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Slide1

Deductive Reasoning: Why People Are Not Always Logical

Pavle ValerjevDepartment of psychologyUniversity of ZadarSlide2

Thinking

Psychology of thinkingReasoningProblem solvingJudgment and decision makingUndirected thinking (Gilhooly, 1996)Cognitive approach: Thinking as

a process of mental representation manipulationSlide3

Deductive reasoning

- examples

Conditional reasoningModus ponens (MP) If it rains, the streets are wet.It rains.Therefore, the streets are wet.

Logical form of MP:P <implicates> QPTherefore, Q.

Syllogistic reasoningBarbara (AAA) conclusionAll men are mortal.Socrates is a man.Therefore, Socrates is mortal. Logical form:Major premise: MaPMinor premise:

SaM

Conclusion:

SaPSlide4

Deductive reasoning

– more examples

Conditional reasoning If it rains, the streets are wet.The streets are wet.Therefore, it rains.WRONG

There is no valid conclusion.Proof? Truth table.

Syllogistic reasoningAll males are animals.Some animals are aggressive.Therefore, some males are aggressive.

WRONG CONCLUSION AGAIN

There is no valid conclusion.

Proof? Euler circles.

P

Q

If P, then Q.

1

1

1

100011001Slide5

Non-deductive types of reasoning

Inductive reasoning making generalizationsThe proportion Q of the sample has attribute A.Therefore, the proportion Q of the population has attribute A.

statistical reasoningThe proportion Q of the population has attribute A.Therefore, there is a Q probability that member x of population has attribute A.analogical reasoningP and Q are similar in respect to properties a, b. Object P has been observed to have further property x.

Therefore, Q probably has property x also.Slide6

Reasoning process

Task presentationMental representations of the situation expressed in taskMental manipulation which generates the answer

AnswerEvaluation of the answer Slide7

Cognitive biases and perceptive illusions

Cognitive biases can be as useful for research on thinking as perceptual illusions are useful for understanding perception.For example:Representativeness h

euristics → conjunction fallacy; gambler’s fallacyAvailability and simulation heuristics → hindsight bias Slide8
Slide9

Wason selection task

Example:Rule: If there is a vowel on one side of the card, then there is an even number on the opposite side.

Which cards would you turn over in order to test the rule?

P not-P Q not-QSlide10

Wason selection task

Original research:Wason (1966) – 4% of valid answers (P and not-Q)Some other evidence of the classic effect:

Valerjev & Pedisić (2001) – 4-8% valid (depending on condition); 47-49% typical error (P and Q)Valerjev (2000) – 14% valid; 74% typical error (participants were instructed to choose TWO cards)Valerjev & Dujmović (2016) – 4% valid; 58% typical error; and on average 85% confidence rating that they choose the right answer.Slide11

Confirmation bias and other biases

Evans (1989) – Biases in human reasoningConfirmation bias – tendency to search, interpret and remember information that confirms someone’s preconceptionsKlayman & Ha (1987) – „positive test strategy”

Nickerson (1998) – looking for supportive evidenceQuick intuitive heuristic that is useful in realistic conditionsSlide12

Other biases in

reasoningMatching bias and belief bias (Evans, 1989; 1998, 2007) Belief bias:Valerjev, Bajšanski

& Gulan (2011) Testing of belief bias and Type 1 vs Type 2 reasoningModus ponens tasks with (or without) content conflictContent conflict conditional: If the child cries, then the child is happy.Non-conflict conditional: If the child cries, then the child is sad. 2 different instructions: To make conclusions according to one’s BELIEF

To make conclusions according to LOGICAL RULESSlide13

Bias in base-rate task

Dujmović & Valerjev (2016)Stereotypical base-rate task (De Neys, 2014; Pennycook

, Fugelsand & Koehler, 2015)Examples:(Congruent stereotype and base rate) Person A is organized. Person A is a member of this group. The group consists of 874 accountants and 126 artists.What is more probable? Person A is an accountant or an artist?

(Incongruent stereotype and base-rase)Person B is physically strong. Person B is a member of this group. The group consists of 860 teachers, and 140 boxers.What is more probable? Person B is a teacher or a boxer?Slide14

Bias in base-rate task - results

Results:High proportion of stereotypical answers even in incongruent situations. Participants neglected the base-rate and answered according to the content.Participants also made high metacognitive judgments (80-90% confident) These judgments were negatively correlated with response times.

