Reasoning and Deduction

1. Reasoning and Deduction The psychology of human reasoning

2. The problem of circularity • PARADOX standard against which reasoning is set quality of human reasoning against standard

3. So we need to measure our reasoning against some standard.

4. Independent mathematical models Provide normative standards for good reasoning Normative standards are taken as the ‘right answer’ on a defined reasoning task . Normative standards Propositional logic (avoid contradictions) Probability theory (avoid certain losses) Decision theory Game Theory How well does human reasoning fit these norms?

5. Prepositional Logic If…then = conditional rule ‘If’ is the antecedent clause = ‘p’ Then is the consequent clause = ‘q’ Abstract version if p…… then q Concrete version if ‘it is raining’ [p]…..then ‘the ground is wet’ [q].

6. Watson Selection Task (1966) A 2 K 7 4 cards Cards have a letter on one side & a number on the reverse. RULE = If there is a vowel on one side then there is an even number on the reverse TASK = “which cards would you select to turn over to determine whether the rule is true or false?

7. Write down your answer

8. Watson Selection Task (1966) A 2 K 7 4 cards Based on the conditional rule ‘if p then q’ Cards have a letter on one side & a number on the reverse. RULE = If there is a vowel on one side [p] then there is an even number on the reverse [q] TASK = “which cards would you select to turn over to determine whether the rule is true or false?

9. A A card is a vowel = ‘p’ K card is a Consonant [not a vowel] = -p 2 is an even number = ‘q’ 7 is an odd number [not even] = -q K 2 7

10. Correct answer by normative logic standard :A [p]& 7 [not-q] So how well did people adhere to this standard?

11. Johnson & Wason (1970a) • Johnson & Wason (1970a) 46% participants A & 2 [p & q] 33% A [p only] 7% A, 2, 7 [p, q & not-q] 4% 7 [not-q only]

12. But………….. Conclusion : people do not use normative logic Is it correct to make the assumption that we are illogical?

13. There is an implicit assumption in the Wason Selection Task • The assumption is that it is a deductive reasoning task • If we accept this premise then logically we are illogical?????

14. Assumption: Wason Selection Task = deduction task Implicit acceptanceof Popper’s (1935-1959) hypothetico-deductive philosophy of science as the normative Standard against which to judge performance. Popper’s assumption was that evidence can only falsify, evidence can never confirm or prove scientific theories.

15. A hypothesis leads to predictions that follow deductively from the scientific theory. The experiment must therefore have the potential to falsify the hypothesis under test By analogy: hypothesis = conditional rule in the card selection task Choice of experiment = which card is selected Experimental data = the reverse of the selected card has a bearing on the truth of the statement (the hypothesis) i.e the conclusion.

16. By ANALOGY with Popper’s hypothetico-deductive philosophy of science, in the deductive selection task participants should only turn over cards that would be incompatible with the conditional rule because only these cards would be able to falsify the rule. The conditional rule has a material implication (if p then q) So the participant should turn over cards A (p) odd number (not-q) would falsify the rule and 7 (not-q)  a vowel would falsify the rule (p)

17. Assumption: Wason Selection Task = deduction task This is not what people do! Instead they typically select cards that confirm the rule by picking A and 2 cards

18. Popper’s hypothetico-deductive philosophy of falsification rejects the selection of card 2 - a consequent cause (q) - as a confirmation bias that is an irrational strategy. Therefore we BEGIN WITH THE IDEA THAT HUMAN REASONING IS IRRATIONAL from Wason’s Abstract Card Selection Task . Assumed rationality was normative theory, deviation from this was wrong = people are illogical and irrational . The normative system itself was never questioned!

19. Historical context to human reasoning research - I • Piaget formal operational thinking as a normative, invariant, inevitable standard. • Not dealing with the nature of human reasoning, instead correctness is judged against ‘logic’ as a normative standard. • To be correct in a deductive reasoning task : accept premises are true, reasoning is only based on these premises (no influence of prior knowledge), statements cannot be logically false if the premises are accepted as true.

