if A then B” is true. “If not B, then not A” must also be true.

9. Armstrong, Gleitman & Gleitman Structure of the Argument If you disprove the contrapositive then the original claim must be false. Contrapositive of Prototype Claim: If a category does not have a prototype structure then it will not show typicality effects.

10. Armstrong, Gleitman & Gleitman Structure of the Argument Goal: disprove the contrapositive by conducting typicality tests on well- defined categories Well-defined categories: ones with necessary and sufficient features –mathematical categories: even number, triangle, plane –gender categories: female, male –kinship terms: uncle, grandmother

11. Exp. 1: Typicality Ratings for ordinary categories FRUIT apple1.3 strawberry2.1 pineapple2.7 fig5.2 olive6.4 SPORT football1.4 hockey1.8 gymnastics2.8 archery4.8 weight-lifting5.1

12. Exp 1. Typicality Ratings for well-defined categories (Armstrong, Gleitman & Gleitman) EVEN NUMBER 41.1 81.5 182.6 343.4 1063.9 FEMALE mother1.7 housewife2.4 princess3.0 policewoman3.9 comedienne4.5

13. Exp. 2 Sentence Verification

14. Exp. 2 Sentence Verification: Prototypical members verified faster

15. Armstrong, Gleitman & Gleitman Conclusion Since well-defined categories also show typicality effects then the presence of these effects, does not prove that ordinary categories have a prototype structure

16. The problem of compositionality A theory of concepts must explain how word meanings combine to yield the meanings of phrases. Prototype Theory fails to do this

17. Pet Fish: Definitional Theory PET [animal] [kept for amusement]

18. Pet Fish: Definitional Theory FISH [aquatic] [water-breathing] [cold blooded] [chambered heart] [animal]

19. Pet Fish: Definitional Theory PET + FISH [aquatic] [water-breathing] [cold blooded] [chambered heart] [animal] [kept for amusement]

20. Pet Fish: Prototype Theory PET [animal] [kept for amusement] [cute] [friendly] [mammal] [furry] [smallish]

21. Pet Fish: Prototype Theory FISH [aquatic] [water-breathing] [cold blooded] [chambered heart] [animal] [elongated] [spindle shaped] [broad caudal fin]

22. Pet Fish: Prototype Theory Predicted Prototype for pet fish: a catlike trout? a fuzzy salmon?

23. The Dual Theory (Armstrong, Gleitman, & Gleitman) 1.Definitions for reasoning and determining category membership Who is a grandmother? –The mother of a parent 2. Prototypes for quick identification How do you find a grandmother in a crowd? –look for the prototyical features (kindly, grey-haired)

24. A 3 rd Story: Exemplar Models Concepts do not have definitions or summary representations. A concept is the set of all examples of the concept that are stored in memory. Concept bird: all exemplars of bird in memory

25. Prototype view: Typicality = similarity to prototype

26. Exemplar view: Typicality = average similarity to all stored instances

27. Challenges for all feature theories…

28. Perceptual Similarity Prototype theory & exemplar models rely on “similarity measure” Typically perceptual similarity But perceptual similarity is unnecessary and insufficient for categorization (lemon, counterfeit, skunk) Though it is useful for categorization

29. The importance of a feature depends on the category X = 3” 12” 1” Which one is more similar to X? (70% quarter) Which one would you categorize with X? (63% pizza) Rips (1989)

30. Example: Gelman & Markman (1986) This bird’s heart has a right aortic arch This bat’s heart has a left aortic arch What does this bird’s heart have? 90% subjects say right aortic arch (like flamingo)

31. Are these any of these features necessary? JUNGLE-DWELLING 4-LEGGED FUR-COVERED GROWLY FIERCE STRIPPED ANIMAL

32. This is a problem for prototypes as well Transplanted Tomcat JUNGLE-DWELLING+ 4-LEGGED+ FUR-COVERED+ GROWLY+ FIERCE+ STRIPPED+ ANIMAL+ Shaved, mutilated but tiger-born JUNGLE-DWELLING0 4-LEGGED0 FUR-COVERED0 GROWLY0 FIERCE0 STRIPPED0 ANIMAL0 No matter what weights we put on these features, the tomcat is more of a tiger, than the altered tiger Moral: typicality does not determine categorization

33. And for the exemplar model Transplanted Tomcat Is similar to the all the other tigers I have seen JUNGLE-DWELLING 4-LEGGED FUR-COVERED GROWLY FIERCE STRIPPED ANIMAL Shaved, mutilated but tiger-born Is not similar to the other tigers I have seen JUNGLE-DWELLING 4-LEGGED FUR-COVERED GROWLY FIERCE STRIPPED ANIMAL

