Philosophy
Higher
Critical Thinking
NQ Support Material
2006
Scottish Further Education Unit
Higher Philosophy Critical Thinking Support Notes
Acknowledgements
SFEU (Scottish Further Education Unit) gratefully acknowledges the contribution made to
this publication by Learning and Teaching Scotland who have granted permission to use
material previously produced by HSDU.
SFEU also thanks the SQA for permission to reproduce parts of the Arrangements
Documents.
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Higher Philosophy Critical Thinking Support Notes
Contents
Introduction
3
National Unit Specification
5
Guidance on Learning and Teaching Approaches
6
Understanding the Nature of Arguments
Introduction
1. The purpose of an argument
2. The distinction between statements and arguments
3. Argument structure
4. Recognising everyday arguments
Reliable and Unreliable Arguments
8
8
11
14
19
36
1. Reliable arguments: what makes a ‘good’ argument?
2. Testing for validity
3. Types of reasoning: deduction and induction
4. Unreliable arguments: fallacies
5. Tying everything together
45
45
50
57
59
81
Appendix 1: Additional Resources
85
Appendix 2: Notes for Teachers
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Introduction
Scotland has long been recognised as providing educational opportunities to its citizens
that encompass both breadth and depth. The need to educate the whole person, and not
simply concentrate on immediately obvious practical skills, is also firmly embedded in all
Scottish educational philosophy. As a result education focuses on the dual objectives of
providing citizens with practical skills and knowledge related to employment, and broader
intellectual and social skills which enable them to participate fully in society and lead rich,
fulfilling lives. It is also recognised that these broader skills are increasingly important as
societies become more complex and ideologically diverse. Scottish society today has
been influenced by a wide variety of cultures and traditions, and it is therefore important
that all its citizens are able to develop and express their own values and perspectives in a
reasoned way. In addition, it is important that they are able to discuss and reflect upon
perspectives and values which may be different from their own. This can only be
accomplished through a process of reasoned debate and discussion which acknowledges
shared human experiences and also the validity of alternative views. Developing a
reasoned and structured approach to all forms of discourse will contribute to this process.
The opportunity for individuals to develop and discuss their own values and perspectives,
and learn to appreciate alternative values and perspectives is an important aspect of
Scottish Primary and Secondary Education. For this reason the process of discussion,
debate and reflection features in many areas of the curriculum from P1-S4. The Higher
Philosophy Course provides the opportunity for candidates to continue to develop the
concepts and skills needed for productive social discourse and offers certificated
progression in S5 and S6. The Course is also suitable for delivery in Further Education
colleges and is appropriate for adult students who have an interest in philosophical
issues.
Candidates who gain a Course award will be in a good position to continue their studies
of philosophical issues in Further Education colleges or Higher Education Institutions.
Those who choose to progress to study alternative subjects will also benefit: developing
critical thinking skills and the ability to reason effectively is an important part of the Higher
Philosophy Course and these skills are of relevance in all subject areas. This will enable
candidates to develop as members of society who can express their own opinions and
values confidently but also appreciate the opinions and values of others.
The Course consists of four mandatory Units. The Critical Thinking in Philosophy Unit
helps candidates to develop an understanding of good and bad arguments and the skills
necessary to reason in an effective manner. In the Metaphysics Unit candidates
investigate a perennial philosophical debate and the different positions adopted in relation
to that debate. The Epistemology Unit focuses on questions surrounding the nature,
sources and possibilities of knowledge. Moral Philosophy involves the study of issues and
positions concerning moral judgements and their nature.
Aims
The Course aims to allow candidates to:
•
develop critical thinking skills which are of importance in all areas of human life and
discourse
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•
•
•
•
•
develop knowledge and understanding of philosophical techniques, issues, positions
and concepts which are relevant in many areas of human life and discourse
develop analytical and evaluative skills which will allow them to examine the
reasoning and assumptions on which the positions and theories they study are based
present their own ideas and opinions in a reasoned and structured manner
gain insight from the ideas and opinions of others which may conflict with their own
engage personally with a range of important questions and issues in order to inform
their own ideas and opinions in a way which contributes to personal and social
development.
Critical Thinking in Philosophy (Higher)
It is strongly recommended that candidates begin the Course by studying this Unit: The
knowledge and skills they acquire are invaluable and directly relevant when studying the
issues, positions and arguments in the remaining Units.
In this Unit candidates develop an understanding of the nature of arguments and some of
the characteristics of effective and ineffective arguments. Candidates then use this
understanding to critically analyse and evaluate previously unseen examples of ordinary
language arguments.
Candidates must study all content. A brief summary of the content of the Unit appears
below:
Candidates gain an understanding of the nature of arguments and of some of the terms
and concepts needed to critically analyse and evaluate arguments in a philosophical
manner. The content is studied under two headings which are:
•
•
understanding the nature of arguments
reliable and unreliable arguments.
This Unit is a mandatory Unit of the Higher Philosophy Course, but it can also be taken as
a freestanding Unit.
This Unit offers progression for candidates who have studied the Intermediate 2
Philosophy Course or Units. It is also suitable as a Higher level introduction for those who
have no background in the subject. In this Unit, candidates develop the skills necessary
to examine arguments and recognise the characteristics of effective and ineffective
arguments. The understanding and skills developed in this Unit are relevant in all areas of
human life. The ability to argue clearly and to recognise strong and weak reasoning in the
arguments of others is a powerful tool in all personal and social contexts. Specific
features of both effective and ineffective arguments are studied in this Unit but the
understanding and critical thinking skills developed are relevant in a wide variety of
contexts. These skills prepare candidates for the study of Philosophy at Advanced Higher
or in Courses at Further Education colleges or Higher Education Institutions. Candidates
will also be prepared for the study of any other subject which requires the ability to
understand and analyse arguments. In addition, candidates will have demonstrated the
skills necessary for entry into any field of employment where the ability to reason
constructively is required.
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Outcomes
1. Demonstrate an understanding of the nature of arguments.
2. Critically analyse ordinary language arguments.
3. Critically evaluate ordinary language arguments.
Acceptable performance in this Unit will be the satisfactory achievement of the standards
set out in this part of the Unit Specification. All sections of the statement of standards are
mandatory and cannot be altered without reference to the Scottish Qualifications
Authority.
Outcome 1
Demonstrate an understanding of the nature of arguments.
Performance Criteria:
(a) describe the difference between statements and arguments
(b) describe the difference between deductive and inductive reasoning
(c) use ordinary language examples to support these descriptions.
Outcome 2
Critically analyse ordinary language arguments.
Performance Criteria:
(a) identify the premises and conclusions of ordinary language arguments
(b) present these arguments in a way which demonstrates the stages of reasoning
involved
(c) explain whether these arguments employ deductive or inductive reasoning.
Outcome 3
Critically evaluate ordinary language arguments.
Performance Criteria:
(a) explain specific examples of fallacious reasoning in ordinary language arguments
(b) explain whether or not the conclusions of these arguments follow from the premises
(c) explain whether these arguments are sound or unsound
(d) state reasons which support the explanations given.
The full Arrangements Documents can be viewed on the SQA website at:
http://www.sqa.org.uk/files_ccc/NQ_Philosophy_Higher_10012006.pdf
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Guidance on Learning and Teaching Approaches
Throughout their study of this Unit, candidates will develop knowledge and skills which
are relevant when analysing all forms of philosophical and everyday human discourse.
This fact should be emphasised at the beginning of the learning and teaching process.
Teachers and lecturers should therefore avoid introducing relevant terms and concepts in
a wholly abstract manner. For example:
•
•
•
•
When investigating the distinction between statements and arguments, candidates
might be asked to distinguish between examples of ordinary language statements and
arguments and to discuss the differences they recognise. This will allow them to
appreciate fully the ways in which statements and arguments function differently in
everyday human discourse. It will also help them to understand that statements are
sometimes used erroneously to create the impression that a point has been
established.
Candidates might also be encouraged to find or compose their own examples of
statements and arguments. This will reinforce their understanding of the distinctions
involved.
When introducing the common fallacy of attacking the person, candidates might be
asked to comment on real-life examples from television/radio debates, newspaper
columns or letters pages. Equally, teachers or lecturers might choose to adapt or
compose topical/relevant examples. By identifying that there is a problem of reasoning
and by discussing the nature of that problem, candidates will gain an understanding of
the fallacy. They will also be more likely to recognise this fallacy when encountering it
in new contexts.
Understanding can also be reinforced by encouraging candidates to find, or compose
their own, examples of the fallacy of attacking the person.
Candidates will be expected to critically analyse and evaluate previously unseen
examples of ordinary language arguments in both Unit and Course assessment.
This ability can be developed only if candidates are continually given practice in applying
the relevant concepts and skills in new and varied contexts. Teachers and lecturers
should ensure that candidates develop techniques to help them analyse and evaluate
previously unseen ordinary language arguments in a reasoned and structured manner.
One possible approach to developing such techniques appears below:
A variety of topical or relevant ordinary language arguments might be sourced or
composed by the teacher/lecturer. Candidates can then critically analyse and evaluate
the arguments by asking the following questions:
•
•
•
•
•
•
•
•
What is the conclusion of the argument?
What are the stated premises?
How can the premises and conclusion be presented to show the stages of reasoning
involved?
Is the argument an example of deductive or inductive reasoning?
Does the structure help to identify any stages of reasoning that might have been
missed out (hidden premises)?
If so, what might these hidden premises be?
If the argument is deductive, must the conclusion necessarily be true if the premises
are true? (valid argument)
Does the argument use any of the forms of fallacious reasoning I have studied?
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•
•
Are any of the premises I have identified either obviously true, false or debatable in
any way?
If the premises are true/undebatable, must the conclusion necessarily be true (sound
argument)?
Some of the content of this Unit can also be studied in the Intermediate 2 Critical Thinking
in Philosophy Unit. If a centre makes the judgement that the Intermediate 2 Unit would be
more appropriate for a particular candidate, the candidate can be assessed at that level
without difficulty. However, it should be noted that there are differences in the skills
assessed at that level. If candidates have already studied the Intermediate 2 Critical
Thinking in Philosophy Unit there will be significant opportunities to build on and develop
the knowledge and skills they have already acquired.
For candidates who study this Unit as part of the Higher Course, there are significant
opportunities to integrate the skills they acquire in the remaining three Units. The ability to
understand, critically analyse and evaluate the reasoning and assumptions on which
specific arguments, theories and/or positions are based is relevant when studying all
other Units in the Higher Course. For this reason it is strongly recommended that this
Unit, Critical Thinking in Philosophy, be delivered as an introductory Unit to the Course.
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Understanding the Nature of Arguments
Introduction: Why study critical thinking?
This unit is intended to introduce students to the role of critical thinking within philosophy.
The study of critical thinking is the study of arguments. What are arguments composed
from? What distinguishes a good argument from a bad one? When should one find an
argument compelling? How should one seek to offer arguments in support of one’s
beliefs?
One question that might come to mind is: why practise evaluating arguments? This looks
like a good question. Isn’t it the case that we are already capable of engaging in such an
activity? Don’t we do it all the time, particularly in philosophy?
Yes – and that is part of the reason why it should be studied. The problem is that we
don’t do it well a lot of the time. People are good at spotting some legitimate and
illegitimate argumentative tactics, but not others. And they are prone to making certain
kinds of mistakes.
We are not always entirely clear as to the connection between a belief and the reasons
for holding it. Often, when trying to argue for a belief we will offer a number of reasons,
without any clear thought as to how these supposed reasons support our assertions. If
our reasons are to hold any weight, they must be able to act as the basis of a good
argument to the conclusion we are advocating. It is always worth asking oneself: why
does that reason support my opinion?
Furthermore, we do not always think critically in another way as well: a large number of
discussions in everyday life rely on non-critical (or non-rational) means to persuade
others. Consider the following four arguments:
1.
We had to go to war, because:
If Saddam Hussein had gained chemical weapons he either would have used them or
made them available to terrorist organisations.
Saddam Hussein was developing such weapons.
We could not allow him to gain such weapons.
Therefore, we had to prevent him from doing so, either by peaceful means or by going to
war.
We could not do it by peaceful means.
2.
Those who would allow Saddam to develop horrendous weapons in light of his previous
use of chemical weapons against the Kurds are naïve pacifists. War is a necessary evil –
we cannot let madmen do what they want just because we do not want to get our hands
dirty. Remember what happened in 1939!!
3.
Blair is just Bush’s poodle, and GWB was just out to finish his dad’s work. It’s all about
American imperialism and the desire for control of oil. Anyone who thinks that war is ever
a good idea is playing into the hands of the American military-industrial complex.
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4.
By going to war, the coalition was able to oust Saddam Hussein.
Ousting Saddam Hussein was a good thing.
However, by going to war, it is likely that the entire Middle East will be further
destabilised, fundamentalism will grow, and religious intolerance will increase.
These consequences outweigh the benefits of ousting Saddam Hussein.
Therefore, we should not have gone to war.
It is relatively easy to spot the well-structured arguments here. Nevertheless, spotting
arguments is not the same as being able to evaluate them thoroughly.
We can identify three main reasons for developing our critical reasoning skills. Firstly, we
can try to avoid being led into error by others. We want to be able to distinguish good
reasons from bad reasons when they are presented to us. This is essential if we are not
to be led astray in our beliefs. Secondly, we want to develop the skills that will allow us to
improve our own skills of persuasion. An increased familiarity with the tools of critical
thinking can only improve our ability to reach agreement with others (or, at least, to know
the means by which we might seek to do this).
We can imagine this second reason to hold for those who engage in debates; not just
members of student debating societies, but also lawyers, politicians and the like. This,
however, should not be our main motivation. This brings us to the third reason, namely,
the pursuit of the truth.
Good reasoning – like philosophy more generally – is concerned with the pursuit of truth,
not just persuasion or victory in a debate. We should not just seek to persuade those
who would disagree with us; we should also seek to ensure that we have good reasons
for believing in the truth of the statements ourselves.
Returning to the matter of our own reasoning abilities, psychologists have identified
certain kinds of mistake in reasoning to which humans appear prone. This is not to say
that we are all not experienced critical thinkers with good critical abilities. We are. Such
abilities, though, can be improved upon, and we can use them in a rather more focused
and explicit way than we might previously have done. Practising saying why we think
certain arguments are good or bad and evaluating our intuitions on particular cases will
allow us to develop our critical skills.
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Exercise 1: Two tests for good reasoning
a) The Wason – Johnson-Laird test
This test was created by Peter Wason and Philip Johnson-Laird.
Four cards are placed on the table on front of you. Each card has a dark side and a light
side, with shapes on the dark side and faces on the light. They look like this:
☺
(Two of the cards are dark side up, two light side up.)
The experimenter suggests the following rule to us:
If there is a circle on one side of the card, then there will be a smiley face on the other
side.
We want to check whether this rule is true. Does it correctly describe the patterns of
shapes and faces on the cards? The question that we have to answer is: which cards
would we have to turn over to establish whether this rule is true or not?
In the original tests run by Wason and Johnson-Laird, only 5 out of 128 American college
students got the right answer.
b) The ‘Conjunction Fallacy’
This comes from Amos Tversky and Daniel Kahneman:
Jacob is a 35-year-old ex-philosophy student who is politically active and highly
intelligent. While at university, he was very active in the animal rights movement. Which
is more likely?
