The document provides examples and explanations of different types of logical reasoning and empirical testing of theories. It includes questions about: 1. Describing a critical test to empirically distinguish between two competing theories about residential segregation. 2. Deciding whether an argument about political inactivity is valid. 3. Demonstrating the validity of a hypothetical syllogism using a truth table. 4. Evaluating the validity of syllogistic arguments using the star test and Venn diagrams. 5. Comparing the empirical content of pairs of statements. The document provides worked examples and evaluation criteria for critically assessing different logical arguments and empirical tests of theories.

1. Test Exam - Solutions
Tutorial Week 7 - Application of Theories
Block A 2013/2014

2. Structure
✤ Quick overview!
✤ YOU propose an answer!
✤ We compare answers !
✤ Evaluation criteria

3. Q1. CriticalTests
✤ When you have two competing explanations of the same
phenomenon make use of a critical test:!
✤ Derive from both underlying theories predictions for the same
situation, so that only the predictions of one theory can be right
(contradicting predictions).!
✤ test them

4. ✤ Q1. Two theories have been proposed to explain residential
segregation in cities. Theory 1 assumes that individuals
prefer to live together with a majority of neighbors of their
own ethnic group. Theory 2 assumes that members of the
ethnic minority have lower incomes and therefore are more
likely to live in neighborhoods with cheaper housing.
Describe a critical test to empirically distinguish these two
explanations. Explain why this is a critical test.
What is your answer?

5. We observe a social phenomenon: Residential Segregation!
What should we see?!
If T1 (homophily) is true, there is majority of one group or the
other in each neighborhood. The reason is that individuals
who are in the minority would prefer to live elsewhere and
therefore leave the neighborhood (or do not enter).!
If T2 (income inequality) is true, there is a majority of
“whites” in expensive neighborhoods and a majority of
“blacks” in cheaper neighborhoods. The reason is that most
blacks cannot afford housing in the expensive neighborhoods
but they would prefer better (more expensive) housing if they
could afford it.!
How can we test (critically) the competing explanations?
Compare (Q1) - 1

6. Experiment - Mixing houses: In a neighborhood where rents are low
and “blacks” are a majority, build expensive houses. The two theories
have contradicting predictions for this experiment and both
predictions can be tested!
T1: Predicts that only blacks with higher incomes will move to
these new houses, because they can afford them and will prefer
to be with a majority of their own. “Whites” on the contrary, will
not move into the new houses because they rather be with a
majority of their own kind - only “blacks” move in.!
T2: Predicts that both blacks and whites with higher incomes
move into the new houses and the neighborhood composition
will not have an effect on their choices - both “blacks” and “whites”
move in.
Compare (Q1) - 2

7. Valid reasoning for each of the two theories about
why it predicts segregation.!
Valid reasoning for each of the two theories on what
it predicts for the critical experiment.!
Predictions are contradictory!
Predictions are testable
Criteria (Q1)

8. Q2.ArgumentValidity
✤ Explanation is formed by the explanandum (the thing that is to be
explained) and the explanans (the things used to explain).!
✤ The explanandum must be a logical consequence of the explanans!
✤ The explanans must contain at least one general law and one
singular statements (necessary to derive the explanandum)!
✤ The explanans must have empirical content!
✤ All statements of the explanans must be true

9. What is your answer?
If citizens are satisfied with the government, then they will not vote!
In 2012, American citizens will be satisfied with the government!
--------------------------------------------------------------------------------!
In 2012, American citizens will be politically inactive
✤ Q2. Decide whether the following argument is valid.
Explain briefly why you arrived at your conclusion:

10. Compare (Q2) - 1
If citizens are satisfied with the government (S),
then they will not vote (N)
General Law
In 2012, American citizens (t) will be citizens
satisfied with the government (S)
Condition
In 2012, American citizens (t) will be politically
inactive (I)
Explanandum

