explanation in intuitive theories tania lombrozo harvard university / uc berkeley
TRANSCRIPT
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?
? ?
??