34. Any two objects can be similar or dissimilar on an infinite number of dimensions –plums and lawnmowers (Murphy & Medin, 1985) –both weigh less than 10,000 kg; both did not exist 10,000,000 years ago; both can be dropped; both cannot hear well; both take up space, etc. How do you know which features are relevant for judging similarity? pandas, newspapers, foods, tools depends on type of category Ex: Parents matter for biological kinds (human, raccoon), not for social roles (writer) The problem with similarity

35. Finding the common features is an example of unconstrained induction (Quine, 1960 again) “Gavagai!”

36. Does Classical Theory really explain it all? 1.What does it mean to have a concept? 2. How can the same concept refer to so many different things and yet not to some similar things? You know the necessary and sufficient features Category membership and allowable variation depend on necessary and sufficient features PROBLEM: failure to identify necessary and sufficient features

37. Classical Theory explains it all 3. How did concepts end up in our heads? Simple concepts: experience + sensory apparatus Complex: experience  association of simple concepts PROBLEM: Sensory Primitives Cannot explain even concrete concepts (chair, lemon) or well-defined concepts (grandmother, odd number, bachelor)

38. Classical Theory explains it all 4. How are concepts related to each other? 5. How do word meanings (concepts) combine to yield the meanings of phrases? Because they have shared features (or no shared features Feature Union: each word contributes its features to the set of necessary and sufficient conditions Seems reasonable…. But depends on finding features Works for small class of adjectives (red) Not others (tall, good, fake)

39. Interlude: Connectionism Review

40. A.____________ B. ____________ C. ____________

41. How is the activation level of the unit determined? How is the output activation level determined

42. Training a network 1.Apply an input 2.You get an output (nonsense) 3.Compare output given with desired output 4.Change the weights If a unit should have been off but was on, decrease any weight which increased its activation If it should have been on and was off, do the reverse 5.Repeat (thousands of times)

43. Concepts are Theories AKA: Theory-Theory or Core Knowledge

44. Borges’ Celestial Empire of Benevolent Knowledge “ In its remote pages it is written that the animals are divided into: (a) belonging to the emperor, (b) embalmed, (c) tame, (d) sucking pigs, (e) sirens, (f) fabulous, (g) stray dogs, (h) included in the present classification, (i) frenzied, (j) innumerable, (k) drawn with a very fine camelhair brush, (l) et cetera, (m) having just broken the water pitcher, (n) that from a long way off look like flies.” - Jorge Luis Borges Are all concepts equally possible?

45. Story #4: Concepts are Theories Concepts gain their meaning from a network of interrelated concepts and beliefs. A concept is defined by its relationship to other concepts and beliefs — it’s “functional” or “inferential” role. Concepts are divided into different domains and concept acquisition within these domains is constrained by evolution (core knowledge)

46. Core Knowledge Some cognitive skills have been important throughout human history. –Understanding others –Language –Physical reasoning –Face perception In these areas children demonstrate advanced cognition despite limited abilities in other areas Claim: we have innate cognitive capabilities that are the product of evolution Computer aided reconstruction of Gibraltar 2 Neanderthal Child

47. Brain as a Pocket Knife Genes are selected because they solve specific problem Evolution creates “a tool for each job” language theory of mind face recognition object recognition

48. Core Knowledge Domain specificity –Development is not global –Development occurs within domains (areas) of cognition Development in each domain guided by set of innate core principles –Define content of domain –Support reasoning within domain

49. Core Knowledge Naive theories organize knowledge within each domain –divide world into basic kinds (animals, objects, people….) –explain many individual events with a few principles –posit unobservable causes for observable events What are the domains? –given by evolution –what children need to know about in order to survive.

50. The Development of Concepts

51. Categories in Infancy Habituation with 3-month- olds perceptual categorization robust in infants allows child to group similar items does not show that they have distinct concepts for the two kinds

52. Children’s concepts are abstract from a young age Early categorization of artifacts is often shape based But attention to object function begins in infancy –1 yo expect object that looks like a rattle to produce a sound –Older children more likely to attend to function than younger ones

53. Children’s use their concepts to make inferences (Mandler & McDonough) Children are shown an action Then they are given a toy from the same category Or one from a different category

54. 14mo infants use concepts to guide inference

55. Conceptual Hierarchies Men, women, boys, girls

56. Categorical Hierarchies Levels: –Superordinate, a general level (animal) –Basic level, level typically used (dog) –Subordinate level, more specific (poodle) Children learn basic level words first –Most commonly used? –Most distinct perceptually? –Conceptually privileged?

