Reasoning Intro

Question 1

deductive vs inductive reasoning

Answer 1

deductive: a judgment that something must be true if other statements are true
inductive: a judgment that some rule is probably true on the basis of experience
syllogism: a basic reasoning puzzle, a set of statements (premises) and a conclusion

Question 2

is reasoning just logic

Answer 2

origins of reasoning in logic

logicism views logic as basis for human thought

great strength is that logic always yields valid conclusions if premises are true

weakness: it always applies, so difficult to account for the errors we know occur

Question 3

true vs valid

Answer 3

true and valid not equivalent

valid conclusion: logically follows from the premises
true conclusion: a statement about the world

sound conclusion: valid conclusion with true premises

Question 4

1. logical inferences are influenced by what we see as plausible

Answer 4

1) If Spot is a lizard then Spot is an animal.
-Spot is not a lizard.
-Therefore, Spot is not an animal
vs
2) If you clean up your room, I will give you $10
-You do not clean up your room.
-Therefore, I do not give you $10.

logically equivalent and invalid

almost nobody agrees with 1 but many agrees with 2

Question 5

2. negation is harder

Answer 5

A) If it is Friday night, then Bill is drunk
It is Friday night.
Therefore Bill is drunk.

(B) If it is Friday night then Bill is drunk.
Bill is not drunk.
Therefore it is not Friday night.

Taplin (1971) found
– virtually everyone endorsed (A)
– substantial proportion didn’t endorse (B).

Question 6

3. quantifiers are harder

Answer 6

3) No CEOs are lazy.
Some rich people are lazy.
Therefore, some CEOs are not rich people.
vs
4) No addictive things are cheap.
Some wines are cheap
Therefore, some addictive things are not wines.

Evans et al (1983) found 10% of subjects accepted (3), but 71% accepted (4).

But (3) and (4) are equivalent (invalid)

Question 7

Are such problems interesting?

Answer 7

World provides us both with too much information, and too little.

Reasoning is like breathing for the mind

Constantly drawing conclusions from premises, but rarely take notice of it.
– Reason when we learn, criticize, analyze, judge, infer evaluate, optimize, apply,
imagine, devise, and create.

But don’t just apply rules of formal logic

Question 8

results of Wason card selection task

Answer 8

‘A’ only turned over
– 33% (applying affirming the antecedent)

‘A’ and ‘4’ turned over
– 45% (applying affirming the consequent)

‘A’ and ‘7’ turned over
– 4% (applying denying the consequent)

Correct answer is ‘A’ and ‘7’

Question 9

Evans (1982) changing relevance of Wason CST

Answer 9

Evans (1982) showed that people do better when rule
is stated as:
“If a card has a vowel on one side then it will not have an even number on the other”

This statement,
– Draws attention.
– Fits to Gricean principles of pragmatics.

But not the whole story, context has a powerful effect.
– Experience with situation helps.

Question 10

Griggs & Cox (1982) beer modification

Answer 10

Better performance than for the abstract rule for the following:
– “If a person is drinking beer, then that person is over 19”.
– Options: “Drinking beer”, “Drinking coke”, “16 years of age”, “22 years of age”

Most subjects said check the people drinking beer and those under 19.

Question 11

Johnson-Laird, Legrenzi & Legrenzi (1972) stamp modification

Answer 11

experience can help

if a letter is sealed, then it has a 50-lira stamp on it

Much better performance for this rule than for the abstract rule for English students
– In England such a rule then existed

Perhaps just because concrete objects are mentioned?
– But Griggs & Cox (1982) found no better performance on this scenario by Florida
students.
– Golding (1981) found better performance by English participants old enough to have used postal rule

Cheng & Holyoak (1985) presented postage problem (and others) to Hong Kong and American students.
– No difference on abstract four-card task
– Hong Kong students performed better on letter problem, had similar rule.

American students with rationale performed as well as Hong Kong
students

Question 12

pragmatic reasoning schemas

Answer 12

Sets of generalized, context-sensitive, rules defined in relations to classes of goals (e.g., permission, social exchange)

Question 13

how to use induction

Answer 13

Use analogies

Reason about causality

Test hypotheses

Question 14

Wason 246 task (Wason, 1960)

Answer 14

– Find a rule that generates a three number sequence
– 2-4-6 is a correct sequence
– Propose a sequence and experimenter tells you if it is correct or not.
– You can announce what you think the rule is and experimenter will tell you if you are correct.

result:
Most initially think rule is “Sequence increasing by 2”

So tried sequences like “6-8-10” and “13-15-17”

Sequences that confirm beliefs, few tried to disconfirm
– e.g. “1-2-3”
– Or more critically, “3-2-1”

Actual rule: “An increasing sequence”
– 28% never found the rule.

Why? Wason proposed a confirmation bias.

Question 15

confirmation bias

Answer 15

Bias: a tendency to perform in a certain way regardless of the situation or information
given

Confirmation bias: the tendency to only look for information that supports your
existing beliefs.

Tweney et al (1980) showed that if it was
two rules “DAX”/”MED” then people did
better than when it was “right”/”wrong”.

Question 16

problems with syllogistic reasoning

Answer 16

1. knowledge of real world strongly influences willingness to accept or reject the conclusions of such problems
2. influenced by whether the surface features of conclusions match those of premises (matching bias)
3. often inaccurate because the meaning of various words and expressions in formal logic differ from their everyday meanings