If it is raining, Frank gets wet.
Frank does not get wet.
Therefore it is not raining.
This conclusion is also valid.
Now the following two forms are invalid. It will be soon considered why. Denying the antecedent
is the third form which procedes the negation of p in the second premise:
If it is raining, Frank gets wet.
It is not raining.
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Therefore Frank does not get wet.
Many people argue the above conclusion is valid, but it is not. The reason for invalidity is that it
does not have to be raining for Frank to get wet (e.g he might have jumped into a swimming pool). Last
but not least the forth form is called affirming the consequent. It is called so, because q is affirmed in
the second premise, which is described more clearly by the following example:
If it is raining, Frank gets wet.
Frank gets wet.
Therefore it is raining.
This conclusion is also invalid for the same reason as before. The fact that Frank gets wet can
follow from another antecedent (again he might have been swimming). The results of many
experiments have shown that most people (close to 100 percent) correctly judge that modus ponens is
valid, but perform lower on modus tollens and the other two forms. Another important point for
peoplès performance in conditional reasoning tasks is the way the task is stated. This means people’s
performance is dependent on whether the task is stated abstractly or concretely. The knowledge
possessed by the person who is evaluating the syllogism is also important for the performance.
Why people make errors in conditional reasoning: The Wason Four- Card- problem
People are often better at judging the validity of syllogisms when real – world items are substituted
for abstract symbols. But it is also known that real – world items can sometimes lead to errors as when
people are influenced by the belief bias. There are many experiments which provide the evidence for
the effect of using real – world items in a conditional reasoning problem. The Wason Four – Card –
problem is one of these experiments. Four cards are shown to the participants. There is a letter on one
side of each card and a number on the other side. The participants task was to indicate the minimum
number of cards they would need to turn over to test the following rule: If there is a vowel on one side
then there is an even number on the other side. In one of the most used versions of this experiment the
cards have the following four symbols visible: ‘E’ ‘K’ ‘4’ ‘7’ 55 percent of participants selected the ‘E’
card which is correct, because turning this card over tests the rule. However still another card needed to
be turned over to fully test the rule. 64 percent indicated the ‘4’ card to be turned over after ‘E’. This
answer indeed is not the best one, because if there is a vovel on the other side of the card it is conistent
with the rule, but if there is a consonant on the other side, then turning the ‘4’ wouldn`t tell anything
about the rule since having a consonant on one side and a vowel on the other side does not violate the
rule. In Wasons`s experiment only 4 percent of participants answered correctly that the ‘7’`card also
needs to be turned over. This is important because turning this card over would disconfirm the rule by
revealing a vowel. Now for solving such a card problem one should be aware of the falsification
principle which says for testing a rule it is necessary to look for situations that falsify the rule.
Stating the Four – Card task in real – world terms: the role of ‘Regulations’
The main reason researchers are interested in the Wason Four – Card problem is that they want to
figure out why participants make so many errors. For answering this, they determined how participants
perform when the problem is restarted in real – world terms. One of the experiments for determining
this was the beer/drinking-age problem used by Richard Griggs and James Cox (1982). This
experiment is identical to the Wason Four – Card problem except that instead of numbers and letters on
the cards everyday terms (beer, soda and ages) were used. Griggs and Cox found out that 73 percent of
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participants provided the correct response for the following rule: ‘If a person is drinking beer then he or
she must be over 19 years old.’ As mentioned before few of the participants answered the abstract Four
- Card task correctly. Now, why is it easier to solve such a problem when using real – world terms?
Apparently being able to relate the beer task to regulations about drinking makes it easier to pick the
right card to turn over. Another experiment was done, the instructions following: ‘Pretend you are a
postal worker sorting letters. A letter which is sealed must have a ‘5d’ stemp on it according to the
postal regulations. Which of the four envelopments (one is shown from the sealed side, the other one is
shown unsealed, the third one is shown with a ‘5d’ stemp and the last one is shown with a ‘4d’ stemp)
would you have to turn over to determine whether the rule is being obeyed?’ The experiment was done
with English and American participants. The fact that English participants performed better (a higher
percentage of them chose the sealed envelope and the one with a 4d-stamp on it to be turned over) than
American was very striking. The reason for this result appeared to be that the American participants
were not familiar with postal regulations like this one but the English were.