•
•
Jacob is a computer programmer for a large multinational company.
Jacob is a computer programmer for a large multinational company and a vegetarian.
It is common for 85% of people to get the answer wrong.
(We will return to these examples later in the course.)
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1. The purpose of an argument
The ability to reason well is an essential philosophical skill; one cannot be a good
philosopher unless one masters key reasoning skills. Philosophy is not just about having
opinions about certain ‘philosophical’ issues: the existence of God, the wrongness or
otherwise of killing animals, what we can or cannot know, and so on. It is also concerned
with the ability to evaluate the arguments for and against these beliefs. There are two
sides to this ability:
•
being able to provide others with good reasons to accept a claim you believe to be
true
•
being able to evaluate whether there are good reasons to accept or reject claims put
forward by others.
Philosophers are as much concerned with why we might believe something as they are
with what it is we believe. To see this, look at the following discussion:
John: It’s wrong to kill animals, even in order to eat them.
Kevin: No it’s not. There’s nothing wrong with eating them, or hunting them, or using them
for sport.
John: That’s rubbish.
Kevin: Watch it, or I’ll thump you.
Now, despite the fact that their discussion concerns one of the most important issues in
philosophy, morality, there is nothing philosophical about it. As it stands, it just isn’t
philosophy. They may be having an argument in the everyday sense of the word, but not
in the sense we are interested in!
To see why, consider the ways in which you might attempt to disprove the views of
another person with whom you disagreed. You wouldn’t just walk away; usually, you
would try to demonstrate the incorrectness of the person’s beliefs or opinions by showing
why she or he was wrong to hold such a view. In other words, you would try to give some
reasons why the person should change his or her mind. To do this would be to engage in
critical reasoning. Compare the discussion above with the following:
Lucie: There are never any good reasons for killing animals.
Mira: That’s not true. Sometimes, humans need to kill animals in order to survive. The
animals might be attacking people, or the people might need to kill the animals for food.
Lucie: Maybe, but you’re assuming that human life is more valuable than the lives of the
animals. All life is equally important.
Mira: Human life is more valuable, because humans are more developed than animals.
They can suffer more, they can think about what will happen if they don’t get more food,
they can read books and do lots of other things that the animals can’t.
Notice the differences. Instead of just stating their view, they offer some reasons for
accepting it as true. They also engage with the claim made by the other; that is, they
consider the claim and respond to it. For example, when Lucie suggests that all life is on
a par, Mira rejects this, giving some reasons why it might be thought that human life is
more important. Once one engages with the views of another and starts to offer reasons
for one’s beliefs, one starts to think philosophically.
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We like to believe that we are rational beings, capable of justifying and arguing for our
beliefs. We also like to think that our beliefs are reasonable: there are good reasons for
believing that men and women have broadly similar abilities, and that having a different
colour of skin or a different sexual preference is irrelevant to one’s rights and one’s skills.
We also like to think that our beliefs are coherent (that is, they do not contradict each
other).
Critical reasoning involves the study of arguments. In philosophy, when we talk about
‘arguments’ we are not talking about shouting matches or fights. John and Kevin may be
about to have an argument in the everyday sense, but it is unlikely that they are about to
have an argument in the sense in which we are interested.
In order to understand what critical thinking or good reasoning is all about, we need to
consider just what an argument is.
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Exercise 2: Spotting arguments
Which of the following do you think contain arguments? For each passage, try to explain
why you gave the answer you did.
Passage 1
I think murderers should be hanged. That way they won’t be able to commit murder
again, and the existence of capital punishment will deter others from taking the life of
another human being.
Passage 2
Of course Descartes is wrong – any half-wit can see that the external world exists. Why
would anyone ever doubt that?
Passage 3
Elaine: Euthanasia is just wrong – I believe that all life must be respected.
Jerry: You’re only saying that because you’re not old and infirm.
Elaine: No, I’d still say it even if I were old.
Jerry: Yeah, right.
Passage 4
Ben: I think everyone in the country should have his or her own gun.
Bill: You know, if you had half a brain, then you’d be dangerous.
Ben: So I’m dangerous, am I?
Bill: No – I said that if you had half a brain, you would be dangerous. But you don’t. So
you’re not.
Passage 5
Blair is just Bush’s poodle, and George W. Bush was just out to finish his dad’s work. It’s
all about American imperialism and the desire for control of oil. Anyone who thinks that
war is ever a good idea is playing into the hands of the American military-industrial
complex.
Passage 6
All bachelors are male.
Paul is a bachelor.
Therefore, Paul is male.
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2. The distinction between statements and arguments
Arguments are the main tools of reasoning; they are attempts to bring someone to believe
the truth of a claim by giving them good reasons for doing so. Before we look at the
nature of arguments, we must first consider the nature of what goes into them – these are
statements.
(a) Statements
Arguments are made up from statements (sometimes also called ‘claims’ or
‘propositions’). When someone makes a statement they assert that something is the
case; they say something that either correctly describes how things are, or does not.
Statements, therefore, are either true or false. The following are statements:
•
•
•
•
•
•
Snow is white.
The sky is blue.
Edinburgh is the capital city of Wales.
Bolivia is larger than Argentina.
God exists.
The cat sat on the mat.
(NB: Saying that a statement must be either true or false does not commit us to holding
that we must know which it is. There are many sentences that express statements about
which we cannot tell whether they are true or not. For example, ‘There is life on at least
three planets in distant galaxies’ must be one or the other, even though we are not in a
position to check which.)
However, attempting to state a fact is not the only role that language plays. Rather,
language can be used for a number of different purposes. To see this, look at the
following sentences:
•
•
•
•
Assertions or statements (‘The door is open’)
Commands or imperatives (‘Open the door!’)
Questions (‘Who is the tallest person in the room?’)
Expressions of emotion or feeling (‘Mmm, lovely!’).
Commands, questions and expressions of emotion or feeling are not statements because
they cannot be true or false. One is not asserting that such-and-such is the case;
instead, one is doing something else, such as asking for information, expressing how one
feels or ordering someone else to do something. In order to test whether a sentence
makes a statement, ask yourself whether it is the kind of sentence that could be true or
false.
Statements should not be confused with sentences, for two main reasons. The first and
most obvious is that some sentences are not statements, as we have just seen. The
other reason is that different sentences can make (or express) the same statement.
‘Tony Blair wears glasses’ and ‘Tony Blair wears spectacles’ both mean the same thing.
In a similar way, sentences in different languages can be used to make the same
statement: ‘snow is white’ in English makes the same statement as the sentence ‘la neige
est blanche’ does in French and ‘Schnee ist weiss’ does in German. This is an important
point, in that when we look at examples of arguments, we need to be able to recognise
whether different sentences are making the same statement or not.
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Exercise 3
Which of the following sentences are statements?
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
I like chocolate.
Chocolate, yum!
Scotland is part of the United Kingdom of Great Britain and Northern Ireland.
Press the button.
Could you press the button please?
I intend to press the button.
Pigs can fly.
Pigs can fly?
Get down!
You should get down.
London is the capital of Scotland.
The Moon is smaller than the Earth.
The Moon is larger than the Earth.
When was the Battle of Hastings?
I prefer France to Germany as a holiday destination.
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(b) Arguments
As we saw above, to provide an argument in support of a claim is to do more than just
state the claim. To give an argument is to offer reasons in support of one’s claim. Those
reasons have to be statements.
Look again at the discussion between Lucie and Mira. After Lucie claims that humans
are never justified in eating animals, Mira rejects this. She goes on to try to justify her
claim by giving a reason in support of it: humans can kill animals if their lives depend
upon it. When Lucie challenges this, Mira offers further support: human lives are more
important because humans have certain abilities not found in other animals. In other
words, Mira gives an argument for her view.
Notice that all of the claims that support Mira’s main claim, that humans can kill animals in
certain circumstances, are statements. We can think of an argument as a set of
statements linked together in an attempt to demonstrate that another statement, which we
can call the conclusion, is true. An argument is, to put it another way, something that
can be used in an attempt to demonstrate or prove the truth of a particular claim.
Here are several examples of arguments:
(A)
All humans are mortal.
Alice is human.
Therefore, Alice is mortal.
(B)
If Doctor Who is on TV, it must be
Saturday.
Doctor Who is on TV.
Therefore, it must be Saturday.
(C)
Holyrood is in Edinburgh.
Edinburgh is in Wales.
Wales is in Europe.
Therefore, Holyrood is in Europe.
(D)
If I had worked hard, then I would have
passed the exam.
I didn’t pass the exam.
Therefore, I didn’t work hard.
All of these are arguments because they attempt to demonstrate that a particular
statement is true or false. This statement, coming after the word ‘therefore’ in each of the
arguments, is the conclusion of the argument. The conclusion of an argument is not
simply asserted. Instead, the arguer attempts to offer a proof of it. To prove some claim
is to demonstrate why it must be true, given that other things are true. Consider
argument (A) above: this is an attempt to prove that Alice is human on the grounds that
the other two preceding statements are true (this is why only statements can feature in
arguments). If all of the other claims featured are true, then the conclusion must be true.
This is so for all of the arguments above, even the one containing the false claim that
Edinburgh is in Wales. This is a major difference between statements and arguments;
statements are asserted (‘statement S is true’), whereas arguments offer proofs of their
conclusions (‘statement S is true because it follows from the truth of statements P and
Q’). In a similar way, to reject the truth of a statement is to deny it; to offer an argument
against it is to attempt to refute it. Only statements can be denials, only arguments can
be refutations.
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Take, for example, the claim: Smoking is good for your health. If someone were to say
‘No it’s not’, then she or he would be denying the statement. However, if someone were
to say ‘No it’s not – smoking causes cancer, which can kill you’, then she or he would be
attempting to refute it.
When we reach a conclusion based on the other claims that feature in the proof, then we
are said to infer (or deduce or draw) the conclusion (‘I infer from the fact that Alice is
human and the fact that all humans are mortal, that Alice is mortal’). ‘Infer’ does not
mean ‘imply’. To imply something is to hint at it or suggest it. This is a very common
mistake, but a serious mistake nevertheless.
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Exercise 4: Conclusions
What are the conclusions of arguments (A) to (D)?
(A)
All humans are mortal.
Alice is human.
Therefore, Alice is mortal.
(B)
If Doctor Who is on TV, it must be
Saturday.
Doctor Who is on TV.
Therefore, it must be Saturday.
(C)
Holyrood is in Edinburgh.
Edinburgh is in Wales.
Wales is in Europe.
Therefore, Holyrood is in Europe.
(D)
If I had worked hard, then I would have
passed the exam.
I didn’t pass the exam.
Therefore, I didn’t work hard.
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3. Argument structure
As we have seen, the conclusion of an argument is the claim that the argument seeks to
prove. Those statements used in the argument in support of the conclusion are known as
premises. Consider again example (B) above. The writer is trying to convince his
audience that it is Saturday – this is the conclusion of the argument. He does this by
pointing out two things: (i) if Doctor Who is on TV, then it must be Saturday; and (ii)
Doctor Who is on TV. These are the premises of the argument.
Arguments can have any number of premises. These premises need not be true; a false
premise, such as that featured in (C), does not mean that (C) is not an argument.
Furthermore, as (C) demonstrates, the argument might even have a true conclusion.
It might be tempting to think that good arguments will be those with true premises and a
true conclusion. This would be a mistake, though. Consider the following:
(E)
Grass is green.
Snow is white.
Therefore, all dogs are mammals.
(E) includes two premises, the word ‘therefore’ and a conclusion; by the above definition,
then, it should count as an argument. Nevertheless, it is clearly not what we would think
of as a good argument. We need to be able to characterise what is required for a good
argument (and to tighten up this terminology somewhat as well).
It is worth noting here that in everyday arguments it is common for some premises to
remain unstated. This is often because the premises will be obvious – all parties in a
debate will agree on their truth, so stating them would be unnecessary. Premises that
play a role in an argument but are not explicitly stated are known as hidden or implicit
premises.
For example, look at this fairly typical example of an everyday argument:
I think murderers should be hanged. That way they won’t be able to commit murder
again, and the existence of capital punishment will deter others from taking the life of
another human being.
In the above argument, the assumption that if you’re dead, you cannot commit murder is
left unstated. This is, of course, fair enough. It seems perfectly sensible to assume that
your listeners will take such a premise for granted. Note, however, that such an
argument would not work in the world of Buffy the Vampire Slayer or Resident Evil.
Presumably, the living dead are just as capable of murder (and probably more prone to it)
as the living living.
Often, however, more serious and potentially objectionable premises will be left unstated.
We have to be on our guard for such occurrences. This is a large part of the practise of
formalising arguments – putting them into a form that makes their evaluation easier.
Without stating hidden or implicit premises, we will be unable to fully evaluate the
argument in question.
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So what distinguishes good arguments from bad arguments? Intuitively, a tighter
connection between premises and conclusion looks essential. We want the premises to
give us reason or justification for accepting the conclusion as true. The colour of grass
and the colour of snow seem irrelevant to whether dogs are mammals. This suggests that
the premises of (E) do not give us any reason to believe the conclusion.
The structure or form of the argument is also important. This provides the connection
between the truth of the premises and the truth of the conclusion. (F) provides a clear
example:
(F)
(p1) If I worked hard, then I will pass the exam.
(p2) I did work hard.
Therefore,
(c) I will pass the exam.
Notice that the first premise – here labelled (p1) – contains two statements, ‘I worked
hard’ and ‘I will pass the exam’, which are connected with ‘if’ and ‘then’. The writer is
suggesting that the statements are connected in this way: if the first is true, then the
second will be true. He goes on to note that the first statement is actually true, so it
follows that the second is also true.
In order to engage with an argument – that is, in order to be in a position to evaluate the
argument, to see whether it offers good reason to believe the truth of the conclusion – we
need to be able to (i) spot the conclusion of the argument, (ii) identify the premises and
(iii) recognise the form of the argument. In other words, we need to establish what the
premises and the conclusion are, and how they are connected.
It is very easy to recognise the premises and conclusion in simplified arguments such as
A) to F) above. In everyday life, however, it is rare to encounter arguments laid out in this
fashion. It is more likely that they will look something like this:
Freedom of speech is more important to society than the offence that certain books might
cause to individuals. People can be offended by anything, from nudity and bad language
to trivial things, such as a person’s choice of clothes or haircut. This shows that we
should not ban books solely because they cause offence.
Or this:
A baby is a lovely little gift from above. Who would ever want to refuse a gift, especially
one from so glorious a benefactor? If something is a gift from above, then it should not
be refused. That’s why contraception should be banned. It would be like refusing a
lottery win or a free two-week holiday abroad!
Notice that when we encounter simplified arguments such as (A) – (F) above, the
conclusion always comes at the end. However, as demonstrated in the second of these
two passages, this will not always be the case for everyday arguments. Instead,
conclusions can appear at any point – beginning, middle or end.
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We need to be able to identify the conclusion of an argument if we are start thinking about
whether or not it is a good or bad argument. There are certain words and phrases that
tend to mark a conclusion (although not every conclusion will be signposted in this way).
