Cognitive Psychology Lecture Notes PDF

# Cognitive Psychology Lecture Six: Thinking and Reasoning <3 ## You Should Understand - Inductive and deductive reasoning - Conditional reasoning - Valid and invalid inferences - The role of context in reasoning - Human performance on reasoning tasks - Abstract rule theory ## What is Reasoning?...

# Cognitive Psychology Lecture Six: Thinking and Reasoning <3 ## You Should Understand - Inductive and deductive reasoning - Conditional reasoning - Valid and invalid inferences - The role of context in reasoning - Human performance on reasoning tasks - Abstract rule theory ## What is Reasoning? - Philosophers and psychologists have long been concerned with the nature of human thinking - It has a history of at least 2,000 years, dating back to Aristotle - In psychology, the history is more recent, and it has only really developed following the cognitive revolution - Although related, you should be aware that psychologists see reasoning, decision-making, and problem-solving as separate areas ## Why is Reasoning Important? - Although the study of reasoning in psychology has altered the ways in which logic is considered as part of thinking it is still an important component in human psychology - Johnson-Laird and Bryne (1991) argued that deductive reasoning was central to activities such as: - Formulating plans - Determining the consequences of hypotheses - Interpreting and formulating instructions - Pursuing arguments and negotiations - An important distinction can be made between deduction and induction ## Inductive Reasoning - Increases semantic information - The burglary was committed at 8:00-8:30 - Adam was seen running from the house at 8:15 - We may conclude that Adam was involved in the burglary - but it is not necessarily the case - We add our knowledge of burglaries to the information presented - Induction often yields plausible conclusions, but they are not necessarily true ## Deductive Reasoning - This is reasoning where conclusions are necessarily true - Deduction is always truth preserving - It does not involve the use of any additional knowledge but requires only the information presented in the premises - When we make a deductive inference, we are making the implicit become explicit - We are not adding anything from our 'world knowledge' - The information to draw the conclusion was already present - To study reasoning we can ask participants to judge the validity of a conclusion or to draw their own conclusion ## Categorical Syllogisms - A syllogism consists of two premises and a conclusion and uses quantity terms like all, some, none, etc. - For example, - All artists are beekeepers - All beekeepers are chemists - Therefore, all artists are chemists - This is a valid argument form - it is truth preserving - This means that if the premises are true then the conclusion will also be true ## Truth vs Validity - A distinction is made between truth and validity - A conclusion may be true and valid, true and invalid, untrue and valid, or untrue and invalid. - Example: - All dogs have tails - The president of the US is a dog - Therefore, the president of the US has a tail - This conclusion is valid but not true - the argument form used is valid, but the premises are not true, so the conclusion is not necessarily true - Validity refers to the form of the argument rather than the content of it - Consider the following argument - All A are B - Some B are C - Therefore, some A are C - This argument is invalid (the 'A's that are 'B's that are C's) - Part of the problem seems to arise from the assumption that all A are B means that all B are A. - If this happens then reasoning might be accurate but on the wrong material - For example, 'all cats are mammals' does not mean ‘all mammals are cats' - This is typical of the errors that we see in human reasoning ## Belief Bias - One notable aspect about human reasoning is that we are seduced by the believability of conclusions rather than their validity - Example 1 - No animals are inhabitants of the island - Some tigers are inhabitants of the island - Therefore, some tigers are not animals - This is valid but unbelievable - Example 2 - No addictive things are inexpensive - Some cigarettes are inexpensive - Therefore, some addictive things are not cigarettes - This is invalid but believable ## How Common is Belief Bias? - Data from Evans, Barston & Pollard (1983) shows clear evidence of belief bias - Valid and believable - conclusion accepted ~ 80% - Valid and unbelievable - conclusion accepted ~ 55% - Invalid and believable - conclusion accepted ~ 70% - Invalid and unbelievable - conclusion accepted ~ 10% ## Propositional Reasoning - A formal system of logic - Symbols are used in place of sentences, typically p and q are used - Conclusions are reached via the application of 'logical operators' or connectives and the rules of logic - Examples of logical operators within propositional logic - Not, and, or, if ... then - If and only if ... then ## Conditional Reasoning - Conditional reasoning is one aspect of propositional reasoning - Reasoning about the operator 'if...then' - The meaning of words used in logic is often different from their meaning in natural, everyday usage - One important difference is that things are only ever true or false in propositional logic - there is no in-between - It is sunny or it is not - there are no overcast days in logic - The fact that these differences exist may have some effect on how people reason and why people often make errors in reasoning ## Inferences in Conditional Reasoning - There are four inferences traditionally associated with conditionals - For example, if you are given a conditional statement and then told that one of the propositions is true or false what can you conclude about the remaining proposition? - If p then q (major premise) - p (minor premise) - Therefore, q (conclusion) - Ideas from logic tell us whether these inferences are valid or not - We use formal logic to assess whether participants' reasoning is accurate or not - Logic is the normative system that psychologists use ## Modus Ponens - If it is sunny then the children will play outside - It is sunny - Therefore, the children will play outside - Formally we could express