C81COG: Cognitive Psychology 1

DEDUCTION AND INDUCTION

Dr. Alastair D. Smith

Room B22 – School of Psychology

alastair.smith@nottingham.ac.uk

Deduction & Induction

Aims

• This lecture will clarify differences between deductive and inductive reasoning and describe key research bearing on human behaviour in such circumstances

Learning Objectives

After this lecture you should be able to:

• Distinguish between Induction and Deduction.

• Describe Wason’s 2-4-6 task and other examples of tasks where subjects show a confirmatory bias.

• Describe Wason’s card selection task and the types of error that people make when doing it.

• Distinguish between strategies that are and are not effective in improving people’s performance in these two tasks.

Deduction

• Reasoning logically from premises to a conclusion such that if the premises are correct the conclusion is necessarily correct.

• Note that a deduction can be valid even if the conclusion is untrue.

• Common examples: Mathematics, Logic, Syllogistic reasoning• Can range from the very easy…

– Major Premise: All of the artists are beekeepers– Minor Premise: All of the beekeepers are chemists

therefore– Conclusion: All of the artists are chemists

(90% correct)

Deduction

• Reasoning logically from premises to a conclusion such that if the premises are correct the conclusion is necessarily correct.

• Note that a deduction can be valid even if the conclusion is untrue.

• Common examples: Mathematics, Logic, Syllogistic reasoning

• Can range from the very easy…to the very difficult…

– Major Premise: All of the artists are beekeepers– Minor Premise: None of the chemists are beekeepers

therefore– Conclusion: Some of the artists are not chemists

(10% correct)

• Deduction draws a specific conclusion from general premises

Induction

• “Any process of thought yielding a conclusion that increases the semantic information in its initial observations or premises” Johnson-Laird (1993).

• This very broad definition could include many types of thinking - reasoning by analogy, practical reasoning, decision making etc.

• Common examples: Science, Everyday thinking.• Reasoning about the future from the past…

– The sun has risen every morningtherefore

– The sun will rise tomorrow morning

• Induction draws a general conclusion from specific premises (the basis of scientific hypothesis-testing)

Scientific Induction

• Francis Bacon (1620) delineated the principles of the inductive method – a breakthrough in the approach to science.

• The only knowledge of importance to man was empirically rooted in the natural world; and that a clear system of scientific inquiry would assure man's mastery over the world. He was the originator of the expression "Knowledge is power."

• Science is about observing nature (i.e. specific instances) and coming up with general laws to describe it (induction).

Scientific induction

• Induction is not necessarily so great for science…

• Bertrand Russell pointed out that a scientist turkey might form the generalization that “Each day I am fed” because this hypothesis has been confirmed everyday of his life.

• But if tomorrow is Christmas the hypothesis is likely to be proved false

• Falsification not confirmation is useful here

Scientific Induction

• Much of real science consists of coming up with a general hypothesis and seeking specific information which confirms it (e.g. NASA scientists: Mitroff, 1974).

• Popper (1959) suggested that good science should involve seeking information which is inconsistent with a particular hypothesis - falsification.

• The hypothetic-deductive method

• Kuhn (1970): if there is too much recalcitrant data then a paradigm shift may occur – scientific revolution

• The importance of falsification is demonstrated by a variety of studies done by Peter Wason and colleagues.

• “I’m thinking of a rule for generating a series of three numbers. One example of a number sequence generated by this rule would be 2-4-6. Your task is to guess what my rule is. You can give me new sequences of numbers and I will tell you if they are possible or not.”

• Write down your hypotheses as to the rule, test them by giving me test sequences, but don’t give me the answer until you are sure.

Wason (1960) - The 2-4-6 task

Wason (1960) - The 2-4-6 task

• Possible rules

1. Any three numbers ascending in twos

2. Any three even numbers in ascending order

• But if subjects ask the experimenter about these they are trying to confirm their hypothesised rule rather than falsify it , unfortunately either could be correct.

• If they hypothesise the rule was 1. They could eliminate (falsify) it by asking about the sequence 3-6-9, if the experimenter says that it conforms to the rule we can eliminate both of these.

Wason (1960) - The 2-4-6 task

• This turns out to a very difficult task. Most subjects announce at least one incorrect hypothesis. Many subjects never discover the correct rule.

• Wason suggests that this is because of confirmation bias – subjects spend too much time giving sequences that confirm their hypothesis Instead of attempting to falsify it (though see Evans 1989)

• Scientists are no better than others at the 2-4-6 task. Interestingly, clergymen seemed slightly more willing to abandon hypotheses (Mahoney, 1976)

• Instructing subjects to use a falsifying strategy, or giving financial incentives generally doesn’t help performance.

Confirmation Bias

• Tweney et al. (1980) found that suggesting to subjects that there are two different rules - a DAX rule and a MED rule does seem to help.