For example, in the first passage above, the phrase ‘this shows that’ leads us to see that
the statement following this, namely ‘we should not ban books solely because they cause
offence’, is the conclusion. Other phrases that might serve to indicate a conclusion
include: ‘therefore’, ‘thus’, ‘this demonstrates that’, ‘we can conclude’. We should not
expect every conclusion to be picked out in this way, though. If we are to be able to
identify a conclusion, we should pay attention to the connections between the various
claims made in the passage.
There are several important connections that we use in everyday discussion. We will
look at the following:
•
•
•
•
‘If… then…’
‘… or…’
‘… and…’
‘All’ and ‘some’.
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a) ‘If… then…’ (conditional) statements
The first, found in (B) and (D) above, concerns the use of the words ‘if’ and ‘then’. By
asserting that ‘if [something-or-other] is true (or happens), then [something else] will also
be true (or will happen)’, the speaker is drawing a link between the two things. Here are
some examples:
•
•
•
•
•
•
•
If 2+2=4, then 4-2=2.
If the Conservative Party wins the election, then Tony Blair will not be PM.
If Edinburgh is in Scotland, then it is in Britain.
If I let go of this pen, it will fall to the floor.
If I steal that book, then I will have committed a crime.
If I go to visit my granny, I will not be going to the cinema.
If I am dreaming, then this is not real.
We can ask: what exactly do the above claim?
Firstly, note that the ‘if… then…’ connects two statements (eg. ‘I am dreaming’, ‘this is not
real’). The speaker is not saying that the separate statements that make up the ‘if…
then…’ claim are true (it may not be the case that the Conservatives win the election, or I
am dreaming, etc.). Instead, something else is being claimed; namely that there is a
connection between the two statements, namely that if the first statement is true, then so
is the second.
Some terminology before we go further: ‘if… then…’ statements are known as
conditional statements (since the truth of the second claim is conditional on the truth of
the first). The statement on which the connection is conditional (the one introduced by
‘if’), is called the antecedent; the other (coming after ‘then’), is the consequent. If you
look at any other texts on critical thinking or reasoning, you will come across these terms.
For this reason, and to avoid any ambiguity, we will use these terms in the following
discussion.
Let us return to the claim made in the conditional statements: when the first statement is
true, so is the second. So, the first conditional in the list above claims that when it is true
that 2+2=4, it will also be true that 4-2=2. Notice that there is no suggestion that the first
causes the second or makes it true; the claim is only that if the antecedent is true, then so
is the consequent. All conditional statements have this form.
Conditionals often feature in arguments such as (B):
(B)
(p1) If Doctor Who is on TV, it must be Saturday
(p2) Doctor Who is on TV
Therefore,
(c) It must be Saturday
Notice that there are two premises in this argument. Given the first premise, we need the
second premise, which tells us Doctor Who is on TV, in order to have the right to infer
that it is Saturday.
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The above example also shows us that sometimes the ‘then’ is left unstated. We have to
watch out for this in everyday contexts.
Do conditionals tell us anything else? Consider (B) again, and assume that premise (p1)
is true. Imagine that we are told that, as a matter of fact, it is not Saturday. Can we infer
anything from that?
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Exercise 5: Conditional statements 1
What conclusions can we draw from the following sets of premises?
(1)
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is not Saturday.
(2)
(p1) If it is raining, then I will get wet.
(p2) I am not getting wet.
(3)
(p1) If it is raining, then I will get wet.
(p2) It is raining.
(4)
(p1) If it is payday, then I will have money in the bank.
(p2) I do not have money in the bank.
(5)
(p1) If it is payday, then I will have money in the bank.
(p2) It is payday.
(6)
(p1) If the Conservatives won the last election, then Michael Howard would be PM.
(p2) Michael Howard is not PM.
(7)
(p1) If the Conservatives won the last election, then Michael Howard would be PM.
(p2) The Conservatives won the last election.
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The preceding should suggest that there are two legitimate conclusions that we can draw
based upon a conditional statement. If we know the conditional and know that the
antecedent is true, then we can infer the consequent. For example:
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) Doctor Who is on TV.
Therefore,
(c) it must be Saturday.
If we know the conditional and know that the consequent is false, then we can infer that
the antecedent is false. For example:
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is not Saturday.
Therefore,
(c) it is not the case that Doctor Who is on TV.
What about anything else? If we know the conditional and know that the consequent is
true, does that tell us anything? Consider:
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is Saturday.
No – specifically, we cannot infer that Doctor Who is on TV. It could be three o’clock on
Saturday morning, or quarter past one in the afternoon. Doctor Who might have been
cancelled to make way for a football match.
What about if we know the conditional and know that the antecedent is false? Again, we
cannot draw any inferences from this. Why?
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Exercise 6: Conditional statements 2
(1)
Use the examples from Exercise 5 to show:
•
if we know that a conditional statement is true and also that its consequent is true, we
cannot infer anything about the truth or falsehood of the antecedent
•
if we know that a conditional statement is true and also that its antecedent is false, we
cannot infer anything about the truth or falsehood of the consequent.
(2)
Construct four conditional statements based on the Wason – Johnson-Laird experiment.
For your first premise, use the conditional claim: if there is a circle on one side of the
card, then there will be a smiley face on the other side.
For your second premise, use a description of the face of the card you can see.
Example: for the first card, you would have:
(p1) If there is a circle on one side of the card, then there will be a smiley face on the
other side.
(p2) There is a circle on one side of the card.
Ask yourself if you can infer anything from the two premises. How does this help us test
the rule?
Now do the same for the other cards.
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b) ‘Or’ statements
The next statements we will consider are those which use the word ‘or’. The word ‘or’,
often used with ‘either’, is one of the most common words in the language. It features in
statements such as:
•
•
•
•
•
•
The baby will be male or it will be female.
Either John will win the election or David will.
You can have the chocolate or the cake.
I will go to the cinema or the concert.
To gain entry to the college, you need three Bs or two As.
I will become a teacher or a social worker.
Such statements have an important place to play within critical thinking. Just as with
conditionals, this is because they serve to connect the truth of two statements, although
in a very different way from ‘if… then…’. Rather than saying that the second statement is
true if the first is, ‘or’ statements claim that at least one of the statements is true. So the
following are true:
•
•
•
•
•
Either the Allies won the war in Europe or Germany and Italy did.
Either Tony Blair won the election or Michael Howard did.
Killing is always wrong or it is not always wrong.
Lee Harvey Oswald shot John Fitzgerald Kennedy or someone else did.
You can get into university with three Bs or you can get into university with 2 As.
Whereas these are not:
•
•
•
The moon is made of cheese or it is made of glass.
Edinburgh is in Germany or it is in France.
Killing is always acceptable or theft is always acceptable.
Before we look at the way in which ‘or’ functions in an argument, there are two points to
which we need to pay attention. Firstly, it is worth stressing the fact that in critical
reasoning ‘or’ is used to connect two statements. This might appear to differ from
ordinary usage, in which ‘or’ does not always appear to connect statements. For example
we might say:
•
You can have cheese or beans on your baked potato.
Notice that ‘or’ is not being used to join statements here. This is not a problem for us, as
we can quite easily rewrite this statement as:
•
You can have cheese on your baked potato or you can have beans on your baked
potato.
This use of ‘or’ connects two different statements. By rewriting it in this way, we can
make the first statement, ‘you can have cheese or beans on your baked potato’, usable in
an argument.
The second thing we should note is that there are two different usages of ‘or’ in everyday
language. To see this, first consider the difference between these two statements:
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•
•
Well done, you’ve won first prize! You can choose either the car or the money!
For my birthday, I would like to get Star Wars or Pirates of the Caribbean on DVD.
In the first example, ‘or’ is used to mean ‘one or the other but not both’. In other words,
you do not have the option of choosing both car and money in the example – you can
only have one. This is called the exclusive sense of or, as it excludes the option of both.
Contrast that with the second example. Here the writer is telling us what she would like
for her birthday. Presumably, she is not saying that she only wants one or the other (the
best outcome would be to get both!). In other words, she is not using ‘or’ in its exclusive
sense. When ‘or’ is used in this other way, we can say that it is used in the inclusive
sense, according to which it means ‘one or the other or both’.
‘Or’ features in arguments in the following way. We are told that at least one of two
statements (joined by ‘or’) is true. When we find out that one of the options is not true,
this entails that the other option is the true statement from the original pair. Looking at
some examples will help clarify this.
Shani is either going to Glasgow University or she is going to Strathclyde University.
She is not going to Strathclyde.
Therefore, she is going to Glasgow University.
Kirsty was going to buy a book with her birthday money or she was going to buy a CD
with her birthday money.
She didn’t buy a book.
Therefore, she bought a CD.
Either we allow the execution of murderers or we condone the actions of murderers.
We do not condone the actions of murderers.
Therefore, we allow the execution of murderers.
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Exercise 7: ‘Or’ statements 1
(1)
Translate the following everyday sentences into sentences that use ‘or’ to connect two or
more statements. Once you have done this, state whether they use the inclusive or
exclusive sense of ‘or’ or whether they are ambiguous. If you think any of the sentences
are ambiguous, explain why.
a) On Monday, I will go to the shops or visit my Gran.
b) When I leave school, I want to be rich or famous.
c) You can study at university if you gain four Bs or two As and one B at Higher level.
d) At the University of Craiglang, you can study French, German, Spanish or
Portuguese.
e) The car key is in my hand or in my pocket.
f)
Sheila’s birthday is either on Monday or on Tuesday.
g) Craiglang FC will play Shieldinch Rovers or Auchterturra Rangers in the cup final.
(2)
Use your translations of a), e), f) and g) above to create arguments. You will have to
invent an appropriate second premise.
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c) ‘… and…’ statements
These statements are also known as conjunctions. We will pass over ‘and’ statements
quickly, as they are very straightforward. As with ‘or’, in critical reasoning we use ‘and’ to
join two statements (try to explain why!). The statements joined by ‘and’ are called
conjuncts.
Look at the following claims:
•
•
•
Grass is green and snow is white.
Grass is green and snow is purple.
2+2=5 and 3-1=3.
Ask yourself: which of these are true?
It seems that only the first of these sentences is true; it is the only example that has two
true statements joined by the word ‘and’. In the case of the second, the second conjunct,
‘snow is purple’, is false; for this reason, we want to say that the whole statement is false.
In the third example, both conjuncts are false. This should suggest to us – correctly –
that an ‘and’ statement is only true when it contains two true statements, otherwise it is
false.
In reasoning, we use ‘and’ statements in two, very straightforward, ways. If we are told
that a conjunction is true, then we can infer that both of the statements ‘and’ joins is true;
if we know that two statements are independently true, then we can create a conjunction
from them.
So, for example, ‘pigs are mammals and iguanas are reptiles’ entails both that ‘pigs are
mammals’ and that ‘iguanas are reptiles’. If we know that ‘December is later than May’
and that ‘May is later than February’ we can infer ‘December is later than May and May is
later than February’.
Notice that this means that it takes more for a conjunction to be true than it does for either
conjunct to be true. ‘A and B’ is a stronger claim than just ‘A’. Look back at the so-called
‘Conjunction Fallacy’ in Exercise 1 and think about your original answer again!
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d) ‘All’ and ‘some’
The fourth group of statements we will consider here are those using the words ‘all’ and
‘some’. These words are called quantifiers, as they are used to discuss quantities –
more than one example – of a particular kind of thing: all dancers are fit; some animals
lay eggs; some Scots can speak Spanish; all Spaniards can speak Spanish.
As you might think, the word ‘all’ is used to talk about every single thing of a particular
sort. If all humans are mammals, then every human is a mammal. If all positive numbers
are greater than zero, then every positive number will be greater than zero. If it is true to
say that all things of some-sort-or-other have this feature, then there is no room for any
exceptions to this.
‘Some’ is used to pick out a group of things of some sort or other. It does not pick out a
specified number of things; instead, we should read ‘some’ as meaning ‘one or more’. If
some dancers are Welsh, then there is at least one dancer who is Welsh. If some
humans are warm-blooded, then at least one human has warm blood. Notice that this is
compatible with the claim that all humans are warm-blooded; the claim that some humans
are warm-blooded is simply a weaker claim, in that it does not try to tell us any wider truth
about all human beings. So we should not take ‘some humans are warm-blooded’ to
imply that not all humans are warm-blooded.
What about sentences using words like ‘none’ or ‘no’? How should we understand the
following claim?
(N) ‘No reptiles have warm blood.’
Sentences of this sort seem to be working like the sentences involving quantifiers above,
yet it does not seem to use any quantifier. If we are to understand what is going on, we
should ask ourselves what this sentence tells us. Look at the following options:
•
•
•
•
•
Some reptiles do not have warm blood.
Some reptiles have warm blood and some reptiles do not have warm blood.
Some reptiles have warm blood or some reptiles do not have warm blood.
It is not the case that all reptiles have warm blood.
It is not the case that some reptiles have warm blood.
Which of the above are consistent with statement N (ie. can be true at the same time as
N), which are inconsistent with N (cannot be true at the same time) and which is
equivalent to N (means the same thing as N)? Let us look at these one by one.
The first sentence, ‘some reptiles do not have warm blood’, makes the claim that at least
one reptile does not have warm blood. This is consistent with statement N but does not
seem to make as strong a claim as N does.
The second, ‘some reptiles have warm blood and some reptiles do not have warm blood’,
seems inconsistent because of the first claim joined by the word ‘and’. If N is true, then it
seems that ‘some reptiles have warm blood’ must be false.
The third, given that it uses ‘or’, only needs one of the two component statements to be
true for the whole statement to be true. As we have just seen, ‘some reptiles do not have
warm blood’ is true but not equivalent to N.
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‘Some reptiles have warm blood’ is false, though this does not have any effect on the
truth-value of the whole disjunction. The third statement does not improve on the first as
an attempt to give the meaning of N.
It might seem that the fourth statement, ‘it is not the case that all reptiles have warm
blood’, is equivalent to N. However, to think so would be a mistake, in that ‘it is not the
case that all reptiles have warm blood’ is consistent with some reptiles having warm blood
– it does not rule out this possibility, after all, whereas N does. The fourth statement is
consistent with N, but is not equivalent to it.
The final option, ‘it is not the case that some reptiles have warm blood’, is equivalent to N.
It entails that not even a few reptiles are warm-blooded; in other words, that no reptiles
are warm-blooded. So when we come across a statement to the effect that no things of
some sort have a certain property, we should read it as saying that it is not the case that
some things of some sort have a certain property.
The ability to tell which statements can be true at the same is crucial to critical thinking
(we will return to why this is so later). Given this, we will have to be able to tell which
sentences using ‘all’ and ‘some’ are consistent with each other (can be true at the same
time).
One way to check for consistency is to use Venn diagrams. These are diagrams that
allow us to graphically represent the connections between different sets through the use
of overlapping shapes such as circles.
For example, if we are interested in two sets of things, say reptiles and warm-blooded
animals, we could use a diagram of the following sort to represent the possible
connections:
Warm-blooded
things
Reptiles
Fig. 1
This gives us four distinct areas within the two circles. The overlapping area is the area
of things which are both reptiles and warm-blooded, since it falls within both circles. The
area to the left of that falls within the set of reptiles but not the set of warm-blooded
things, so it is the set of reptiles that are not warm-blooded. The third area, to the right of
the overlap, is the set of warm-blooded things that are not reptiles. Finally, the fourth
area, the area within the rectangle but outside both circles, is the set of those things that
are neither reptiles nor warm-blooded.
