Critical Thinking
What is Critical Thinking? Is it ‘slagging’ off people in your mind? Is it thinking about
how ridiculous someone looks, about their lack of dress sense or sniggering at
someone who can’t sing? No – unfortunately it is not about any of the above.
Critical Thinking is about examining arguments in a logical way, about assessing the
truth content of an argument and coming to a judgement on whether it is any good.
Critical Thinking in Philosophy is about establishing what we can count as reliable
arguments and not merely accepting rants or ill-informed opinion.
By the end of the unit you will be able to do the following;
Outcomes
1. Demonstrate an understanding of the nature of arguments.
2. Critically analyse ordinary language arguments.
3. Critically evaluate ordinary language arguments.
Outcome 1
Demonstrate an understanding of the nature of arguments.
Performance Criteria:
1. describe the difference between statements and arguments
2. describe the difference between deductive and inductive reasoning
3. use ordinary language examples to support these descriptions.
Outcome 2
Critically analyse ordinary language arguments. Performance Criteria:
1. identify the premises and conclusions of ordinary language arguments
2. present these arguments in a way which demonstrates the stages of reasoning
involved
3. explain whether these arguments employ deductive or inductive reasoning.
Outcome 3
1. Critically evaluate ordinary language arguments. Performance Criteria:
2. explain specific examples of fallacious reasoning in ordinary language arguments
3. explain whether or not the conclusions of these arguments follow from the
premises
4. explain whether these arguments are sound or unsound
5. state reasons which support the explanations given.
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Do you ever argue?
It is fairly safe to say that all of us know what it is like to argue and that sometimes all
we ever seem to do is argue with parents, friends and enemies. Sometimes the
arguments are relatively heated – keeping your room tidy, helping around the house,
what time you have to be home etc. At other times the arguments are about your
mood or even boredom!
Why do we argue?
Most arguments happen because at least two people disagree about something. You
might not think you should be told what to do, when you should do it and so you try
to get what you want by arguing. Some people seem to very good at it and these are
the people that usually get their own way.
Good and Bad Arguments
What is it then that makes a good or bad argument? Look at the examples below and
write down which of the arguments are good and which are bad. Try to give reasons
to support your view.
Tom: I want to go to see the latest Star Wars film
Harry: I don’t
Tom: I don’t care what you want
Harry: See you later then
Sarah: I hate people who eat meat
Donna: I eat meat!
Sarah: I hate you then
Donna: Because I eat meat?
Sarah: No – you stole my boyfriend!
Billy: Scotland will not qualify for the next World Cup
Ron: Of course they will
Billy: No chance. They only have four points from four games
Ron: If they win all the remaining games they then will have twelve points
Billy: That won’t be enough – other teams will pick up more points as well
Watch the Monty Python clips – are these good or bad arguments? Power Point
examples also.
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What is the purpose of an argument?
The purpose of an argument in Philosophy is not just to state opinions on what you
believe to be true. In Philosophy, we need to be able to;
 provide others with good reasons to accept a claim you believe to be true
 evaluate whether there are good reasons to accept or reject claims put forward by
others.
In other words, the whole purpose of an argument is to give good reasons/
evidence to support the point you are trying to make and to analyse the
reasons given by others.
Of the three arguments on the previous page, only the argument between Billy &
Ron comes close to doing this. Once we begin to master this type of reasoning it will
help us to;
1. Avoid being led into error by others.
2. Develop skills that will increase our skills of persuasion.
3. Help us in the pursuit of truth.
Task 1
Construct two separate arguments based around disagreements between at least
two people. The first argument should be a bad one and the second a good one.
Once you have constructed the arguments write a paragraph on how the good
argument provides good evidence and how it evaluates the claims put forward by
others.
Task 2
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.
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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 militaryindustrial complex.
Passage 6
All bachelors are male.
Paul is a bachelor.
Therefore, Paul is male.
Statements
Arguments are made up from statements (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:
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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.
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However, although statements are capable of being either true or false we will not
always be able to prove the claims. To say there is life on other planets is either true
or false but we cannot, at this time prove it. We can say there is a monster in Loch
Ness but can we prove it?
Furthermore, 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:
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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 (rhetorical questions are different and will be covered later)
and expressions of emotion or feeling are not statements because they cannot be
true or false. You are not asserting that such-and-such is the case; instead, you are
doing something else, such as asking for information, expressing how you feel 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.
Task 3
Which of the following sentences are statements?
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I like lager.
Chocolate, yum!
Scotland is part of the United Kingdom of Great Britain and Northern Ireland.
Ring the bell.
Could you ring the bell please?
I intend to ring the bell.
