explanation in intuitive theories tania lombrozo harvard university / uc berkeley

Explanation in Intuitive Theories

Tania Lombrozo

Harvard University / UC Berkeley

Why have theories?• Allow us to generalize from known to unknown

“Among the divers factors that have encouraged and sustained scientific inquiry through its long history are two pervasive human concerns which provide, I think, the basic motivation for all scientific research. One of these is man’s persistent desire to improve his strategic position in the world by means of dependable methods for predicting and, whenever possible, controlling the events that occur in it…”

CarlHempel

Why have theories?• Allow us to generalize from known to unknown

“…But besides this practical concern, there is a second basic motivation for the scientific quest, namely, man’s insatiable intellectual curiosity, his deep concern to know the world he lives in, and to explain, and thus to understand, the unending flow of phenomena it presents to him.”

CarlHempel

Other philosophers say:

“Theories are the crown of science, for in them our understanding of the world is expressed. The function of theories is to explain.”

Rom Harre, The Philosophies of Science, 1985“What is crucial is the insight that the kind of knowledge science produces...permits the development of explanations, and it is those explanations which are the real payoff.”

Joseph Pitt, Theories of Explanation, 1988

What’s so great about explanation?

? ?

??

Quine & Ullian (1970)

“… the hypotheses we seek in explanation of past observations serve again in the prediction of future ones. Curiosity thus has survival value, despite having killed a cat.”

W.V.O. Quine & J.S. UllianThe Web of Belief (1970)

Craik (1943)

“It is clear that, in fact, the power to explain involves the power of insight and anticipation, and that this is very valuable as a kind of distance-receptor in time, which enables organisms to adapt themselves to situations which are about to arise.”

Kenneth CraikThe Nature of Explanation (1943)

Heider (1958)

“If I find sand on my desk, I shall want to find out the underlying reason for this circumstance. I make this inquiry not because of idle curiosity, but because only if I refer this relatively insignificant offshoot event to an underlying core event will I attain a stable environment and have the possibility of controlling it.”

Fritz HeiderThe Psychology of Interpersonal Relations (1958)

Quick Recap

• Theories serve the function of:– Prediction– Intervention– Explanation

• But is explanation intrinsically valuable?

• Perhaps explanation contributes to fulfilling the other functions of theories, .e.g. prediction.

The Plan

• What’s the relationship between theories and explanation?

• How might explanation contribute to the function of theories, e.g. prediction?– “Off-line” explanation-based learning– “On-line” explanation-based inference

• Case study: Simplicity in explanation-based inference

• What’s the relationship between theories and explanation?

• How might explanation contribute to the function of theories, e.g. prediction?– “Off-line” explanation-based learning– “On-line” explanation-based inference

• Case study: Simplicity in explanation-based inference

Theories & Explanation I

A theory is “characterized by the phenomena in its domain, its laws and other explanatory mechanisms, and the concepts that articulate the laws and the representations of the phenomena”

Susan Carey, 1985

Theories generate explanations

FOLK BIOLOGY

…why living things need food……why birds have wings…

…why Bob the bird flew towards the worm…

Causal LawsExplanatory Mechanisms

Theories & Explanation II

A theory is “any of a host of mental ‘explanations,’ rather than a complete, organized, scientific account.”

Greg Murphy & Doug Medin, 1985

Theories contain explanations

FOLK BIOLOGY

…why living things need food……why birds have wings…

…why Bob the bird flew towards the worm…

Theories generate and contain explanations

FOLK THEORY

…specific explanations…

Causal LawsExplanatory Mechanisms

(“Framework level” explanations)

The Plan

• What’s the relationship between theories and explanation?

• How might explanation contribute to the function of theories, e.g. prediction?– “Off-line” explanation-based learning– “On-line” explanation-based inference

• Case study: Simplicity in explanation-based inference

• What’s the relationship between theories and explanation?