Every statement we can make with a quantifier can be represented on a diagram like this.
Furthermore, if statements are consistent, we should be able to represent all of the
statements on the one diagram.
Let us look briefly at the way we represent statements on Venn diagrams.
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To say that ‘no reptiles are warm-blooded’, we shade out the overlapping area to indicate
that it is empty (that nothing exists that is in both sets):
Warm-blooded
things
Reptiles
Fig. 2
To show that there is something in a set, for example that there are as a matter of reptiles
with warm blood, we put an ‘x’ in the relevant area:
Warm-blooded
things
Reptiles
x
Fig. 3
If we want to represent a statement involving a name, such as ‘Sid the Snake is a coldblooded reptile’, we could write an ‘S’ in the relevant area. Underneath the diagram, we
would have to provide a key that made it clear that ‘S’ represented Sid the Snake.
What should we do if we just want to indicate that there are reptiles, though? We cannot
put an ‘x’ in either the overlap or non-overlapping areas of the left circle, since we do not
know whether these reptiles are warm-blooded or not. Instead, we can put a question
mark in each of the areas indicating that there might be something within:
Warm-blooded
things
Reptiles
?
?
Fig. 4
(In a similar way, if we were only told ‘Sid is a reptile’, we would put ‘S?’ in the two
relevant sectors.)
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Combining statements within a Venn diagram can be very informative. For example, look
at what would happen if we combined the two statements, ‘no reptiles are warm-blooded’
and ‘some reptiles exist’. By the first statement, we would shade out the overlapping
area. So when it came to representing the second, there would be no need to put a
question mark in the overlapping area, as we would already know that nothing was to be
found in here. This would allow us to place an ‘x’ in the area representing the set of
reptiles which are not warm-blooded:
Warm-blooded
things
Reptiles
x
Fig. 5
Diagrams like this can be used to test for consistency and inconsistency. For example, if
you were to try to represent the statement ‘some warm-blooded things are reptiles’ on this
diagram, you would find yourself trying to put an ‘x’ in an area that was shaded out – an
area in which nothing exists, to put it another way. This would show that the statements
you were trying to represent could not all be true at the same time – that they were
inconsistent, in other words. That we were able to represent both of the statements ‘no
reptiles are warm-blooded’ and ‘Some reptiles exist’ in Figure 5 showed that they were
consistent with each other.
If we needed a Venn diagram with three overlapping sets, we would have to use one that
looked like the following (notice that all possible overlaps are represented).
Fig. 6
Sometimes, whether statements are consistent or not will be obvious to us. However,
using Venn diagrams provides us with a good and quick way of checking this.
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Higher Philosophy Critical Thinking Support Notes
Exercise 8: Quantifiers
We have to be very careful when considering arguments that use quantifiers. For each
set of statements below, use Venn diagrams try to identify a set of three consistent
statements.
(1)
All pens are writing tools.
Some writing tools are pens.
Some pens are not writing tools.
Some writing tools are not pens.
(2)
Some superheroes wear capes.
Some supervillains wear capes.
No superheroes are supervillains.
Only superheroes wear capes.
(3)
All philosophers are smart.
No philosophers are scientists.
All smart people are philosophers.
All scientists are smart.
(4)
Some politicians are deceitful.
All well paid people are deceitful.
All politicians are well paid.
Some politicians are not deceitful.
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4. Recognising everyday arguments
It will be obvious that very few of the arguments we encounter in everyday life are
presented as a list of premises followed by a conclusion, all neatly numbered and
labelled. Instead, the conclusion is often mixed in with the premises and not clearly
indicated. Occasionally, important parts of the argument are often left implicit and not
openly stated – we will see just how important this can be when we look at fallacious
reasoning later.
In order to apply our critical thinking skills to the kinds of arguments we encounter in the
classroom, on television and in the newspapers, we need to be able to pick out those
crucial features of arguments that we have been considering; namely, the conclusion, the
premises and the structure.
This is a skill that we all possess to some degree. When we read newspapers, we can
tell what the writer is arguing for, even if she has not written ‘the conclusion of this
argument is that…’ or other words to this effect. One of the reasons for this is that we are
all competent speakers of the language, and one of the main purposes of language is to
convey information. We are usually very good at recognising what someone is trying to
bring us to believe.
Nevertheless, there are some good rules of thumb for trying to identify the conclusion of
an everyday argument. Conclusions are often indicated by words and phrases such as
‘therefore’, ‘so’, ‘thus’, ‘for these reasons’, ‘this shows us that’, ‘that is why’, etc.
Look at the following argument:
A baby is a lovely little gift from above. Who would ever want to refuse a gift, especially
one from so glorious a benefactor? If something is a gift from above, then it should not
be refused. That’s why contraception should be banned. It would be like refusing a
lottery win or a free two-week holiday abroad!
What is the conclusion here?
The answer is ‘contraception should be banned’. Notice that it follows the phrase ‘That’s
why’ – this indicates that reasons have been given for believing whatever it is that comes
after ‘that’s why’. This argument should also draw our attention to the fact that
conclusions can feature at the beginning, middle or end of an everyday argument.
Not every conclusion will be so indicated, though. When we look at passages of text with
the aim of identifying the conclusion, we have to look at the all of the text with the aim of
getting some idea of how it all fits together. What work is each sentence playing? Is it
the conclusion, a premise or just extra padding? The best way of developing your skills in
identifying conclusions is just to practice. Read letters in newspapers, editorial pieces,
opinion columns. Listen to speeches and debates, whether on television or in the
classroom. The more you do this, the better you will be at detecting how the various
claims made fit together.
One further point: conclusions can contain the sorts of connecting phrases we looked at
above. ‘France is in Europe and Brazil is in South America’ could be a conclusion. So
might ‘if dinosaurs still existed, humans would be in trouble’. We should not always
expect conclusions to be simple sentences.
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Exercise 9: Conclusions for everyday arguments
Look at the following arguments. Try to identify the conclusion.
(A)
There are good reasons why capital punishment should be banned. It devalues human
life and reduces us all to the level of murderer. If something treats life as worthless, then
it ought to be made illegal.
(B)
All killing is wrong. Squashing a fly is a way of causing a death. So squashing a fly must
be wrong.
(C)
The weather forecaster said it would rain today. I better take an umbrella. I don’t want to
get wet, after all.
(D)
France is in Europe. I’ve been there and they use Euros as money. They wouldn’t do
that anywhere else in the world.
(E)
I won’t do well in the exam. If I were to do well, I would’ve had to work hard. But I didn’t.
(F)
Scotland has the worst rate of heart disease in Europe, and bad diet is a major cause of
this. We ought to do something about it. That’s why we should stop selling burgers,
chips and fizzy drinks in the school dining room. There are plenty of healthier foods that
we could be selling instead.
(G)
Scooby is a coward and so is Shaggy. Any time something scary happens, they both run
away. If they run away all of the time something frightening happens, then they are
cowards!
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Once we have developed our skills in identifying conclusions, we should turn our attention
to the rest of the passage. What are the premises? What is the structure of the
argument?
In order to establish this, we have to look for two features in the passage: recurring
phrases (or, at least, phrases that have the same meaning) and key terms that indicate
sentence structure: ‘all’, ‘some’, ‘if…, then…’, ‘and’, ‘or’. We can then try to fit the
sentences together in a way that best captures the speaker’s intentions. This is not
always possible; some speakers might just blurt out a stream of sentences, with little or
no obvious connections. We do not need to worry about such things at this stage,
though. The passages we will be looking at will contain arguments that a competent
critical thinker should be able to detect after a little practice.
As mentioned in passing a moment ago, in everyday language speakers and writers do
not always use identical phrases when repeating a point. For example, someone might
say:
We should not accept what the Prime Minister has said. Tony Blair has got it wrong on
many occasions.
Or:
Capital punishment should be reintroduced in this country for football hooligans. The
death penalty should stop them from causing mayhem!
Clearly, the name ‘Tony Blair’ and the phrase ‘the Prime Minister’ are intended to pick out
the same person in the first example, and ‘capital punishment’ and ‘the death penalty’ are
used to talk about the same form of punishment in the latter. When we spell out the
argument in terms of labelled premises and a conclusion, we should try to use the same
phrase to make the structure of the argument completely clear.
How do we tackle this? In order, we should try to:
•
•
•
•
identify the main conclusion
identify the premises
identify any hidden premises
find the structure of the argument.
Let us look at an example of an everyday argument to see how this works in practice.
If Highers were difficult, lots of people would fail them. The pass rates are very high. So
our exams are easier than we are being told. It’s not like it was in my day!
What is going on here?
Firstly, we have to identify the conclusion. Let us write the sentences out one by one to
make it easier to spot.
1. If Highers were difficult, lots of people would fail them.
2. The pass rates are very high.
3. So our exams are easier than we are being told.
4. It’s not like it was in my day!
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Notice the use of the word ‘so’ at the start of sentence 3 – this is usually an indication that
what comes next is the conclusion. This seems to be the case here, in that it appears
that the author is arguing for the claim that ‘our exams are easier than we are being told’.
So far, then, we have:
Therefore,
(c) Our exams are easier than we are being told.
(We don’t need to write the ‘So’ – this indicates a conclusion but is not part of it. The
‘therefore’ plays the same role.)
It would be useful at this point to note that we do not need to write ‘Therefore’ in this
fashion in every argument. Instead, it is acceptable to draw a line between the premises
and the conclusion like this:
_________________________________________
(c) Our exams are easier than we are being told.
(This line is called the inference bar.)
Returning to our argument, the next things we need to look for are the premises. There
are three other sentences.
1. If Highers were difficult, lots of people would fail them.
2. The pass rates are very high.
4. It’s not like it was in my day!
Are all of these premises? Look for repeated phrases, or phrases that mean the same
thing. There are no repeated phrases, but sentences 1 and 2 seem plausibly to be about
the same thing – the numbers of people passing exams.
Are there any words relating to argument structures? Yes – sentence 1 uses the word ‘if’
– it is an ‘if…, then…’ sentence, even though the ‘then’ is left unwritten. This gives us:
(p1) If Highers were difficult, lots of people would fail them.
(p2) The pass rates are very high.
_________________________________________
(c) Our exams are easier than we are being told.
What about sentence 4? Is this doing any significant work in an argument? It appears
not. Instead, the author is simply giving some anecdotal information about what went on
when he was at school.
So, does that mean we have finished with our argument? Not quite – the phrases used
are different, this making it more difficult than it might be to see the structure. We should
ensure that similar phrases are used to make the argument explicit.
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One option would be this:
(p1) If Highers were difficult, lots of people would fail Highers.
(p2) It is not the case that lots of people fail Highers.
_________________________________________
(c) It is not the case that Highers are difficult.
(Are there others?)
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Exercise 10: Formalising everyday arguments
Look at the following arguments. Try to put them into the standard argument form.
(A)
There are good reasons why capital punishment should be banned. It devalues human
life and reduces us all to the level of murderer. If something treats life as worthless, then
it ought to be made illegal.
(B)
All killing is wrong. Squashing a fly is a way of causing a death. So squashing a fly must
be wrong.
(C)
The weather forecaster said it would rain today. I better take an umbrella. I don’t want to
get wet, after all.
(D)
France is in Europe. I’ve been there and they use Euros as money. They wouldn’t do
that anywhere else in the world.
(E)
I won’t do well in the exam. If I were to do well, I would’ve had to work hard. But I didn’t.
(F)
Scotland has the worst rate of heart disease in Europe, and bad diet is a major cause of
this. We ought to do something about it. That’s why we should stop selling burgers,
chips and fizzy drinks in the school dining room. There are plenty of healthier foods that
we could be selling instead.
(G)
Scooby is a coward and so is Shaggy. Any time something scary happens, they both run
away. If they run away all of the time something frightening happens, then they are
cowards!
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We should not forget that some arguments feature hidden premises in addition to their
explicitly stated ones. We have to be on the lookout for these when formalising
arguments.
Hidden premises are usually those premises that are thought too obvious to state out
loud. Recall that we noted one example earlier when hidden premises were first
introduced.
How should we spot hidden premises? In general, they will be fairly easy to spot once
the conclusion has been identified. Most hidden premises will be fairly straightforward –
to see this, consider the following example:
The Police Chief (to his squad): Look, only two people knew where the informer was
hiding. Either Lieutenant Kojak here told the hitman where he was, or the new District
Attorney did. The DA must be the leak.
What is going on here? It looks like the argument runs as follows:
(p1) Either Lt. Kojak told the hitman where the informer was hiding or the District Attorney
told the hitman where the informer was hiding.
__________________________________
(c) The District Attorney told the hitman where the informer was hiding.
This is not enough to give us a valid argument, though. Is the speaker leaving something
implicit? Is there a hidden premise?
Yes there is: that it is not the case that Lt. Kojak told the hitman where the informer was
hiding. This gives us:
(p1) Either Lt. Kojak told the hitman where the informer was hiding or the District Attorney
told the hitman where the informer was hiding.
(p2) It is not the case that Lt. Kojak told the hitman where the informer was hiding.
__________________________________
(c) The District Attorney told the hitman where the informer was hiding.
Why did the Police Chief not make this premise explicit to his squad?
Here’s a rather more difficult example.
A baby is a lovely little gift from above. Who would ever want to refuse a gift, especially
one from so glorious a benefactor? If something is a gift from above, then it should not
be refused. That’s why contraception should be banned. It would be like refusing a
lottery win or a free two-week holiday abroad!
(p1) A baby is a gift from above.
(p2) If something is a gift from above, then it should not be refused.
(p3) Contraception amounts to the rejection of gifts from above.*
(p4) Anything that amounts to the rejection of gifts from above should be banned.*
_____________________________
(C1) Contraception should be banned.
(Notice the way in which I have marked hidden premises with an asterisk. Any hidden
premises you find should clearly be indicated.)
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Note the two hidden premises. Why did we need these?
To see why, compare the other, explicit premises with the conclusion. In the first
argument, the conclusion mentions contraception and banning; neither appear in either of
the two explicit premises. We need something to tie claims about gifts from above to
claims about banning contraception; in other words, we need further premises that link
these ideas. (p3) links contraception to gifts from above and (p4) links gifts from above to
banning. This provides the argument with the structure required in order to allow for
detailed evaluation.
The general idea is that much of the connecting work, and therefore much of the
structural work, is often done by hidden premises. When looking for hidden premises we
need to look for those claims that would serve to connect the premises to the conclusion
and make explicit the structure of the argument. One way to do this is to look for phrases
or terms that we would expect to be repeated given their importance to the argument.
Of course, it is always possible that there will be more than one plausible reconstruction
of the argument using hidden premises. When we look for hidden premises, we should
try to stay as close as we can to the speaker’s intentions, as we perceive them. We
should always be ready to make a case for saying why a particular hidden premise has
been proposed.
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Exercise 10a: Formalising everyday arguments with hidden premises
Look at the following arguments. Try to put them into the standard argument form.
Include any hidden premises that are required.