Pigs can fly.
Pigs can fly?
Stand up!
You should stand up.
Oban is the capital of Scotland.
A 20 pence coin is larger than a £2 coin.
A 20 pence coin is smaller than a £2 coin.
When was the Battle of Bannockburn?
I prefer Portugal to Turkey as a holiday destination.
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So, only statements are capable of being true or false and as such only statements
can be used to form arguments. 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.
Argument structure
How can we prove a statement/ proposition to be either true or false? Well, we know
it must have supporting evidence and that we must have good reasons to accept
that it is true. So, how do we prove that a statement such as Edinburgh is in Europe
is true? The short answer is that we need to build an argument to show why it is
true.
Arguments are formed using premises and these premises when taken together
lead to a conclusion. In this argument the conclusion we are aiming for is that
Edinburgh is in Europe. So, what evidence can we give to support this claim?
Premise 1 (p1) Edinburgh is in Scotland
Premise 2 (p2) Scotland is in the U.K.
Premise 3 (p3) The U.K. is in Europe
So or ---------Conclusion or (c) Therefore Edinburgh is in Europe.
We can construct an argument around the statement ‘Alice is mortal’ in the same
way.
(p1) All humans are mortal
(p2) Alice is human
-------(c) Therefore Alice is mortal
Task 4
Re-arrange the following statements into two arguments using the format known as
standard form (p1) (p2) & (c).
Therefore, it must be Saturday. I didn’t work hard. If Doctor Who is on TV, it must be
Saturday. Therefore, I didn’t work hard I didn’t pass the exam. Doctor Who is on TV.
If I had worked hard, then I would have passed the exam.
Arguments then are made from statements that try to give proof that they are true or
false – they try to offer proof that the claim is either true or false. In a similar way, to
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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.
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. To infer
means that we can be sure of the conclusion.
Task 5
a) In Philosophy and Critical Thinking, what is an argument?
b) What is the purpose of an argument?
c) What is the difference between denying and refuting something in Critical Thinking?
d) Explain the difference between inferring and implying in Philosophy?
Identifying premises & conclusions
We already know that questions, commands and expressions of taste cannot play
any part in an argument – only statements make up arguments. The conclusion is
merely a statement with other statements giving supporting evidence – these are
called premises. Look at the following argument;
Stop doing that! That’s why I won’t listen to you. Do you think it is ok for you to slag
my friend? Either say something nice or say nothing at all. I tell you what, say
nothing at all.
There are 5 sentences in the above argument but not all are statements. Stop doing
that is a command, Do you think it is ok for you to slag my friend? is a question.
These two sentences can be scored out. We are now left with 3 sentences – two
premises and a conclusion.
Remember that conclusions will have supporting evidence from the premises and
will usually begin with ‘That’s why’ ‘Therefore’ or ‘So’.
Task 6
What is the conclusion to the above argument? What are the premises?
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Task 7
Re-write the following arguments into standard form
Do you think abortion is wrong? Why? If abortion is wrong then we are killing unborn
children. Stop talking rubbish! Killing unborn children is murder. Really? That’s why
we need to stop abortion.
Will you ask your sister to go out with me? Oh yuk! What’s wrong with that? You are
a girl. So what? Girl’s should only go out with boys. Who made up that rule? I don’t
know but it’s disgusting! Will you ask her or not? I really like her! It’s not natural for
girls to go out with girls. So, that’s why I won’t ask her.
The legal drinking age should be raised to twenty one. Why do you think that we
need to do this? There are so many problems caused by underage drinking. But I
love drinking lager! Either we raise the legal drinking age limit or we have to live with
the consequences. Really?
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!
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!
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.
Hidden Premises
Arguments don’t appear from thin air and they are always caused by at least two
people disagreeing about something. The people arguing usually start arguing
because they believe they are right and the other person is wrong.
If there was an argument about who was the best footballer in the world then the
people involved would be arguing for who they thought the player was. People not
interested in the subject would either not get involved or only get involved to support
a friend.
The point here is that all arguments are based upon a viewpoint they believe to be
true. Richard Dawkins argues against the existence of God because he is an atheist
and doesn’t accept God as real. SNP supporters argue that Scotland should be
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separate from the UK because they believe Scotland would be better on their own.
People who prefer different styles of music believe their choice is the best. All
arguments then are based on a stated position that is accepted but not necessarily
mentioned in the argument.
In the above argument, the person arguing against abortion believes that abortion is
murder. A Hidden Premise can usually be inserted between (p2) and the conclusion.
