Grice knew how to lecture.
When invited to deliver the Kant lectures across the bay, at Stanford, he chose the right topic: "Aspects of reason and reasoning."
When invited to deliver the Locke lectures across the pond, at Oxford, he chose the right topic -- for surely Locke predates Kant and understands English idioms like 'to reason' better: "Aspects of reason and reasoning".
Reasoning is related to problem solving, because people trying to solve a
reasoning task have a definite goal and the solution is not obvious.
However, problem solving and reasoning are typically treated separately. Reasoning
problems differ from other kinds of problems in that they often owe their
origins to systems of formal logic, as symbolised by Frege and 'laughed'
metaphorically by Grice in "Logic and Conversation".
There are clear overlaps between the two areas, which may differ less than
one might initially suppose. Inductive reasoning involves making a
generalised conclusion from premises referring to particular instances. Hypotheses
can never be shown to be logically true by simply generalising from
confirming instances (i.e., induction). Generalisations provide no certainty for
future events. Deductive reasoning allows us to draw conclusions that are
definitely valid provided that other statements are assumed to be true. For
example, if we assume
i. Grice is taller than Popper
ii. Popper is taller than Johnson-Laird
the conclusion
iii. Grice is taller than Johnson-Laird.
is necessarily true.
It is well known that Popper argues for a distinction between confirmation
and falsification. Confirmation involves obtaining evidence to confirm the
correctness of one’s hypothesis. Falsification involves attempting to
falsify hypotheses by experimental tests.
Popper argued that it is impossible to achieve confirmation via hypothesis
testing. Rather, scientists should focus on falsification.
When Johnson-Laird and Wason devised their tests, such as "the 2–4–6
task", in which participants have to discover a relational rule underlying a set
of three numbers, they found performance was poor on the task because
people tended to show confirmation bias – they generated numbers conforming to
their original hypothesis rather than trying hypothesis disconfirmation. A
positive test is when numbers produced are an instance of your hypothesis.
A negative test is when numbers produced do not conform to your hypothesis.
Wason’s theoretical position predicts that people should perform better
when instructed to engage in disconfirmatory testing.
The evidence was mixed.
Cowley and Byrne argue that people show confirmation bias because they are
loath to abandon their own initial hypothesis.
Tweney finds that performance on the 2–4–6 task was enhanced when
participants were told to discover two rules, one the complement of the other.
Gale and Ball argue that it was important for participants to identify the
crucial dimensions of ascending vs. descending numbers.
Performance on the Johnson-Laird's and Wason's 2–4–6 task involves
separable processes of:
hypothesis generation;
hypothesis testing.
Cherubini (not the author of "Medea") argues that participants try to
preserve as much of the information contained in the example triple (i.e., 2–4–
6) as possible in their initial hypothesis. As a result, this hypothesis is
typically much
more specific than the correct rule. Most hypotheses are sparse or narrow
in that they apply to less than half the possible entities in any given
domain (vide Navarro & Perfors).
The 2–4–6 problem is a valuable source of information about inductive
reasoning. The findings from the 2–4–6 task may not be generalisable because,
in the real world, positive testing is not penalised. Additional factors
come into play in the real world. Hypothesis testing in simulated and
real-world settings.
There is a popular view that "scientific discovery is the result of genius,
inspiration, and sudden insight" (Trickett & Trafton).
That view is largely incorrect.
Scientists (that Grice never revere -- 'we philosophers are into
hypostasis; while mere scientists can only grasp hypothesis') typically use what
Klahr and Simon describe as weak methods.
Kulkarni and Simon found scientists make extensive use of the unusualness
heuristic, or rule of thumb.
This involves focusing on unusual or unexpected findings and then using
them to guide future theorising and research.
Trickett and Trafton argue that scientists make much use of “what if”
reasoning in which they work out what would happen in various imaginary
circumstances.
Dunbar uses a simulated research environment. He found that participants
who simply tried to find data consistent with their hypothesis failed to
solve the problem.
It is believed that scientists should focus on falsifying their hypotheses.
However this does not tend to happen.
Nearly all reasoning in everyday life is inductive rather than deductive.
Hypothesis testing is a form of inductive reasoning.
It is well known that Popper argued that it is impossible to confirm a
hypothesis via hypothesis testing. Rather, scientists should focus on
falsification. However, it is now accepted that Popper’s views were oversimplified
and confirmation is often appropriate in real scientific research.
When Johnson-Laird and Wason devised stuff like the 2–4–6 task, they
found people tended to show confirmation bias, producing sequences that
confirmed their hypotheses rather than seeking negative evidence. However, later
studies demonstrated that people’s behaviour is often more accurately
described as confirmatory or positive testing.
"What if", or conditional reasoning is basically reasoning with “if”.
It has been studied to decide if human reasoning is logical.
In propositional logic, meanings are different from those in natural
language.
There are different types of logical reasoning statements:
"Affirmation of the consequent":
Premise (if P then Q), (Q), Conclusion (P).
Invalid form of argument.
"Denial of the antecedent":
Premise (if P then Q), (not P), Conclusion (not P).
Invalid form of argument.
"Modus tollens":
Premise (If P, then Q), (not Q), Conclusion (not P).