Faster = more confident.Slide15

Dual process theory

Cognitive biasesHeuristicsIntuitiveUnconsciousRapidLow effort

High capacityAutomatic Type 1 processesSystem 1 thinkingMental skillsAnalytical

Non-intuitiveConsciousSlow and serialHigh effortLow capacity

Deliberate, access to working memoryType 2 processSystem 2 thinkingEvans (1989, 2007, 2013), Evans & Stanovich (2013), Sloman

(1996), ect.

Properties of the two thinking systems:Slide16

Some misconceptions about dual process theory

Distinction between two systems is not always so simpleThere are many dual-process theories but they are not all the sameType 2 is not always slowThere is not only one „System 1” that performs all Type 1 processing; TASS „the set of automated subsystems” (Stanovich

, 2004)Slide17

Theories of deductive reasoning

Formal rules theoriesDomain-specific reasoning theoriesProbability theories Mental model theorySlide18

Mental model theory

Johnson-Laird (1983, 2001, 2013); Johnson-Laird & Byrne (1991)Mental model –representations of the states of affairs; possible valid conclusionsMental models in conditionalExample:

If P, then Q. If it rains, then the streets are wet. [p] [q] [it rains] [streets are wet] [¬ p] [q] [it does not rain] [streets are wet] [¬ p] [¬ q] [it does not rain] [streets are not wet]Slide19

Computational constraints and limitations described by mental model theory

Initial model representationNumber of modelsContent of modelsArrangement of modelsSlide20

Initial model

Premise can be represented with more than one modelConditional has three possible modelsInitially, only the first model is constructed to represent the conditional [it rains] [streets are wet]

… [it does not rain] [streets are wet] [it does not rain] [streets are not wet]Implication: Modus ponens (MP) is easier then Modus tollens (MT)Evidence:Valerjev (2006); Valerjev, Bajšanski

& Gulan (2013a, 2013b)Mental chronometry studiesMPs are significantly faster and more accurate than MTs Slide21

How models are generated?

Valerjev (2009)Likelihood judgment experimentConditional form: If P, then Q.Biconditional

form: If and only if P, then Q. Possible cases: P Q; P not-Q; not-P Q; not-P not-Q Slide22

Number of mental models

Greater number of models = greater working memory load = less efficiencyMT (3) is harder than MP (1)Valerjev (2006) – mental chronometry experiment Conditional and disjunctive tasks with different number of required models.

Accuracy as function of number of

m

.m. Response time as function of number of m.m.Slide23

Content effects

Models content:Abstract content, spatial relations, events, processes etc.Knauff

& Johnson-Laird (2002)Bajšanski, Valerjev, & Gulan (2011) – conditionals with up-down relations and with content that was expected to be placed up or down (congruent and incongruent)Example: If the roof is up, then the cellar is down. (congruent)If the road is down then the car is up. (congruent)

Orientation effect:

F(1, 23)=17.44, p<.001Content congruence effectF(1, 23)=5.16, p<.05Slide24

Arrangement of the models

Girrotto, Mazzocco, & Tasso (1997) – different order of premises made MT more accurateValerjev,

Bajšanski, & Gulan (2010)Manipulation of the conditional orderStandard: If P, then Q.Reverse: Q, if P. Congruent and incongruent spatial content. If A is left, then B is right. MPs processed more efficient in standard orderMTs processed more efficient in reverse order

MPs and MTs have an opposite reasoning directionSlide25

Spatial priming of mental models

Valerjev, Bajšanski, & Gulan

(2013) – visual priming experiment where visual prime was antecedent and consequent in congruent or incongruent spatial order that interfered with mental model Congruent priming: If A is left, then B is right. [prime stimulus] A B Incongruent priming: If A is left, then B is right. [prime stimulus] B ACongruent prime: faster MPsIncongruent prime: faster MTsBoth effects, directionality and visual-spatial priming were significant and opposite for MPs and MTsSpatial order of mental representation significantly affects reasoningSlide26

Conclusion

Many biases and computational constraints affect reasoningTwo important properties of mind:Bounded rationality which is fastSystem 1Flexibility – opportunity to switch from system 1 to system 2 if neededSlide27

References

De Neys, W. (2014). Conflict detection, dual processes, and logical intuitions: Some clarifications. Thinking & Reasoning, 20

, 169-187.Dobelli, R. (2013): The Art of Thinking Clearly. New York: Harper Collins Publishers. Dujmović, M., & Valerjev, P. (2016

). Metacognitive assessment in a base-rate task: The effect of Type 1 and Type 2 processing. 20th Days of Psychology in Zadar. Zadar, 19-21.05.2016.