(p1) If abortion is wrong then we are killing unborn children
(p2) Killing unborn children is murder
(HP) Abortion is murder
--------(c) That’s why we need to stop abortion
Task 8
Write out the other arguments formally including the Hidden Premises.
Types of Premises
As we have seen, there are ways to identify what counts as a premise but how do we
sort them into order? There are several types of statements that will act as premise 1
(p1).
 ‘If… then…’
 ‘… or…’
 ‘… and…’
 ‘All’ and ‘some’.

Rhetorical questions
If…then… statements are known as conditional statements. An example of this
could be ‘If there is a red sky at night then the weather will be good tomorrow’.
The first part of the statement ‘If there is a red sky at night’ is known as the
antecedent while the second part ‘then the weather will be good tomorrow’ is known
as the consequent. The consequent depends on the antecedent being true for the
conditional statement to be true. In other words the consequent is the consequence
of the antecedent being true. So, if the antecedent is true then we can accept the
consequent as also being true. Look at the following sentences.
There is a red sky tonight. So what? Well, if there is a red sky at night then the
weather will be good the next day. Oh, I like red. That’s why the weather will be good
tomorrow.
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When we rewrite the argument it looks like this.
(p1) If there is a red sky at night then the weather will be good tomorrow
(p2) There is a red sky tonight
-------(c) The weather will be good tomorrow
As before, we can identify which sentences should be in the argument and we can
spot the conclusion. However, we are left with two possible premises so which one
comes first. Where conditional statements are involved then the full conditional
statement will act as the first premise. In logic formula it reads
If A then B
A
----B
Task 9
Construct arguments for the following conditional statements
If Celtic are the best team then they will be top of the league
If you disrespect me then I will slap you
If I eat prawns then I will be sick
If I am dreaming, this is not real
If I am at school I am not at home
We already know if the antecedent is true then the consequent must be accepted to
make the conditional true. Look at the example below.
(p1) If I drink 8 pints of Stella then I will be drunk
(p2) I have drunk 8 pints of Stella
--(c) I am drunk
This follows the if A then B, A so B rule. But what if we know the consequent is
false? This means we can infer that the antecedent is also false.
(p1) If I drink 8 pints of Stella then I will be drunk
(p2) I am not drunk
-(c) It is not the case that I drank 8 pints of Stella
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This formula goes If A then B, not B therefore not A. Let’s look at the WasonJohnson-Laird experiment.
‘Or’ statements
Unlike conditional statements, ‘or’ statements simply join two statements together.
‘Or’ statements do not mean that we have to accept the whole thing as true.
‘You can have Coke or you can have Pepsi’.
‘Either the Universe has an original cause or it doesn’t’.
Or statements offer a straight forward choice and an argument can be built around it.
It has a simple formula: A or B, A, not B. It can also be: A or B, B not A.
‘Or’ statements can also be inclusive or exclusive. Inclusive statements mean you
have a choice from a range of options while exclusive means it must be one or the
other.
Task 10
Which of the following are inclusive and which are exclusive? Once you have done
this then rewrite a, e & g into formal arguments.
a) On Saturday, I will go to Edinburgh or Glasgow.
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 Edinburgh, you can study French, German, Spanish or
Portuguese.
e) The car key is in my hand or in my pocket.
f) David’s birthday is either on Monday or on Tuesday.
g) Celtic will play Aberdeen or Rangers in the Cup Final.
‘And’ statements
‘And’ statements are the most straight-forward in this section. They simply join two
statements together and are called conjunctions. The individual statements are
called conjuncts.
3 x 5 = 15 and 15 x 2 = 30. Obviously, a conjunction is a much stronger statement
than a conjunct. However, if one of the conjuncts is false then the whole statement
cannot be true.
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Grass is green and water is slightly blue is a true conjunction
Grass is green and water is clear is a false conjunction as the second conjunct is
false.
So, if we are told the conjunction is true then we have to assume that both conjuncts
are also true. Look at the following ‘and’ statements
Dundee is north of Edinburgh and Aberdeen is north of Dundee. What can we say
about the position of Edinburgh in relation to Aberdeen? We can infer that Edinburgh
is south of both Aberdeen and Dundee.
(p1) Dundee is further south than Aberdeen
(p2) Edinburgh is further south than Dundee
-(c) Edinburgh is further south than Aberdeen
We can be certain of this knowledge if we know the conjunction is true. However, if
one of the conjuncts is false the conclusion will be wrong.
‘All’ and ‘Some’ statements
‘All’
All statements simply tell us that there are no exceptions to the group and acts as a
quantifier. So, if there is a statement like ‘All humans’ are mortal’ then we know that
there are no humans who are not mortal. This leads us to infer the following:
(p1) All humans are mortal
(p2) Alice is human
(c) Alice is mortal.