Pragmatic Reasoning Schemas in the Wason Task: The role of ‘Permission’
Patricia Chena and Keith Holyoak (1985) proposed the concept of pragmatic reasoning schemas. A
pragmatic reasoning schema is a way of thinking about case and effect in the world that is learned as
part of experiencing everyday life. One of these schemas that people learn is called the permission
schema which states that if a person satisfies condition A, then he/ she get to carry out action B. As an
example the permission schema for the beer’/ drinking – age problem (‘If you are 19 years old, then
you are allowed to drink beer.’) has already been learned by most of the participants, so they were able
to apply that schema to the card task.
This makes it easier to people to understand the difference between the abstract version or the
‘drinking beer’ or ‘postal regulation’ version of the card task. Apparently activating the permission
schema helps people to focus on attention on the right card, which is often ignored by them in the
abstract task.
An evolutionary approach to the Four – Card – problem: The role of ‘Cheating’
The Wason Four – Card – problem did not only prove the evidence for the effect on using it in a
conditional reasoning problem, but it also had led cognitive psychologists to another controversy in
which there were different explanations offered for the result of various experiments. As already
mentioned the permission schema is one of them. Now there is a proposed alternative to this idea which
states that the performance on the Wason task is governed by a built – in cognitive program for
detecting cheating.
Some psychologists (among them are Leda Cosmides and John Tobby (1992)) do have an
evolutionary perspective on cognition in which they argue that human beings can trace many properties
of their minds to the evolutionary principle of natural selection. Now according to this natural selection
adaptive characteristics (characteristics that help a person or an animal to survive to pass their genes to
the next generation) will become a basic characteristic of humans.
Applying to this idea it follows that a highly adaptive feature of the mind would become a basic
characteristic of the mind. According to the evolutionary approach, one such characteristic is related to
the idea of social exchange theory. This theory states that an important aspect of human behavior is the
Chapter 13
ability for two persons to cooperate in a way that is beneficial to both of them. As long as each person
is receiving a benefit for whatever he/ she gives up, everything works well in social exchange. But if
someone cheats, some problem arises. Therefore it is important that people are able to detect cheating
behavior to avoid it. Because this is an important tool for them to have better chances to survive,
‘detecting cheating’ has become a part of the brain’s cognitive makeup.
Now with this evolutionary approach the Wason Four – Card – problem can be understood in
terms of cheating. Cosmides and Tobby devised a number of experiments to determine whether
‘detecting cheating’ is helping by decisions or not. They created unfamiliar situations in Four – Card
scenarios which include cheating. It was obvious that the participants’ performance was high, though
even task was unfamiliar to them. They also ran some other experiments which did not include
cheating to prove that participants perform better in experiments which include it.
However other researchers have created scenarios with unfamiliar situations, but which did not
include cheating. It was astonishing that stating problems in this way caused an increase in
performance. An example of these experiments was one devised by Ken Maktelow and David Over
(1990) in which they tested people using a rule that says ‘If you clean up spillt blood, you must wear
gloves’. Now there are a lot more examples for controversial research in the field of cognitive
reasoning and for each of the mechanisms presented for and against it.
What will be left is the important finding that the context within which conditional reasoning
occurs makes a big difference. All this controversy can be inferred from the behavioral evidence. This
shows how complex the mind is and that it can have a number of different ways of approaching such a
task like the Wason task, depending on the situation.
Inductive Reasoning
In the previous chapters we discussed deductive reasoning, reaching conclusions based on logical
rules applied to a set of premises.
However, many problems cannot be represented in a way that would make it possible to use these
rules to get a conclusion. In this chapter we will talk about a way to be able to decide in terms of these
problems as well: inductive reasoning.
Inductive reasoning means making simple observations of a certain kind and apply these
observations via generalization to a different problem to make a decision.
One famous example for this kind of reasoning is the following:
All crows I have ever seen are black.
Therefore, every crow in the world is black.
This is an example for the so called ‘strong inductive reasoning’. It is easy to see that inductive
reasoning leads to a quick conclusion that is likely but not certain, since it is impossible to check the
color of every crow in the world. An example for ‘weak inductive reasoning’ would be a statement like
this:
I always cook noodles in a frying pan.
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Therefore, noodles are cooked in a frying pan.
(For this kind of reasoning the same conditions hold than stated before for strong inductive
reasoning.)
