psychology of proof

Question 1

chernobyl - (a failed) deduction

Answer 1

• If the experimenter continues, then the reactor must be cool
  
  • The reactor is not cool
  • Therefore?:
  • The experiment must be stopped…
  • But it was not stopped

Question 2

what is proof

Answer 2

• Proof - evidence or argument establishing a fact or the truth of a statement = drawing an inference
  
  • Other tasks related to proof:
  • Explanation
  • Diagnosis
  • Prediction
    Imagination

Question 3

types of inference

Answer 3

· Deduction - specific inference:
- “When the Uk leaves the EU, reaching an agreement will be the easiest deal in human history” - Liam Fox, 2017. The Uk is leaving the EU in January 2020…. Therefore?
· Induction - general inference:
- ‘the Uk parliament has rejected deals negotiated between the Uk prime minister and the EU on five occasions (out of vie)’. Therefore?
· Abduction - ‘best explanation available’
- ‘the areas of the Uk that voted most highly in favour of leaving the EU have received the most money from the EU over the past 25 years’. The reason why these regions voted to leave is…..?

Question 4

how does the mind undertake deduction

Answer 4

· E.g., ‘If the plane crashes the pilot will die’ and ‘The plane crashed’
· Structure (form) - if crash then die. Given crash, die follows
· Semantics (function) - dying as a result of a crash is possible
· Statistics (frequency) - dying as a result of a crash is possible

Question 5

inference as logical reasoning

Answer 5

· Assumption - individuals draw conclusions from premises by applying stored rules of logic to derive a single valid inference
· Types of inference:
- Classical syllogisms - all artists are beekeepers, some beekeepers are chemists, therefore?
- Conditional inferences - if I work hard, then I will get a pay rise. I didn’t get a pay rise. Therefore?
- Transitive inferences - john is faster than mike, john is slower than bill, therefore?

Question 6

structural view

Answer 6

· Formal logic - the use of syntactic structure (form) to determine the validity of an argument
· Piaget - stage of ‘formal operational thinking’

Question 7

Braine and O’Brien (1994); Rips (1983) - natural deduction:

Answer 7

· Direct inferences - when “p or q” and “not p” are held in memory, then conclusion “q” follows
· Indirect inferences - when “if p then q” and “not q” are held in memory, “not p” is inferred by applying inference rules

Question 8

Evidence - Wason’s selection task:

Answer 8

· Wason & Evans (1975)
· I have a set of cards, each with a letter on one side and a number on the other. There are four cards face down on the table, showing either a letter or a number. Select those cards, and only those cards, that will test the truth of the following rule:
· “If a card has a D on one side, then it has a 5 on the other side”
- D H 5 8
· “If a card has a B on one side, then it does not have a 7 on the other side”
- W B 7 4

Question 9

Evidence - Wason’s selection task: 2

Answer 9

· Cheng & Holyoak (1985) - Pragmatic reasoning schemas
· You are an immigration officer, checking that your staff are applying a rule that passengers coming from areas where Cholera is epidemic have had an immunization injection. If a passenger comes from a Cholera epidemic area, it is marked on one side of their visa, and if they have had the immunization, it is marked on the other side. In front of you are four visas on the table. Which should you turn over to ensure that the staff are applying the rule correctly?
· Cholera area No Cholera Immunized Not immunized

Question 10

Inference as searching for mental models:

Answer 10

· Johnson-Laird (1983)
· Inferences are drawn by searching mental representations for possibilities that have no counter-examples
· Construction of and search for models is constrained by
i) Principle of truth
ii) working memory capacity
· ʻIf the plane crashes the pilot diesʼ allows….
- Crash Dies
- No crash Lives
- No crash Dies

Question 11

Evidence - Ormerod and Richardson (2003):

Answer 11

paraphrasing between different kinds of logically equivalent conditional statement

Question 12

Ormerod and Richardson results:

Answer 12

Generation:
- C -> D = 70%
- D -> C = 55%
Evaluation:
- C -> D = 45%
- D -> C = 45%

Question 13

Explaining Ormerod and Richardson (2003) results:

Answer 13

• generation easier than evaluation
• generation = flesh out + match against stored template
• evaluation = compare model sets

Question 14

Bayes (simplified):

Answer 14

· Posterior probability - updated probability after the evidence is considered
· Prior probability - the probability before the evidence is considered
· Likelihood - probability of the evidence, given the belief is true
· Marginal probability - probability of the evidence, under any circumstance

Question 15

Information gain (Oaksford and Chater 1994;2007):

Answer 15

· Information = reduction in uncertainty
· Reasoning is about expected information gain (“what if….”) à utility
· Rarity – most events/things are rare compared with the number of instances where they donʼt occur
· Example: a Ford Fiesta is a common car, but its presence is rare when compared to the times when you donʼt see one

Question 16

Example - the ‘meningitis’ test:

Answer 16

· The small print….
· It is a common misconception that a meningitis rash appears in every case of meningitis. This is not true. If someone has meningitis but not septicaemia, they will not have a rash that does not fade, but they can still be seriously unwell.

Question 17

Rarity as informative:

Answer 17

· “If rash remains under pressure, then patient has meningitis”
· p: rash remains – rare
· not p: some other symptom – common
· q: meningitis – rare
· not q: some other outcome - common

Question 18

Dual system accounts:

Answer 18

· Example - why don’t firefighter drop their tools when ordered to do so in an evacuation?
· Naturalistic decision-making (Klein)
· E.g., Kahneman and Klein (2009)

Question 19

Where are we now dual system accounts:

Answer 19

· System 1 (heuristic, pragmatic)
- Fast
- Recognition-driven
- Effortless
- Prone to errors of inaccuracy
· * System 2 (analytic, logical)
- Slower
- Inference-driven
- Effortful
- Prone to errors of incompletion