In the same way, if we assert that all living things are the result of an Intelligent
Designer we can infer:
(p1) All living things are the result of an Intelligent Designer
(p2) Tigers are living things
(c) Tigers are the result of an Intelligent Designer.
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Task 11
Construct arguments based on the following propositions:
All blondes are stupid
All teachers are grumpy
All Scotsmen have ginger hair
‘Some’
‘Some’ statements are not quite as certain as ‘All’ statements. ‘Some’ statements
merely claim at least one or more things are included in the category. To say ‘some
teachers are nice’ means that at least one teacher is like this! It is a weaker claim
than ‘All’ statements because we do not know which teachers are included in the
category.
Task 12
Construct some arguments using your own ‘some’ statements.
‘No’ and ‘None’ statements
These act the same way as ‘All’ statements – there are no exceptions to the rule. If I
assert that no brothers are female it simply means what it says. If I were to claim that
no humans were polar bears….?
Rhetorical Questions
We already know that questions are not capable to being either true or false so they
are not part of an argument. However, rhetorical questions can, and do, play a role in
everyday language and arguments.
A rhetorical question is a question that is asked in order to state a point or for a
dramatic effect. Rhetorical questions can sometimes be thought of as statements. If
someone were to ask the question ‘does God exist?’ the answer might be ‘who
knows?’ This can be interpreted as ‘nobody knows’ and rewritten as ‘there is no way
anyone can answer that question’. A student misbehaving in a classroom might be
asked by the Teacher ‘what do you think you are doing?’ Someone who hears
something incredible might ask ‘do you expect me to believe that?’
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In both cases a question is asked and the question can be interpreted in different
ways. The Teacher is really saying ‘stop that’ but this is a command a therefore is
not capable if being true or false and cannot play any part in an argument. However,
the question could also be seen as saying ‘if you think this type of behaviour is
acceptable then I’m afraid you are wrong’. On this occasion it becomes a conditional
statement and can play a role in an argument. How could ‘do you expect me to
believe that?’ be interpreted?
Rhetorical questions are also difficult to identify in written language due to
understanding of grammar and identify punctuation. It will always be possible to
identify rhetorical questions as either commands or conditional statements.
Create three rhetorical questions of your own and show how they might be
interpreted as commands or as conditional statements.
Summary
Generally speaking, ‘If…Then…’ statements (conditionals), ‘Or’ statements, ‘And’
statements and ‘All’ and ‘Some’ statements will be (p1) and the conclusion will begin
with therefore’, ‘so’, ‘thus’, ‘for these reasons’, ‘this shows us that’, ‘that is why’, etc.
(p2) will always follow from (p1) and between (p2) and the conclusion there may be a
hidden or implicit premise. Rhetorical questions may also play a role.
Task 13
Rewrite the following into standard form
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.
All killing is wrong. Squashing a fly is a way of causing a death. So squashing a fly
must be wrong.
Either God exists or God doesn’t exist. For these reasons we must believe in God.
Existence can’t spring into life own its own.
France is in Europe. I’ve been there and they use Euros as money. Euros are only
used by some countries within Europe.
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.
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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.
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
Task 14
Fill in the hidden premises for the following arguments rewriting into a formal
structure as you go;
If Descartes was an empiricist, then every philosophy book published about
Descartes has been wrong. Descartes was no empiricist.
Muir and Elizabeth should be sacked. Anyone who badly mismanages a company
doesn’t deserve to remain in charge.
Smacking infants is no way to instill 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.
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.
All blood sports are evil. They all involve inflicting unnecessary suffering and taking
pleasure in another creature’s pain.
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!
Valid and Invalid arguments
When we talk about a valid argument we are talking about the structure of the
argument and how sure we can be that the argument is a good one. There are very
few people who would enter a lift in a high-rise building if they had any doubt about
the structural safety of the building. In the same way, Philosophers will not accept
badly structured arguments as reliable. So, what makes an argument reliable? The
first thing is that it must be valid.
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Validity is all about the connections between the premises and the conclusion. If an
argument is valid then it cannot have true premises and a false conclusion – if the
premises are true then the conclusion must also be true. This is because the
conclusion must be inferred from the premises – they must be deduced.
(p1) All humans are mortal (true)
(p2) Alice is human (true)
-(c) Alice is mortal
Task 15
Construct three valid examples of your own.
However, an argument becomes invalid and so unreliable if we can’t infer the
conclusion from the premises. Look at the next one
(p1) All humans are mortal (true)
(p2) Alice is human (true)
-(c) Edinburgh is in Scotland (true)
All of the propositions are true but we cannot get evidence for Edinburgh being in
Scotland from the two premises. So, while the premises are true and the conclusion
is true there is no way of inferring the conclusion from the premises. It is invalid.