Valid form of argument.
"Modus ponens"
Premise (If P, the Q), (P), Conclusion (Q).
Valid form of argument.
Invalid inferences (denial of the consequent, affirmation of the
consequent) are accepted much of the time, the former typically more often (Evans).
De Neys finds evidence that conditional reasoning is strongly influenced
by the availability of knowledge in the form of counterexamples appearing to
invalidate a given conclusion. He also found performance on conditional
reasoning tasks depends on
individual differences.
Bonnefon argues that reasoners draw inferences when presented with
conditional reasoning problems.
According to Markovits, there are two strategies people can use with
problems: a statistical strategy and a counterexample strategy.
Various findings suggest many people fail to think logically on conditional
reasoning tasks.
Conditional reasoning is closer to decision making than to classical logic
(Bonnefon).
The Johnson-Laird/Wason selection task has four cards, each with a number
on one side and a letter on the other.
Participants
are told a rule and asked to select only those cards that must be turned
over to decide if the rule is correct.
The correct answer is only given by 5–10% of those who are engaged in the
experiment.
Many attempts have been made to account for performance on this task.
Evans identifies matching bias as an important factor.
This is the tendency for participants to select cards matching items named
in the rule regardless of whether the matched items are correct.
Stenning and van Lambalgen argue that people have difficulties interpreting
precisely what the selection problem is all about.
Oaksford argues that the logical answer to the Johnson-Laird/Wason
selection task conflicts with what typically makes most sense in everyday life.
Performance in the Johnson-Laird/Wason selection task can be improved by
making the underlying structure of the problem more explicit (Girotto) or by
motivating participants to disprove the rule (Dawson).
A syllogism consists of two premises or statements followed by a
conclusion. The validity of the conclusion depends only on whether it follows
logically from the premises. Belief bias is when people accept believable
conclusions and reject unbelievable conclusions, irrespective of their
logical validity or invalidity. Klauer finds various biases in syllogistic
reasoning, including a base-rate effect, in which performance is influenced by
the perceived probability of syllogisms being valid. Stupple and Ball find
with syllogistic reasoning that people took longer to process unbelievable
premises than believable ones. Stupple finds participants were more likely
to accept conclusions that matched the premises in surface features than
those not matching.
Conditional reasoning has its origins in a system of logic known as
propositional logic. Performance on conditional reasoning problems is typically
better for the modus ponens inference than for other inferences (e.g., modus
tollens). Conditional reasoning is influenced by context effects (e.g., the
inclusion of additional premises). Performance on the Wason selection task
is generally very poor, but is markedly better when the rule is deontic
rather than indicative. Performance on syllogistic reasoning tasks is
affected by various biases, including belief bias and the base rate. The fact that
performance on deductive reasoning tasks is prone to error and bias
suggests people often fail to reason logically.
The mental models approach is one of the most influential approaches and
was proposed by Johnson-Laird.
A mental model represents a possibility, capturing what is common to the
different ways in which the possibility could occur. People use the
information contained in the premises to construct a mental model.
Here are the main assumptions of mental model theory. A mental model
describing the given situation is constructed and the conclusions that follow
are generated. The model is iconic (its structure corresponds to what it
represents). An attempt is made to construct alternative models to falsify the
conclusion by finding counterexamples to the conclusion. If a
counterexample model is not found, the conclusion is assumed to be valid.
The construction of mental models involves the limited resources of working
memory. Reasoning problems requiring the construction of several mental
models are harder to solve than those requiring only one mental model because
of increased demands on working memory. The principle of truth states that
individuals minimise the load on working memory by tending to construct
mental models that represent explicitly only what is true, and not what is
false (Johnson-Laird).
Successful thinking results from the use of appropriate mental models.
Unsuccessful thinking occurs when we use inappropriate mental models.
Knauff finds deductive reasoning was slower when it involved visual
imagery. Copeland and Radvansky test this assumption. They find a moderate
correlation between working memory capacity and syllogistic reasoning. They also
found that problems requiring more mental models had longer response times.
Legrenzi tested the principle of truth. He found performance was high on
problems when adherence to the principle of truth was sufficient. In
contrast, there were illusory inferences when the principle of truth did not
permit correct inferences to be drawn. People are less susceptible to such
inferences if explicitly instructed to falsify the premises of reasoning
problems (Newsome & Johnson-Laird).
Newstead, Eysenck, and Keane also found participants consistently failed to
produce more mental models for multiple-model syllogisms than for
single-model ones.
Most predictions of mental model theory have been confirmed experimentally.
In particular, evidence shows that people make errors by using the
principle of truth and ignoring what is false. Limitations with the theory are
that it assumes that people engage in deductive reasoning to a greater extent
than is actually the case. The processes involved in forming mental models
are underspecified.
There are two process involved in human reasoning. One system involves
unconscious processes and parallel processing, and is independent of
intelligence. The other system involves conscious processes and rule-based serial
processing, has limited capacity and is linked to intelligence. Evans
proposes the heuristic–analytic theory of reasoning, which distinguishes between
heuristic processes (System 1) and analytic processes (System 2). Initially,
heuristic processes use task features and
knowledge to construct a single mental model. Later, effortful analytic
processes may intervene to revise this model. This is more likely when task
instructions tell participants to use abstract or logical reasoning;
participants are highly intelligent; sufficient time is available for effortful
analytic processing; or participants need to justify their reasoning.