(A)
If Descartes was an empiricist, then every philosophy book published about Descartes
has been wrong. Descartes was no empiricist.
(B)
Muir and Elizabeth should be sacked.
doesn’t deserve to remain in charge.
Anyone who badly mismanages a company
(C)
Smacking infants is no way to instil a sense of morality in children. If something is to
make children think in terms of right and wrong, it has to do more than inflict pain in a
brutal fashion.
(D)
If something is human, then it must be capable of sophisticated thought and appreciate
art, culture and the like. By these standards, we have to say that Jonah isn’t a human.
(E)
All bloodsports are evil. They all involve inflicting unnecessary suffering and taking
pleasure in another creature’s pain.
(F)
The choice is stark: either we ensure that cannabis abuse remains a criminal offence or
we face a generation of children addicted to killer drugs, sharing potentially infected
needles with a criminal underclass. We should ban cannabis now!
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Reliable and Unreliable Arguments
1. Reliable arguments: what makes a ‘good’ argument?
We have now covered the basic building blocks of arguments and looked at some
important argument structures and connectives. The time has now come to look into
what makes an argument good or bad.
Earlier, we noted that the premises of an argument should give us reason or justification
to accept the conclusion as true. We also noted that the relationship between the
premises and the conclusion was of central importance for this idea of justification or
support. Intuitively, good arguments are those arguments that give us good reason to
accept the truth of the conclusion.
There is, however, a crucial distinction we need to make here in order to clarify the idea
of a good argument. Some arguments will help us to identify the reason why such a
distinction is required.
(A)
(p1) If John has £10 and is over 12, then he can buy Batman Begins from Amazon.
(p2) John is over 12.
(p3) John has £10.
(c) Therefore, John can buy Batman Begins from Amazon.
(B)
(p1) All Bryan Singer films are worth seeing.
(p2) Superman Returns is a Bryan Singer film.
(c) Therefore, Superman Returns is worth seeing.
(C)
(p1) All arguments used as examples in philosophy classes are really dull.
(p2) This is an argument used in a philosophy class.
(c) Therefore, this argument is really dull.
(D)
(p1) All students are lazy and work-shy.
(p2) [insert your name here] is a student.
(c) Therefore, [insert your name here] is lazy and work-shy.
What can we say about each of these arguments? Do the premises give us reason to
accept the truth of the conclusion?
It appears that they do (we will see why in a moment). Nevertheless, we might be
hesitant about endorsing some of them. You might be reluctant to accept (p1) from (D),
for example, given the conclusion it leads to! In a similar way, you might find Bryan
Singer’s films not worth seeing (or the arguments used in philosophy classes exciting,
unlikely as this might seem).
This shows that we need to be clearer about what a ‘good’ argument is. The distinction
between validity and soundness is used for just this purpose. We will look at these in
turn.
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a) Valid and invalid arguments
Turning first to validity, we need to draw a distinction between valid and invalid
arguments. Validity concerns the structure of an argument, more specifically the
connections between the premises and the conclusion. If an argument is valid, you
cannot have true premises and a false conclusion.
All of the arguments (A) – (D) above are valid. That is to say, if their premises are true,
then their conclusions must also be true. The conclusions cannot be false while the
premises are true. It doesn’t say that the premises are true, we should note. Valid
arguments can have false premises – they just cannot have true premises yet false
conclusions.
Note one interesting consequence of the fact that validity is concerned with the structure
of arguments. If two arguments have the same structure, then either they both must be
valid or they both must be invalid. Consider:
(p1) If Babe is a piglet, then he will be lovely and cuddly.
(p2) Babe is a piglet.
(c) Therefore, Babe will be lovely and cuddly.
(p1) If Babe is a piglet, then he will taste nice fried.
(p2) Babe is a piglet.
(c) Therefore, Babe will taste nice fried.
These have the same structure. In both, we have two premises, consisting of (i) a
conditional and (ii) the antecedent of a conditional. The conclusion is then the
consequent of the same conditional. Such arguments are valid due to the structure they
possess.
Clearly, not every argument is valid. If an argument can have true premises but a false
conclusion, then it is an invalid argument. Here, again, is a very obvious one:
Grass is green.
Snow is white.
Therefore, all dogs are mammals.
This argument is unlikely to fool anyone into believing the truth of the conclusion. It is
perfectly consistent with grass being green and snow being white that all dogs are not
mammals.
This reveals an interesting feature about invalid arguments: they can have true premises
and a true conclusion. The reason for this is that validity concerns the relations between
the premises and the conclusion – or the structure of the argument, in other words.
More interesting are those invalid arguments that might convince the inattentive reader.
These are the arguments that we have to be on the lookout for – we do not want to be
poor critical thinkers, after all.
We can find some interesting examples of invalid arguments by looking back at
conditional statements. As you will remember, we looked at the following arguments:
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(p1) If Doctor Who is on TV, it must be Saturday.
(p2) Doctor Who is on TV.
Therefore,
(c) it must be Saturday.
and
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is not Saturday.
Therefore,
(c) it is not the case that Doctor Who is on TV.
We can now say that these two arguments are valid. If the premises are true, the
conclusion will also true. It is not possible for the premises to be true while the conclusion
is false.
What about the other possible arguments involving conditional statements?
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is Saturday.
Therefore,
(c) Doctor Who is on TV.
and
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is not the case that Doctor Who is on TV.
Therefore,
(c) It is not the case that it is Saturday.
Are these valid or invalid? We will look at some tactics for determining this shortly.
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b) Sound and unsound arguments
Given that valid arguments can have false premises (and also false conclusions), we
clearly need some other distinction between those valid arguments with true premises
and those without. This is where the notion of soundness comes in. Sound arguments
are just those valid arguments that also have true premises. With these two distinctions
in place, we can drop our ambiguous talk of ‘good’ and ‘bad’ arguments. Instead, we can
talk of invalid and valid arguments, and sound and thus valid and unsound arguments.
Arguments can be unsound in one of two ways: either by being invalid or by having false
premises. Obviously, the arguments that you want to offer in your attempts to persuade
others are sound ones.
To labour the point somewhat, validity concerns the truth-preserving structure of
arguments, whereas soundness also concerns the truth of the premises.
Notice a consequence of this: you can have valid arguments for two opposing sides of a
debate (eg. ‘Britain should join the Euro’ and ‘it is not the case that Britain should join the
Euro’), but you cannot have sound arguments on both sides.
The above also points to two ways of countering an argument:
•
We could attempt to show that the conclusion does not follow from the premises – the
premises could be true but the conclusion still false. This would be to try to
demonstrate that the argument is invalid.
•
We could attempt to show that at least one of the premises is false. This would be to
try to demonstrate that the argument is unsound (even if it was valid).
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Exercise 11: Validity and soundness
(1) Are the following arguments valid or invalid, sound or unsound?
(A)
(p1) All Kryptonians are super-powered.
(p2) Superman is super-powered.
_____________________________
(c) Therefore, Superman is a Kryptonian.
(B)
(p1) All humans are mortal.
(p2) Clark Kent is human.
__________________________
(c) Therefore, Clark Kent is mortal.
(C)
(p1) If David Cameron is the leader of the opposition, then the leader of the opposition is
not Scottish.
(p2) The leader of the opposition is Scottish.
__________________________
(c) David Cameron is not the leader of the opposition.
(D)
(p1) All Premier League football players are rich.
(p2) All rich people own more than one house.
__________________________
(c) All Premier League football players own more than one house.
(E)
(p1) All stars in the Horsehead Nebula are either red giants or white dwarfs.
(p2) Star EP4162X is not a white dwarf.
___________________________
(c) Star EP4162X is a red giant.
(2) Look at the above arguments. Why is it more difficult to check whether an argument
is sound than it is to check its validity?
(3) Explain why you can have valid arguments for two opposing sides of a debate.
(4) Try to construct two valid arguments, one for each side of a debate.
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2. Testing for validity
It is not enough to know what makes an argument valid. Given that we use arguments in
everyday life, we also need to know how to check whether an argument is valid. In other
words, even when we recognise that the premises are true, we need to know whether the
argument really gives us any reason to believe in the truth of the conclusion.
One way of doing this would be to try to memorise all of the valid argument structures.
However, this will not help as there are infinitely many of them! Skilled critical thinkers
will be able to recognise some common invalid argument forms, though – we will look at
some of these when we consider fallacious arguments below.
a) Counterexamples
The most straightforward way of testing for validity is through the use of
counterexamples. Recall that validity relates to the structure of arguments and that
arguments with the same structure are all valid or all invalid. If we are concerned that an
argument might be invalid, then we should try to see if it would be possible for an
argument with the same structure to have true premises but a false conclusion. To look
for an argument with these features is to look for a counterexample to the argument you
are trying to evaluate.
Imagine that you are trying to determine whether the following argument is valid:
(p1) If David Cameron is the leader of the opposition, then the leader of the opposition is
not Scottish
(p2) The leader of the opposition is not Scottish
__________________________
(c) David Cameron is the leader of the opposition
At the time of writing, both premises and conclusion are true. So we do not have true
premises leading us to a false conclusion in this case – we will have to investigate further
if we are to determine whether or not it is valid. In order to test its validity, we should pay
attention to the structure of the argument. Notice that the first premise is a conditional
statement – it asserts that if the antecedent statement is true, then so will the consequent.
We should also be able to see that the second premise is just an assertion of the
consequent. Finally, the conclusion is the antecedent of the conditional statement. In
other words, we have something that looks like this:
(p1) If [antecedent], then [consequent]
(p2) [consequent]
_________________________
(c) [antecedent]
Are arguments with this structure valid?
Well, one way to check is to try to find another argument with this structure that has true
premises but a false conclusion. If we can do this, then we will have demonstrated that
all arguments with this structure are invalid.
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Compare the above argument with this one:
(p1) If Keira Knightley is a man, then Keira Knightley is mortal.
(p2) Keira Knightley is mortal.
_______________________
(c) Keira Knightley is a man.
What can we say about this? The structure is the same as that of the argument in which
we are interested. Yet the premises are true (remember, the first premise does not assert
that Keira Knightley is a man!) and the conclusion false. This shows us that it is invalid.
The second argument is a counterexample to the first: it has the same structure, but has
true premises and a false conclusion. We should be able to construct similar
counterexamples for any invalid argument.
In order to be able to use counterexamples, it is helpful to develop a stock of statements
that can be used in the construction of counterexamples. If you have some favourite
statements, then you can bring them out when required in order to test any argument you
are worried about.
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Exercise 12: Counterexamples
Look at the following invalid arguments. Try to identify their structure by looking for
repeated statements and then try to develop counterexamples.
(1)
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is Saturday.
Therefore,
(c) Doctor Who is on TV.
(2)
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is not the case that Doctor Who is on TV.
Therefore,
(c) It is not the case that it is Saturday.
(3)
(p1) All Kryptonians are super-powered.
(p2) Superman is super-powered.
_____________________________
(c) Therefore, Superman is a Kryptonian.
(4)
(p1) All stars in the Horsehead Nebula are either red giants or white dwarfs.
(p2) Star EP4162X is not a white dwarf.
___________________________
(c) Star EP4162X is a red giant.
(5)
(p1) David Bowie is either a rock star or actor.
(p2) David Bowie is a rock star.
___________________________
(c) It is not the case that David Bowie is an actor.
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b) Venn diagrams, quantifiers and validity
Counterexamples are not the only way of testing validity. There is another way of testing
arguments that use quantifiers.
Recall that conclusions have to be more than consistent with their premises; instead, their
premises should entail their truth. In other words, we should be able to read off the
conclusion from the diagram once all of the premises have been represented. If we
cannot do this, then either the premises are inconsistent with the conclusion or both the
conclusion and its negation are consistent with them – either way, we would not have a
valid argument.
Here are two examples, one valid argument and one invalid argument:
All female birds lay eggs.
Henrietta is a female bird.
Therefore, Henrietta lays eggs.
and
All chickens have wings.
Henrietta has wings.
Therefore, Henrietta is a chicken.
Firstly, we should draw the appropriate Venn diagram:
Female birds
Egg-laying things
Fig. 7
Next, we have to look at how the first premise should be represented. It says that all
female birds lay eggs; so, in other words, if there are any female birds then they must be
in the overlapping area – the area of female birds that are also egg-laying things. This
entails that the left hand area is empty (there are no non-egg-laying female birds).
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Egg-laying things
Female birds
Fig. 8
Note that the order of the premises does not matter. We should tackle them in whichever
order makes it easiest to create an appropriate diagram.
Next, we need to represent Henrietta’s place on the map. She is a female bird, so she
should go into the left circle somewhere. The left circle is divided into two sections, as
can be seen from the diagram, so into which section should we place her? The answer
should be clear after a moment’s reflection: the left area is empty, so it must be the centre
overlapping area.
Egg-laying things
Female birds
H
Fig. 9
So, is the argument valid? Does Henrietta lay eggs? Yes; and we can read this off the
diagram.
Next, have a look at the following argument.
All chickens have wings.
Henrietta has wings.
Therefore, Henrietta is a chicken.
As always, we start by setting up our diagram. Notice that this time, the categories are
‘chickens’ and ‘things with wings’.
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Things with
wings
Chickens
Fig. 10
How do we represent the first premise?
Like this:
Things with
wings
Chickens
Fig. 11
What about the second premise?
This does not look as straightforward, since we have two possible places for things with
wings to reside.
Can we read off the conclusion, that Henrietta is a chicken? No, we cannot. So the
argument is invalid. All we know about Henrietta is that she has wings. This is consistent
with her being a dove, a pigeon, an aeroplane, etc.
Things with
wings
Chickens
H?
H?
Fig. 12
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Exercise 13: Quantifiers and validity
Which of the following arguments are valid? Test with Venn diagrams.
(I)
All humans are mortal.
Socrates is human.
Therefore,
Socrates is mortal.
(II)
All humans are mortal.
Socrates is mortal.
Therefore,
Socrates is human.
(III)
No chickens are athletes.
Foghorn Leghorn is a chicken.
Therefore,
It is not the case that Foghorn Leghorn is an athlete.
(IV)
Some chickens are athletes.
Foghorn Leghorn is a chicken.
Therefore,
Foghorn Leghorn is an athlete.
(V)
Some chickens are athletes.
Foghorn Leghorn is a chicken.
Therefore,
Foghorn Leghorn is not an athlete.
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3. Types of reasoning – deduction and induction
There is another distinction that it would be useful to draw at this stage, between
deductive and inductive arguments. This is a distinction that is of central importance,
within both the history of philosophy and everyday practice.
All of the arguments we have discussed so far are deductive arguments. Deductive
arguments are those arguments that aim at validity, as outlined above. In other words,
deductive arguments are arguments that attempt to give us reason to believe the truth of
a conclusion by giving us arguments that are truth-preserving: if the premises are true,
then the conclusion will also be true. With a valid argument, a true starting point always
guarantees a true conclusion.
Nevertheless, many useful everyday arguments do not share this feature. These are
inductive arguments. Rather than attempting to give premises that entail the truth of the
conclusion, inductive arguments attempt to generalise from evidence. That is, they
attempt to offer a conclusion about all things of a type by making observations about a
limited number of things of that type.