Invalid arguments can have true premises and even a true conclusion but they don’t
have any justification or evidence to support them – they are merely statements.
Construct three invalid examples of your own.
Look at the following and decide whether it is valid or invalid.
(p1) All cats are dogs
(2) Fluffy is a cat
-(c) Fluffy is a dog
The argument is valid as the structure is entirely logical because we can infer the
conclusion from the premises. It doesn’t matter that both premise 1 and the
conclusion are false because the structure is correct.
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However, although the argument is valid it is unsound. Unsound arguments are
where either the premises or the conclusion is false or where there is no reason for
us to accept the conclusion from the premises.
On the other hand, valid arguments with true premises and a true conclusion are
sound arguments and can be described as justified, true belief.
Task 16
Look at the following and decide if they are valid or invalid. Then, decide whether
they are sound or unsound. Remember, for an argument to be sound it must first be
valid and we can never have and invalid but sound argument although we can have
a valid but unsound argument.
(p1) All Brazilians are great footballers
(p2) Marquinhos is Brazilian
(c) Marquinhos is a great footballer
(p1) All Celtic fans are Roman Catholics
(p2) Mr Cassie is a Celtic fan
(c) Mr Cassie is a Roman Catholic
(p1) All fish eat other fish
(p2) Penguins eat fish
(c) Penguins are a type of fish
(p1) All dogs are mammals
(p2) All Munroes are over 3000 feet high
(c) Ben Nevis is the highest mountain in the U.K.
(p1) All bachelors are unmarried males
(p2) Freddie is a bachelor
(c) Freddie is an unmarried male
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Task 17
a) What is a valid argument? Your answer should describe both valid and invalid
structures and illustrate your answer by giving an example of each.
b) What is a sound argument? Your answer should describe both sound and unsound
arguments by making reference to validity and giving examples.
c) Can an invalid argument have a true conclusion? Illustrate your answer with an
example.
d) Can a sound argument have a false conclusion? Illustrate your answer with an
example.
e) Can an invalid argument ever be sound? Illustrate your answer with an example.
f) Can a valid argument ever be unsound? Illustrate your answer with an example.
g) Why is it more difficult the check whether an argument is sound than it is to check
for validity?
Deductive & Inductive thinking
So far all of the arguments we have covered have been deductive arguments. They
are deductive because we infer or deduce the truth claim of the conclusion from the
premises and as such the truth of the conclusion cannot go beyond the evidence of
the premises. If we say that all humans are mortal we know there are no humans
who do not fit into this category. If we then claim that Alice is human we can deduce
mentally that Alice must be mortal. We do not have to physically check that Alice is
human or that she is mortal as we can know the truth of the conclusion a priori by
thought alone. In short, deductive arguments aim at being valid and sound and as
such they claim to guarantee knowledge.
Inductive arguments base the truth of the conclusion on prior experience (a
posteriori) and are less certain than deductive arguments. In other words they only
claim a probability not a certainty. Look at the examples;
(p1) Every swan I have ever seen is white
(c) All swans are white.
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(p1) Every relationship I have ever been in has been a nightmare
(c) My next relationship will be a nightmare as well
(p1) Every day in the history of the world the sun has risen in the morning
(c) Tomorrow the sun will rise in the morning
These arguments are clearly basing what will happen in the future based upon what
has happened in the past but the truth of the conclusions are not certain merely
probable. It was thought to be true that all swans were white until Europeans
observed black swans when they first went to Australia. It may well be the case that
your next relationship will be a nightmare but it is not certain.
The probability of the sun rising tomorrow is very high but it is not certain.
Inductive arguments go beyond the truth claim of the conclusion by claiming a
general truth and as such never aim at validity as they do not try to deduce the
conclusion. It is possible for inductive arguments to have true premises but false
conclusions and so can never be valid. It is also very difficult to sort out good from
bad inductive arguments.
(p1) Everyone in this room speaks English
(p2) Everyone I know speaks English
(c) Everyone speaks English
This argument was definitely true at one time but has been shown to be false even
though the premises are true.
(p1) Every episode of Hollyoaks is brilliant
(c) The next one will be brilliant as well
Well that conclusion is entirely subjective – it depends on the person watching or not
watching.
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Inductive Arguments and Cogency
We have already seen that some inductive arguments seem to be stronger than
others. Inductive arguments that have lots of supporting evidence are clearly
stronger than those that do not! Look at the following 2 inductive arguments – which
is the stronger and why?