Human reasoning is based on the use of three principles: the Singularity
principle, the Relevance principle (not to be confused with Grice's
conversational category of Relatio, after Kant), and the Satisficing principle.
In contrast to the mental model theory, the heuristic–analytic theory
predicts that people initially use their world knowledge and immediate context
in reasoning. Deductive reasoning is regarded as less important.
Belief bias is a useful phenomenon for distinguishing between heuristic
and analytic processes. Evans finds less evidence of belief bias when
instructions emphasised logical reasoning. Stupple compares groups of participants
who showed much evidence of belief bias and those showing little belief
bias. Those with high levels of belief bias responded faster on syllogistic
reasoning problems. De Neys finds high working memory capacity was an
advantage only on problems requiring the use of analytic processes. A secondary
task impaired performance only on problems requiring analytic processes.
Evans and Curtis-Holmes find belief bias was stronger when time was strictly
limited.
Thompson suggests two processes are used in syllogistic reasoning:
Participants provided an intuitive answer. This is followed by an assessment of
that answer’s correctness (feeling of rightness). After which, participants
have unlimited time to reconsider their initial answer and provide a final
answer (analytic or deliberate answer). Thompson argues that we possess a
monitoring system (assessed by the feeling-of-rightness ratings) that
evaluates the output of heuristic or intuitive processes. Evidence that people are
more responsive to the logical structure of reasoning problems than
suggested by performance accuracy was reported by De Neys. The heuristic–analytic
theory of reasoning has several successes: the notion that cognitive
processes used by individuals to solve reasoning problems are the same as those
used in other cognitive tasks seems correct. Evidence supports the notion
that thinking is based on singularity, relevance and satisficing principles.
There is convincing evidence for the distinction between heuristic and
analytic processes. The theory accounts for individual differences, for
example in working memory capacity.
Limitations with the approach are that it is an oversimplification to
distinguish between implicit heuristic and explicit analytic processes. Also,
the distinction between heuristic and analytic processes poses the problem of
working out exactly how
these two different kinds of processes interact. It is not very clear
precisely what the analytic processes are or how individuals decide which ones
to use. Logical processing can involve heuristic or intuitive processes
occurring below the conscious level.
The assumption that heuristic processing is followed by analytic processing
in a serial fashion may not be entirely correct.
According to mental model theory, people construct one or more mental
models, mainly representing explicitly what is true. Mental model theory fails
to specify in detail how the initial mental models are constructed, and
people often form fewer mental models than expected. Dual-system theories
answer the two main limitations of most other research into human reasoning
because they take account of individual differences in performance and
processes. There is now convincing evidence for a distinction between relatively
automatic, heuristic-based processes and more effortful analytic-based
processes. However, it is unlikely that we can capture all the richness of human
reasoning simply by assuming the existence of two cognitive systems.
Prado finds the brain system for deductive reasoning is centred in the
left hemisphere involving frontal and parietal areas. Specific brain areas
activated during deductive reasoning included: inferior frontal gyrus;
middle frontal gyrus; medial frontal gyrus; precentral gyrus; basal ganglia.
Goel studies patients having damage to left or right parietal cortex. Those
with left-side damage perform worse than those with right-side damage on
reasoning tasks in which complete information is provided. Prado finds the
precise brain areas associated with deductive reasoning depended to a large
extent on the nature of the task. Prado also finds that the left inferior
frontal gyrus (BA9/44) is more activated during the processing of categorical
arguments. Prado finds found the left precentral gyrus (BA6) was more
activated with propositional reasoning than with categorical or relational
reasoning.
Language seems to play little or no role in processing of reasoning tasks
post-reading (Monti & Osherson). Reverberi identifies three strategies used
in categorical reasoning: sensitivity to the logical form of problems (the
left inferior lateral frontal (BA44/45) and superior medial frontal (BA6/8)
areas); sensitivity to the validity of conclusions (i.e., accurate
performance) -- the left ventro-lateral frontal (BA47) area, use of heuristic
strategies, no specific pattern of brain activation. More intelligent
individuals exhibit less belief bias because they make more use of analytic
processing strategies (De Neys). Individual differences in performance accuracy
(and thus low belief bias) were strongly associated with activation in the
right inferior frontal cortex under low and high cognitive load conditions
(Tsujii & Watanabe).
Fangmeier uses mental model theory as the basis for assuming the existence
of three stages of processing in relational reasoning. Different brain
areas were associated with each stage: Premise processing: temporo-occipital
activation reflecting the use of visuo-spatial processing. Then there's
Premise integration: anterior prefrontal cortex (e.g., BA10), an area associated
with executive processing. Finally, there is Validation: the posterior
parietal cortex was activated, as were areas within the prefrontal cortex
(BA6, BA8) and the dorsal cingulate cortex.