This is the difference between inductive and deductive reasoning. While deduction brings
conclusions that are inevitably based on certain rules (arguments are called ‘sound’ or ‘valid),
induction is concerned rather with the probability of an event or a statement based on previously
gathered evidence (the correct terminology here is ‘cogent’).
Induction vs deduction
Induction is the form of reasoning that is used more often and much more easily. Most of the time
we use it without even realizing that we do some kind of reasoning at the moment. Whether it is the
sunrise every morning and the sunset in the evening, the change of seasons, the TV program, the fact
that a chair does not collapse when we sit on it or the lightbulb that flashes after we have pushed a
button, all of these are examples for inductive reasoning. We think that certain events will occur or that
our actions have certain kinds of effects because this is the way it always is and has been and therefore
we have good reason to believe that it is going to happen in just the same way. It would take way too
much time and effort to think about all these things every time anew.
Deduction and induction are also regarded as being the complement of one another and inductively
reached conclusions are usually deductively invalid. But it would be a mistake to say that these two are
totally independent from each other. It is often the case that one needs inductive reasoning first to get to
deductive reasoning. A good example for this is the whole field of science. To be able to compile a
formula in physics for example, one needs a theory at first that can be tested. This is nothing but
inductive reasoning:
I realize that everything I see, including myself, is somehow fixed to the surface of the earth. I
have been to different places on this planet and noticed the same. Although I have not seen every single
corner in the world, I assume that this principle holds for every piece of matter with a certain mass.
This is a prime example for inductive reasoning because it shows that it can be regarded as making
an assumption that is thought quite probable to be the case but not foolproof.
How reliable are conclusions reached through induction?
What it also shows is an important aspect for evaluating conclusions reached through induction:
The size of the sample, also called the ‘law of large numbers’.
If I have been to many countries and saw the same circumstances everywhere, it is much more
likely that these circumstances can be found on the whole planet than if I have seen nothing but my
own town. It might be the case that in the next town people are walking on the ceiling. I cannot say
anything about that because I have never been out of town to check on it.
Other factors that contribute to the so-called ‘strength’ of the argument is the representativeness of
the observations and the quality of the evidence.
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To ask only members of a reigning political party about the current government of their country is
certainly not very representative because it only takes into account the opinion of people that are very
likely to approve it.
And it is no better idea to ask other people the same question when it is in the middle of the night
and they have spent the last five hours in a pub. It would be quite doubtful that their answers were of
the quality we want for doing proper reasoning.
Processes and constraints of inductive reasoning
But how does inductive reasoning happen in more special cases than strong inductive reasoning?
And what kinds of psychological pitfalls are there to it? To get a little bit deeper into this subject, we
will introduce some processes and consraints related to inductive reasoning:
The availability heuristic
Things that are more easily remembered are judged to be more prevalent. Examples are two
experiments that have been made. One of them asked people to say which one of two different causes
of death occurs more often (Lichtenstein et al., 1978). Because of the availability heuristic people
judged more ‘spectacular’ causes like homicide or pregnancy to cause more deaths than others, like
asthma. In another similar experiment participants had to say whether there were more words in a list
starting with an ‘r’ or more words having ‘r’ as the third letter (Tversky & Kahneman, 1973). Most
people picked the former although there were actually three times as many words having ‘r’ in third
position.
The representativeness heuristic
Judgements are often made based on how much an event resembles another event. If I hear loud
scratching noises in the back of my car while parking, I know that I bumped into another car. If I hear
the same kind of noise from the front of the car, I will be much more likely to think about an accident
than if I heard a soft sound like when I drive my car into a heap of freshly fallen snow in winter. Even
if the noise comes from another direction, it is much more similar to the first scenario than the snow
scenario.
Illusory correlations
People tend to judge according to stereotypes. This is what is known by the term ‘prejudice’. It
means that a much oversimplified generalization about a group or a class of people is made. Usually
this focuses on the negative and has absolutely no proof in reality. This property of inductive reasoning
can be very dangerous. Examples for this are racist believes about Afro-Americans or Jews during the
time of the Third Reich.
The conjunction rule
The conjunction of two events is never more likely to be the case than the single events alone. An
example for this is the case of the femininist bank teller (Tversky & Kahneman, 1983). If we are
introduced to a woman of whom we know that she is very interested in women’s rights and has
participated in many political activities in college and we are to decide whether it is more likely that
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she is a bank teller or a feminist bank teller, we are drawn to conclude the latter based on our
knowledge about her. But it is in fact much more likely that somebody is just a bank teller than it is that
someone is a feminist in addition to being a bank teller.