(p1) There are 30 students in the class
(p2) The first 25 own mobile phones
(c) The next one I ask will have a mobile phone.
(p1) I have seen 2 pit-bull terriers in my life
(p2) Both were bad tempered and bit me
(c) The next pit-bull I see will be bad tempered and bite me.
The first argument is a strong inductive argument because the premises make the
conclusion highly probable. This is because there is lots of evidence to support a
likely or probable conclusion. The second argument is a weak inductive argument
because the evidence is so small that the conclusion becomes less likely or
probable.
However, inductive arguments can also be Cogent or not cogent. Cogency means
that the inductive argument is strong and has true premises.
(p1) Scotland has a population of around 6 million people
(p2) Most of the people in Scotland use English as their first language
(c) The next person I meet will speak English as their first language
This argument can be said to be cogent because it is a strong argument based on
lots of evidence and the premises are true.
(p1) Oban has a population of 20 thousand
(p2) 18 thousand people in Oban speak Gaelic
(c) The next person I meet will speak Gaelic
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This is not a cogent argument because although the premises look like they give us
lots of evidence to support the claim, the premises are not true.
Before some think that inductive arguments are useless it is worth remembering that
this is the method used by science and medicine and has brought great advances to
our lives. When scientists are developing new drug treatments it is usually through
strong inductive arguments that are cogent. The treatment will be tested and
retested until the results are fairly certain.
One further thing about inductive arguments – they can all easily be turned into
deductive arguments by inserting a hidden premise. However, it would not achieve
much as the hidden premise would also rely on past events or experiences i.e.
(p1) Every swan I have ever seen is white
(HP) No-one has seen a swan that was not white
(c) Therefore all swans are white
Clearly, the hidden premise here is suggesting that no-one else has seen a swan
that wasn’t white but this is also based on experience even though the experience is
from other people. In order to check the certainty of the conclusion we would need to
check all over the world for non-white swans before we could claim the conclusion to
be certain.
Task 18
a) Give an example of a valid, sound deductive argument
b) Why can deductive arguments be described as a priori?
c) Give an example of an inductive argument and explain why these types of
arguments can be useful.
d) Why can inductive arguments be described as a posteriori?
e) What is the difference between deductive and inductive arguments? Use relevant
examples to illustrate the answer.
f) Give an example of a cogent argument and a non-cogent argument. Explain why
these are different.
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Fallacies
A fallacy is basically a faulty argument and come in two main forms – Formal
Fallacies which are always invalid and Informal Fallacies which can be valid or
invalid.
Formal Fallacies
Formal Fallacies, in this course, are limited to conditional statements (If…then…).
Remember, when we are talking about conditional statements we are talking about
the form – If A then B – A therefore B or If A then B – not B therefore not A.
Construct a conditional statement of your own for the following tasks.
(p1) If you are Scottish then your are British
(p2) You are Scottish
-(c) You are British
Or
(p1) If you are Scottish then you are British
(p2) You are not British
-(c) You are not Scottish
Both of the above are valid arguments. It is fine, in a conditional statement, to affirm
the antecedent as the consequent relies on it for it to be true. In a similar way, it is
also fine to deny the consequent because we know that for the whole conditional to
be true then both the antecedent and the consequent must also be true.
However, if we deny the antecedent then we cannot imply that the consequent is
true. We cannot say that just because you are not Scottish then you cannot be
British – of course you can as you can be English or Welsh and still be British.
In the same way I cannot affirm the consequent and imply that the antecedent is
true. Just because I can say I am British does not mean I have to be Scottish.
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Task 19
Construct three examples of invalid conditional statement of your own.
Informal Fallacies
Informal fallacies are flaws in critical thinking and can take many forms.
Attacking the person
This is an unreliable form of reasoning because it attacks the person presenting the
argument rather than the argument put forward.
This type of fallacy also takes the form of a conditional statement and will usually
be valid (it is structurally correct).
It can take three different forms:
Ad Hominem Abusive (a personal attack on the person),;
Ad Hominem Circumstantial (where the arguer profits from their position) and;
Ad Hominem Tu Quoque (when the arguer is being a hypocrite).
Task 20
Which of the Ad Hominem fallacies is being made in the following example?
(p1) If Davie is a politician then he is not capable of telling the truth
(p2) Davie is a politician
-(c) We can ignore his views as he will never tell the truth.
In the above example we have no right to come to such a conclusion even though it
is valid. The argument here merely attacks the person.