11. All S* is N!
t is S!
------------!
t is I*
The explanandum does not follow logically
from the explanans!
We do not need the explanans to obtain the
explanandum!
We can test validity (star test)
All statements are wffs (+)!
There is only one star on the
right hand side (+)!
N is not starred (-)
The argument is not valid
Compare (Q2) - 2

12. How about implicit assumptions? -!
This is not a necessary part of the answer
Politically inactive citizens (I) reject
political mechanisms (R)
The rejection of political mechanisms
(R) is expressed when citizens do not
vote (N)
Citizens who do not vote (N) are
politically inactive citizens (I)
All S* is N!
All N* is I!
t is S!
------------!
t is I*
The argument is valid
( but it is not the original argument)All N is I
Compare (Q2) - 3

13. Criteria (Q2)
Explain what “validity of an argument” means.!
Show why this argument is not valid given your
explanation (here: conclusion does not follow from
premises)!
You can use syllogistic logic and the star test, but
this was not asked here!
If you do not use this, you have to explain in your
own words clearly why the conclusion does not
follow from the premises.

14. Q3. Propositional Logic
✤ Propositional Logic - single objects!
✤ Propositions are statements which are either true or false - not valid or
invalid!
✤ Propositions can be combined to form new propositions - using
operators!
✤ Operators define the truth-value of the combined propositions based
on the truth-values of the propositions that it consists of!
✤ We make use of truth tables

15. What is your answer?
erence 1: Hypothetical syllogism
(p), then he is a Marxist (q).
), then he hates capitalism (r)
(p), then he hates capitalism (r).
General form:
p⊃q
q⊃r
p⊃r
✤ Q3. Demonstrate that the following argument is valid,
using a truth table. Explain why your truth table
demonstrates that the argument is valid.

16. Compare (Q3) - 1
p q r p⊃q q⊃r (p⊃q).(q⊃r) p⊃r ((p⊃q).(q⊃r))⊃(p⊃r)
1 1 1 1 1 1 1 1
1 1 0 1 0 0 0 1
1 0 1 0 1 0 1 1
1 0 0 0 1 0 0 1
0 1 1 1 1 1 1 1
0 1 0 1 0 0 1 1
0 0 1 1 1 1 1 1
0 0 0 1 1 1 1 1

17. Compare (Q3) - 2
✤ The task is to demonstrate that the hypothetical syllogism is valid: Is
((p⊃q)·(q⊃r))⊃(p⊃r) valid?!
✤ The implication of p and q is false only if p is true and q is false!
✤ We make use of a truth table!
✤ Why truth table: Because it shows that for every combination of p.q,r, it
is true that the conclusion of this reasoning(p⊃r) is an implication of
(follows logically from) the conjunction of the premises (which is
((p⊃q)·(q⊃r)) )

18. Q4. Syllogistic Logic
Syllogistic Logic - domains objects!
We study the implication of general statements (wffs)!
There are five words (All, No, Some, Is, Not)!
There are 8 possible forms of wffs!
We make use of the Star Test and Venn-Diagrams to test
validity of the arguments

19. What is your answer?
All hominids have a tail!
Humans are hominids!
---------------------------!
No human has a tail
No X is Y!
z isX!
------------!
Z is
Some L is M!
g is not L!
----------------!
g is not M
a b c
✤ Q4. Below, you find a list of syllogisms. Demonstrate
whether they are valid or not, using the star test and a
Venn-diagram. If necessary, translate the statements

20. All hominids (H) have tail (T)!
Humans (U) are hominids (H)!
---------------------------!
No human (U) has tail (T)
Start Test
All H* is T!
All U* is H!
-------------!
No U is T
H
TU
Venn-D.
All are wffs!
T is not *!
No * right side
Conclusion needs to be drawn!
There cannot be a U with no T
The argument is not valid
Compare (Q4) - 1

21. Start Test
X
YZ
Venn-D.
Not all statements are wffs!
Z is not *!
Z is not in the premises
The conclusion is not a wff
The argument is not valid
No X is Y!
z is X!
------------!
Z is
No X* is Y*!
z is X!
------------!
All Z is
z
Compare (Q4) - 2