Bonnefond studies the brain processes associated with conditional
reasoning focusing on modus ponens: There is enhanced brain activity when premises
and conclusions do not match and anticipatory processing before the second
premise occurs when they match. Limited progress has been made in
identifying the brain systems involved in deductive reasoning. This is because of
simple task differences and individual differences that affect the results.
Informal reasoning is a form of reasoning based on one’s knowledge and
experience. People make extensive use of informal reasoning processes such as
heuristics in formal deductive reasoning tasks. However, there are also
differences between processes in formal and informal reasoning: content;
contextual factors; informal reasoning concerns probabilities; and motivation.
Ricco identifies common informal fallacies: Irrelevance (seeking to
support a claim with an irrelevant reason); Slippery slope.The myside bias is the
tendency to evaluate statements with respect to one’s own beliefs rather
than solely on
their merits (Stanovich & West). Support for the probabilistic approach
was reported by Hahn and Oaksford.They identify several factors influencing
the perceived strength of a conclusion: degree of previous conviction or
belief; positive arguments have more impact than negative arguments; and
strength of the evidence.
Hahn and Oaksford find a Bayesian model predicted informal reasoning
performance very well. However, Bowers and Davis argue that the Bayesian
approach is too flexible and thus hard to falsify. Sá finds unsophisticated
reasoning was more common among those of lower cognitive ability. Informal
reasoning is more important in everyday life than deductive reasoning. However,
most reasoning research is far removed from everyday life. Hahn and Oaksford
propose a framework for research on informal reasoning based on
probabilistic principles. There is reasonable support for their model, particularly
for the role of prior belief and new evidence on strength of argument. In
future, it will be important to establish the similarities and differences
in processes underlying performance on informal and deductive reasoning
tasks.
Are humans rational? Much evidence seems to indicate that our thinking and
reasoning are often inadequate, suggesting that we are not rational, even
if Grice thought he was. Human performance on deductive reasoning tasks
does seem very prone to error.
Most people cope well with problems in everyday life, yet seem irrational
and illogical when given reasoning problems in the laboratory. However, it
may well be that our everyday thinking is less rational than we believe.
Heuristics allow us to make rapid, reasonably accurate, judgements and
decisions, as Maule and Hodgkinson point out. Laboratory research findings
suggest people can think rationally when problems are presented in a readily
understandable form. Many of the apparent "errors" on deductive reasoning tasks
may also be less serious than they seem. There is reasonable support for
the notion that factors such as participants’ misinterpretation of problems,
or lack of motivation, explain only a fraction of errors in thinking and
reasoning
(e.g., Camerer & Hogarth). Individual differences in intelligence and
working memory also influence performance on conditional reasoning tasks. Some
researchers have found inadequacies in performance even when steps are
taken to ensure that participants fully understand the problem (e.g., Tversky &
Kahneman’s conjunction fallacy study). Interestingly, those who are
incompetent have little insight into their reasoning failures; this is the Dunning
–Kruger effect (Dunning). Deciding whether humans are rational depends on
how we define “rationality”. Sternberg points out that few problems of
consequence in our lives had a deductive or even any meaningful kind of ‘
correct’ solution. Normativism “is the idea that human thinking reflects a
normative system one conforming to norms or standards against which it should
be measured and judged. (Elqayam & Evans).
An alternative approach is that human rationality involves effective use
of probabilities rather than logic. Oaksford and Chater put forward an
influential probabilistic approach to human reasoning. Simon suggests the notion
of bounded rationality should be considered in human reasoning. This means
an individual’s informal reasoning is rational if it achieves his/her goal
of arguing persuasively. Many “errors” in human thinking are due to
limited processing capacity rather than irrationality. Toplak reports a
correlation of +0.32 between cognitive ability and performance across 15 judgement
and decision tasks. Stanovich (2012) developed the tripartite model with
two levels of processing: Type 1 processing (e.g., use of heuristics) within
the autonomous mind is rapid and fairly automatic. Type 2 processing (also
called System 2 processing), which is slow and effortful.
There are three different reasons why individuals produce incorrect
responses when confronted by problems: the individual lacks the mindware (e.g.,
rules, strategies) to override the heuristic response; or the individual has
the necessary mindware but fails to realise the need to override the
heuristic response; or the individual has the necessary mindware and realises
that the heuristic response should be overridden, but doesn’t have sufficient
decoupling capacity.
Stanovich uses the hybrid term (that scared Grice) dysrationalia to refer
to "the inability to think and behave rationally despite having adequate
intelligence". Most people (including those with high IQs) are cognitive
misers, preferring to solve problems with fast, easy strategies than with more
accurate effortful ones. Humans can be considered rational because errors
are caused by limited processing capacity (Simon). Classical logic is almost
totally irrelevant to our everyday lives because it deals in certainties.
Our thinking and reasoning are rational when used to achieve our goals.
However, humans can be considered irrational because many humans are cognitive
misers. There is a widespread tendency on judgement tasks to de-emphasise
base-rate information. They fail to think rationally because they are
unaware of limitations and errors in their thinking. Apparently poor performance
by most people on deductive reasoning tasks does not mean we are illogical
and irrational because of the existence of the normative system problem,
the interpretation problem and the external validity problem.
