Cognitive Psychology by K. Gilhooly, F. Lyddy, and F. Pollick (first edition) – Summary chapter 11

Reasoning is the cognitive process of deriving new information from old information. Deductive reasoning is drawing logically necessary conclusions from given information. It’s going from the general to the specific. Inductive reasoning is the process of inferring probable conclusions from given information. It’s going from the specific to the general. Premises are statements assumed to be true from which conclusions are drawn. Valid arguments are those in which the conclusions must be true if the premises are true.

Deductive reasoning has two types:

1. Propositional reasoning
   This is reasoning about statements connected by logical relations, such as ‘and’, ‘or’, ‘not’ and ‘if’.
2. Syllogistic reasoning
   This is reasoning about groups or sets using statements connected by logical relations of ‘some’, ‘none’, ‘all’ and ‘some not’.

Inference rules are rules for reaching a conclusion given a particular pattern of propositions. There are multiple inference rules:

1. Modus ponens
   ‘If A, then B. ‘A’, so ‘B. It’s affirming the first premise.
2. Modus tollens
   ‘If A, then B’. Not ‘B’, so not ‘A’.
3. Double negation
   Not ‘not A’, so ‘A’.

There are two main mistakes:

1. Confirming the consequent
   ‘If A, then B’. ‘B’, so ‘A’. This is invalid reasoning. If the consequent is confirmed, this does not mean that the first premise is correct.
2. Denying the antecedent
   ‘If A, then B’. Not ‘A’, so not ‘B’. This is invalid reasoning. If the antecedent is denied, this does not mean that the second premise is incorrect.

People are better at reasoning with the modus ponens (100%) than with the modus tollens (60%). The two fallacies are rejected in about 25% of the cases. It could be that people do poorly on the modus tollens because of misinterpretation of the premises. The ‘if’ is often interpreted as ‘if and only if’. When more antecedents are added, then the fallacies are suppressed. This is called the suppression effect.

Braine argued that people have mental logic rules that they can apply to solving reasoning problems. He argued that people have a set of mental inference rules or schemas that permit direct inferences. They include the modus ponens, but not the modus tollens.

The mental models approach is the view that people tackle logical reasoning problems by forming mental representations of possible states of the world and draw inferences from those representations. Mental models are used for reasoning and the more mental models reasoning requires, the more difficult it will get for people. People minimise the load on the working memory by tending to construct mental models that represent explicitly only what is true and not what is not true. This can cause people to draw the wrong conclusion when they have to answer questions about things that are implicitly not true according to the premises. The principle of truth leads people to form models in which the possibility of the premise being wrong is not represented and this is the illusory inference. The number of mental models needed correlates strongly with the difficulty reported. Mental illness can enhance reasoning about matters related to that specific mental illness.

In syllogism reasoning, people tend to perform better with concrete arguments than with abstract arguments. People might make mistakes in syllogism reasoning because of the atmosphere effect. This is a tendency to draw conclusions in syllogisms that are over-influenced by the form of the premises rather than the logic of an argument (e.g: concrete arguments are easier to understand than abstract arguments). The atmosphere effect is weaker with familiar as opposed to abstract or unfamiliar material and the atmosphere effect does not explain this difference.

Some people answer logical arguments based on facts, instead of as a purely logical exercise. This is fairly typical of people from cultures with little formal education. People do not reason irrationally, but they misinterpret premises, add premises that were not given and ignore some premises. There are differences in answering logical questions between collectivistic cultures and individualistic cultures. The collectivistic mindset stresses practical and contextualized knowledge to be used in real social settings against theoretical abstract knowledge.

The four figures of syllogism are the four possible layouts of terms which give four syllogistic figures (e.g: A-B, B-C; B-A, B-C and so on). These layouts affect what valid conclusions are preferred. The figural bias is the effect of a figure on preferred conclusions. An explanation for figural bias is that it arises from processes of combining premise representations in working memory. The load of the working memory changes when more than one model has to be evaluated and syllogisms load working memory, particularly the central executive and phonological loop components. The figural bias may arise from assumptions made about which term in the premise is the topic. The belief bias is a tendency to accept invalid but believable conclusions and to reject valid but unbelievable conclusions to arguments.

There are two types of inductive tasks:

1. Hypothesis testing
   This is assessing hypotheses for truth/falsity against data (e.g: hypothesising that all swans are white).
2. Hypothesis generation
   This is deriving possible hypotheses from data for later testing.

Hypothesis generation can use the hypotheticodeductive reasoning method. This is a form of inductive reasoning in which a hypothesis is tested by deducing necessary consequences of the hypothesis and determining whether the consequences are true or false. Implications are deduced from the hypothesis and the implications are then checked against data for truth or falsity.

Watson created a card selection task used to test the hypotheticodeductive reasoning method. People are better at this task in the concrete version than in the abstract version, but they do it wrong often because they are trying to confirm the rule, instead of trying to disprove it. This is called the confirmation bias. The poor performance of people on the Watson card selection test could possibly be explained by ambiguities in the task. It could be that people misinterpret the instructions and the rules. This has been tested and showed that when there are no ambiguities, the performance is much better.

In the abstract version of the card selection task, most people show a matching bias. This is choosing the cards mentioned in the rule. It could be that prior experience of specific counter-examples helps performance on the card selection task. Memory cueing or the availability approach is the use of memory when you already know the concrete task Performance on the card selection task is better when the rule and thus the solution is already known (e.g: people are not allowed to drink under the age of 18). People already know that from memory. Performance in the card selection task also improves when people can make use of pragmatic reasoning schemes. These are schemes about situations you already know (e.g: knowing how to behave in a certain situation).

Cosmides proposed the social contract theory. This states that rules expressing payment of costs for privileges will be easily solved in 4 cards tasks as the correct choices would uncover cheating. This implies that people are evolutionarily prepared to uncover cheaters. An alternative explanation for the results found by the social contract theory is that the pragmatic reasoning schemes might be activated, because pragmatic reasoning schemes also include schemes for permission, as all social contract theory situations are.