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Explanation in Intuitive Theories Tania Lombrozo Harvard University / UC Berkeley.

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1 Explanation in Intuitive Theories Tania Lombrozo Harvard University / UC Berkeley

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4 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…” Carl Hempel

5 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.” Carl Hempel

6 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

7 What’s so great about explanation? ? ? ? ?

8 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. Ullian The Web of Belief (1970)

9 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 Craik The Nature of Explanation (1943)

10 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 Heider The Psychology of Interpersonal Relations (1958)

11 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.

12 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

13 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

14 Theories generate explanations FOLK BIOLOGY …why living things need food… …why birds have wings… …why Bob the bird flew towards the worm… Causal Laws Explanatory Mechanisms

15 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

16 Theories contain explanations FOLK BIOLOGY …why living things need food… …why birds have wings… …why Bob the bird flew towards the worm…

17 Theories generate and contain explanations FOLK THEORY …specific explanations… Causal Laws Explanatory Mechanisms (“Framework level” explanations)

18 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

19 “Off-line” Explanation-Based Learning FOLK THEORY T1 …explanation of D1… Causal Laws Explanatory Mechanisms (“Framework” explanations) DATA D1 Time 1 FOLK THEORY T1’ DATA Causal Laws Explanatory Mechanisms (“Framework” explanations) Time 2 Predict data like D1 Prevent or cause data like D1

20 “Off-line” Explanation-Based Learning FOLK COOKERY …Cake was overcooked… Causal Laws Explanatory Mechanisms (“Framework” explanations) DRY CAKE Time 1 FOLK COOKERY T1’ TIME & MOISTURE Causal Laws Explanatory Mechanisms (“Framework” explanations) Time 2 Predict dry cakes Prevent dry cakes

21 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

22 O’Reilly et al. (1998) Knowledge of circulatory system, university students

23 Wong et al. (2002) Geometry problem solving, 9 th graders Kinds of problems: Training: Equal Near transfer: 10% better Far Transfer: 40% better

24 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

25 “On-line” Explanation-Based Inference FOLK THEORY T1 Causal Laws Explanatory Mechanisms (“Framework” explanations) (hypothetical) DATA D1 Predict data like D1 Prevent or cause data like D1

26 “On-line” Explanation-Based Inference FOLK COOKERY T1 Causal Laws Explanatory Mechanisms (“Framework” explanations) Prevent DRY CAKE Compute probability of DRY CAKE with 1 hour cooking time (hypothetical) DRY CAKE

27 “On-line” Explanation-Based Inference FOLK COIN FLIPPING Causal Laws Explanatory Mechanisms (“Framework” explanations) Probability of someone having a trick coin that repeats sequence HHTHT (hypothetical) HHTHT

28 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

29 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%)

30 Class Experiment: Data

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

32 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

33 Pennington & Hastie (1988) Juror Decisions, university students Percent Guilty Verdicts

34 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

35 Read & Marcus-Newhall (1993) Social and biological reasoning, university students Cheryl has FELT TIRED, GAINED WEIGHT, and had an UPSET STOMACH

36 Explanation-based learning is great! But explanation-based inference seems to lead to systematic bias. Why the difference? ? ? ? ?

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

38 Siegler (1995)

39 Putting it together: Speculation FOLK COOKERY …Cake was overcooked… Causal Laws Explanatory Mechanisms (“Framework” explanations) DRY CAKE Time 1 FOLK COOKERY T1’ TIME & MOISTURE Causal Laws Explanatory Mechanisms (“Framework” explanations) Time 2 Predict dry cakes Prevent dry cakes Change probability?

40 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?

41 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

42 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

43 “On-line” Explanation-Based Inference FOLK THEORY T1 Causal Laws Explanatory Mechanisms (“Framework” explanations) (hypothetical) DATA D1 Predict data like D1 Prevent or cause data like D1

44 Read & Marcus-Newhall (1993) Social and biological reasoning, university students Cheryl has FELT TIRED, GAINED WEIGHT, and had an UPSET STOMACH

45 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?

46 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.

