Theories of Reasoning Flashcards
What does the data suggest reasoning involves?
Reasoning is not purely logic, but logic is not irrelevant
Reasoning is influenced by context
Reasoning evokes heuristics
What are the three main theoretical approaches that account for reasoning?
- Mental Models (Johnson-Laird)
- Mental Logics (Braine, Rips)
- Bayesian reasoning (Chater, Oaksford)
What does the Mental Logics model posit about reasoning? What are its assumptions? What is an example of this rule?
People often respond inconsistently with formal logic, but does not mean there isn’t a mental logic
Braine and O’Brien (1991) and Rips (1994) - both assume propositional representations: represent knowledge as statements, describing the knowledge
• Errors occur because the rules in mental logics are incomplete, and requires taking different steps to reach conclusions
E.g. Modus Ponens: Proof by confirmation. Turning over the “A” card
Modus Tollens: Proof by contradiction. Turning over the “7” card
- We don’t have a direct rule for Modus Tollens/it’s not part of our set –> hard
How are mental logics used?
Use a limited set of logical rules, rather than all the ones in formal logic
(e.g. We have Modus Ponens, but not Modus Tollens)
Chains of inferences can be forward (premises –> concl) or backward (concl –> premises), but eventually all suppositions are rejected/accepted - reasoning.
Rules in mental logic depends on individuals
- e.g. Musicians may reason differently to others, due to their skill set?
How does the Mental Logics model explain errors?
- Chain of inferences –> greater chance of error
- Exceed WM
- Exec control limitations: can’t keep track of chain in argument
- Wrong rule: Lack of appropriate inference rule, failure to apply appropriate rule, or application of inappropriate rule
- Garbled output of rule.
What evidence is there to support the Mental Logics model?
Tasks where people judge the logical correctness of a series of arguments.
Braine et al (1984): When asked to judge 85 syllogisms, participants applied more complex rules as the difficulty of syllogisms increased. (r=0.79)
Rips (1994): People found problems more difficult if backwards reasoning was required
Forward reasoning seems more automatic
- Lea et al (1990) found more false recog for forward reasoning conclusions
Rips (1989) found evidence of mental logic type reasoning in verbal protocols
Good evidence for this approach.
What does the Mental Models approach suggest about how we reason?
Reasoning involves building >1 representation (model) of the situation, then making conclusions from introspection
Mental model = a representation of a possible state-of-affairs in the world
E.g. Black behind cue
Green on right of cue
Red ball between them
How can Euler circles be used? (Erickson, 1974)
Euler circles: Creating circles to represent info (sort of like Venn diagram)
e.g. Some artists (A) are beekeepers (B). All the beekeepers (B) are chemists (C). Therefore some of the artists (A) are chemists (C). (refer to notes for actual circles)
Do people use Euler circles to reason?
- Can be ambiguous when used in situations.
- Need to be taught this in maths - no evidence that people do this spontaneously
What form of Mental Models does Johnson-Laird (1983) propose?
Comprehending text –> Construct different critical, concrete possibilities
e.g. lots of ways of tossing a coin, but only two models of outcomes: H/T
e.g. Some of the artists are beekeepers
All the beekeepers are chemists
Therefore some of the artists are chemists
Set up the following model:
A B C
A
B C, etc.
However, one model is not always enough.
E.g. None of the artists are chemists. All the beekeepers are chemists. Therefore some of the artists are beekeepers
A
B C … no valid conclusion?
More possible models:
A
B C
C
Valid conclusion: Some chemists are not artists.
What evidence is there to support mental models?
Johnson-Laird and Byrne (1991) predicted:
Inferences based on one model will be easier than those based on multiple models
Systematic errors are likely to correspond to initial models of premises - knowledge can influence the process of inference
Copeland and Radvansky (2004): When participants asked to rate validity of syllogisms, depending on the number of mental models that needed to be constructed for the correct response,
- Fewer models necessary –> More accurate, faster, more confident conclusions
- WM capacity corr. .42 with accuracy (higher WM –> more space to store more models)
- Higher corr with accuracy for multiple than single model syllogisms (more models = more accurate)
Supports Mental Models theory.
How does the Mental Models approach explain for contextual effects on reasoning?
The context of the syllogism influences the first model that is created.
- If the first model is incorrect, it can lead the person to make the wrong conclusion, and also hinder the person from creating other models that lead to different conclusions.
- Whether or not the conclusions reflect reality also influences the endorsement of conclusions
E.g. All athletes are bakers. Some of the bakers are chemists. Therefore some of the athletes are chemists.
People tend to endorse this invalid conclusion.
Woodsworth and Sells (1935) proposed the “Atmosphere of the premises” hypothesis: “Some” in the premise biases us towards “some” in the conclusion
- Suggests people do not reason, but take a guess at what looks right - not well supported.
Mental model to this approach:
Model 1:
A B C
A B
C --> statement is correct (false)
Model 2:
A B
B C
C
--> Contradicts conclusion, but requires going beyond first model
--> First model created is critical
Knowledge influences first model created --> Knowledge can influence whether or not the correct conclusion is reached
How does the Mental Model approach explain the error in Wason selection task?
Model 1 created:
[Vowel] Even ….
- Easy to see that need to turn over vowel card (Modus Ponens)
- Also makes sense to look at the even card, due to model –> error (due to no other models having been created)
To turn over odd card, another model needs to be developed:
[Vowel] Even
Not vowel Even
Not vowel not even
Error in Wason’s because we don’t expand on the first model enough.
Mental logics vs Mental models?
- Testing theories requires critical tests that can distinguish them.
- Hard to do for mental logics and mental models - Tend to be able to explain each others’ results post-hoc
May be due to fact that each is under-constrained - What is a model and which ones do we build?
- What mental logics do we have and not have?
Thus argument continues, but both provide possible explanation of reasoning phenomena.
What does the Bayesian approach propose about reasoning?
People reason about syllogisms based on the probability that a conclusion is correct.
- Probabilistic strategy in an uncertain world
- Probability theory better than logic, because it’s a computational level of reasoning
But: Judgements of probability are hard, so this makes reasoning fundamentally subjective.