Confirmation bias
This phenomenon describes the fact that people tend to decide in terms of what they themselves
believe to be true or good. If we go back to the example of the members of the political party, let us
imagine that they are strictly against abortion. If they are presented with a bill that prohibits abortion
but features in addition to that a list of some arguments pro and contra abortion, they would judge the
prohibition as being a good thing although the list might contain twice as many arguments for abortion
than against it.
The hindsight bias
Estimations are reconsidered after getting more infromation. If you ask someone about the
percentage of water on the planet's surface and after a while you give him the answer and ask what it
was that he had estimated before, he is quite likely to give another number that is closer to the actual
percentage.
The probability heuristic
This is simply the term for the fact that the subjective probabilities one would give for an event
might differ to a smaller or larger extent from the actual probabilities of the event. Reasons for this can
be all of the above.
The gambler’s fallacy
And a little tidbit at the end of the list: Against most intuitions the rolling of a dice is totally
independent from earlier outcomes, of course. Throwing a six has exactly the same probability after the
throwing of five, one and four than it has after three sixes have been thrown already. This is also an
example for the representativeness heuristic.
So, why inductive reasoning at all?
All of these introduced phenomenons are responsible for leading our reasoning by induction. And
as we can easily see, quite often they lead us on the wrong track. But they are important nevertheless
because they act as shortcuts for our reasoning. We have said that inductive reasoning is used in
everyday situations much more often than deductive reasoning because it is faster and easier. The
attributes featured in the above list are the reason for that.
And this shows exactly what inductive reasoning is and why it is so useful:
It is a way of making decisions that might not ground on real facts, but on what best suits the
purposes of the individual in a particular situation and it is a very quick way of making these decisions.
And this is much more important because most of the time decisions are supposed to serve the purposes
of a person and are made within parts of seconds without us even noticing that we just made a decision.
Chapter 13
Decision Making: Choosing Among Alternatives
About the Process
The psychological process of decision making constantly goes along with situations in daily life.
Determining preferences among different alternatives can have minor consequences (e.g. deciding
between chocolate and vanilla ice cream), but it can also have relevant influence on important
circumstances of life in the future (e.g. job decisions, influencing also family life, hobbies, self-esteem,
salary, …). The mentioned examples are both characterized by personal decisions, whereas
professional decisions, dealing for example with economic or political issues, are just as important.
According to the different levels of consequences, each process of making a decision requires
appropriate effort and various aspects to be considered. Such a process can be roughly structured into
three steps, beginning with the information-gathering stage, proceeding through likelihood
estimation and deliberation and being completed by the final act of choosing.
There are three different approaches to the analysis of decision making. The normative approach
assumes a rational decision-maker with well-defined preferences. While the rational choice theory is
based on a priori considerations, the descriptive approach is based on empirical observation and on
experimental studies of choice behavior. The prescriptive enterprise develops methods in order to
improve decision making.
The Utility Approach
According to Manktelow and Reberś definition, “utility refers to outcomes that are desirable
because they are in the person’s best interest” (as cited in Goldstein, 2005, p. 468). An early economic
approach characterizes optimal decision making by the maximum expected utility (in terms of
monetary value). This approach can be helpful in gambling theories, but simultaneously inhales several
disadvantages. People do not necessarily focus on the monetary payoff, since they find value in things
other than money, such as fun, free time, family, health, … Therefore not choosing the maximal
monetary value does not automatically describe an irrational decision process.
Misleading Effects
Situation Models
By imagining the most intuitive consequences of different decisions, people often create situation
models (Kahneman & Tversky, 1982; Dunning & Parpal, 1989) which might be misleading, since they
rely on subjective speculations. An example could be deciding where to move by considering typical
prejudices of the countries (e.g. always good pizza,nice weather and a relaxed life-style in Italy in
contrast to some kind of boring food and steady rain in Great Britain). The predicted events are not
equal to the events occurring indeed.
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Focusing Illusion
Another misleading effect is the so-called focusing illusion. By considering only the most obvious
aspects in order to make a certain decision (e.g. the weather) people often neglect various really
important outcomes (e.g. circumstances at work). This effect occurs more often if people judge about
others than in case of judging about thei