• How might explanation contribute to the function of theories, e.g. prediction?– “Off-line” explanation-based learning– “On-line” explanation-based inference

• Case study: Simplicity in explanation-based inference

“Off-line” Explanation-Based Learning

FOLK THEORY T1

…explanation of D1…

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

DATA D1

Time 1

FOLK THEORY T1’DATA

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

Time 2

Predict data like D1Prevent or cause data like D1

“Off-line” Explanation-Based Learning

FOLK COOKERY

…Cake was overcooked…

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

DRYCAKE

Time 1

FOLK COOKERY T1’TIME &

MOISTURE Causal LawsExplanatory Mechanisms

(“Framework” explanations)

Time 2

Predict dry cakesPrevent dry cakes

Evidence for explanation-based learning

• “Self-Explanation Effect”: You learn and gain understanding as a result of explaining something to yourself or others– Word problems in math– Facts about biology– Properties of number– Strategies in Tic-Tac-Toe– Folk Psychology

O’Reilly et al. (1998)

02

46

810

121416

1820

Cued recall Recognition

Repetition

ElaborativeInterrogationSelf-Explanation

Knowledge of circulatory system, university students

Wong et al. (2002)

0

5

10

15

20

25

30

35

40

Pre-Test Post-Test

"Think out loud"Self-Explanation

Geometry problem solving, 9th graders

Kinds of problems:Training: EqualNear transfer: 10% betterFar Transfer: 40% better

The Plan

• What’s the relationship between theories and explanation?

• How might explanation contribute to the function of theories, e.g. prediction?– “Off-line” explanation-based learning– “On-line” explanation-based inference

• Case study: Simplicity in explanation-based inference

“On-line” Explanation-Based Inference

FOLK THEORY T1

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

(hypothetical)DATA D1

Predict data like D1Prevent or cause data like D1

“On-line” Explanation-Based Inference

FOLK COOKERY T1

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

Prevent DRY CAKECompute probability of DRY

CAKE with 1 hour cooking time

(hypothetical)DRY CAKE

“On-line” Explanation-Based Inference

FOLK COIN FLIPPING

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

Probability of someone having a trick coin that repeats

sequence HHTHT

(hypothetical)HHTHT

Evidence for explanation-based inference

• Generating explanations influences assessments of probability

• Facility with which explanations can be generated influences assessments of probability

• “Goodness” of explanations can influence assessments of probability

• Generating explanations influences assessments of probability

• Facility with which explanations can be generated influences assessments of probability

• “Goodness” of explanations can influence assessments of probability

Class Experiment: Task

Imagine the Republican candidate wins (loses) the 2008 presidential election. Please list three reasons why a Republican might win (lose) the election:_____________________________________________________________________________________________________________________________________________________________________

How likely do you think it is that a Republican will win the 2008 presidential election? ________ (0-100%)

Class Experiment: Data

0102030405060708090

100

P(Win)

Explained WinExplained Loss

Anderson & Sechler (1985)Social theories (e.g. risk & fire-fighting), university students

Evidence for explanation-based inference

• Generating explanations influences assessments of probability

• Facility with which explanations can be generated influences assessments of probability

• “Goodness” of explanations can influence assessments of probability

Pennington & Hastie (1988)

0102030405060708090

100

Defense-Story Defense-Witness

Prosecution-Story

Prosecution-Witness

Juror Decisions, university students

Per

cent

Gui

lty

Ver

dict

s

Evidence for explanation-based inference

• Generating explanations influences assessments of probability

• Facility with which explanations can be generated influences assessments of probability

• “Goodness” of explanations can influence assessments of probability

Read & Marcus-Newhall (1993)Social and biological reasoning, university students

0102030405060708090

100

mononucleosis stoppedexercising

virus previous 3 pregnant

ProbabilityGoodness

Cheryl has FELT TIRED, GAINED WEIGHT, and had an UPSET STOMACH

Explanation-based learning is great! But explanation-based inference seems to lead to systematic bias.

Why the difference?

? ?

??

Siegler (1995)Number conservation, non-conserving 5-year-olds

Siegler (1995)

Putting it together: Speculation

FOLK COOKERY

…Cake was overcooked…

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

DRYCAKE

Time 1

FOLK COOKERY T1’TIME &

MOISTURE Causal LawsExplanatory Mechanisms

(“Framework” explanations)

Time 2

Predict dry cakesPrevent dry cakes

Change probability?

Interim Discussion Questions

• Is the effect of explanation on learning simply a result of probabilistic (Bayesian?) inference?

• Does explanation play the same role in science as it does in everyday cognition?

• What’s the relationship between theories and explanation?