57. Further development in artifact concepts What is the nature of mature artifact concepts? Is identity based on: 1.The object’s current function? 2.Its past history of use? 3.The intentions of it’s creator? Tested by asking adults and children to make category judgments

58. Ex: How many cups are there? Gutheil, Bloom, Valderrama & Freedman, 2003 Adults say 3 Remains a cup even if it cannot serve the function of a cup. Preschoolers say 2 To be a cup, object must serve function of a cup

59. Ex: Is it a plate of frisbee? I found it. I use it to play catch with my friends! I made this to put food on at dinnertime! Matan & Carey, 2001 Adults: Plate Creator’s intent or original function Preschoolers: Inconsistent in responses Don’t appeal to creator’s intent

60. Further development in artifact concepts Adults often rely on creator’s intention and history Young children rely more on appearance and function But preschoolers can use creator’s intention for some categorization tasks –naming artwork –deciding if thing is an artifact (is a candle or just wax?) Does the early reliance on physical properties reflect: –More concrete concepts in early childhood? –Use of perceptually accessible properties to make inferences about abstract properties which are perceptually available?

61. Children’s changing theories of natural kinds The development of naïve biology

62. Young children’s knowledge living things Infants distinguish among animals, humans & inanimate objects. Preschoolers –understand elementary aspects of inheritance –know living things grow bigger and more complex, not smaller and less complex Children are essentialists –believe living things have an “essence” (internal causal property) which makes them what they are

63. By 4 children begin defining animals by internal properties What is it now? A cat or a dog? Young children say CAT Natural kinds are not defined by their properties

64. How Do Children Acquire Biological Knowledge? 1.Socio-cultural: Knowledge comes from the input they receive from general culture, parents, and teachers 2.Modularity Nativism: We’re born with innate “biology module” allowing us to learn quickly about living things 3.Theory-theory: Initial theory based on naïve psychology & theory of artifacts (Carey) –Both animals and humans defined as “behaving” beings –Preschoolers personify living things –Often believe natural kinds have functions like artifacts (bats are for eating bugs)

65. Changes in Biological Theories Theory 1 (4-8 yo) Alive = able to behave & move Not alive (dead, inanimate, imaginary) = unmoving Death as life under altered circumstances (underground, sleep) Theory 2 (9  ) Alive = having bodily functions These concepts distinguished Death defined as cessation of bodily function Claim: concepts in Theory 2 cannot be built out of the concepts from Theory 1

69. Changes in Biological Theories Theory 1 (4-8 yo) Alive = able to behave & move Not alive (dead, inanimate, imaginary) = unmoving Death as life under altered circumstances (underground, sleep) Theory 2 (9  ) Alive = having bodily functions These concepts distinguished Death defined as cessation of bodily function Claim: concepts in Theory 2 cannot be built out of the concepts from Theory 1

70. What causes the transition from T1 to T2? (Johnson & Carey, 1998) 3 groups: –Young kids (5-7) –Older kids (8-12) –Adolescents with Williams’ Syndrome: matched in vocabulary to older kids WS = developmental disorder argued to effect deep conceptual analysis but not acquisition of “encyclopedic knowledge”

71. What causes the transition from T1 to T2? (Johnson & Carey, 1998) Tests of biological knowledge (theory neutral) –Name all the animals you know –Animal properties: do cats have legs? Test of Theory 2 concepts –Animacy: Are bicycles/cars/cars/moon alive? –What happens when you die? –Attribution of living properties to plants

72. What causes the transition from T1 to T2? (Johnson & Carey, 1998) If theory change is caused by acquiring knowledge about animals –Performance on neutral questions should predict T2 performance for WS & typically developing children. –Young < WS & Old If theory change requires more than knowledge accretion –WS should perform like younger children regardless of general biological knowledge

73. Results: older kids better at both questions (Johnson & Carey)

74. Knowledge alone doesn’t ensure theory change

75. Example of T1 in Williams Syndrome SK is a 21 year old with WS who reads novels about vampires E: What is a vampire? SK: Oooh, a vampire is a man who climbs into ladies’ bedrooms in the middle of the night and sinks his teeth into their necks E: Why do vampires do this SK…..I’ve never thought about that…..vampires must have an inordinate fondness for necks. Missing biological concepts of life and death (vampires as “living-dead”)

76. What causes change in biological theory? Correlated with biological knowledge in typical children But also requires conceptual reanalysis Remaining question: how exactly does reanalysis happen?

77. The Exam for Psych 1020 Is graded and will be returned over the next two days Drop by to pick it up: –2-3:30 Thrs, 2-3:15 Fri –Or email me to arrange a place to pick it up –After Tues: Dr. Griffin will have Redemption assignment: will be posted by Thrs Cut-off point values posted on the website

78. Redemption Assignment Psych 13 If you got below a B- You can rewrite any questions that you got wrong or partially wrong (except fill in blanks or matching) You can regain points –Up to half the points you missed –With a maximum grade set at 91 (bottom of B-)