This is a familiar way of arguing within science. Some experiments will be performed
concerning, say the behaviour of a substance at certain temperatures. Once a decent
number of experiments have been carried out, all giving the same results, a hypothesis
will be introduced to the effect that the substance in question always behaves that way at
that temperature. So the argument attempts to reach a general rule based upon a finite
number of experiments.
Some examples should help to clarify the idea of an inductive argument.
All of the previous Harry Potter books have been good.
Therefore, the next Harry Potter book will also be good.
All shops in the UK took £ sterling yesterday.
All shops in the UK took £ sterling before yesterday and for as long as I can remember as
well.
Therefore, all shops in the UK will take £ sterling tomorrow.
The sun rose yesterday, and everyday before that for as long as the Earth has existed.
Therefore, the sun will rise tomorrow.
These are clearly useful. They provide a good guide as to what we should expect, given
what has happened in the past. It would seem reasonable to belief, based upon prior
experience, that shops in Scotland will take £ sterling tomorrow. Likewise, we should not
lie awake worrying whether the sun will rise tomorrow. Since we will not have read any
new Harry Potter book that might be published in the future, all the evidence we can have
about its quality comes from the quality of the preceding books.
We can identify bad inductive arguments, though.
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All of the people in this room speak English.
Therefore, all people speak English.
I wear glasses.
Therefore, all humans wear glasses.
These arguments have the same structure as the earlier ones, and thus are
counterexamples to the arguments. The fact that we can find such counterexamples
shows us that inductive arguments – by their very nature – are deductively invalid.
There are serious problems with inductive reasoning – it is extremely difficult to
distinguish between good and bad inductive arguments. One reason is that such
arguments do not carry the guarantee that deductive ones do. For all inductive
arguments, it remains the case that their conclusions could be false while their premises
are true. Logic cannot rule out the possibility that the next Harry Potter book might be
awful, nor that the UK will sign up for the Euro some time in the near future. Whether we
can determine what makes an inductive argument good or bad is a significant
philosophical issue, and we will not explore it here.
In light of our earlier discussion of hidden premises, it is worth noting that every inductive
argument can be converted into a valid deductive argument through the addition of an
extra premise – usually ‘all unobserved “x”s will be like observed “x”s or ‘all future “y”s will
be like past “y”s’. Try adding an extra premise into each of the examples above to render
them valid.
This raises the question: why don’t we just do that? Why not just treat inductive
arguments as valid deductive arguments of a certain sort? One reason concerns the
extra premise that would be required. What grounds could we possibly have for holding
that all unobserved things are like observed things, or that the future will be like the past?
We haven’t seen the unobserved things or the future, so the only grounds we would have
for accepting the truth of the premises would be that arguments like this had worked in
the past – and this is inductive evidence!
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4. Unreliable arguments: fallacies
a) Introduction to fallacies
Fallacies are types of arguments that display errors in reasoning of a certain kind. As we
will go on to see, they tend to be persuasive, common and hard for the uncritical thinker
to spot. Fallacies crop up everywhere – it is rare to watch a debate on Question Time for
example and not find a fallacy or two cropping up. As serious critical thinkers – as
people, in other words, who are determined not to be swayed by poor arguments or nonrational reasons – we have to be on the lookout for fallacies. In a similar way, we should
seek to avoid using fallacies when giving our own arguments. To do this is to cheat in
reasoning – it is to seek to persuade listeners without giving them good reason to accept
whatever it is we are arguing for. For these reason, we should familiarise ourselves with
some of the more common fallacies that appear in everyday contexts. That way we will
recognise them when we encounter them and should be able to avoid using them in our
own arguments.
Not every mistake in reasoning counts as a fallacy, though – arguments that just offer any
old false premise are not, for example. Instead, fallacies are genuine arguments – that is,
genuine attempts to persuade us to accept a conclusion on the strength of the premises
and the structure of the argument – it is just that the arguments contain particular sorts of
flaws in their reasoning. Sometimes there is a structural error in the reasoning,
sometimes it will display a common pattern of bad reasoning that will not give the
audience any reason to accept the conclusion offered, other times the argument will
contain a false premise of a very general sort. In the case of the last sort, these very
general premises usually will remain implicit. Making them explicit is often enough to
reveal why we should not believe any conclusion that is based on such a premise. We
have already seen two fallacies of the first sort:
(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is Saturday.
Therefore,
(c) Doctor Who is on TV.
This has the structure:
(p1) If [antecedent] then [consequent]
(p2) [consequent]
____________
(c) [antecedent]
This is called the fallacy of affirming the consequent, as the second premise asserts or
affirms the consequent. What makes this a fallacy is that it involves a systematic error in
reasoning. Specifically, it involves using arguments with a faulty connection between the
premises and the conclusion – any argument with this structure will allow for the
possibility of true premises plus false conclusion. (Fallacies with structural faults like this
are often called formal fallacies.)
The other mistake in reasoning involving a conditional that we noticed earlier was:
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(p1) If Doctor Who is on TV, it must be Saturday.
(p2) It is not the case that Doctor Who is on TV.
Therefore,
(c) It is not the case that it is Saturday.
This has the structure:
(p1) If [antecedent] then [consequent]
(p2) It is not the case that [antecedent]
____________
(c) It is not the case that [consequent]
This is called the fallacy of denying the antecedent, as the second premise states the
opposite of or denies the antecedent. As with the previous fallacy, there is a mistake
concerning the connection between the premises and the conclusion – the truth of the
former does not guarantee the truth of the latter.
Remember, validity is a feature of the structure of arguments. If an argument is valid,
then any other argument with the same structure is also valid. If an argument is invalid,
then any other argument with the same structure is also invalid. That these two
structures are invalid can be demonstrated through the use of counterexamples. You
should be able to construct a counterexample for each of these arguments.
In the remainder of this section, we will look at the following fallacies:
•
•
•
•
•
•
•
•
circularity/begging the question
slippery slope
post hoc ergo propter hoc
false dilemma
attacking the person
appeals to consequences
appeals to illegitimate authorities
arguments from ignorance (or appeals to ignorance).
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b) Begging the question/circularity
One of the most famous fallacies is a rather obvious one that involves a particular pattern
of reasoning, one that fails to give the audience any ground for accepting the truth of the
conclusion. Despite this, it is not uncommon and even can be plausibly found in one of
the greatest works of Western philosophy, René Descartes’ Meditations on First
Philosophy (published in 1641).
‘Begging the question’ is a phrase that is often misused in everyday discussion. It does
not mean ‘raising the question’. For example, this is an incorrect usage of the phrase:
Tajinder: We will see how Gordon Brown does in the next general election. That will tell
us whether or not people prefer his policies and beliefs to those of Tony Blair.
Ruth: That begs the question of whether Brown will take over as Labour leader from Tony
Blair.
Ruth means that Tajinder has raised the question of whether Brown will succeed Blair as
leader of the Labour Party. This is to misunderstand the meaning of the phrase.
To beg the question is to presuppose the conclusion being argued for. Here is an
example:
David: Look, women shouldn’t become soldiers.
Anna: Why not?
David: Because it’s a job for men only!
What is wrong with this argument? It could be shown to be valid, after all. To see the
problem, ask yourself if the argument would give someone who didn’t accept the truth of
the conclusion any reason to accept it.
The answer is that it would not. The conclusion, that women shouldn’t be soldiers, is
already presupposed by the premises, in which it is asserted soldiering is a job for men
and only men. To say this is just to say that women should not do it.
Here is another example:
(p1) The Bible says that God exists.
(p2) The Bible is the true Word of God.
___________________________
(c) God exists.
Do the premises give someone who does not already believe in the existence of God
reason to do so? No – because they presuppose that God exists! Begging the question
involves using an argument with a structure like this:
{Premises including the claim that p (where p is some statement)}
___________________________
(c) p
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Circular arguments are closely related to the fallacy of begging the question. Instead of
one argument featuring its conclusion amongst its premises, it involves a chain of
reasoning that is circular in the following way: the first argument uses premise p to
argument for conclusion q and the second argument uses q as a premise to argue for
conclusion p.
As with begging the question, circular reasoning will be valid and can be sound. It does
not, however, offer the listener any good reasons for accepting the truth of the
conclusions.
Here is an example of circular reasoning:
(Argument I)
(p1) The Bible says that God is no deceiver.
(p2) Whatever the Bible says is true.
___________________________
(c1) God is no deceiver.
(Argument II)
(p3) God is no deceiver.
(p4) The Bible is the Word of God.
___________________________
(c2) Whatever the Bible says is true.
(The conclusions have also been numbered to make it easier to refer to them.)
These arguments are both valid. However, if we follow the reasoning for each of the
conclusions we find that one of the premises for that conclusion is base on another
argument that takes that conclusion for granted. To see this, look at the chain of
reasoning for each of the conclusions.
Start with the reasoning to the conclusion ‘whatever the Bible says is true’. We get this
conclusion from two premises, (p3) ‘God is no deceiver’ and (p4) ‘the Bible is the Word of
God’. But what grounds do we have for believing the first of these? The arguer tries to
base this on two other premises (p1) ‘the Bible says that God is no deceiver’ and (p2)
‘whatever the Bible says is true’. But look: (p2) is just the conclusion for which we are
looking for justification! (Try to give details of the chain of reasoning to the other
conclusion yourself.)
The following is a more advanced example that will be of relevance if you go on to study
the writings of René Descartes.
Descartes is accused of circular reasoning in relation to a couple of key moves that he
makes over the course of his Meditations. The accusation against Descartes arises in
relation to the connection between what has come to be known as his ‘clear and distinct’
rule (‘all that we clearly and distinctly perceive is true’) and the role that God plays in his
philosophical system. Consider the following sketch of an argument:
(p1) If God exists, then he is no deceiver.
(p2) If God is no deceiver, then all I clearly and distinctly perceive will be true.
(p3) God exists.
__________________
(c1) All I clearly and distinctly perceive is true.
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Is this valid? Now consider the following simplified argument:
(p4) All I clearly and distinctly perceive is true.
(p5) I clearly and distinctly perceive the idea of God.
(p6) The idea of God is a true idea.
_________________
(c2) God exists.
Is this a valid argument, or could it be made into one? Let us assume that it could be.
Then we will have two perfectly valid arguments. So what’s wrong?
The key to getting to the heart of the problem with this pair of arguments is in
remembering the purpose of an argument. An argument is a device for rationally
persuading another to accept your conclusion. The suggestion here is that while an
argument may be valid, it need not be rationally persuasive. Why this is so concerns the
reasons we have or lack for accepting the truth of the premises of the argument.
Descartes is attempting to argue from his methodological sceptical position back to the
claim that he can safely believe pretty much everything he believed before free from
worries about deceiving demons and the like. What’s more, he is trying to convince the
reader of the validity and soundness of his arguments too.
What is deeply unsatisfying about Descartes’ arguments is that they are supposed to help
us build upon one’s certainty about one’s own existence and re-establish that our beliefs
are true. The problem is that both of the arguments above use more premises than he
seems entitled to: in the first case, we have ‘God exists’; in the second ‘all that we clearly
and distinctly perceive is true’. Given Descartes’ sceptical challenge, we cannot accept
these without further reason.
This is where the circularity comes in. Descartes apparently provides arguments in
support of the key premises, but each of the argument employs the other disputed
premise. In other words, in each case the desired conclusion has actually already been
assumed as a premise.
It is worth stressing that both of these arguments are valid, even though a fallacy is being
committed. So fallacious arguments needn’t be invalid.
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Exercise 14: circularity and begging the question
1. Construct an argument that begs the question for each of the following claims:
(a) Killing is wrong.
(b) I exist.
(c) The Arctic Monkeys have no talent.
(d) The TV programme Casualty has no educational value.
(e) Chocolate tastes nice.
Explain why the arguments beg the question.
2. Construct circular arguments for the following pairs of claims:
(a) Killing is wrong; killing is illegal.
(b) I think; I exist.
(c) The Arctic Monkeys are rubbish; The Arctic Monkeys have no talent.
(d) Wonder Woman is brave, strong and good; Wonder Woman is heroic.
(e) Stephen Hawking is intelligent; Stephen Hawking is not stupid.
Explain why the arguments are circular.
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c) The slippery slope fallacy
The slippery slope fallacy involves arguing that one thing will inevitably lead later to
another, without further argument. It is a favourite of politicians and such arguments
often appear in discussions concerning the legalisation of something or other –
homosexuality, some drug or other, the genetic modification of crops, stem cell research,
and so on.
The standard move made by arguments committing this fallacy is that once one step has
been taken in a certain direction, there is nothing to prevent further (and therefore more
extreme) steps being taken in that direction.
Here are two examples:
I’m not giving you any exam tips! The next thing I know, you’ll be asking me to sit the
exam for you!
and
We shouldn’t legalise cannabis – if we do, they’ll be selling crack from ice cream vans
within a year or two.
Notice that in each of these, a suggestion is rejected (that the teacher give exam tips, that
cannabis be legalised) on the grounds that it would lead to some further undesirable state
(the teacher sitting an exam for a student, crack cocaine being sold by ice cream vans).
There is, however, no argument given to the effect that the former suggestion if accepted
would lead to the latter, undesirable state of affairs.
Here is an everyday argument that commits the slippery slope fallacy:
There are too many people begging on our streets and some of them make a good living
out of it. If we don’t stop people begging we’ll soon find that most of the unemployed
people will start doing it to top up their benefits. Once they do it, people on low wages will
not want to work when they see people making money for doing nothing. Once those on
low wages take up begging, students at school won’t see the need for getting
qualifications. They’ll start begging rather than go to school. It won’t be long before
begging is the main option for people and our whole economic system will collapse.
As you can see the author has gone very quickly from people begging on the streets to
the collapse of our whole economic system. The problem is that the moves the author
makes are all too big to be justified and if we are not examining each move it is not too
long before we are well on the way down the slope.
The moves in the argument above are suspect right from the word go. Moving from the
fact that there are a lot of beggars to the idea that most unemployed people will start
begging is not justified. The next step to the low-paid becoming beggars is not justified
either and already we are sliding down the slope fast.
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Exercise 15: Slippery slopes
1. Create your own slippery slope argument for each of the following conclusions:
(a) The age at which people can legally drink should not be lowered.
(b) Scientists should not be allowed to engage in research on stem cells.
(c) Alcohol should not be advertised on television.
(d) Euthanasia should be legalised.
Explain what is wrong with the arguments.
2. Try to find other examples of slippery slope arguments from newspapers, television,
etc.
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d) Post hoc ergo propter hoc
Post hoc ergo propter hoc is a causal fallacy that involves a mistake concerning the
causal relationship holding between events. That is, the fallacy involves the formation of
beliefs concerning whether one event caused another based upon a false general
principle. The fallacy is committed when one argues that because an event, call it e2,
follows another event, e1, then e1 is the cause of e2. The Latin name basically states
this, translating as it does into ‘after this, therefore because of this’. Consider the all too
familiar argument:
Most ‘hard’ drug users start off as ‘soft’ drug users. This demonstrates that ‘soft’ drug use
causes ‘hard’ drug use
We can represent this as:
(p1) Most ‘hard’ drug users start off as ‘soft’ drug users
_________________
(c) ‘Soft’ drug use causes ‘hard’ drug use
What is assumed by those who put forward such arguments? It is the idea that because
soft drug use precedes hard drug use, then the former is a cause of the latter. This
fallacy is another of those that involve a substantive, general and usually hidden premise.
