- The document discusses explanation as one aim of science according to the deductive-nomological (DN) account of explanation. - Under the DN account, understanding a phenomenon is achieved by deducing it from laws of nature and specifying the particular circumstances. - However, the DN account is not sufficient for explanation as there can be intuitive explanations that do not satisfy the DN conditions, such as singular causal explanations.

1. Explanation as an
Aim of Science

2. Understanding
reasons for why the
phenomenon to be
explained is
expected on a lawful
basis (Hempel 1965)
Functioning artifacts
reasons for expecting
that a manipulation
satisfies certain
functions
Forecasts
reasons for expecting
a phenomenon to
occur in a particular
way.
S C I E N T I F I C K N O W L E D G E
Design
Prediction
Explanation
Is explanation the same as prediction, just
applied to phenomena already observed?

3. … a DN explanation answers the question “Why did the explanandum-
phenomenon occur?” by showing that the phenomenon resulted from
certain particular circumstances, specified in C1, C2,…, Ck, in accordance
with the laws L1, L2,…, Lr. By pointing this out, the argument shows that,
given the particular circumstances and the laws in question, the occurrence
of the phenomenon was to be expected; and it is in this sense that the
explanation enables us to understand why the phenomenon occurred.
Hempel 1965
The Deductive-Nomological (DN) Account

4. Question Why E? Why was Mars at position X at time t?
Law-like L1=("If C1,…,Ck then E"),
generalisations L2,…,Lr
Newton's laws of motion, the Newtonian
inverse square law governing gravity
Circumstances C1, C2,…,Ck the mass of the sun, mass of Mars, their
present position, their velocity
Explanandum E Mars at position X at time t

5. • Explanation as one aim of science
• Explanation provides understanding
• DN account: understanding a phenomenon achieved
through deducing it from laws of nature
Summary

6. Achieving
Understanding

7. Which variable can provide an
explanation of the other variable?
A. The shadow's length explains the height of the flagpole
B. The flagpole's height explains the length of its shadow
C. Either variable explains the other
Please pause the video and answer the question before continuing!

8. Explain the flagpole's
length by its shadow?
• If we know the values of any two of the variables
x, h, θ, we can calculate the third
• However, the productive relationships between
these variables is not symmetric:
• Intervening on h or θ will change x
• Intervening on x will not change h or θ
• To understand means to be able to say what
would have happen if things had been different
Judea Pearl
(*1936)
Michael Strevens
(*1965)
James Woodward
(*1945)

9. Explain the flagpole's
length by its shadow?
• If we know the values of any two of the variables
x, h, θ, we can calculate the third
• However, the productive relationships between
these variables is not symmetric:
• Intervening on h or θ will change x
• Intervening on x will not change h or θ
• To understand means to be able to say what
would have happen if things had been different
• Such what-if questions can be answered by
tracing productive relationships
• Explanations help us understand by identifying
the productive relationships – i.e. the relevant
causes

10. Explain the
pendulum's length
by its period?
T = 2π*√(l/g)
ó
l = T2 * g / 4π2

11. Explain the
pendulum's length
by its period?
T = 2π*√(l/g)
ó
l = T2 * g / 4π2
These cases satisfy the DN
conditions, but intuitively do not
constitute genuine explanations
àDN account is not sufficient for
explanation

12. (L) All biological males who take birth control pills regularly
fail to get pregnant
(K) Mr. Jones is a biological male who has been taking
birth control pills regularly
---------
(E) Why does Mr. Jones fail to get pregnant?

13. (L) All biological males who take birth control pills regularly
fail to get pregnant
(K) Mr. Jones is a biological male who has been taking
birth control pills regularly
---------
(E) Why does Mr. Jones fail to get pregnant?
These cases satisfy the DN
conditions, but intuitively do not
constitute genuine explanations
àDN account is not sufficient for
explanation

14. • Vase stood on table
• 1 m above marble floor
• Hit table with my knee
• Vase fell…
Singular Causal Explanations

15. When explaining a specific event, at least in everyday
context we seem to do without laws.
Singular Causal Explanations

16. Singular Causal Explanations
These cases do not satisfy the DN
conditions, but intuitively constitute
genuine explanations
àDN account is not necessary for
explanation

17. To explain phenomenon E is to identify the
contributing cause of E that makes a difference in the
situation to be explained
Identifying the difference-making contributing causes
is sufficient to answer what if things had been different
questions – i.e.sufficient to provide understanding