Yet, when Grandy and Warner decided for a festschrift for P. Grice, they
came up with "Philosopical Grounds of Rationality: Intentions, Categories,
Ends", but then it's an acronym: PGRICE ("and Clarendon didn't notice!")
reasoning task have a definite goal and the solution is not obvious.
However, problem solving and reasoning are typically treated separately. Reasoning
problems differ from other kinds of problems in that they often owe their
origins to systems of formal logic, as symbolised by Frege and 'laughed'
metaphorically by Grice in "Logic and Conversation".
There are clear overlaps between the two areas, which may differ less than
one might initially suppose. Inductive reasoning involves making a
generalised conclusion from premises referring to particular instances. Hypotheses
can never be shown to be logically true by simply generalising from
confirming instances (i.e., induction). Generalisations provide no certainty for
future events. Deductive reasoning allows us to draw conclusions that are
definitely valid provided that other statements are assumed to be true. For
example, if we assume
i. Grice is taller than Popper
ii. Popper is taller than Johnson-Laird
the conclusion
iii. Grice is taller than Johnson-Laird.
is necessarily true.
It is well known that Popper argues for a distinction between confirmation
and falsification. Confirmation involves obtaining evidence to confirm the
correctness of one’s hypothesis. Falsification involves attempting to
falsify hypotheses by experimental tests.
Popper argued that it is impossible to achieve confirmation via hypothesis
testing. Rather, scientists should focus on falsification.
When Johnson-Laird and Wason devised their tests, such as "the 2–4–6
task", in which participants have to discover a relational rule underlying a set
of three numbers, they found performance was poor on the task because
people tended to show confirmation bias – they generated numbers conforming to
their original hypothesis rather than trying hypothesis disconfirmation. A
positive test is when numbers produced are an instance of your hypothesis.
A negative test is when numbers produced do not conform to your hypothesis.
Wason’s theoretical position predicts that people should perform better
when instructed to engage in disconfirmatory testing.
The evidence was mixed.
Cowley and Byrne argue that people show confirmation bias because they are
loath to abandon their own initial hypothesis.
Tweney finds that performance on the 2–4–6 task was enhanced when
participants were told to discover two rules, one the complement of the other.
Gale and Ball argue that it was important for participants to identify the
crucial dimensions of ascending vs. descending numbers.
Performance on the Johnson-Laird's and Wason's 2–4–6 task involves
separable processes of:
hypothesis generation;
hypothesis testing.
Cherubini (not the author of "Medea") argues that participants try to
preserve as much of the information contained in the example triple (i.e., 2–4–
6) as possible in their initial hypothesis. As a result, this hypothesis is
typically much
more specific than the correct rule. Most hypotheses are sparse or narrow
in that they apply to less than half the possible entities in any given
domain (vide Navarro & Perfors).
The 2–4–6 problem is a valuable source of information about inductive
reasoning. The findings from the 2–4–6 task may not be generalisable because,
in the real world, positive testing is not penalised. Additional factors
come into play in the real world. Hypothesis testing in simulated and
real-world settings.
There is a popular view that "scientific discovery is the result of genius,
inspiration, and sudden insight" (Trickett & Trafton).
That view is largely incorrect.
Scientists (that Grice never revere -- 'we philosophers are into
hypostasis; while mere scientists can only grasp hypothesis') typically use what
Klahr and Simon describe as weak methods.
Kulkarni and Simon found scientists make extensive use of the unusualness
heuristic, or rule of thumb.
This involves focusing on unusual or unexpected findings and then using
them to guide future theorising and research.
Trickett and Trafton argue that scientists make much use of “what if”
reasoning in which they work out what would happen in various imaginary
circumstances.
Dunbar uses a simulated research environment. He found that participants
who simply tried to find data consistent with their hypothesis failed to
solve the problem.
It is believed that scientists should focus on falsifying their hypotheses.
However this does not tend to happen.
Nearly all reasoning in everyday life is inductive rather than deductive.
Hypothesis testing is a form of inductive reasoning.
It is well known that Popper argued that it is impossible to confirm a
hypothesis via hypothesis testing. Rather, scientists should focus on
falsification. However, it is now accepted that Popper’s views were oversimplified
and confirmation is often appropriate in real scientific research.
When Johnson-Laird and Wason devised stuff like the 2–4–6 task, they
found people tended to show confirmation bias, producing sequences that
confirmed their hypotheses rather than seeking negative evidence. However, later
studies demonstrated that people’s behaviour is often more accurately
described as confirmatory or positive testing.
"What if", or conditional reasoning is basically reasoning with “if”.
It has been studied to decide if human reasoning is logical.
In propositional logic, meanings are different from those in natural
language.
There are different types of logical reasoning statements:
"Affirmation of the consequent":
Premise (if P then Q), (Q), Conclusion (P).
Invalid form of argument.
"Denial of the antecedent":
Premise (if P then Q), (not P), Conclusion (not P).
Invalid form of argument.
"Modus tollens":
Premise (If P, then Q), (not Q), Conclusion (not P).
Valid form of argument.
"Modus ponens"
Premise (If P, the Q), (P), Conclusion (Q).
Valid form of argument.