• How might explanation contribute to the function of theories, e.g. prediction?– “Off-line” explanation-based learning– “On-line” explanation-based inference

• Case study: Simplicity in explanation-based inference

The Plan

Revisiting evidence for explanation-based inference

• Generating explanations influences assessments of probability

• Facility with which explanations can be generated influences assessments of probability

• “Goodness” of explanations can influence assessments of probability

“On-line” Explanation-Based Inference

FOLK THEORY T1

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

(hypothetical)DATA D1

Predict data like D1Prevent or cause data like D1

Read & Marcus-Newhall (1993)Social and biological reasoning, university students

0102030405060708090

100

mononucleosis stoppedexercising

virus previous 3 pregnant

ProbabilityGoodness

Cheryl has FELT TIRED, GAINED WEIGHT, and had an UPSET STOMACH

Open Questions

• Do the explanation “goodness” judgments lead to the probability judgments, or the other way around?

• Are simpler explanations judged better because they’re simpler, or because in this case they’re more likely to be true?

Goals of Simplicity Case Study

• Determine whether simpler explanations are judged better independently of probability.– When no probability information?– When simpler explanation is less probable?

• Determine how simplicity and probability trade off: does probability trump simplicity?– When probability information is unambiguous?– When probability information is uncertain?

• Determine whether simpler explanations are judged disproportionately likely to be true.

Simplicity: The Task

S2S1

D3D2D1

S2S1 S2S1

D1

(a)

Most satisfying explanation for the alien’s symptoms?

D2

(b)D3

(c)D1&D2

(d) D1&D3

(e)D2&D3

(f)

Simplicity: The Task

S2S1

D3D2D1

S2S1 S2S1

D1

(a)

Most satisfying explanation for the alien’s symptoms?

D2

(b)D3

(c)D1&D2

(d) D1&D3

(e)D2&D3

(f)

Simplicity: The Task

S2S1

D3D2D1

S2S1 S2S1

D1

(a)

Most satisfying explanation for the alien’s symptoms?

D2

(b)D3

(c)D1&D2

(d) D1&D3

(e)D2&D3

(f)

Figure 1

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

0

20

40

60

80

100

NoProbability

DirectProbability

vs.Simplicity

OpaqueProbability

vs.Simplicity

Simplicity: The Task

S2S1

D3D2D1

S2S1

50/750 73/750

S2S1

D1

(a)

Most satisfying explanation for the alien’s symptoms?

D2

(b)D3

(c)D1&D2

(d) D1&D3

(e)D2&D3

(f)

Figure 1

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

0

20

40

60

80

100

No Probability UnambiguousProbability vs.

Simplicity

Opaque Probabilityvs. Simplicity

Simplicity: The Task

S2S1

D3D2D1

S2S1

50/750 220/750

S2S1

D1

(a)

Most satisfying explanation for the alien’s symptoms?

D2

(b)D3

(c)D1&D2

(d) D1&D3

(e)D2&D3

(f)

250/750

Some MathP(D1 | S1 & S2)

= P(S1 & S2 | D1) * P(D1) / P(S1 & S2)

= 1 * (50/750) / P(S1 & S2)

= .067 * (1 / P(S1 & S2))

P(D2 & D3 | S1 & S2)

= P(S1 & S2 | D2 & D3) * P(D2 & D3) / P(S1 & S2)

= 1 * (250/750 * 220/750) / P(S1 & S2)

= .098 * (1 / P(S1 & S2))

D1

D2&D3

S2S1

.067 : .0982 : 3

Figure 1

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

0

20

40

60

80

100

No Probability UnambiguousProbability vs.

Simplicity

Uncertain Probabilityvs. Simplicity

Goals of Simplicity Case Study

• Determine whether simpler explanations are judged better independently of probability.– When no probability information?– When simpler explanation is less probable?

• Determine how simplicity and probability trade off: does probability trump simplicity?– When probability information is unambiguous?– When probability information is uncertain?

• Determine whether simpler explanations are judged disproportionately likely to be true.

Yes!It depends.

Yes.No.

Figure 1

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

0

20

40

60

80

100

NoProbability

DirectProbability

vs.Simplicity

OpaqueProbability

vs.Simplicity

Simplicity: The Task

S2S1

D3D2D1

S2S1

50/750 220/750

S2S1

D1

(a)

Most satisfying explanation for the alien’s symptoms?