20. Historical context to human reasoning research - II • Tversky & Kahneman (1972) people’s rationality is bounded (loss frame - risk seeking, gain frame – risk adverse.) • Using Popperian deductive logic Wason (1970a) showed people were prone to confirmation bias (logical error)

21. Historical context to human reasoning research - III BUT The Wason Abstract Selection Task is not just about deducing reasoning. To be ‘correct’ you have to know & understand the Falisification Principle It was thought that the paradigm was studying deductive reasoning, but behaviour on the task had nothing to do with deductive reasoning! The premise was to test if those not trained in formal logic could reason logically in an ill-defined task, BUT the task merely asked for necessary conclusions from premises, it did not ask participants to perform a well defined task to manipulate formal logic rules. Logic was only implicitly given in the instructions because they were trying to discover is we were innately logical! If the falsification principle had been made explicit to participants they would have used it!

22. Historical context to human reasoning research - IV • There has been a shift in emphasis away from formal logic in human reasoning research. • Evidence suggests that pragmatic strategies cause responses. • Responses are influenced by prior knowledge and belief that the deductive paradigm defines as errors & biases! • If human reasoning is based on prior belief and the degree of confidence they feel then human reasoning may be probabilistic. • Still need to explain how prior general knowledge affects reasoning. (shared / unshared knowledge bases, e.g. are you an expert in formal logic?

23. Deductive Reasoning Paradigm : Empirical Findings Important distinction between abstract and themed tasks (content and context). Abstract reasoning as domain-general - independent of problem content. - as free of prior knowledge and belief • so abstract tasks = ideal task to discover whether the mind has an inherent logicality. Deductive reasoning paradigm shows biases & context effects

24. Deductive Reasoning Paradigm : Empirical findings • Deductive competence • Negative conclusion bias & double negation effect • Matching Bias • Influence of Content & Context 5. Thematic Facilitation effect

25. Deductive Reasoning Paradigm : (1) Deductive Competence • Deductive competence is lacking! • Do not understand the logical distinction between necessity and possibility • Fallacies: draw conclusions that could but need not be true given the premises • Despite error, validity of argument are above chance levels – needs explanation.

26. Deductive Reasoning Paradigm : (1) Deductive Competence • Logic errors are systematic (bias). ‘Bias’ presupposes logic is standard and systematic error is irrational. Neither are valid deductions! – because the logic paradigm was set up to identify non-logical psychological influences, you could equally argue that systematic bias is rational.

27. Deductive Reasoning Paradigm : (2) negative conclusion bias & double negation effect • Introducing negatives into rules produces bias (Evans, 1982; Evans et al, 1995) Asked to reason using 4 rules. (i)If p then q (ii)If p then not-q (iii)If not-p then q (iv)If not-p then not-q The arguments have equal validity but the insertion of a negation into the antecedent of the rule makes it much harder for participants to judge its veracity.

28. Example: (1) RULE: If the letter is P, then the number is 2 The number is not 2 therefore the letter is not P Is this statement true or false 74% of participants said True (2) RULE: If the letter is not P, then the number is 2 The number is not 2 therefore the letter is not P Is this statement true or false? 45% of participants said true. Both statements are equally true.

29. Negation Bias Effect Evans et al (1995) found the effect mostly when the inference required the denial of a negative component suggesting Negation bias is a difficulty in the processing of a double negation. Schaeken & Schronens (2000) suggest that the negation phenomenon is due to the difficulty of processing implicit negations. Better not to talk in double negatives if you want to be understood!

30. Deductive Reasoning Paradigm : (3) Matching Bias (Evans, 1972) Tendency to pay attention to features of the problem information that have a lexical match with items explicitly named in the conditional statement.

31. Example (1) Find a falsifying example of the statement: “If the letter B, then the number is not 4” Almost everyone said B & 4 (2) Find a falsifying example of the statement “If the letter is not D, then the number is 7” MOST said D & 7 Few gave the logically equivalent answer to (1) : pairing a letter that was not D with a number that was not 7 [as in S3], The bias suggests attention to named attributes is independent of logical context of the instructions.

