Reasoning - summary of chapter 11 of Cognitive Psychology by Gilhooly, K & Lyddy, F, M

Cognitive Psychology
Chapter 11
Reasoning

Reasoning: the cognitive process of deriving new information from old information.
People who can correctly derive new information by reasoning do well on tests of general ability or intelligence and in turn do better in education and in the occupational world.

Deductive reasoning

Deductive: drawing logically necessary conclusions from given information.
Inductive: the process of inferring probable conclusions from given information.

In deductive tasks, people are required to determine what conclusions, if any, must follow when they are given statements that are assumed to be true.
Premises: statements assumed to be true from which conclusions are drawn.
Valid arguments: those in which the conclusions must be true if the permisses are true.

Deductive reasoning is of two types:

• Propositional reasoning: reasoning about statements connected by logical relations such as ‘and’ ‘or’ ‘not’ ‘if’
• Syllogistic reasoning: reasoning about groups/ sets using statements connected by logical relations of ‘some’, ‘none’, ‘all’, ‘some not’

Propositional reasoning

Propositional logic is a set of rules devised by logicians which enable valid arguments to be developed.

Inference rules: rules for reaching a conclusion given a particular pattern of propositions, e.g. modus pones, which states that given ‘if p then q’ and ‘not q’ we can infer ‘not p’.
Can be used to derive correct conclusions from patterns of propositions, such that different patterns trigger different inference rules.
Three examples:

• Modus pones.
  If p then q. p → q
• Modus tollens
  If p then q. not q → not p
• Double negation
  Not p → not q

Two main mistakes or fallacies when arguing from conditionals:

• Affirming the consequent:
• Denying the antecedent

Suppression effects

It has been suggested that what are usually classes as fallacies in conditional reasoning could result from misinterpretations of the premises.
The importance of premise interpretation and how surrounding context can affect interpretations ans so influence reasoning.

Mental logic approaches

People have mental logic rules that they can apply to solving reasoning problems.
People generally have available a set of mental inference rules (or schema’s in their terminology) that permit direct inferences when the schema conditions are met.
The schema typically match some rules of logic but may not include others.
The mental rules/schemas may also include fallacious inferences, such as denying the antecedent. Thus, schemas may or may not match the formal inference rules.
Schemas can take the form of ‘premises→ conclusion’.

Ratings of problem difficulty would depend on the length of the problem in words and on the difficulty of the schemas used in solving the problem.
People reason using a limited number of schemas.

Mental models

The mental models approach: the view that people tackle logical reasoning problems by forming mental representations of possible states of the world and draw inferences from those representations.
The meaning of connectives (and, or, if, etc.) can be represented by mental representations of possible states in the world, known as mental models.

Deductive propositional reasoning then begins with the construction of one or more mental models with represent the first premise.
One source of variation lies in how completely the models are developed to take all possibilities into account.
To draw a conclusion from ‘denial the consequent’, the representation must include two models.
As an argument is build up, premises are added and the set of models is modified until a conclusion is drawn from the final set of models.

Mental models, is argued, offer economical forms of representation that appear psychologically plausible.
Models are built in accordance with the principle of truth. Thus, mental model representations tend to be incomplete from the strictly logical point of view and this incompleteness is a source of error in dealing with reasoning tasks.

The number of mental models needed per problem correlated highly with rated problem difficulty reported.

Syllogistic reasoning

To determine what conclusion, if any, follows assumptions about category membership.
Categorical syllogisms.

Basic findings from syllogistic reasoning studies

Some of the main factors associated with the difficulty of syllogisms:

• Beneficial effects
• Concrete material as against abstract materialism

Atmosphere effect: a tendency to draw conclusions in syllogisms that are over influences by the form of the premises rather than the logic of the argument.

The atmosphere effect

The form of the premises influences people’s expectations about the form of the conclusion.
In particular, if both premises involve ‘all’, people are disposed to accepting an ‘all’ conclusion. And also for the others like ‘some and not’.

Atmosphere versus conversion errors (illicit conversion) and probabilistic inference

People apply heuristic which are not appropriate.

• Conversion
  Two. All X are Y. and All Y are X.
  That some As are not Bs implies ‘Some Bs are not As.’
  People tend to make conversions unless they have information to the contrary (which they do not have in abstract material).
• Probabilistic inference
  Involved ‘plausible reasoning’ that is not valid in deductive reasoning.

Henle on ‘rationality’

Many apparent instances of illogical thinking involve the implicit introduction of additional premises, the ignoring of some of the given premises and the misinterpretation of still other premises. But! The inferences people make are generally rational, given how they have interpreted the premises.
People often fail because they have worked with materials different from those intended or because they undertaken a task different from the one intended.

Culture and logic

Just because someone gives the correct answer to a reasoning problem, that does not mean the answer was reached by applying rules of logic.

Collectivistic mindset: stresses practical and contextualized knowledge to be used in real logical settings against theoretical abstract knowledge to be used in artificial classroom settings.