18. Understanding
Identify difference-
making contributing
cause for
phenomenon to be
explained
Functioning artifacts
reasons for expecting
that a manipulation
satisfies certain
functions
Forecasts
reasons for expecting
a phenomenon to
occur in a particular
way.
S C I E N T I F I C K N O W L E D G E
Design
Prediction
Explanation
Explanation NOT the same as prediction

19. The Format of
Explanation

20. Why did the vase break?
Explanandum
Features of phenomenon to be explained.
Because it was dropped.
Explanans
Statements that increase understanding of explanandum

21. Singular Explanandum General Explanadum
Thus, despite national averages that indicate boys’ performance was consistently higher
in science than that of girls relative to their personal mean across academic areas, there were
substantial numbers of girls within nations that performed relatively better in science than in
other areas. Within Finland and Norway, two countries with large overall sex differences in the
intra-individual science gap and very high GGGI scores, there were 24% and 18% of girls who
had science as their personal academic strength, respectively; relative to 37% and 46% of boys.
Finally, it should also be noted that the difference between the percentage of girls with a
strength in science or mathematics was always equally large or larger than the percentage of
women graduating in STEM; importantly, again this difference was larger in more gender equal
countries (rs = .41, CI = [ .15 , .62 ] , n = 50, p = .003). In other words, more gender equal
countries were more likely than less gender equal countries to lose those girls from an academic
STEM track who are most likely to choose it based on personal academic strengths.
Figure 3: Gender equality (y-axes) is related to sex differences in intra-individual science
strength and STEM graduation. The Global Gender Gap Index (GGGI) assesses the
extent to which economic, educational, health, and political opportunities are equal for
substantial numbers of girls within nations that perform
other areas. Within Finland and Norway, two countrie
intra-individual science gap and very high GGGI score
had science as their personal academic strength, respec
Finally, it should also be noted that the differ
strength in science or mathematics was always equally
women graduating in STEM; importantly, again this d
countries (rs = .41, CI = [ .15 , .62 ] , n = 50, p = .003)
countries were more likely than less gender equal coun
STEM track who are most likely to choose it based on
Figure 3: Gender equality (y-axes) is related to
strength and STEM graduation. The Global Ge
extent to which economic, educational, health,

22. 22
Contrastive Explanandum:
Why did the vase break into fragments rather than just show
fissures?
Contrastive Explanans:
Because it was dropped from height X onto a floor with
stiffness Y rather than from height <X onto floor with
stiffness <Y

23. Why did the crash occur
in this situation while it doesn't
occur in situations in which similar
cars moving at similar speeds
with similarly competent drivers
traverse other curves?
Why did the crash occur
with this driver while other
drivers did traverse this
curve safely?
(i) Because the driver was intoxicated
(ii) Because the curve was too tightly banked

24. What makes
Explanations powerful

25. 1. Accuracy – whether the explanans describes
the actual state/properties of the world
• Explanation needs to identify only the difference-making
contributing cause(s)

26. 2. Precision (of the Explanandum) – the more
precise the contrast is stated in the explanandum,
the better the explanation.

27. 3. Difference-Making (of the Explanans) – The
explanans must identify all the contributing causes
that produced the difference asked for in the
explanadum.

28. 4. Non-sensitivity (of the Explanans) – Some
explanans causes are more sensitive to
background causes than others

29. Illustration: A Very Sensitive Explanans
“I don’t want to listen to
[Beethoven’s Appassionata]
because it makes me want
to stroke people’s heads,
and I have to smash those
heads to bring the revolution
to them.”

30. 4. Non-sensitivity (of the Explanans) – The less
sensitive an accurate difference-making
explanans, the more powerful the explanation

31. 5. Cognitive Salience – The more easily a given
explanation can be grasped, the more powerful it
is.

