Concepts Part 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

The Classical Theorya.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

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)

SMITH

beard 1.0

brown hair .75

big nose .75

big ears .75

mustache .625

Representation of Concept in Prototype Theory

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

Problems with Prototypes

Armstrong, Gleitman & GleitmanStructure 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.

Armstrong, Gleitman & GleitmanStructure 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.

Armstrong, Gleitman & GleitmanStructure 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

Exp. 1: Typicality Ratings for ordinary categories

FRUIT

• apple 1.3

• strawberry 2.1

• pineapple 2.7

• fig 5.2

• olive 6.4

SPORT

• football 1.4

• hockey 1.8

• gymnastics 2.8

• archery 4.8

• weight-lifting 5.1

Exp 1. Typicality Ratings for well-defined categories(Armstrong, Gleitman & Gleitman)

EVEN NUMBER

• 4 1.1

• 8 1.5

• 18 2.6

• 34 3.4

• 106 3.9

FEMALE

• mother 1.7

• housewife 2.4

• princess 3.0

• policewoman 3.9

• comedienne4.5

Exp. 2 Sentence Verification

stimuli Ordinary Well-defined

+ proto orangebaseball

housewife4

-proto figfishing

comedienne56

Exp. 2 Sentence Verification:Prototypical members verified faster

results Ordinary Well-defined

+ proto fast fast

-proto slow slow

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

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

Pet Fish: Definitional Theory

PET

[animal]

[kept for amusement]

Pet Fish: Definitional Theory

FISH

[aquatic]

[water-breathing]

[cold blooded]

[chambered heart]

[animal]

Pet Fish: Definitional Theory

PET + FISH

[aquatic]

[water-breathing]

[cold blooded]

[chambered heart]

[animal]

[kept for amusement]

Pet Fish: Prototype Theory

PET[animal]

[kept for amusement]

[cute]

[friendly]

[mammal]

[furry]

[smallish]

Pet Fish: Prototype Theory

FISH[aquatic] [water-breathing][cold blooded][chambered heart][animal][elongated][spindle shaped][broad caudal fin]

Pet Fish: Prototype Theory

Predicted Prototype for pet fish:

a catlike trout?

a fuzzy salmon?

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)

A 3rd 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

Prototype view: Typicality = similarity to prototype

Exemplar view: Typicality = average similarity to all stored instances

Challenges for all feature theories…

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

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)

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)

Are these any of these features necessary?

• JUNGLE-DWELLING

• 4-LEGGED

• FUR-COVERED

• GROWLY

• FIERCE

• STRIPPED

• ANIMAL

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-DWELLING 0• 4-LEGGED 0• FUR-COVERED 0• GROWLY 0• FIERCE 0• STRIPPED 0• ANIMAL 0

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

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

• 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 si

milarity

Finding the common features is an example of unconstrained induction

(Quine, 1960 again)

“Gavagai!”

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 necessaryand sufficient features

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)

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)

Interlude: Connectionism Review

A.____________

B. ____________

C. ____________

A1 A2 .. .. .. A8

w1

w2

w8

Activation Level

Output Activation

How is the activation level of the unit determined?

How is the output activation level determined

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)

Concepts are Theories

AKA: Theory-Theory or Core Knowledge

Borges’ Celestial Empire ofBenevolent 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 BorgesAre all concepts equally possible?

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)

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

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

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

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.

The Development of Concepts

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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

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

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

14mo infants use concepts to guide inference

Conceptual Hierarchies

Men, women, boys, girls

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?

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

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

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

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?

Children’s changing theories of natural kinds

The development of naïve biology

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

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

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)

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

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

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”

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

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

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

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Biological Knowledge

Theory 2

Knowledge alone doesn’t ensure theory change

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Biological Knowledge

Theory 2

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”)

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?

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

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-)