Invalid inferences (denial of the consequent, affirmation of the
consequent) are accepted much of the time, the former typically more often (Evans).
De Neys finds evidence that conditional reasoning is strongly influenced
by the availability of knowledge in the form of counterexamples appearing to
invalidate a given conclusion. He also found performance on conditional
reasoning tasks depends on
individual differences.
Bonnefon argues that reasoners draw inferences when presented with
conditional reasoning problems.
According to Markovits, there are two strategies people can use with
problems: a statistical strategy and a counterexample strategy.
Various findings suggest many people fail to think logically on conditional
reasoning tasks.
Conditional reasoning is closer to decision making than to classical logic
(Bonnefon).
The Johnson-Laird/Wason selection task has four cards, each with a number
on one side and a letter on the other.
Participants
are told a rule and asked to select only those cards that must be turned
over to decide if the rule is correct.
The correct answer is only given by 5–10% of those who are engaged in the
experiment.
Many attempts have been made to account for performance on this task.
Evans identifies matching bias as an important factor.
This is the tendency for participants to select cards matching items named
in the rule regardless of whether the matched items are correct.
Stenning and van Lambalgen argue that people have difficulties interpreting
precisely what the selection problem is all about.
Oaksford argues that the logical answer to the Johnson-Laird/Wason
selection task conflicts with what typically makes most sense in everyday life.
Performance in the Johnson-Laird/Wason selection task can be improved by
making the underlying structure of the problem more explicit (Girotto) or by
motivating participants to disprove the rule (Dawson).
A syllogism consists of two premises or statements followed by a
conclusion. The validity of the conclusion depends only on whether it follows
logically from the premises. Belief bias is when people accept believable
conclusions and reject unbelievable conclusions, irrespective of their
logical validity or invalidity. Klauer finds various biases in syllogistic
reasoning, including a base-rate effect, in which performance is influenced by
the perceived probability of syllogisms being valid. Stupple and Ball find
with syllogistic reasoning that people took longer to process unbelievable
premises than believable ones. Stupple finds participants were more likely
to accept conclusions that matched the premises in surface features than
those not matching.
Conditional reasoning has its origins in a system of logic known as
propositional logic. Performance on conditional reasoning problems is typically
better for the modus ponens inference than for other inferences (e.g., modus
tollens). Conditional reasoning is influenced by context effects (e.g., the
inclusion of additional premises). Performance on the Wason selection task
is generally very poor, but is markedly better when the rule is deontic
rather than indicative. Performance on syllogistic reasoning tasks is
affected by various biases, including belief bias and the base rate. The fact that
performance on deductive reasoning tasks is prone to error and bias
suggests people often fail to reason logically.
The mental models approach is one of the most influential approaches and
was proposed by Johnson-Laird.
A mental model represents a possibility, capturing what is common to the
different ways in which the possibility could occur. People use the
information contained in the premises to construct a mental model.
Here are the main assumptions of mental model theory. A mental model
describing the given situation is constructed and the conclusions that follow
are generated. The model is iconic (its structure corresponds to what it
represents). An attempt is made to construct alternative models to falsify the
conclusion by finding counterexamples to the conclusion. If a
counterexample model is not found, the conclusion is assumed to be valid.
The construction of mental models involves the limited resources of working
memory. Reasoning problems requiring the construction of several mental
models are harder to solve than those requiring only one mental model because
of increased demands on working memory. The principle of truth states that
individuals minimise the load on working memory by tending to construct
mental models that represent explicitly only what is true, and not what is
false (Johnson-Laird).
Successful thinking results from the use of appropriate mental models.
Unsuccessful thinking occurs when we use inappropriate mental models.
Knauff finds deductive reasoning was slower when it involved visual
imagery. Copeland and Radvansky test this assumption. They find a moderate
correlation between working memory capacity and syllogistic reasoning. They also
found that problems requiring more mental models had longer response times.
Legrenzi tested the principle of truth. He found performance was high on
problems when adherence to the principle of truth was sufficient. In
contrast, there were illusory inferences when the principle of truth did not
permit correct inferences to be drawn. People are less susceptible to such
inferences if explicitly instructed to falsify the premises of reasoning
problems (Newsome & Johnson-Laird).
Newstead, Eysenck, and Keane also found participants consistently failed to
produce more mental models for multiple-model syllogisms than for
single-model ones.
Most predictions of mental model theory have been confirmed experimentally.
In particular, evidence shows that people make errors by using the
principle of truth and ignoring what is false. Limitations with the theory are
that it assumes that people engage in deductive reasoning to a greater extent
than is actually the case. The processes involved in forming mental models
are underspecified.
There are two process involved in human reasoning. One system involves
unconscious processes and parallel processing, and is independent of
intelligence. The other system involves conscious processes and rule-based serial
processing, has limited capacity and is linked to intelligence. Evans
proposes the heuristic–analytic theory of reasoning, which distinguishes between
heuristic processes (System 1) and analytic processes (System 2). Initially,
heuristic processes use task features and
knowledge to construct a single mental model. Later, effortful analytic
processes may intervene to revise this model. This is more likely when task
instructions tell participants to use abstract or logical reasoning;
participants are highly intelligent; sufficient time is available for effortful
analytic processing; or participants need to justify their reasoning.