Task 21
Construct examples for all versions of valid attacking the person arguments using the
following
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Tabloid newspapers accusing a politician of trying to stir up controversy
Teachers telling students to work harder
Rich people demanding that taxes be lowered
Arguments from Ignorance
These are usually conditional statements as well. The flaw in this way of reasoning
is that it assumes the lack of proof of one thing acts as proof of another.
(p1) If there is no evidence that aliens exist then we are the only life in the universe
(p2) The is no conclusive prove of alien life
-(c) We are alone in the universe.
In the above example we have no right to come to that conclusion. Just because we
can’t prove something doesn’t mean the thing we can’t prove offers evidence that
something else is true.
Task 22
Construct three examples of valid Arguments from Ignorance arguments.
Appeals to Authority
Again, these are usually conditional statements but not always. However, when they
do not take the form of a conditional it is easy to re-write them into one. This fallacy
bases truth claims on the view of an expert.
(p1) If Richard Dawkins says there is no God then I believe him
(p2) Dawkins does say there is no God
-(c) I believe there is no God.
In the above example we do seem to have grounds to accept the word of an expert.
However, should we base truth claims merely on the word of an expert?
Experts have been wrong in the past and will be in the future. Let’s face it, every time
England play in a major football tournament they are odds-on favourites to win and
we all know how that turns out!!!
Task 23
Construct three fallacious, but valid Appeals to Authority arguments of your own.
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Illegitimate Appeals to Authority
The worst kinds of appeal to authority are those where the alleged authority isn’t an
authority on the subject matter in question. The conclusion is inferred from the fact
that some person or group asserts the conclusion without justifying the right of that
person or group to be regarded as authoritative in this matter.
Task 24
Rewrite the following argument into a fallacious, but valid illegitimate appeal to
authority argument. Explain why this is fallacious.
Mr Fyfe told me that Global Warming is a real danger for the future of the planet. Mr
Fyfe is a teacher.
Appeals to Consequences
This fallacy attempts to prove/disprove something on the basis that if it were true
then the results of that would be horrible.
(p1) If evolution is correct then we are all just sophisticated monkeys
(p2) I am not just a sophisticated monkey
-(c) Evolution is incorrect.
This is a perfectly valid argument (If A then B – not B therefore not A) but we are
saying that evolution is not true just because we don’t want to be classed as clever
monkeys!
Task 25
Construct three valid appeals to consequences arguments of your own.
False Dilemma
These are arguments that presume without argument that there are only two choices
when there may be more, ie, they are exclusive. If the conditional is that you must
either support Celtic or Rangers it can be written as follows
(p1) You must support Celtic or Rangers
(p2) You do not support Celtic
-(c) You must support Rangers
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We have no right to infer that this valid argument is sound because it is entirely
possible that you could support Hibs, Hearts, Aberdeen or any other team. In
arguments for the existence of God, Aristotle claims that either the universe needs a
cause or it doesn’t. He concludes that to say it doesn’t is ridiculous (reduction ad
absurdum). Is this a possible false dilemma? Construct three false dilemma
arguments of your own.
Slippery slope arguments
This is where it is assumed (without further argument) that x will lead inevitably to y.
(p1) If we ban junk food then we should also ban alcohol
(p2) If we ban alcohol then we ban choice
(p3) If we ban choice then we ban freedom
-(c) If we ban junk food then we ban freedom
The main problem with this type of invalid argument is that we affirm the consequent
in each case and use a ‘slippery slope’ to justify the position. We have no right to
infer the conclusion based on the premises. It is simply not the case that banning
junk food will result in the loss of freedom.
David Hume would argue that there are no necessary links present here and while
it may be the case, in extreme cases, that banning junk food could lead to the loss of
freedom it is by no means certain. There are many other possibilities such as
(p1) If we ban junk food then the nation will be healthier
(p2) If we are healthier then the NHS will not need so much money to fund it
(p3) If the NHS needs less money then that money stays in my pocket
-(c) If we ban junk food then I will be richer.
However, there are no guarantees that this will be the case either as the argument is
invalid – we cannot infer or deduce the conclusion from the premises. The
government could simply spend the money elsewhere.
Task 26
Construct valid slippery slope arguments from the following:
The age at which people can legally drink should not be lowered.
Scientists should not be allowed to engage in research on stem cells.
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Post hoc ergo propter hoc
(after this – because of this)
These fallacies are based around one thing causing another and the idea that cause
and effect are directly connected.
They usually arise around health scares such as Mexican Swine Flu.
(p1) Anyone who has recently been in Mexico has been exposed to the flu virus
(p2) My neighbour has just come back form Mexico
-(c) My neighbour has Swine Flu
Another example might be
(p1) If skin cancer rates increase then the sun is dangerous
(p2) Skin cancer rates have increased
-(c) The sun is dangerous
Again, these are valid arguments but we have no right to assume that because one
thing is the case it is directly caused by another.