32. What is the necessary amount of detail
required in the explanans to explain the
explanandum?
Aggregate demand & supply
Actual interactions on trading
floors
Neural basis for decisions
Accuracy Salience
goes up goes up

33. Summary
• Causal explanations, i.e. those that identify difference-
making contributing causes of an explanandum, can be
better or worse
• 5 dimensions of making them better

34. What is Causation?

35. X is a direct cause of Y with respect to
a background variable set V
ó
there is a possible intervention on X
that will change Y when all other
variables in V are held fixed.
(Woodward 2003)
I
Y
X
V2
V1

36. Pause the video and answer this question before continuing.
A B C
In which of the following models is X a direct
cause of Y?
I
Y
X
V2
V1
V3
I
Y
X
V2
V1
V3
I
Y
X
V3
V1
V4
V2
V4

37. X is a contributing cause of Y with
respect to a background variable set V
ó
there is a causal chain, each link of
which consists in a direct cause,
extending from X to Y
(Woodward 2003)
I
Y
X
V2
V1
V2
X not a direct cause of Y,
but a contributing cause,
wrt to {Vi}

38. Summary
• Manipulability account of direct cause
• Derived from that: account of contributing cause

39. How to learn about
Causes?

40. Correlation
≠
Causation

41. Correlation
• measures the association between two variables
Causation
• measures the productive influence of one variable on another

42. We only observe
correlation but
never causation.
David Hume
(1711-1776)
Observing
correlation is an
important kind of
evidence for
causation.
Judea Pearl
(*1936)

43. Correlation Not Necessary for Causation

44. Correlation Not Necessary for Causation
Y
X
Z
+
-
Cov (X,Y) = 0

45. Correlation Not Sufficient for Causation
Cov (X,Y) >> 0
Y
X
Y
X
X causes Y Y causes X
Y
X
X, Y
independent but
correlated
C
Y
X
A common cause C
causes both X and Y

46. Examples:
• Per capita candy consumption correlated with divorce rate– common cause: age
• hormone replacement therapy correlated with coronary heart disease – common cause:
socio-economic status
Correlation Not Sufficient for Causation
Cov (X,Y) >> 0
Y
X
Y
X
X causes Y Y causes X
Y
X
X, Y
independent but
correlated
C
Y
X
A common cause C
causes both X and Y

47. Correlation Not Sufficient for Causation
Cov (X,Y) >> 0
Y
X
Y
X
X causes Y Y causes X
Y
X
X, Y
independent but
correlated
C
Y
X
A common cause C
causes both X and Y

48. Correlation Not Sufficient for Causation
Cov (X,Y) >> 0
Y
X
Y
X
X causes Y Y causes X
Y
X
X, Y
independent but
correlated
C
Y
X
A common cause C
causes both X and Y
Many different causal models are compatible with correlation
data! How to determine the correct one?

49. Strategy 1: Controlled Experiments
Mill's Method of Difference
1. Control all background variables influencing X and Y
2. Intervene on hypothesized cause to see whether it
makes a difference on hypothesised effect

50. Strategy 1: Controlled Experiments
Y
X
V2
V1
I
X causes Y

51. Strategy 1: Controlled Experiments
X
Y
V2
V1
I
Y causes X

52. Strategy 1: Controlled Experiments
C
Y
X
V2
V1
I
A common cause C
causes both X and Y

53. Strategy 1: Controlled Experiments
Y
X
V2
V1
I
X, Y
independent but
correlated

54. Strategy 2: Instrumental Variable Analysis
For detecting causes from observational data
1. Observe correlation between X and Y
2. Find a variable Z that you know affects X, but not Y (the instrument)
3. Use the instrument Z instead of X when estimating the effect of X
on Y
Example
Cov (Smoking,Health) >> 0
Health
Smoking

55. Strategy 2: Instrumental Variable Analysis
For detecting causes from observational data
1. Observe correlation between X and Y
2. Find a variable Z that you know affects X, but not Y (the instrument)
3. Use the instrument Z instead of X when estimating the effect of X
on Y
Example
Cov (Smoking,Health) >> 0
Health
Smoking
Depression

56. Strategy 2: Instrumental Variable Analysis
For detecting causes from observational data
1. Observe correlation between X and Y
2. Find a variable Z that you know affects X, but not Y (the instrument)
3. Use the instrument Z instead of X when estimating the effect of X
on Y
Example
Cov (Smoking,Health) >> 0
Cov (Taxes,Health) = ?
Health
Smoking
Cigarette taxes

57. These Strategies Require Causal Knowledge!
Health
Smoking
Cigarette taxes I
Y
X
V2
V1
Need to know that tax
increases do not cause
health decreases
Less
money
Need to know all
relevant background
conditions for control
"No causes in, no causes out"
Nancy Cartwright
(*1944)

58. Summary
• Causes ≠ Correlations
• Correlations as evidence
for causes
• Experimental &
observational strategies
for generating that
evidence