Human reasoning is based on the use of three principles: the Singularity
principle, the Relevance principle (not to be confused with Grice's
conversational category of Relatio, after Kant), and the Satisficing principle.
In contrast to the mental model theory, the heuristic–analytic theory
predicts that people initially use their world knowledge and immediate context
in reasoning. Deductive reasoning is regarded as less important.
Belief bias is a useful phenomenon for distinguishing between heuristic
and analytic processes. Evans finds less evidence of belief bias when
instructions emphasised logical reasoning. Stupple compares groups of participants
who showed much evidence of belief bias and those showing little belief
bias. Those with high levels of belief bias responded faster on syllogistic
reasoning problems. De Neys finds high working memory capacity was an
advantage only on problems requiring the use of analytic processes. A secondary
task impaired performance only on problems requiring analytic processes.
Evans and Curtis-Holmes find belief bias was stronger when time was strictly
limited.
Thompson suggests two processes are used in syllogistic reasoning:
Participants provided an intuitive answer. This is followed by an assessment of
that answer’s correctness (feeling of rightness). After which, participants
have unlimited time to reconsider their initial answer and provide a final
answer (analytic or deliberate answer). Thompson argues that we possess a
monitoring system (assessed by the feeling-of-rightness ratings) that
evaluates the output of heuristic or intuitive processes. Evidence that people are
more responsive to the logical structure of reasoning problems than
suggested by performance accuracy was reported by De Neys. The heuristic–analytic
theory of reasoning has several successes: the notion that cognitive
processes used by individuals to solve reasoning problems are the same as those
used in other cognitive tasks seems correct. Evidence supports the notion
that thinking is based on singularity, relevance and satisficing principles.
There is convincing evidence for the distinction between heuristic and
analytic processes. The theory accounts for individual differences, for
example in working memory capacity.
Limitations with the approach are that it is an oversimplification to
distinguish between implicit heuristic and explicit analytic processes. Also,
the distinction between heuristic and analytic processes poses the problem of
working out exactly how
these two different kinds of processes interact. It is not very clear
precisely what the analytic processes are or how individuals decide which ones
to use. Logical processing can involve heuristic or intuitive processes
occurring below the conscious level.
The assumption that heuristic processing is followed by analytic processing
in a serial fashion may not be entirely correct.
According to mental model theory, people construct one or more mental
models, mainly representing explicitly what is true. Mental model theory fails
to specify in detail how the initial mental models are constructed, and
people often form fewer mental models than expected. Dual-system theories
answer the two main limitations of most other research into human reasoning
because they take account of individual differences in performance and
processes. There is now convincing evidence for a distinction between relatively
automatic, heuristic-based processes and more effortful analytic-based
processes. However, it is unlikely that we can capture all the richness of human
reasoning simply by assuming the existence of two cognitive systems.
Prado finds the brain system for deductive reasoning is centred in the
left hemisphere involving frontal and parietal areas. Specific brain areas
activated during deductive reasoning included: inferior frontal gyrus;
middle frontal gyrus; medial frontal gyrus; precentral gyrus; basal ganglia.
Goel studies patients having damage to left or right parietal cortex. Those
with left-side damage perform worse than those with right-side damage on
reasoning tasks in which complete information is provided. Prado finds the
precise brain areas associated with deductive reasoning depended to a large
extent on the nature of the task. Prado also finds that the left inferior
frontal gyrus (BA9/44) is more activated during the processing of categorical
arguments. Prado finds found the left precentral gyrus (BA6) was more
activated with propositional reasoning than with categorical or relational
reasoning.
Language seems to play little or no role in processing of reasoning tasks
post-reading (Monti & Osherson). Reverberi identifies three strategies used
in categorical reasoning: sensitivity to the logical form of problems (the
left inferior lateral frontal (BA44/45) and superior medial frontal (BA6/8)
areas); sensitivity to the validity of conclusions (i.e., accurate
performance) -- the left ventro-lateral frontal (BA47) area, use of heuristic
strategies, no specific pattern of brain activation. More intelligent
individuals exhibit less belief bias because they make more use of analytic
processing strategies (De Neys). Individual differences in performance accuracy
(and thus low belief bias) were strongly associated with activation in the
right inferior frontal cortex under low and high cognitive load conditions
(Tsujii & Watanabe).
Fangmeier uses mental model theory as the basis for assuming the existence
of three stages of processing in relational reasoning. Different brain
areas were associated with each stage: Premise processing: temporo-occipital
activation reflecting the use of visuo-spatial processing. Then there's
Premise integration: anterior prefrontal cortex (e.g., BA10), an area associated
with executive processing. Finally, there is Validation: the posterior
parietal cortex was activated, as were areas within the prefrontal cortex
(BA6, BA8) and the dorsal cingulate cortex.
Bonnefond studies the brain processes associated with conditional
reasoning focusing on modus ponens: There is enhanced brain activity when premises
and conclusions do not match and anticipatory processing before the second
premise occurs when they match. Limited progress has been made in
identifying the brain systems involved in deductive reasoning. This is because of
simple task differences and individual differences that affect the results.
