Deductive reasoning

What is deductive reasoning

• Reasoning to a conclusion from a set of premises or statements where the conclusions follows from the assumption

• Conclusions can be drawn with certainty

What is conditional reasoning

• ‘if P then Q’

• The ‘if P’ part is the antecedent then the ‘if Q’ part is the consequent

• Eg ‘if i attend all of my lectures’ (P) then ‘I will do well on my exams’ (Q) (major premise)

• Eg ‘I attend all of my lectures’ then ‘I do well on my exams’ (minor premise)

• P= modus ponens, attend lectures

• not Q= modus tollens, not do well on exams, we are denying this statement

• not P= denial of the antecedent, not attend all lectures

• Q= affirmation of the consequent, do well on exam

• Modus ponen and tollens are logically valid inferences

• Denial of the antecedent and affirmation of the consequent are logically invalid

Theories of reasoning

• Mental model theory, (Johnson-Laird, 1983)

• Mental models represent possibilities given premise information

• Alternative models are created to identify counter examples but if no counterexamples are found then the conclusion is invalid

• Counterexamples include your own experiences and opinions

• Limited WM capacity means that sometimes not all possible models are created

Valid Inferences of mental models

• Valid inferences require 1 model

• Modus ponens, attend lectures= you do well

• Modus tollens, not do well= not attend lectures

Invalid inferences of the mental models

• Invalid inferences require 2 models

• Denial of the antecedent, Not attend lectures= do well, not attend lectures= not do well

• Affirmation of the consequent, do well= not attend lectures, do well= attend lectures

Mental model evaluation

• Strengths:

• Predictions have been confirmed experimentally

• Predicts participants responses to a 95% accuracy (Khemlani and Johnson-Laird, 2012)

• Weaknesses:

• Assumes more deductive reasoning occurs than actually does, why we always need a sufficient sample size as we can’t predict what participants will do

• Under specification of the process involved in mental model formation

• Doesn’t account for ambiguous reasoning problems

Role of prior knowledge

• (De Neys et al, 2005)

• Conditionals differed in terms of number of alternatives or disabled that can be generated

• Conditionals with few/many alternatives/disables

• Working memory is tested

• His study showed that inference accepted is affected by a number of counterexamples

• High working memory capacity is better at logical reasoning

What is Wason’s selection task

• Provided with 4 cards and each card has a number on one side and a colour on the other

• A rule applies to the 4 cards

• The task is to select only those cards that would need to be turned over to decide whether or not the rule is correct

• There is a lot of matching bias in this as people tend to select cards mentioned in the rule

• This is a logical solution in conflict with what makes sense in real life (Oaksford, 1997)

Denial of the antecedent

• ‘If I attend all of my lectures, then ‘I will do well on my exams’ (major premise)

• ‘ I do not attend all of my lectures’ then ‘I may or may not do well on my exam’ (minor premise)

Affirmation of the consequent

• ‘If I attend all of my lectures then ‘I will do well on my exam’ (major premise)

• ‘ I do well on my exam’ then ‘I attend all of my lectures’ (minor premise)

Modus tollens

• ‘If I attend all of my lectures’ then ‘I will do well on my exam’ (major premise)

• ‘I do not do well on my exam’ then ‘I did not attend all of my lectures’ (minor premise)

Can we influence reasoning?

• Alternative and additional premises (Byrne,1989)

• Eg, ‘if she meets her friend then she will go to a play’

• Further premises:

• Alternative, ‘If she meets her family she will go to a play’

• Additional, ‘If she has enough money then she will go to a play’

• Was testing what happens to people’s ability to reason from the original conditional statement, wanted to test what impact does additional information have in people’s ability to reason logically

Byrne, 1989 results

• For the original condition:

• 96% of participants made the modus ponens inference

• 92% made the modus tollens inference

• Participants didn’t struggle to make the valid inferences

• 46% denial of the antecedent

• 71% affirmation of the consequent

• Participants should not be making these inferences as they are invalid, “She may or may not have gone to the play”

• After additional information:

• After compared to other conditions, (alternative) the denial of the antecedent and affirmation of consequent decreased dramatically

• Participants inferred she may or may not have gone to the play with her friend because she went with her family

• Giving people an alternative argument improves the conditional reasoning abilities

• However giving people an additional requirement hinders reasoning abilities and couldn’t reason logically