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1

What are the two main domains of formal reasoning (logic)?

1. Syllogisms.
2. Conditional reasoning.

2

What is the formula for syllogisms?

_________ + __________ = syllogism

Premise 1 + Premise 2 + Conclusion = syllogism

3

To be correct, a syllogism must be _____ (i.e. logical) and ___.

To be correct, a syllogism must be valid (i.e. logical) and true.

4

Label the formula for these statements and put them in order to create a syllogism:

Therefore, Socrates is mortal.
Socrates is a man.
All men are mortal.

P1: All men are mortal. + P2: Socrates is a man. = C: Therefore, Socrates is mortal.

5

To solve a syllogism, what two things must we evaluate?

1. It's validity.
2. The truth of its premises.

6

Evaluate the validity and truth of the premises to solve this syllogism:

P1: All apples are fruit. + P2: All fruit can swim. = C: Therefore, apples can swim.

The argument is valid, but it is not true because the second premise is false. We cannot accept this syllogism.

7

What are the two basic heuristics for solving syllogisms?

1. Venn diagrams.
2. Replacing abstract entities with more concrete ones.

8

How do venn diagrams help solve syllogisms?

They show the relationships among sets of things.

9

How does replacing abstract entities with more concrete ones help solve syllogisms?

Makes an abstract syllogism more concrete.

10

When solving syllogisms using venn diagrams, always look for _____ _______.

When solving syllogisms using venn diagrams, always look for counter examples.

11

The tendency when reasoning to look for examples that confirm the truth of some argument is called:

Confirmation bias.

12

How may we avoid confirmation bias when evaluating the truth of syllogisms?

Using counter-examples to arguments.

13

Who first proposed that people's performance solving syllogisms improves with training, but only if they are explicit taught to avoid confirmation bias by looking for counter examples?

Helsabeck (1975)

14

Evaluating the truth of a two-part statement that specifies the relationship between 2 assertions (cause and effect) is called:

conditional reasoning.

15

What is an antecedent?

A thing that existed before, or logically goes before another.

16

What is a consequent?

The following result or subsequent effect of something.

17

In conditional reasoning, statements take the general form: if _ then _.

_ = cause/antecedent
_ = effect/consequent

In conditional reasoning, statements take the general form: if P then Q.

P = cause/antecedent
Q = effect/consequent
C = conclusion

18

What does 'modus ponens' mean?

Affirming the antecedent.

19

What does 'modus tollens' mean?

Denying the consequent.

20

"If it's raining (P), then I'm carrying an umbrella (Q)."

P: it's raining.
Q: I'm carrying an umbrella

This is called:

Affirming the antecedent.

21

"If it's raining (P), then I'm carrying an umbrella (Q)."

~P: it's not raining.
C: None is possible. I always carry my umbrella, irrespective of whether or not it's raining.

This is called:

Denying the antecedent.

22

"If it's raining (P), then I'm carrying an umbrella (Q)."

Q: I'm carrying an umbrella
C: None is possible. I always carry my umbrella, irrespective of whether or not it's raining.

This is called:

Affirming the consequent.

23

"If it's raining (P), then I'm carrying an umbrella (Q)."

~Q: I'm not carrying my umbrella.
C: It's not raining.

This is called:

Denying the consequent.

24

Describe Rips and Markus (1977) experiment on human reasoning.

Procedure:

Results:

Procedure:

Gave conditional reasoning problems to college students.

Results:
Modus ponens problems = 100% correct.
Modus tollens problems = 60% correct.

25

In the 19_0's's, Peter Cathard _____ introduce a test of logical reasoning he called a _______ ____. This was used to test his theory of _________ ____.

In the 1960's's, Peter Cathard Wason introduce a test of logical reasoning he called a selection task. This was used to test his theory of confirmation bias.

26

Describe the procedure of Wason and Johnson-Laird (1972) experiment on human reasoning.

Procedure:

Procedure:

Developed variant of conditional reasoning task using cards. If a card has a vowel on one side, then it should have an even number on the other side.

[A] [D] [4] [7]

Participants were asked to turn over the minimal number of cards to validate the rule.

27

Describe the results of Wason and Johnson-Laird (1972) experiment on human reasoning.

[A] [D] [4] [7]

Results:

__% picked the A card, and then the 4 card.
__% picked the A card alone.
__% picked the A card, and the 7 card
__% picked another combination of cards.

[A] [D] [4] [7]

Results:

45% picked the A card, and then the 4 card.
35% picked the A card alone.
4% picked the A card, and the 7 card
9% picked another combination of cards.

28

Solve the puzzle:

If a card has a vowel on one side, then it should have an even number on the other side.

[A] [D] [4] [7]

Turn over the minimal number of cards to validate the rule.

Turn over A and 7.

29

Describe the procedure of Johnson-Laird et al. (1982) experiment on human reasoning.

Procedure:

Procedure:

Used a modified version of the Wason task on college students. Participants were given 4 orange cards, with each having a drink on one side of the card and the age of the drinker on the another side.

[Beer] [Coke] [ 35 ] [ 19 ]

If a patron is drinking a beer, they must be 21 yrs+. Turn over the minimum number of cards (check the minimum number of ID's) to validate the rule.

30

Describe the results of Johnson-Laird et al. (1982) experiment on human reasoning.

[Beer] [Coke] [ 35 ] [ 19 ]

Results:
__% picked the beer and 35 card.
__% pick the beer card alone.
__% pick the beer, 35, and 19 card.
__% pick the beer and 19 card.
__% pick another combination of cards.

[Beer] [Coke] [ 35 ] [ 19 ]

Results:
0% picked the beer and 35 card.
20% pick the beer card alone.
3% pick the beer, 35, and 19 card.
72% pick the beer and 19 card.
5% pick another combination of cards.