32. Deductive Reasoning Paradigm : (4) influence of content & context: evidence for probabilistic reasoning Oaksford er al (2000) Premises and conclusions are not seen as true/false Instead they are seen in terms of degrees of belief. The new normative of conditional reasoning is Probability, replacing logic. As the deductive paradigm is based on formal logic, then probability reasoning based upon content and context will have been considered by definition - illogical!

33. Belief Bias Stanovich (1999) We tend to contextualise all problems with regard to prior knowledge and belief Evans et al (1983) Conclusions are more likely to be accepted as valid if they concur with prior belief (confirmation bias) especially if the conclusion is potential fallacy (false)

34. Belief Bias: Evans (1983) Percentage of participants accepting a conclusion 89% acceptance of valid believable conclusions No police are vicious therefore some highly trained dogs are not police dogs

35. Belief Bias: Evans (1983) Percentage of participants accepting a conclusion 56% acceptance of valid unbelievable conclusions No nutritional things are inexpensive, some vitamin tablets are inexpensive, therefore, some vitamin tablets are not nutritional

36. Belief Bias: Evans (1983) Percentage of participants accepting a conclusion 71% acceptance of invalid believable conclusions No addictive things are inexpensive, some cigarettes are inexpensive, therefore some addictive things are not cigarettes

37. Belief Bias: Evans (1983) Percentage of participants accepting a conclusion 10% acceptance of invalid unbelievable conclusions No millionaires are hard workers, some rich people are hard workers, therefore, some millionaires are not rich people.

38. Belief Bias Evans (1983) An endorsement of believable conclusions Evans et al (2001) A debiasing effect against unbelievable conclusions • fallacies are endorsed in abstract tasks (no content), • Fallacies are only suppressed when content makes conclusions unbelievable.

39. Other content effects: • Nature of the qualifiers in the premises • Order effects • Additional premises

40. In the light of new evidence we withdraw a deduction. suggesting……….

41. We construct a limited number of mental models to support our inferences and that these block other inferences. • A new premise undermines belief in the original conditional. • We are reluctant to draw conclusions from premises we believe to be false. • A second premise reduces the likelihood of the conclusion suggesting we reason probabilistically. • Beliefs about the premises in the conditional information or contextual information have an influence.

42. Ellis et al (1997): promises & threats are endorsed more than tips & warnings because probabilistically they are stronger. Newstead et al (1997): promises and threats are endorsed because it is perceived that the speaker has more control over the consequent event.

43. Three problems with probabilistic & logic accounts

44. (i). People are not asked to judge probability, but to judge the necessity rule (true/false) in the deduction task. Polister & Carles (2001) people do not respond in absolute true/false deductions, instead they respond in degrees of belief.

45. (ii) Inferences do not follow from the logical truth of a conclusion from premises, instead the reasoner makes inferences by extending the logical possibilities.

46. (iii) In the real world when new premises that contradict the conclusion are introduced, what do people ‘give up’ to resolve the contradiction? Elio & Pelletier (1997) show we relinquish conditional premises and not minor premises.

47. Deductive Reasoning Paradigm : (5) Thematic facilitation effect Griggs & Cox (1982) if an abstract selection task is transposed into a rule about drinking age, performance increases to 75% (from 10%). Griggs (1983) There is no transference of performance from a thematic deduction task to a subsequently given abstract deduction Task. People do not transfer logical deduction from the contexturalised problem, suggesting that the thematic task was not based on logical reasoning. Manktelow & Over (1991) suggest that the task changes hypothetical reasoning (true/false) to reasoning about rules and Regulations. The two tasks differ.

48. Try this one! You have to 18 to drink alcohol in a pub! There are 4 people standing at a bar One was drinking beer, one was drinking orange, one was 14 and one was 19. Who would you approach to check if they were breaking the law?

49. Deductive Reasoning Paradigm : (5) Thematic facilitation effect Griggs & Cox (1982) if an abstract selection task is transposed into a rule about drinking age, performance increases to 75% (from 10%).

50. Pollard & Evans (1987) In the thematic task the correct answer (under-aged drinker & beer drinker) can be analysed in terms of p & q BUT if the police officer role instructions are removed, performance falls to that of the abstract task. .