47 Simplicity: The Task S2S2 S1S1 D3D3 D2D2 D1D1 S2S2 S1S1 S2S2 S1S1 D1D1 (a) Most satisfying explanation for the alien’s symptoms? D2D2 (b) D3D3 (c) D 1 &D 2 (d) D 1 &D 3 (e) D 2 &D 3 (f)

48 Simplicity: The Task S2S2 S1S1 D3D3 D2D2 D1D1 S2S2 S1S1 S2S2 S1S1 D1D1 (a) Most satisfying explanation for the alien’s symptoms? D2D2 (b) D3D3 (c) D 1 &D 2 (d) D 1 &D 3 (e) D 2 &D 3 (f)

49 Simplicity: The Task S2S2 S1S1 D3D3 D2D2 D1D1 S2S2 S1S1 S2S2 S1S1 D1D1 (a) Most satisfying explanation for the alien’s symptoms? D2D2 (b) D3D3 (c) D 1 &D 2 (d) D 1 &D 3 (e) D 2 &D 3 (f)

50 Figure 1 % Ss choosing simpler explanation

51 Simplicity: The Task S2S2 S1S1 D3D3 D2D2 D1D1 S2S2 S1S1 50/75073/750 S2S2 S1S1 D1D1 (a) Most satisfying explanation for the alien’s symptoms? D2D2 (b) D3D3 (c) D 1 &D 2 (d) D 1 &D 3 (e) D 2 &D 3 (f)

52 Figure 1 % Ss choosing simpler explanation

53 Simplicity: The Task S2S2 S1S1 D3D3 D2D2 D1D1 S2S2 S1S1 50/750220/750 S2S2 S1S1 D1D1 (a) Most satisfying explanation for the alien’s symptoms? D2D2 (b) D3D3 (c) D 1 &D 2 (d) D 1 &D 3 (e) D 2 &D 3 (f) 250/750

54 Some Math P(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)) D1D1 D 2 &D 3 S2S2 S1S1.067 : : 3

55 Figure 1 % Ss choosing simpler explanation

56 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.

57 Figure 1 % Ss choosing simpler explanation

58 Simplicity: The Task S2S2 S1S1 D3D3 D2D2 D1D1 S2S2 S1S1 50/750220/750 S2S2 S1S1 D1D1 (a) Most satisfying explanation for the alien’s symptoms? D2D2 (b) D3D3 (c) D 1 &D 2 (d) D 1 &D 3 (e) D 2 &D 3 (f) 250/750

59 Probability Conditions D1D2D3P(D1):P(D2&D3) 50 15: : : : : : : :10

60 Simplicity & Probability P(D 1 ) : P(D 2 & D 3 ) % Ss choosing simpler explanation P(D1|S1&S2) = P(S1&S2|D1)*P(D1) / P(S1&S2)

61 Simplicity & Probability P(D 1 ) : P(D 2 & D 3 ) % Ss choosing simpler explanation P(D1|S1&S2) = P(S1&S2|D1)*P(D1) / P(S1&S2)

62 Simplicity & Probability P(D 1 ) : P(D 2 & D 3 ) % Ss choosing simpler explanation

63 Simplicity & Probability P(D 1 ) : P(D 2 & D 3 ) % Ss choosing simpler explanation Data (n = 144)

64 Simplicity & Probability P(D 1 ) : P(D 2 & D 3 ) % Ss choosing simpler explanation 80% Data (n = 144)

65 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?

66 Frequency Estimation Most satisfying explanation for symptoms? S2S2 S1S1 D1D1 D2D2 D3D3 or S2S2 S1S1 D1D1 S2S2 S1S1 D2D2 D3D3  3 3

67 Computer Replication Data (n = 108) % Ss choosing simpler explanation

68 Frequency Estimation Most satisfying explanation for symptoms? S2S2 S1S1 D1D1 D2D2 D3D3 or D1D1 D2D2 D3D3 Percent ? S2S2 S1S1 D1D1 S2S2 S1S1 D2D2 D3D3  3 3

69 D1D1 What percent of the population has D 1 ?

70 D2D2 D3D3 What percent of the population has D 2 /D 3 ?

71 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?

72 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.

73 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

74 “On-line” Explanation-Based Inference FOLK THEORY T1 Causal Laws Explanatory Mechanisms (“Framework” explanations) (hypothetical) DATA D1 Predict data like D1 Prevent or cause data like D1

75 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?

76 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

77 General Questions? Comments? Thoughts on theories or explanation? ? ? ? ?

78 The End. Thanks! Tania Lombrozo


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