What is deductive reasoning?
- Starting with some sort of premises, then you deduce a conclusion
- Determining the conclusions that must follow given that certain statements are true
- Premise 1: All planets are made of cheese
- Premise 2: Earth is a planet
- Conclusion: Earth is made of cheese
-If it is raining, then Fred’s hair gets wet.
-It is raining.
-Fred’s hair gets wet.
HOW MANY PEOPLE (%) AGREED THIS WAS A VALID INFERENCE?
-98% agreed this was a valid inference (Marcus & Rips, 1979)
-If it is raining, then Fred’s hair gets wet.
-Fred’s hair does not get wet.
-It is not raining.
HOW MANY PEOPLE (%) AGREED THIS WAS A VALID INFERENCE?
- 52% agreed this was a valid inference (Marcus & Rips, 1979)
- Need to go off what the first premise says
-If it is raining, then Fred’s hair gets wet.
-Fred’s hair gets wet.
-It is raining.
HOW MANY PEOPLE (%) AGREED THIS WAS A VALID INFERENCE?
-33% agreed this was a valid inference (Marcus & Rips, 1979)
-If it is raining, then Fred’s hair gets wet.
-It is not raining.
-Fred’s hair does not get wet.
HOW MANY PEOPLE (%) AGREED THIS WAS A VALID INFEFENCE?
-21% agreed this was a valid inference (Marcus & Rips, 1979)
Why do people make mistakes?
- People can reason logically, but often fail to understand formal, logical tasks (e.g. Braine, 1978). E.g. not tasks they’re used to
- People do not reason logically (e.g. Woodworth & Sells, 1935)
- We should not expect people to reason in line with formal logic (e.g. Oaksford & Chater, 1994). Argued that it is not the right type of test, not evolved to think this way
What are the Theories of deductive reasoning?
- Abstract-rule theories
- Mental models
- Dual systems approach
- Probabilistic approach
What is the Abstract rule theory?
-Braine (1978)
-People reason logically but make mistakes:
– if they misunderstand the task
– if the required reasoning places too many demands on working memory
-Limited capacity to make sense of the task, can’t store and process
What can improve reasoning performance? (Abstract rule theory)
- Performance can be improved by presenting additional clarifying sentences (to reduce comprehension errors, e.g. Braine et al., 1984)
- However, such additional information can also impair performance on some tasks (e.g. Byrne, 1989)
What is the Mental model theory?
- Johnson-Laird (e.g. 1999)
- Everyday comprehension processes (mental models) are used on reasoning problems
- People create mental models to represent premises
- Reasoning involves examination of mental model and/or attempts to create alternative models
What is principle of truth?
- Conclusions are drawn based on the initial model. People then try to falsify that conclusion by constructing alternative models
- The creation of alternative models is very demanding on working memory.
- THEREFORE “individuals … tend to construct mental models to represent explicitly only what is true…” (principle of truth) Johnson-Laird (1999)
What did Newstead et al (1999) look into?
- Mental models theory predicts that people will consider more conclusions in problems where they must create more mental models
- Gave tasks permitting one or several mental models
- No difference in number of conclusions considered
What is the Dual systems approach?
-Reviewed by Evans (2003)
-Reasoning involves two systems
-Fast, automatic, based on prior knowledge, belief and heuristics (rules of fun, e.g. shortcuts)
– Slow, deliberate, abstract, based on logic
What did -Oaksford and Chater (e.g. 2001) find about probabilistic reasoning?
-People use ‘probabilistic reasoning’ rather than logic to solve deductive reasoning tasks
What are Thematic materials?
- Perhaps people are better at reasoning when the material is meaningful?
- BUT correct answer does not necessarily imply correct reasoning
- Memory cuing hypothesis (Griggs & Cox, 1982)
- Good memory, not meaning you are good at reasoning
What is Social contract theory?
- We have strategies for detecting cheats who receive benefits without incurring the appropriate costs.
- We should be particularly good at versions of the Wason task that involve social contracts.
- Cosmides & Tooby (1989)
What did Gigerennzer and Hug (1992) find about pensions?
- ‘If an employee gets a pension (P) then s/he has worked for 10 years (Q)’
- Who is violating the rule?
- Pension P
- No Pension not-P
- Worked 10 years Q
- Worked 8 years not-Q
- Imagine you are the employer OR imagine you are the employee
Problems for social contract theory
- Some facilitatory contexts do not involve costs and benefits that are socially exchanged – BUT these have not always replicated
- Only applies to ‘deontic versions of the Wason task (‘if you do X you must do Y’) and not to ‘indicative’ versions (‘if there is a P then there is a Q’)
What did Oaksford and Chater (1994) find about selection tasks?
- Selection task is not deductive, but a matter of ‘optimal data selection’
- Confirming instances may be useful, as well as counterexamples
- What matters is the expected reduction in uncertainty concerning whether rule is true or false. According to this measure: P > Q > not-Q > not-P
- Meta analysis of over 30 experiments using different versions of the selection task
- 89% choose A P
- 62% choose 4 Q
- 25% choose 7 NOT Q
- 16% choose D NOT P
Deductive reasoning: summary
-People make characteristic errors in deductive reasoning
-These are attributed to:
– Failure to understand the task
– Lack of logical approach
– Tendency towards probabilistic approach in line with real-life reasoning
What is Inductive reasoning?
- Going beyond the information provided to draw generalised conclusions – Hypothesis testing
- Note that conclusions may not always be true
What were the results of the Wason 2-4-6 task?
- Only 21% correct with first statement of rule (but over 70% correct in the end)
- Tendency to attempt to confirm (rather than disconfirm) original hypothesis
- 1960
What did Tweney et al (1980) find when looking at performance?
-Performance does not improve when specifically instructed to use a disconfirmatory approach
What did Mynatt et al (1977) look at when Firing particles?
- Select direction in which to fire particle across the screen
- Then choose one of a pair of possible screens on which to test hypothesis (by firing additional particles)
- Confirmation, disconfirmation & control groups