22. Start Test Venn-D.
M is not *
g can be an M although all
premises are true!
it is not clear where to draw g
The argument is not valid
Some L is M!
g is not L!
----------------!
g is not M
Some L is M!
g is not L*!
----------------!
g is not M
Compare (Q4) - 3
L
M
x

23. Q5. Empirical Content
✤ Recall: explanations must be empirically testable!
✤ Theories should be as informative as possible!
✤ The set of objects in the if part should be larger (general), and the
set of objects in the then part should be smaller (specific).!
✤ The empirical content of a statement is higher the more possible states
there are which would falsify the statement. One way to achieve this:!
✤ More states: if part contains a disjunction!
✤ More states: then part contains a conjunction

24. What is your answer?
A. If citizens are dissatisfied with the living conditions in their
country, then they will vote for conservative parties!
B. If citizens are dissatisfied with the living conditions in their
country and if they are religious, then they will vote for conservative
parties
A. People who do not vote will participate in demonstrations or
sign a petition.!
B. People who vote will participate in demonstrations.
a
b
✤ Q5. Below you find 2 boxes which contain pairs of
statements. Decide for each pair which statement has more
empirical content. Sketch why.

25. Compare (Q5) - 1
A. If citizens are dissatisfied with the living conditions in their
country, then they will vote for conservative parties!
B. If citizens are dissatisfied with the living conditions in their
country and if they are religious, then they will vote for
conservative parties
There is a conjunction in the if part of statement B!
The informational content of statement B is smaller than of A
because due to the conjunction, the set of objects referred to in the
if part of B is only a subset of those referred to in A (not all citizens
– but only the religious ones)
A has more empirical content

26. Compare (Q5) - 2
A has more empirical content
Dissatisfied
Citizens
Religious
Voting for
conservative
parties
A
B

27. Compare (Q5) - 3
A is about non voters and B about voters - we do not
know if the two set are of the same size (which is larger) !
There is a disjunction in the then part of A!
There are less states that can be falsified in the then
part of B
We cannot answer the question
A. People who do not vote will participate in demonstrations or
sign a petition.!
B. People who vote will participate in demonstrations.

28. Compare (Q5) - 4
Non voters
Demonstrate
A
Voters
Sign a
petition
A
B
We cannot answer the question

29. Q6. Social Phenomena &
Individual Behavior
✤ Micro-level explanations provide information that might be
overlooked if only macro-relationships are considered!
✤ Explain the macro-to-micro relationship (bridge assumption)!
✤ Explain the theory of action!
✤ Explain the micro-to-macro relationship (transformation assumption)!
✤ Assess validity for all!!
✤ Explanations lead to predictions (Advice)!
✤ Consider the ceteris paribus assumptions

30. What is your answer?
✤ Q6. Read the following article. The author argues that the quality
of teaching in the US can be raised by giving teachers more
autonomy. Both variables “quality of teaching in the US” and
“autonomy given to teachers” are collective phenomena. Develop an
explanation of this relationship based on assumptions about
individual behavior. You can use arguments of the author and/or
include own assumptions.!
✤ a. Draw a “Coleman-boat” of your theory!
✤ b. Make explicit all bridge assumptions, the theory of action of your
theory, and the transformation assumptions you make. Justify these
assumptions, using general theories or empirical background knowledge.
Demonstrate that your arguments are valid!
✤ c. Do you think that the advice to increase teachers’ autonomy is valid?
explain your answer.