Evans, J. St. B. T. (1989). Bias in Human Reasoning: Causes and Consequences. Hove: LEA. Evans, J. St. B. T. (1998). Matching Bias in Conditional Reasoning: Do We Understand it After 25 Years? Thinking & Reasoning, 4,1, 45-110.Evans, J. St. B. T. (2007). Hypothetical Thinking : Dual Processes in Reasoning and

Judgement

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Essays

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Psychology

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Hove

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Psychology

Press.Evans, J. St. B. T. (2009). How many dual-process theories do we need? One, two, or many? In J. S. B. T. Evans & K. Frankish (Eds.), In two minds: Dual processes and beyond (pp. 33-54). New York, NY, US: Oxford University Press. Evans, J. St. B. T. (2012). Questions and challenges for the new psychology of reasoning. Thinking & Reasoning, 18, 1, 5–31.Evans, J. St. B. T. (2013). Dual-process theories of deductive reasoning: Facts and fallacies. In K. J. Holyoak and R. G. Morrison (Eds.), The Oxford Handbook of Thinking and Reasoning. Oxford: Oxford University Press. Evans, J. St. B. T., & Stanovich, K. E. (2013). Dual-Process Theories of Higher Cognition: Advancing the Debate. Perspectives on Psychological Science, 8, 3, 223–241.Gilhooly, K. J. (1996). Thinking: Directed, Undirected and Creative. London: Academic Press.Johnson-Laird, P. N., & Byrne, R. M. J. (1991). Deduction. Hillsdale: Erlbaum. Johnson-Laird, P. N. (2013). Inference with mental models. In K. J. Holyoak and R. G. Morrison (Eds.), The Oxford Handbook of Thinking and Reasoning. Oxford: Oxford University Press. Nickerson, R. S. (1998). Confirmation bias: A ubiquitous phenomenon in many guises. Review of General Psychology, 2, 2, 175-220.Sloman, S. A. (1996) The empirical case for two systems of reasoning. Psychological Bulletin, 119, 3–22.Valerjev, P. (2000). Wasonov izborni zadatak: Stabilnost efekata pristranosti i tematskog materijala. [Wason selection task: Stability of bias and thematic material effects]. Radovi: Razdio filozofije, psihologije, sociologije i pedagogije, 39, 16, 97-111.Valerjev, P. (2006). Deduction and Conditionals: A Mental Chronometry Experiment. Psihologijske teme. 15, 1, 151-176. Valerjev, P., Bajšanski, I., & Gulan, T. (2011). Logičko i sadržajno zaključivanje: efekti upute i sadržajne konfliktnosti [Logical and content reasoning: the effects of instruction and content conflict]. Savremeni trendovi u psihologiji. Novi Sad, 14-16. 10. 2011.Valerjev, P., Bajšanski, I., & Gulan, T. (2013a). Directionality of conditional and accuracy of reasoning. Suvremena psihologija 16, 1

,

49-62

.

Valerjev

, P.,

Bajšanski

, I., &

Gulan

,

T

. (

2013b).

Directionality of conditionals in the context of visual priming.

Review

of

psychology 20

, 1

,

61-68.

Valerjev

, P.

&

Dujmović

, M.

(2016

)

.

Metacognitive judgments during solving of

Wason

selection

task

.

Unpublished

.

Valerjev

, P. &

Pedisić

, A. (2002).

Wasonov

izborni

zadatak

-

utjecaj

upute

,

tipova

kondicionala

i

tematskog

materijala

. [

Wason

Selection Task - Influence of Instruction, Conditional Types and Thematic Material].

Radovi

:

Razdio

filozofije

,

psihologije

,

sociologije

i

pedagogije

40

, 17, 45-64

Wason

, P. C. (1966). Reasoning. In B. M. Foss, (Ed.),

New Horizons in psychology 1

.

Harmondsworth

: Penguin.

Wason

, P. C. (1968). Reasoning about the rule.

Quarterly Journal of Experimental Psychology, 20

, 3, 273-281.Slide28

Thank you for your attention