We can see this from the fact that, as it stands, the argument above is clearly invalid –
there is little to connect the premise to the conclusion, this suggesting that there is a
hidden premise in play.
(p1) Most ‘hard’ drug users start off as ‘soft’ drug users
(p2) When one thing precedes another, then the former is the cause of the latter*
_________________
(c) ‘Soft’ drug use causes ‘hard’ drug use
Notice that the hidden premise (marked by an asterisk) is very general and is effectively
just a translation of post hoc ergo propter hoc. Any argument using this premise is bound
to be a bad argument given that it is both highly general and false.
Look at the argument with the hidden premise added. Is this now valid?
In any case, it clearly isn’t sound. The second premise is false, as this less-familiar
parallel argument demonstrates:
(p1) Most hard drug users start off as breast milk users
_________________
(c) Banning breast milk use will prevent hard drug use
When we insert the hidden premise we get:
(p1) Most hard drug users start off as breast milk users
(p2) When one thing precedes another, then the former is the cause of the latter*
_________________
(c) Banning breast milk use will prevent hard drug use
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Inserting the hidden premise turns these into valid arguments, but the very general
principle (post hoc ergo propter hoc) is false. This does not, incidentally, show that there
is no causal connection between the two classes of events or kinds of behaviour; ‘soft’
drug use could cause ‘hard’ drug use – it’s just that the above argument does nothing to
demonstrate this, in that it makes no attempt to argue for the claim and relies instead on a
general, false premise.
Post hoc ergo propter hoc often rears its head in arguments about health scares. It is
often suggested that diseases or medical conditions are caused by some factor, which in
fact may just happen to temporally precede them. It has been suggested that this was
what was going on in the MMR jab controversy of a few years ago. Think of your own
examples.
More generally, the causal fallacy involves confusing the fact that two things are always
(or usually) found together for a relation of cause and effect. Just because there is a
correlation between x and y, it doesn’t follow that x causes y (or vice versa). The
following argument commits this fallacy:
(p1) The crime rate amongst the poorest in society is far higher than the crime rate
amongst the better off
_________________
(c) Poverty is a cause of crime
Now, it may be true that poverty is a cause of crime but the above argument doesn’t
constitute a sound argument towards this conclusion. There are probably statistical
correlations between those beings who understand language and those who cut their
toenails, but understanding language is not a cause of toenail cutting (or, possibly even
more obviously, vice versa). Instead, they are both just typically human activities.
The hidden premise will be something like:
(p1) The crime rate amongst the poorest in society is far higher than the crime rate
amongst the better off
(p2) Whenever two things are found together, one is the cause of the other*
_________________
(c) Poverty is a cause of crime
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Exercise 16: Post hoc ergo propter hoc
(1) Create arguments using post hoc ergo propter hoc involving the following statements:
(a) All humans are born; all humans die.
(b) Spider Man’s spider sense tingles; Spider Man gets into a fight.
(c) The students sat the course; the students sat the exam.
(2) Try to create some post hoc ergo propter hoc arguments of your own.
(3) Explain what is wrong with the above arguments.
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e) False dilemmas
Yet another bad way of arguing can be found in the use of false dilemmas. These use
‘either/or’ claims to suggest that there are only two options – two things that we might
believe or two ways of responding to a situation – one of which is clearly awful, so we
should accept the other. Consider this example of a rather common bad argument:
The country is being swamped by ‘asylum seekers’. We must prevent this. Either we
double the tax rate to pay for the easy lifestyle of these poor souls, or we stop allowing
immigrants into the country at all.
Look at what is going on here. Ask yourself: how does the arguer get to the conclusion?
Let us reconstruct the argument.
Presumably, the argument is supposed to look something like this:
(p1) We should do something to sort out the problem of false asylum seekers
(p2) If we have to do something about the problem of false asylum seekers, we can either
double the tax rate or stop all immigration
(p3) We should not double the tax rate
_______________________
(c) We should stop all immigration
Is there anything wrong with it? Look at (p2). Are these really the only two options?
False dilemmas are committed when an arguer presents the audience with only two
options or choices when in fact there are more. In the above example, it is clear that
there is a whole range of options other than just halting all immigration or doubling the
rate of tax, yet the arguer does not mention any of these.
When a couple’s marriage is in trouble they can do one of two things. They can just stand
back and let their relationship fall apart or they can get help from a counsellor. A
counsellor will help them talk through their problems and change their behaviour before it
is too late.
What is wrong with this argument? The answer is that it only considers two options
where there are actually many more. They could, for example, talk to each other. The
options do not have to be limited to two. The fallacy of false dilemma occurs when the
arguer does not give all the options that exist.
One recent example of a false dilemma concerned the ultimatum put to countries such as
France and Germany by George W. Bush at the start of the second Gulf war. The
suggestion was that ‘either you're with us, in which case you will support military action
and send troops when required, or you're against us, in which case you're against us’.
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Speaking after talks with French President Jacques Chirac, Mr Bush bluntly stated that
those nations not ‘for’ the US were ‘against us’.
‘A coalition partner must do more than just express sympathy,’ he said. ‘A coalition
partner must perform.’
‘All nations, if they want to fight terror, must do something... You're either with us or you're
against us.’
(http://news.bbc.co.uk/1/hi/world/europe/1642130.stm)
President Bush is certainly emphasizing the need for more active engagement by many
of those who have professed support for his coalition. ‘A coalition-builder must do more
than just express sympathy,’ he said Tuesday. ‘A coalition-builder must perform. All
nations, if they want to fight terrorism, must do something. It's time for action.’ And just in
case anybody missed the message, he added, ‘It's going to be important for nations to
know they will be held accountable for inactivity. You're either with us or you're against us
in the fight against terror.’
(http://www.time.com/time/columnist/karon/article/0,9565,183631,00.html)
Irrespective of one’s political views, it seems that the above is a false dilemma. It leaves
no room for those who agree on certain matters (eg. condemnation of terrorism and
states sponsoring terrorism) but disagree on others (eg. the appropriate response to such
terrorist attacks).
False dilemmas are valid arguments, it should be noted. They are of the form:
(p1) Either A or B
(p2) It is not the case that A
_______________________
(c) B
The problem comes with the ‘either-or’ premise, as can be seen from the above
examples. False dilemmas are valid but they are not sound.
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Exercise 17: False dilemmas
Create your own false dilemma for each of the following conclusions:
(a) Children should exercise for three hours a day.
(b) The age at which people can legally drink should be raised.
(c) Scientists should be banned from engaging in stem cell research.
(d) Alcohol advertising should be banned.
Explain what is wrong with these arguments by noting options other than those
mentioned in the dilemma.
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All of the remaining fallacies we will look at involve appeals to irrelevant considerations,
ie. factors that are not relevant to the truth of the conclusion.
f) Attacking the person
A very common fallacy is what is usually called the ad hominem fallacy. ‘Ad hominem’
means ‘to the man’. This sort of fallacious move involves an attack on the person
putting forward a claim, rather than a response to the claim itself.
Here are two examples:
George W. Bush tells us that terrorism is the greatest threat facing the world today.
George W. Bush was put into power by his father’s money and doesn’t have a brain
between his ears. Given this, it is safe to think that whatever he says about terrorism will
be wrong.
and
There is no reason to listen to academics concerning the depletion of fish stocks in the
North Sea. They sit in their ivory towers all day long and have never worked a day at sea
in their lives.
You can no doubt see what else would be required to turn these into valid arguments.
Attacks against the person of this sort have the following structure:
(p1) Academics tell us that fish stocks are being depleted in the North Sea.
(p2) Academics have never worked at sea.
_________________
(c) Academics are wrong about fish stocks in the North Sea.
Work out the structure of the other argument yourself.
Think about the extra premises that seem to be involved here and are needed to make
the arguments valid. Are they true? Something like this would do:
(p3) Anyone with this characteristic will be wrong about such claims*
The characteristic and claim will differ in each case, of course.
There is a temptation to accept attacks against the person of such a sort. This comes
from an understandable reluctance to believe those whom we regard as unreliable. If
someone has misled you on repeated occasions, it certainly looks like you have little
reason to believe anything they say (this, of course, is the point of the story of the boy
who cried ‘wolf!‘). Such reluctance looks reasonable when taken as a claim about how
much credibility we should give their claim, but it is problematic when we focus on the
aims of critical reasoning. What we are interested in is the truth of the claim being made:
this looks to be entirely separate from the character of the person making it. Just
because the person who ran off with your girlfriend/boyfriend, stole your lunch money and
kicked your dog tells you that there’s a fire in the school doesn’t mean that there isn’t
actually a fire in the school.
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Denying the truth of someone’s claims purely on the basis of that person’s past record is
unacceptable; any argument that works in this way is bound to be fallacious. We can
take a sceptical stance with regard to such a person’s claim, but we cannot legitimately
assume that it is false. This would be bad critical thinking.
The people who are against genetically modified crops say that they are damaging to the
environment. This is clearly not true. These people are just determined to stop a valuable
method of research if necessary by acting illegally. They are a bunch of emotional dogooders who behave like yobs.
The speaker giving this argument is trying to show that genetically modified crops are not
damaging to the environment (the first two sentences). But instead of giving reasons to
support this conclusion, the people who disagree with the speaker’s point of view are
attacked.
Even if the accusations against the protesters were true the argument does not work
because there are no reasons given to show that genetically modified crops do not
damage the environment.
It is worth noting here that there are some times when it is justified to refer to a
person’s character. This would not be inappropriate in an argument over is the best
candidate for a job, for example. This is not committing a fallacy.
Of all the people who have applied for the job of nursery nurse, Mrs. Scream is the last
person we should consider. In her previous job she was given a written warning for
shouting at the children.
In this example the evidence about Mrs. Scream’s character is relevant to the conclusion
that she should not be given the job. The evidence about her character gives a relevant
reason to say she is not the best candidate for the job.
Notice that the implicit premise here will not be the general false premise discussed
above. Instead, this argument works in this way:
(p1) Mrs. Scream was given a written warning for shouting at the children.
(p2) We want someone who is good with children for the job.
(p3) If someone gets a written warning for shouting at the children, then that person is not
good with children.
__________________________________________
(c) We do not want Mrs. Scream for the job.
There are also two other specific ways of committing the ad hominem fallacy. The first
(sometimes called the ad hominem circumstantial fallacy), points towards the fact that
an individual putting forward a claim or argument has something to gain from our
acceptance of the argument. In other words, it relates to the speaker’s circumstances.
Imagine an environmental scientist putting forward an argument to the effect that we have
to increase spending on anti-pollution measures in order to combat the greenhouse
effect. To object to this on the grounds that the scientist stands to gain from an increase
in funding is beside the point. It would be to commit the ad hominem circumstantial
fallacy.
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All these dentists tell us that we need to go for more regular check-ups. You know why
that is? It’s because we pay through the nose for some poorly educated half-wit to look
into our mouths and tell us the obvious. They do this and then drive home in their little
sports cars – cars that we‘ve paid for! There’s absolutely no need to go to the dentists
that often.
This is an obvious example. It claims that we have no reason to listen to what dentists
tell us because they make money from treating us. Be attuned to such arguments arising
in the political sphere. Just because you don’t like a politician doesn’t mean that she or
he might not be right sometimes. Good critical thinkers will always listen to the
arguments they are presented with – if you can do this and then reject them, you can
defeat your opponent is a clear and thorough fashion.
The other form of attacking the person is to draw attention to the fact that the individual in
question fails to act in accordance with the conclusion that they are asserting (to argue in
this way is to commit the kind of ad hominem fallacy known as tu quoque (meaning ‘you,
also’). This approach focuses upon certain aspects of an individual’s behaviour rather
than their motivations or character:
The event that stands out most for me was when the Home Secretary was caught driving
at 100 mph on the motorway and was allowed to keep his job. That speaks volumes
about how much he really cares about law and order.
The suggestion is that because someone is clearly not doing what he or she advocates
his or herself, then we have no reason to do it either. Home secretaries speeding,
doctors smoking and drinking, parents not looking both ways when they cross the road,
teachers being lazy with their teaching preparation – these can all give rise to attacks on
the person of this sort.
Doctors and nurses always tell us that we should limit our drinking and give up smoking.
They say that we need to do this for our health. But if you ever see doctors and nurses
on nights out, they are always smoking and drinking as much as they can! If they’re not
going to do it, then why should we?
Think for yourself what implicit false generalisation is assumed here.
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Exercise 18: Attacking the person
1. Construct fallacious arguments about the following subjects:
(a) Anti-war protesters claiming that the war in Iraq was immoral.
(b) Teenagers arguing that smoking should be banned in pubs.
(c) Teachers telling students to work harder.
(d) Politicians trying to encourage people to be more energy efficient.
(e) Tabloid newspapers accusing a politician of trying to stir up controversy.
Explain why these arguments are fallacious.
2. Look at the following examples and work out whether they are examples of the fallacy,
ie. whether they are attacking the arguer unjustifiably.
(a) The headteacher, Mrs. Sharp, is calling for the return of corporal punishment in
schools. We need to bring back the cane, she says, to bring back proper discipline.
However, her argument looks shaky when we consider that her own children are not
shining examples of well-behaved children. Jane smokes even though she is only 12 and
Jack has been convicted of assault.
This example is/is not an example of attacking the person fallacy.
(b) The male protest group ‘Society Against Dating’ (SAD) has said that all singles clubs
should be shut because they encourage immoral behaviour. But these men are, as their
title suggests, ‘sad’ and probably lonely. We should not therefore listen to anything they
say.
This example is/is not an example of attacking the person fallacy.
(c) The Chief Executive of the council Mr. George Big has recommended that the contract
for the new school should go to Big Contractors Ltd. However, since Mr. George Big and
his brother Jerry jointly own the company, we should question whether his judgement has
been coloured by his personal link with the company. Therefore, the recommendation
should not be accepted until other members of the council check the bid.
This example is/is not an example of attacking the person fallacy.
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g) Appeals to irrelevant consequences
There won’t be any epidemic as a result of bird flu! If the public believed that there was
going to be such an epidemic, shops would be looted, tinned food would disappear off the
shelves and I would stop going to work!
Look at what is going on in this example. It is as if the speaker is suggesting that there
will be no bird flu epidemic just because the consequences of people accepting that there
will be an epidemic are undesirable. To argue in this way is to appeal to irrelevant
consequences. There are several ways in which this fallacy can be committed. A
speaker might argue that some statement is true because if people accepted its truth, this
would have good consequences. Alternatively, it could be argued that we should hold a
statement to be false, as accepting its truth would have negative consequences.
Santa exists! Think of how much better the world would be if every child believed this.
There would be no more truancy, no more gangs of kids mugging pensioners, no more
rude behaviour – they would all be too worried about not getting any presents next year!
To argue in this way is to commit a fallacy, for the straightforward reason that the
consequences of the statements being true or false have no relevance to the question of
whether it is as a matter of fact true or false. To commit this fallacy is to be guilty of
wishful thinking – accepting that the world must be such-and-such a way because it
would be nicer if it were.