Mental-model approaches to syllogisms

Four figures of syllogism:

• A-B, B-A
• B-A, B-C
• A-B, C-B
• B-A, C-B

Figural bias: the effect of figure on preferred conclusions.
Premises of the form A-B, B-C produced a bias towards conclusions of the form A-C (even if C-A conclusion where also valid).

Mental-modal theory.
Stages:

• Interpretation of premises
• Initial heuristic combination of the representations of the two premises
• Formulation of a conclusion corresponding to the combination of premises
• A logical test

In the mental-model approach, the premise representations are assumed to take the form of examples of the items of the premises.
Having representations of the individual premises, the next step is to combine them in some way. There is a heuristic bias towards forming connections that link up all the classes if possible.
The mental models theory proposes a combination of premises to yield a tentative conclusion, followed by a logical testing process. Differences in persistence of testing preliminary conclusions would lead to differences in the conclusions finally drawn by different individuals to the same premises.

With a syllogism of the form A-B, B-C, people encode the first premise and then add on to it a representation of the second premise with a resulting bias towards a conclusion of the form A-C.

Of certain syllogisms two or three different combined models of the premises are possible and all the possible models must be considered before a correct conclusion can be drawn.
The rate of drawing correct conclusions declined sharply as the number of possible combined models increased from one to three.
These results are due the load on working memory.

Belief bias and dual system theory

Arguments can vary independently in validity and in the truth or believability of the conclusions.
With real-life materials prior beliefs would be expected to influence judgments of how valid an argument is.

Belief bias: a tendency to accept invalid but believable conclusions and to reject valid but unbelievable conclusions to arguments.

Inductive reasoning: testing and generating hypotheses

Two types of inductive tasks:

• Hypothesis testing: assessing hypotheses for truth/ falsity against data
• Hypothesis generation: deriving possible hypotheses from data for later testing

People are required the implications, if any, of some particular observation(s) for the truth of possible generalizations (hypotheses).
In hypothesis generation, the person can obtain observations on the objects of interest and seeks to make a generalization supported by the evidence.
Such hypotheses may need further testing and again cannot be conclusively proved but could be disproved.

Hypothetico-deductive reasoning: 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.

Testing hypotheses: the four-card selection task

People are biased towards verification or conformation and so choose the potentially confirming cards and ignore the potentially falsifying case.

Procedural variations

Performance is improved with concrete material.
The main facilitating effects on selection task performance were those of using realistic material.
Reasons below:

• Interpretation factors
  People make interpretations different from that intended, but then go on reason correctly on their interpretations.
  The success rate with clarified instructions is much higher than that obtained with standard instructions.
• Matching bias
  In the four cart task, the matching bias is choosing the cards mentioned in the rule.
  The responses match the input and not deeper processing is involved.
• Memory-cueing (availability) accounts
  Prior experience of specific counter-examples helped performance.
  People for whom the rule was a real everyday rule would be more likely to think of possible counter-examples from memory.
  Falsifying possibilities would be more available to people familiar with the rule in real life.

Pragmatic reasoning schemas

People do not use formal ‘syntactic’ rules for logical implication in these tasks.
Specific memory cueing.
A marked increase in correct performance when given the rationale for the rule.

Social contract theory

As a result of evolutionary pressures, people have a number of innate special purpose mechanisms to handle problems that have been critical to survival over many millennia.

Social contract theory: proposes that rules expressing payment of cost for privileges will be easily solved in 4 cards tasks as the correct choices would uncover cheating.
Humans have evolved so that they possess a ‘cheat detecting algorithm’ which will focus on possible cases of cheating.

The only reliable facilitations of the four-cards task with thematic materials occur when the rule used is a social contract and is understood as such by the participants.

Deontic rules: rules regarding obligations and typically involve terms such as ‘should’, ‘must’,
Ought, may and so on.
Rules regarding what may or must be done.

The selection task as optimal data selection

If the proposed rule and the alternative null hypothesis are viewed as equally likely initially, and the probabilities of p’s and q’s are seen as fairly low, then the best choices on Bayes’s theorem to discriminate between the two hypotheses are the p card, the q card and then not-q card in that order.
The not-p card would yield no discriminating information.

The optimal data selection model argues that people will home in on rare events as being most informative and the predictions are based on that assumption.

Generating and testing hypotheses

Wason’s reversed 20 question task

A special task in which people generate over-restrictive hypotheses.

The overwhelming tendency is for people simply to generate series consistent with their particular hypotheses and to keep on doing so until they felt sufficiently confident to announce their own hypothesis as correct.

Simulated research environments

Naive people tend neither to consider alternative hypotheses nor to seek out potentially falsifying data.

Confirmation bias: in hypothesis testing, is a tendency to seek out and attend only to information consistent with the hypothesis while ignoring falsifying information.

If participants did obtain explicit falsifying information, they generally used this information to reject incorrect hypotheses.