D2

(b)D3

(c)D1&D2

(d) D1&D3

(e)D2&D3

(f)

250/750

Probability ConditionsD1 D2 D3 P(D1):P(D2&D3)

50 50 50 15:1

50 197 190 1:1

50 195 214 9:10

50 225 210 4:5

50 250 220 2:3

50 268 280 1:2

50 330 340 1:3

50 610 620 1:10

Simplicity & Probability

0

20

40

60

80

100

15:1 1:1 9:10 4:5 2:3 1:2 1:3 1:10

P(D1) : P(D2 & D3)

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

P(D1|S1&S2) = P(S1&S2|D1)*P(D1) / P(S1&S2)

Simplicity & Probability

0

20

40

60

80

100

15:1 1:1 9:10 4:5 2:3 1:2 1:3 1:10

P(D1) : P(D2 & D3)

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

P(D1|S1&S2) = P(S1&S2|D1)*P(D1) / P(S1&S2)

Simplicity & Probability

0

20

40

60

80

100

15:1 1:1 9:10 4:5 2:3 1:2 1:3 1:10

Bayesian PosteriorBiased PriorConservatism

P(D1) : P(D2 & D3)

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

Simplicity & Probability

0

20

40

60

80

100

15:1 1:1 9:10 4:5 2:3 1:2 1:3 1:10

P(D1) : P(D2 & D3)

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

Data (n = 144)

Simplicity & Probability

0

20

40

60

80

100

15:1 1:1 9:10 4:5 2:3 1:2 1:3 1:10

P(D1) : P(D2 & D3)

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

80%

Data (n = 144)

Goals of Simplicity Case Study

• Determine whether simpler explanations are judged better independently of probability.– When no probability information?– When simpler explanation is less probable?

• Determine how simplicity and probability trade off: does probability trump simplicity?– When probability information is unambiguous?– When probability information is uncertain?

• Determine whether simpler explanations are judged disproportionately likely to be true.

Yes!It depends.

Yes.No.Bayesian inference?

Frequency Estimation

Most satisfying explanation for

symptoms?S2S1

D1 D2 D3or

S2S1

D1

S2S1

D2 D3

3

Computer Replication

0

0.25

0.5

0.75

1

15:1 9:10 1:2 1:10

Probability Ratio: P(D1):P(D2&D3)

Data (n = 108)

% S

s ch

oosi

ng

sim

pler

exp

lana

tion

Frequency Estimation

Most satisfying explanation for

symptoms?S2S1

D1 D2 D3or D1

D2

D3

Percent ?

Percent ?

Percent ?

S2S1

D1

S2S1

D2 D3

3

Frequency estimates for D1

0

0.1

0.2

0.3

0.4

0.5

1:15 9:10 1:2 1:10

1 cause

2 causes

Actual

D1

What percent of the population has D1?

Frequency estimates for D2

0

0.2

0.4

0.6

0.8

1

1:15 9:10 1:2 1:10

Frequency estimates for D3

0

0.2

0.4

0.6

0.8

1

1:15 9:10 1:2 1:10

D2 D3

What percent of the population has D2 /D3?

Goals of Simplicity Case Study

• Determine whether simpler explanations are judged better independently of probability.– When no probability information?– When simpler explanation is less probable?

• Determine how simplicity and probability trade off: does probability trump simplicity?– When probability information is unambiguous?– When probability information is uncertain?

• Determine whether simpler explanations are judged disproportionately likely to be true.

Yes!It depends.

Yes.No.Bayesian inference?

Simplicity: Data Summary

• All else being equal, simpler explanation are preferred.

• When probability information is unambiguous it trumps a simplicity difference.

• When probability information is opaque, simplicity informs judgments (80% prior).

• Committing to a simple but unlikely explanation can lead to overestimating the frequency of causes invoked in the explanation.

Revisiting evidence for explanation-based inference

• Generating explanations influences assessments of probability

• Facility with which explanations can be generated influences assessments of probability

• “Goodness” of explanations can influence assessments of probability

“On-line” Explanation-Based Inference

FOLK THEORY T1

Causal LawsExplanatory Mechanisms

(“Framework” explanations)

(hypothetical)DATA D1

Predict data like D1Prevent or cause data like D1

Simplicity Discussion Questions

• It looks like simplicity of an explanation may influence its perceived probability. Is this rational or a cognitive bias?

• Scientists often wax poetic about simplicity. Is the sense of simplicity assumed in these experiments like simplicity in scientific theories?

• What’s the relationship between theories and explanation?

• How might explanation contribute to the function of theories, e.g. prediction?– “Off-line” explanation-based learning– “On-line” explanation-based inference

• Case study: Simplicity in explanation-based inference

The Plan

General Questions? Comments?

Thoughts on theories or explanation?

? ?

??

The End.

Thanks!

Tania Lombrozolombrozo@wjh.harvard.edu