How one should represent appeals to irrelevant consequences is something of an open
question. We can either portray the argument as valid and propose that there is a hidden
false premise – along the lines of ‘anything with such terrible premises cannot be true’ or
‘anything with such great consequences cannot be false’ – or we can claim that it is
invalid in a very straightforward way. The issue turns upon what we take the speaker to
be doing and how good a critical thinker we take the speaker to be. In the case of most
of the other fallacies we have looked at, there is clearly an extra premise in play. This is
less obvious here.
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h) Unjustified or illegitimate appeals to authority
Many arguments make use of appeals to authority. This involves claiming that
something or other is true because someone else – the ‘expert’ in question – says so. To
see that there need be no problem with many of these, consider the following:
Dr. Smith announced that the prelim exam is taking place on Thursday 6 June, and Dr.
Smith is the teacher in charge of scheduling exams. If someone is the teacher in charge
of scheduling exams, then she or he will know the details of the exam. Therefore, I have
good reason to believe that the exam is taking place on Thursday 6 June
This looks fine. Dr. Smith appears to be a legitimate expert when it comes to examination
dates.
Not all appeals to authority will be of this kind though. Any argument that works by saying
something like the following looks problematic:
Taking recreational drugs is clearly wrong. I saw an old television interview just the other
day in which Marilyn Monroe was saying just the same thing.
Unless there are facts concerning Marilyn Monroe’s drug counselling qualifications of
which we are all unaware, she is not actually an authority on the matter. Nevertheless,
we see celebrities endorsing charities and products in adverts, giving their opinions about
current affairs, politics and moral issues on chat shows, and so on. To accept the truth of
a claim on the grounds that some celebrity advocated it would be to accept an illegitimate
appeal to authority. The only exception is when the celebrity also happens to be an
authority on the matter – but then it is not their celebrity but their expertise that will be
cited in support of the claim. Don’t forget – just because a celebrity presents a show
about, say, animals, it doesn’t follow that he or she is an expert on the topic! You
wouldn’t take a sick pet to a celebrity for medical treatment even if he or she were a
presenter of Animal Hospital or Sick Pets!
All appeals to illegitimate authorities do not involve celebrities, though. Serious examples
can be found in the treatment of the victims of crime and those who have suffered in
serious accidents. Victims of accidents, such as train crashes, are often interviewed by
the media on the subject of rail safety. The fact that they suffered a terrible experience,
though, does not make them experts on safety issues. Likewise, victims of crime are
often consulted on issues such as the rise in crime in the UK as a whole. The unfortunate
relatives of those who have suffered a loss as a result of drug use, for example, are often
given special status by the media and the authorities with regard to the problem of how
society should deal with drug use and abuse.
Such individuals may be experts – their situation might have led them to read up on all
the facts, consult with all the appropriate organisations and individuals, and so on.
Unless they have done this, though, we have reason to question the legitimacy of their
claim to authority. Do I become an expert on crime and the way we should treat
offenders solely because I have been mugged?
Notice that attacks on the person involve the unjustified rejection of a claim on the basis
of certain irrelevant facts about its advocate(s). Conversely, illegitimate appeals to
authority involve accepting a conclusion on the basis of certain irrelevant facts about its
advocate(s).
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i) Arguments from ignorance/Appeals to ignorance
Arguments from ignorance, also known as appeals to ignorance, work by assuming
that if there is no evidence against the truth of a statement, then we can legitimately infer
that it is true. The name of the fallacy comes from the fact that it is the fact that the
speaker is ignorant of any reasons against the truth of the statement that is taken to
justify acceptance of the statement itself.
There is life on other planets. We know that many, many other planets exist outside of
our Solar System. Furthermore, we have no evidence to support the claim that there is
no life anywhere else in the universe. It follows from this that life must exist somewhere
else as well as on Earth.
Note the writer’s tactic here. The conclusion ‘there is life on other planets’ is offered and
the only evidence given in support of this is the fact that there is no evidence available for
not believing it!
The structure of the argument looks something like this:
(p1) There is no evidence to believe that there is not life on other planets.
___________________________________________________________
(c) There is life on other planets.
This is barely an argument at all! Note that there only appears one premise: there is no
reason not to believe [some statement].
Sometimes, we are justified in believing that something is true given the lack of evidence
against it. For example, when scientists conduct large-scale trials of a drug – call it
Kleanskin – to see whether it causes some negative effects – say bad acne – and do not
find a single instance of bad acne arising in all of the trial’s patients, then it seems fair to
infer that it does not have this negative effect.
The argument involved in such a case would not be the straightforwardly invalid one
above, though. Instead, it would look something like this:
(p1) If Kleanskin causes acne, then large-scale trials would reveal this.
(p2) It is not the case that large-scale trials have revealed this.
___________________________________________________
(c) It is not the case that Kleanskin causes acne.
This, as you will have noted, is a valid argument.
It is also the case that inductive arguments might be used to argue for a conclusion based
on the absence of evidence against it. Try to think of some examples.
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Exercise 20: Appeals to irrelevant consequences, illegitimate appeals to
authority and appeals to ignorance
1. Construct arguments that use appeals to irrelevant consequences to argue for the
following conclusions:
(a) God exists.
(b) An asteroid will destroy the Earth in 15 years’ time.
Explain what is wrong with these arguments.
2. From the media, find two examples of illegitimate appeals to authority. Use these to
create arguments to present to the others in your class. Explain what is wrong with the
arguments.
3. Construct arguments that use appeals to ignorance to argue for the following
conclusions:
(a) God exists.
(b) An asteroid will destroy the Earth in 15 years’ time.
Explain what is wrong with these arguments.
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5. Tying everything together
We should now be in a position to tackle some fairly complex everyday arguments. If we
are to check whether these arguments are the sorts of arguments that should be
accepted by a good critical thinker, we will have to be able to evaluate whether or not the
arguments are valid and whether or not they are fallacious.
To do this, we should approach arguments in this way:
•
•
•
•
•
•
•
try to identify the main conclusion
try to identify the explicit premises
reconstruct the structure as best as you can
use your structure to spot hidden premises
see if any of these premises constitute substantive fallacies
check the argument for formal fallacies
construct a counterexample if required.
The justification for suggesting that we approach an argument in this manner is as
follows. Before we can do anything else, we need to know the claim for which the
speaker is arguing. This is the first step outlined.
Next, we need to disentangle those sentences that are doing the work from those that are
mere padding. To do this is just to establish the premises of the argument.
When we have done this, we are in a position to figure out the structure of the argument.
Remember, this might involve rephrasing some sentences to make the structure more
obvious.
As has been discussed at some length above, doing this should make obvious any gaps
in the argument. Often, these gaps are filled by hidden premises. When we find the
gaps, we will see what premises are required to fill them. This can only be done after we
have some idea of the structure of the argument – so the search for hidden premises
should come after the first attempt at working out the structure of the argument.
Furthermore, it makes sense to look at these hidden premises to see if they are
symptomatic of any of the fallacies we have considered. Formal fallacies can also be
looked for at this stage to see if the argument is invalid.
Don’t forget that counterexamples can be used for this purpose.
Let’s look at an example of this procedure in practice.
The security guard told me that the building was unsafe to play in. But he is a stupid,
nasty man who gets pleasure from telling kids to buzz off. We have got no reason to
believe someone like that. The security is wrong when he says the building is unsafe!
Firstly, what is the conclusion? Presumably it is given in the last sentence, ‘the building
will be safe’.
(c) The security guard is wrong in claiming that the building is unsafe.
What about premises? It looks like all of the sentences have some role to play.
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(p1) The security guard told me that the building was unsafe to play in.
(p2) He is a stupid, nasty man who gets pleasure from telling kids to buzz off.
(p3) We have got no reason to believe someone like that.
________________________
(c) The security guard is wrong in claiming that the building is unsafe.
Let’s tighten it up a bit to make the structure explicit. Something like the following would
do:
(p1) The security guard claims that the building is unsafe.
(p2) He is a stupid, nasty, etc.
(p3) If someone is stupid, nasty, etc., then they will be wrong about such things.
________________________
(c) The security guard is wrong in claiming that the building is unsafe.
Is this valid? No – the truth of the premises does not entail the truth of the conclusion.
The argument seems to commit the fallacy of attacking the person.
Here’s another example.
Violent youth crime is out of control in Britain today. The liberal laws that we have today
are no deterrent to those bent on committing serious crimes. Capital punishment should
be reintroduced in the United Kingdom. If we are to solve this problem, then either the
death penalty is brought back or thuggery and anarchy will continue to prevail.
What is the conclusion? Presumably, it is the sentence ‘Capital punishment should be
reintroduced in the United Kingdom’. This is the claim about which the speaker is trying
to convince us.
Next, we have to ask: how is the speaker trying to convince us of this conclusion?
It seems that the first sentence is giving background information. The next sentence
plausibly is also just padding – it only provides background information and does not
contribute to the argument. The conclusion follows immediately after this.
The final sentence, ‘if we are to solve this problem, then either the death penalty is
brought back or thuggery and anarchy will continue to prevail’, is clearly important.
Again, this looks like a premise.
Let’s put these together:
(p1) If we are to solve this problem, then either the death penalty is brought back or
thuggery and anarchy will continue to prevail.
_______________________________________
(c) Capital punishment should be reintroduced in the United Kingdom.
This is not enough to give us an argument. Is there anything implicit here? Presumably,
the speaker is assuming the following hidden premise:
(p2) We must do something to stop the violent youth crime that is out of control in Britain
today
Adding this gives us:
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(p1) If we are to solve this problem, then either the death penalty is brought back or
thuggery and anarchy will continue to prevail.
(p2) We must do something to stop the violent youth crime that is out of control in Britain
today.
_______________________________________
(c) Capital punishment should be reintroduced in the United Kingdom.
We need to tighten this up somewhat – notice how the same phrases do not reoccur in
the way we might expect. One plausible suggestion would be:
(p1) Either capital punishment is reintroduced in the UK or violent youth crime in the UK
will not be stopped.
(p2) Violent youth crime in the UK should be stopped.
_______________________________________
(c) Capital punishment should be reintroduced in the United Kingdom.
This has the form of an ‘or’ argument. The first premise states ‘we either do one thing
(call it ‘p’) or another (q)’, the second premise claims ‘we should not do q’ and the
conclusion follows that we should do p.
Is there a fallacy committed here? Well, the argument looks valid – it runs ‘either p or q,
not q, therefore p’ and this is valid. So there will no possibility of constructing a
counterexample. Is there a fallacy of another sort committed, though?
It looks as if the answer is ‘yes’. The argument is a false dilemma.
Try to work through the arguments in the following exercise either by yourself or in
groups.
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Exercise 21: Spotting fallacies in everyday arguments
Do the following arguments contain fallacies? Give details of any fallacies you find.
Support your answer by showing the structure of the argument.
a) The senior MP Alice Winterbottom should not have been sacked for telling a racist
joke. Other politicians say the joke was racist, and that senior politicians should be
dismissed if they are racist. But that’s just because they want to win more support for
themselves.
b) Lorraine will win the race. If she doesn’t, British athletics will be shamed in front of the
world and other athletes will see this and not want to compete. This will filter down to
schools and ruin sport in our country.
c) The council is planning to stop homeless people begging on the streets. This is wrong
and must be opposed. The councillors who are putting forward this idea have no idea
what poverty is. They sit in the comfort of their centrally heated homes and think
everyone should be like them.
d) Batman tells all the children in Gotham that they ought to obey the law. But he is a
masked vigilante who ignores the law on a daily basis! We have no obligation to obey the
law.
e) I will win the lottery! All the other people who have entered are nasty, immoral
creatures who would spend the money making good folks like you and me miserable!
f) The popularity of rap music is a sign of the downfall of civilisation. We should stop kids
listening to rap music. If we don’t they’ll soon be joining criminal street gangs. In my day,
we only ever listened to Mozart and Bach.
g) Who would have thought New Labour would have been responsible for so many bad
things! The number of children infected with measles rose to a new high after New
Labour came into office. New Labour causes measles in children!
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Appendix 1: Additional resources
Students should be warned that they should expect to encounter variant terminology if
they consult other texts and resources.
Terminological differences with the following textbooks should be minimal:
Recommended textbooks
•
Bowell, T. and Kemp, G. (2005) Critical Thinking: A Concise Guide. 2nd edition,
Routledge.
•
Thomson, A. (2001) Critical Reasoning. Routledge.
The main fallacy websites tend to be more complex and to favour the Latin names for
fallacies. Nevertheless, these should be of some use.
Helpful websites
•
http://www.fallacyfiles.org
A thorough site dedicated to the study of fallacies. Very detailed.
•
http://www.iep.utm.edu/f/fallacies.htm
From The Internet Encyclopedia of Philosophy.
•
http://www.datanation.com/fallacies
Another thorough site at a reasonably appropriate level.
•
http://www.nizkor.org/features/fallacies
Another good guide to fallacies.
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Appendix 2: Notes for teachers
The purpose of these notes is to provide a teaching resource for teachers. However, the
notes have been written in a style that should be accessible to students. Teachers might
consider distributing copies of sections to students over the duration of the course. To
facilitate this, any comments for teachers have been left until this appendix.
Exercise tips
•
Students will find the exercises more engaging if the examples are kept up to date.
For this reason, you might consider replacing some of the examples with newer ones
if this is seen as desirable. Clip art illustrations can be inserted into handouts if this is
desired.
•
The Wason – Johnson-Laird Exercise and the ‘Conjunction Fallacy’: teachers
may want to run one or both of these with the class. Withholding the correct answer
until a later lesson may help to increase students’ interest in the material. The
reasoning involved in each test can be discussed at a later stage in the course. This
might allow students to see an improvement in their reasoning skills.
•
Exercise 3: teachers may want to follow this up with a similar exercise, using different
sentences, which asks students to identify whether any of the sentences express the
same statement (or have the same meaning). Students could be asked to provide
their own examples of statements, questions, commands, etc., as well as examples of
different sentences with the same meaning.)
•
Section 3: for bi-level teaching, teachers may prefer to avoid using technical terms
such as ‘antecedent’ and ‘consequent’. This will not affect the content of this
discussion but will help facilitate teaching of Intermediate 2 students. If other
textbooks are used, students should be warned to expect this terminology.
•
Exercise 6:This is a difficult exercise. You can only derive a conclusion for the first
and fourth cards. If these cards were turned over to reveal a different image from that
expected in light of the conclusion, then the rule has been disproved. Students may
find this easier if they are guided through the examples one-by-one in a group
exercise.
•
Counterexamples: Students should be encouraged to develop a repertoire of
phrases and arguments that can be used to construct counterexamples should these
be required. One way of doing this would be to have students print a selection of
phrases and connectives on to card that could be cut out and used to assemble
arguments. This could be added as a freestanding exercise at an appropriate stage
during the course.
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Examples
Teachers are encouraged to collect appropriate examples of arguments, including
fallacious arguments, from the media. These could be used as the basis of additional or
alternative exercises to those in the main section of the notes. Good resources include
editorial columns and letters to the editor from newspapers and the BBC News website’s
‘Have Your Say’ section (http://news.bbc.co.uk/1/hi/talking_point/default.stm). Further
examples can be found on the sites listed in Appendix A.
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