• (DAX is the normal 2-4-6 rule, MED is any other rule)

• Rather than being told that sequences are right or wrong, subjects are told whether they are DAX or MED.

• Now most subjects generate the correct rule first time!

• This is despite the fact that they are still seeking to confirm MED, rather than attempting to falsify DAX.

Confirmation Bias

• Mynatt, Doherty & Tweney (1977) examined a more scientific example of hypothesis testing.

• Constructed a virtual world in which subjects fire particles at circles and triangles that are either bright or dark.

• Test the rule “Dim shapes reflect particles” - subjects had to discover what influenced motion of particles.

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90270

Confirmation Bias

• Subjects again select information to confirm their hypotheses and ignore disconfirming information.

• Understand the logic of falsification, but fail to eliminate hypotheses that are misguided (e.g. shape of objects, rather than brightness).

• Disconfirmatory instructions led to poorer performance – a need to establish at least one viable hypothesis that can account for a range of data.

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180

90270

• Wason (1966, 1968): There are four cards on the table. Each has a number on one side, and a letter on the other.

• Here is a rule that might apply to the four cards - “If a card has a vowel on one side, it has an even number on the other side”.

• Which card(s) must you turn over in order to test this rule?

A K 4 7

The Wason Card Selection Task

• The majority choose: A and 4, or just A• Only a few choose: A and 7 (is there an odd number on the

other side of A and a vowel on the other side of 7)

• A – if even it confirms, but if odd then it’s definitely not true• K – irrelevant since rule says nothing about consonants• 4 – if vowel then it confirms, but cannot prove. If a

consonant then the card is irrelevant• 7 – if a consonant then irrelevant, but if a vowel it falsifies

the rule

A K 4 7

The Wason Card Selection Task

Card (type) Number or Status of card letter on reverse-----------------------------------------------------------------------------------------------P (A) even number confirming odd number falsifyingNot-P (K) even number irrelevant odd number irrelevantQ (4) vowel confirming

consonant irrelevantNot-Q (7) vowel falsifying consonant irrelevant

The Wason Card Selection Task

P and Q are from propositional calculus (like x and y in algebra

• Using a concrete task improves results (Wason & Shapiro, 1971)

• “Every time I go to Manchester I go by car”

• 62% of subjects correctly selected the Manchester and Train cards, compared to 12% in the experiment with abstract stimuli (AK47)

MANCHESTER LEEDS TRAINCAR

A concrete example (1)

• Johnson-Laird et al. (1972).

“If a letter is sealed, then it has a 5d stamp on it”

5d 4d

• 92% success on envelopes, 8% on abstract task.• Older subjects better than younger subjects.

A concrete example (2)

• Griggs & Cox (1982) did this task with American students and found no difference between the abstract and concrete version.

• In contrast their students could do “if a person is drinking beer, then the person must be over 19 years of age”.

• In this case, the instruction to determine whether the rule had been violated improved performance (unlike “disconfirmation”)

• The drinking rule had recently been introduced in Florida – people require specific experience of the situation to reason adequately about it. The Memory Cueing hypothesis - if people can remember cases which would disconfirm the rule they are more likely to try to falsify it.

Memory cueing

• But it can’t just be memory - version of the task which involve wholly novel situation can still facilitate performance. For example:

“If a purchase exceeds $30, then the receipt must be approved by the department manager.” (Griggs & Cox, 1983)

• Even without direct experience subjects made correct choices about 70% of the time

$45 $15 APPROVED NOT APPROVED

Memory Cueing or Pragmatic Reasoning

• Cheng & Holyoak (1985) suggest that this is an example of a common real-world situation that people do have to reason about (e.g. needing permission to do something)

• So the key thing is not that you have experienced the exact situation, but that you are used to this type of pragmatic reasoning.

• Normal reasoning may make falsification an extremely inefficient way to gain information

– Are all swans white? (Oaksford, 1997)

– The probability of confirmation is high – therefore an apparently irrational negative conclusion bias can be seen as a rational “high probability conclusion” effect

Memory Cueing or Pragmatic Reasoning

• Pragmatic reasoning experience can also be gained with the right instructions

• Cheng & Holyoak (1985) manipulated content and context:

– Subjects in Hong Kong and Michigan

– If a letter is sealed, then it has a 5d. stamp on it

– If the form says “Entering” on one side, then the other side includes cholera among the list of diseases

• Half of the subjects also given a rationale for the judgement (e.g. revenue, inoculation)

• With no rationale, Hong Kong subjects performed better with postal problem (due to experience) – all subjects improved on all tasks when the rationale was explained

Memory Cueing or Pragmatic Reasoning

Example questions

• In the 2-4-6 task participants tend to try and:

a. Confirm their hypothesisb. Falsify their hypothesisc. Base their decisions on past experienced. Generalize to new examples

• Reasoning is improved:

a. When problems are realisticb. With a scientific educationc. When problems are abstractd. With financial incentives