this as: - If p then q - p - Therefore, q - This is a valid inference form - it is truth preserving and will always yield true conclusions from true premises ## Modus Tollens - If it is sunny then the children will play outside - The children are not playing outside - Therefore, it is not sunny - Formally we could express this as: - If p then q - Not-q - Therefore, not-p - Again, this is a valid argument form and is truth preserving ## Affirmation of The Consequent - If it is sunny then the children will play outside - The children are playing outside - Therefore, it is sunny - Formally we could express this as: - If p then q - q - Therefore, p - This is not a valid argument form as it will not necessarily always give true conclusions from true premises ## Denial of The Antecedent - If it is sunny then the children will play outside - It is not sunny - Therefore, the children are not playing outside - Formally we could express this as: - If p then q - Not-p - Therefore, not-q - Again, this is an invalid argument form as it will not necessarily always give true conclusions from true premises - We can use truth tables from logic to assess the validity of these arguments ## Are Humans Logical? - Now we can assess human performance - Boole (1854) stated that the laws of logic are the laws of thought - When assessing human performance, we can use - Generation tasks - Evaluation tasks - Some form of logical problem - There have been many studies that have looked at the rates at which participants generate or endorse the valid and invalid conclusions outlined above ## Reasoning Performance - A graph from Marcus and Rips (1979) regarding inference and percentage of conclusions shows a number of interesting issues immediately: - The modus ponens inference is drawn almost universally - The modus tollens inference is drawn less frequently - Both the affirmation of the consequent and denial of the antecedent inferences are drawn some of the time - Evans, Newstead, and Bryne (1993) reviewed many studies and reported similar endorsement rates regarding percentage of conclusions endorsed ## Theories of Reasoning - Any proposed theory of reasoning will need to be able to account for the pattern of performance that has been observed - We have seen that in the psychology of reasoning there are a number of factors that a theory must be able to account for: - Competence - Errors (biases) - A number of studies show an effect of content - One possible theoretical explanation is that offered by Abstract Rule Theories ## Abstract Rule Theories - Braine and O'Brien (1991) and Rips (1994) Braine (1994) Braine and O'Brien (1991) - There are numerous versions of mental logic, and they are not all the same (although they share some basic principles) - People are rational - we have some rules of logic or specialised processes for logical thinking - We make mistakes because: - We misunderstand or misrepresent the task (Henle, 1962) - We lack the necessary rules of logic - Resource limitations ## Braine's Abstract Rule Theory - **Comprehension component** - In the first stage of the theory, the premises must be converted into a mental representation that can be held in working memory - **Application of rule schemas** - Incompatibility rules - Check for inconsistent or contradictory reasoning (such as concluding both p and not-p) ## The Data - Valid Inferences - Modus ponens is easy - it is assumed that we have a rule for this - Thus, when we are confronted with an argument of the form: - If p, then q - p - We can easily draw a valid conclusion (q) - Modus tollens is harder because a series of rules must be applied and the longer the derivation, the more likely that error will occur - It includes complex ideas like making assumptions and testing them via mental proofs - There is no single rule for modus tollens - hence the difficulty ## The Data - Invalid Inferences - Errors are made here because the conditional (if p then q) is reinterpreted into its everyday usage and then rules of logic are applied - **Affirmation of the consequent** - If it is sunny then the children will play outside - The children are playing outside - Therefore, it is sunny - Braine et al. (1994) - the conditional is assumed to be the same as 'if the children are playing outside then it is sunny' if you make this error, you could then apply modus ponens and conclude that 'it is sunny' - Braine et al. (1984) - supported this through showing that such inferences can be blocked by additional premises - ‘if they have a football then the children will play outside’ ## Denial of The Antecedent - If it is sunny then the children will play outside - It is not sunny - Therefore, the children will not play outside - It is possible that participants interpret the conditional as 'if it is not sunny then the children will not play outside' - Then again by the application of modus ponens it is erroneously concluded that 'the children will not play outside' - This reinterpretation is perfectly reasonable - if you mow the lawn, I will give you £5 - We could assume that this also means if you do not mow the lawn, I will not give you £5 - this is known as an invalid inference ## However… - The theory is incomplete - it states little about the comprehension component, so predictions are not always clear - Context and content have a dramatic effect on reasoning, and this is difficult to reconcile with a theory that proposes abstract, content-free rules of reasoning, this includes belief bias - Ignores individual differences - Propositional reasoning is only one type of reasoning - it is unclear whether abstract rules can account for other types - There is ultimately no compelling evidence that people use any type of logic when attempting to solve deductive problems - Numerous alternative explanations - mental models, information gain, pragmatic reasoning schemas ## Summary - Induction and deduction - Truth and validity - Conditional reasoning and the inferences associated with it - modus ponens, modus tollens, affirmation of the consequent, denial of the antecedent - Performance is not always in line with the dictates of formal logic (e.g. Marcus and Rips, 1979) - Abstract rule theory - Reasonable account of the data but limited in places