Informal reasoning is a form of reasoning based on one’s knowledge and
experience. People make extensive use of informal reasoning processes such as
heuristics in formal deductive reasoning tasks. However, there are also
differences between processes in formal and informal reasoning: content;
contextual factors; informal reasoning concerns probabilities; and motivation.
Ricco identifies common informal fallacies: Irrelevance (seeking to
support a claim with an irrelevant reason); Slippery slope.The myside bias is the
tendency to evaluate statements with respect to one’s own beliefs rather
than solely on
their merits (Stanovich & West). Support for the probabilistic approach
was reported by Hahn and Oaksford.They identify several factors influencing
the perceived strength of a conclusion: degree of previous conviction or
belief; positive arguments have more impact than negative arguments; and
strength of the evidence.
Hahn and Oaksford find a Bayesian model predicted informal reasoning
performance very well. However, Bowers and Davis argue that the Bayesian
approach is too flexible and thus hard to falsify. Sá finds unsophisticated
reasoning was more common among those of lower cognitive ability. Informal
reasoning is more important in everyday life than deductive reasoning. However,
most reasoning research is far removed from everyday life. Hahn and Oaksford
propose a framework for research on informal reasoning based on
probabilistic principles. There is reasonable support for their model, particularly
for the role of prior belief and new evidence on strength of argument. In
future, it will be important to establish the similarities and differences
in processes underlying performance on informal and deductive reasoning
tasks.
Are humans rational? Much evidence seems to indicate that our thinking and
reasoning are often inadequate, suggesting that we are not rational, even
if Grice thought he was. Human performance on deductive reasoning tasks
does seem very prone to error.
Most people cope well with problems in everyday life, yet seem irrational
and illogical when given reasoning problems in the laboratory. However, it
may well be that our everyday thinking is less rational than we believe.
Heuristics allow us to make rapid, reasonably accurate, judgements and
decisions, as Maule and Hodgkinson point out. Laboratory research findings
suggest people can think rationally when problems are presented in a readily
understandable form. Many of the apparent "errors" on deductive reasoning tasks
may also be less serious than they seem. There is reasonable support for
the notion that factors such as participants’ misinterpretation of problems,
or lack of motivation, explain only a fraction of errors in thinking and
reasoning
(e.g., Camerer & Hogarth). Individual differences in intelligence and
working memory also influence performance on conditional reasoning tasks. Some
researchers have found inadequacies in performance even when steps are
taken to ensure that participants fully understand the problem (e.g., Tversky &
Kahneman’s conjunction fallacy study). Interestingly, those who are
incompetent have little insight into their reasoning failures; this is the Dunning
–Kruger effect (Dunning). Deciding whether humans are rational depends on
how we define “rationality”. Sternberg points out that few problems of
consequence in our lives had a deductive or even any meaningful kind of ‘
correct’ solution. Normativism “is the idea that human thinking reflects a
normative system one conforming to norms or standards against which it should
be measured and judged. (Elqayam & Evans).
An alternative approach is that human rationality involves effective use
of probabilities rather than logic. Oaksford and Chater put forward an
influential probabilistic approach to human reasoning. Simon suggests the notion
of bounded rationality should be considered in human reasoning. This means
an individual’s informal reasoning is rational if it achieves his/her goal
of arguing persuasively. Many “errors” in human thinking are due to
limited processing capacity rather than irrationality. Toplak reports a
correlation of +0.32 between cognitive ability and performance across 15 judgement
and decision tasks. Stanovich (2012) developed the tripartite model with
two levels of processing: Type 1 processing (e.g., use of heuristics) within
the autonomous mind is rapid and fairly automatic. Type 2 processing (also
called System 2 processing), which is slow and effortful.
There are three different reasons why individuals produce incorrect
responses when confronted by problems: the individual lacks the mindware (e.g.,
rules, strategies) to override the heuristic response; or the individual has
the necessary mindware but fails to realise the need to override the
heuristic response; or the individual has the necessary mindware and realises
that the heuristic response should be overridden, but doesn’t have sufficient
decoupling capacity.
Stanovich uses the hybrid term (that scared Grice) dysrationalia to refer
to "the inability to think and behave rationally despite having adequate
intelligence". Most people (including those with high IQs) are cognitive
misers, preferring to solve problems with fast, easy strategies than with more
accurate effortful ones. Humans can be considered rational because errors
are caused by limited processing capacity (Simon). Classical logic is almost
totally irrelevant to our everyday lives because it deals in certainties.
Our thinking and reasoning are rational when used to achieve our goals.
However, humans can be considered irrational because many humans are cognitive
misers. There is a widespread tendency on judgement tasks to de-emphasise
base-rate information. They fail to think rationally because they are
unaware of limitations and errors in their thinking. Apparently poor performance
by most people on deductive reasoning tasks does not mean we are illogical
and irrational because of the existence of the normative system problem,
the interpretation problem and the external validity problem.
Yet, when Grandy and Warner decided for a festschrift for P. Grice, they
came up with "Philosopical Grounds of Rationality: Intentions, Categories,
Ends", but then it's an acronym: PGRICE ("and Clarendon didn't notice!")
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