31. !
!
!
a. Draw a “Coleman-boat” of your theory
!
!
macrolevel
Autonomy given
to teachers
Quality of
teaching
indiv.level
Perception of safety
for disagreeing with
the principal
Choice of teaching
techniques based
on their knowledge
Compare (Q6) - 1

32. Compare (Q6) - 2
Autonomy given
to teachers
Quality of
teaching
Perception of safety
for disagreeing with
the principal
Choice of teaching
techniques based on
their knowledge
b. Make explicit all bridge assumptions, the theory of action of your theory,
and the transformation assumptions you make. !
+ Justify these assumptions, using general theories or empirical
background knowledge. !
+ Demonstrate that your arguments are valid
Bridge Assumption
T. of Action - RCT
Transf. Assumption

33. Autonomy given to
teachers
Perception of safety for
disagreeing with the principal
Bridge Assumption: If teachers have more autonomy, they perceive that
it is safer for them to disagree with the school principal
The higher the autonomy given to teachers (I) the less likely they will feel obliged to
choose teaching techniques they dislike (R)!
The less obliged teachers feel to chooses teaching techniques they dislike (R) the more
likely teachers perceive safety for disagreeing with the school principal (B)!
--------------------------------------------------------------------------------!
The higher the autonomy given to teachers (I) the more likely teachers perceive safety
for disagreeing with the school principal (B)
Compare (Q6) - 3

34. All I* is R!
All R* is B!
------------!
All I is B*
All statements are wffs!
All capital letters are * once!
There is one * on the right
Compare (Q6) - 4
Bridge Assumption: If teachers have more autonomy, they perceive that
it is safer for them to disagree with the school principal
Autonomy given to
teachers
Perception of safety for
disagreeing with the principal

35. Perception of safety for
disagreeing with the principal
Choice of teaching techniques
based on their knowledge
The higher the autonomy given to teachers (I) the more likely teachers perceive safety for
disagreeing with the school principal (B) !
The more likely teachers perceive safety for disagreeing with the school principal (B), the
more likely teachers will choose their teaching techniques based on their own knowledge (T)!
--------------------------------------------------------------------------------!
The higher the autonomy given to teachers (I), the more likely teachers will choose their
teaching techniques based on their own knowledge (T)
T. of Action: If teachers perceive that it is safer for them to disagree with the
school principal, it is more likely they will choose teaching techniques based on
their own knowledge.
Compare (Q6) - 5

36. All I* is B!
All B* is T!
------------!
All I is T*
All statements are wffs!
All capital letters are * once!
There is one * on the right
Compare (Q6) - 6
Perception of safety for
disagreeing with the principal
Choice of teaching techniques
based on their knowledge
T. of Action: If teachers perceive that it is safer for them to disagree with the
school principal, it is more likely they will choose teaching techniques based on
their knowledge.

37. Transf. Assumption: An increase in the use of the teaching techniques based
on teachers’ own knowledge increases the quality of teaching in the classroom
Quality of
teaching
Choice of teaching
techniques based on their
knowledge
The higher the autonomy given to teachers (I), the more likely teachers will choose
their teaching techniques based on their own knowledge (T) !
The more likely teachers will choose their teaching techniques based on their own
knowledge (T), the higher the quality of teaching in the classroom (Q)!
--------------------------------------------------------------------------------!
The higher the autonomy given to teachers (I), the higher the quality of teaching in the
classroom (Q)
Compare (Q6) - 7

38. All I* is T!
All T* is Q!
------------!
All I is Q*
All statements are wffs!
All capital letters are * once!
There is one * on the right
Compare (Q6) - 8
Transf. Assumption: An increase in the use of the teaching techniques based
on teachers’ own knowledge increases the quality of teaching in the classroom
Quality of
teaching
Choice of teaching
techniques based on their
knowledge

39. c. Do you think that the advice to increase
teachers’ autonomy is valid? explain your answer.
The advice is valid, as it has been shown in the arguments
of points a and b. Nonetheless, there are problems that
might arise given the ceteris paribus assumptions of the
explanations and the advice.!
It is assumed that if given safety about keeping their
jobs (autonomy), teachers will always use the best
teaching techniques. This implies that they know them -
how about teachers that are not well trained?!
Even if assumed that all teachers know what are the
best teaching techniques, their implementation has no
cost (requires the same effort than using traditional
techniques)- how about lazy teachers?
Compare (Q6) - 9

40. Definitions of concepts!
Multiple choice!
Matching
Good luck in the exam!
Other types of questions