Task 27
Construct valid post hoc propter hoc arguments of your own from the following
statements
Most ‘hard’ drug users start off as ‘soft’ drug users
Most hard drug users start off as breast milk users
Fallacy of Composition*
The arguments are when it is assumed that just because a part of something has a
certain property then the whole must also have this property. Hume thinks this fallacy
occurs in arguments about the existence of God and will be covered in more detail in
the Metaphysics unit.
(p1) If the tyre is made from rubber then the whole car is made of rubber
(p1) The tyre is rubber
-(c) The car is rubber
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When arguing for the existence of God, theists often claim that if we know everything
in the world needs a cause then it is reasonable to assume everything in the
universe also needs a cause. David Hume rejects this as a Fallacy of Composition
(p1) If everything in the world needs a cause then so must everything in the Universe
(p2) We know everything in the world needs a cause
-(c) The Universe must need a cause
This argument commits the same fallacy as the car being made from rubber. Clearly,
we have no right to infer the universe needs a cause just because an orange does.
Task 28
Construct three fallacy of composition arguments of your own.
Construct three valid appeals to force arguments of your own.
Glossary
It is accepted that different critical thinking and logic textbooks may use different
terminology from one another or use the same terminology in different contexts.
Therefore, for the purposes of clarity and consistency, the following definitions are
those which will be used in SQA documents, Unit and Course assessments and
associated marking schemes:
Affirming the consequent: this fallacy is committed when an argument has the
following structure. If P then Q, Q, therefore P‘ e.g., If you are Spanish then you are
an EU citizen. You are an EU citizen, so you must be Spanish‘.
Argument from ignorance: this fallacy is committed if it is argued that since p has
not been proved true, it must be false (or that since p has not been proved false, it
must be true)
Argument: a collection of statements (the premises) put forward to support a central
claim (the conclusion).
Attacking the person: this fallacy is committed if it is argued that p is false on the
ground that it is advanced by a particular person, for example because that person
stands to gain from our acceptance of it as true or because that person‘s behaviour
is not consistent with the truth of p.
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Cogency: a strong inductive argument which also has true premises is said to be
cogent. False premises or premises which can provide only weak evidence for the
conclusion make the argument either not cogent or less cogent.
Deductive argument: an argument which attempts to prove certain conclusions
based on what is contained in the premises alone. E.g. All cats have tails. Felix is a
cat, therefore Felix has a tail.
Denying the antecedent: this fallacy is committed when an argument has the
following structure ‗If P then Q, Not P, therefore Q‘ e.g. If you are Spanish then you
are an EU citizen. You are not Spanish, so you can‘t be an EU citizen‖.
False dilemma: this fallacy is committed if, in the course of an argument, it is
presumed without argument that p and q are the only two possibilities, when in fact
there are other possibilities.
Formal Fallacy: a common error in reasoning that is fallacious by virtue of having an
invalid structure or form.
Hidden Premise: a statement which is not explicitly stated in an argument but on
which the argument may rest for its strength or validity e.g. the argument ‗All dogs
are carnivores so Fido is a carnivore‘ rests on the hidden premise that Fido is a dog‘
to make it formally valid.
Illegitimate appeals to authority: this fallacy is committed if a conclusion c is
inferred from the fact that some person or group asserts c, without justifying the right
of that person or group to be regarded as authoritative in this matter.
Inductive argument: an argument based on experiential premises where the
conclusion goes beyond what is said in the premises. The conclusions of an
inductive argument are usually said to be probable rather than certain. E.g., Every
cat I have seen has a tail. Felix is a cat therefore, Felix has a tail‘.
Informal Fallacy: an argument which may be formally valid yet is fallacious because
it has false premises or ambiguous terminology or grammar.
Post hoc ergo propter hoc: this fallacy is committed if it is assumed, in the course
of an argument, that because x and y occur one after the other that the one causes
the other.
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Rhetorical Question: a question that is asked in order to state a point or for
dramatic effect rather than to elicit an answer. Rhetorical questions can therefore
sometimes be interpreted as statements. E.g. the question ‗Who knows?‘ might be
interpreted as being equivalent to the statement ‗Nobody knows‘.
Slippery slope: an informal fallacy which claims that one thing will inevitably lead
later to another, usually worse, state of affairs, without further argument.
Soundness: a deductive argument which has true premises and is valid is said to be
sound. An unsound argument is therefore one which has either a false premise or is
invalid or both.
Standard form: a consistent way of organizing and presenting arguments which
involves identifying the premises and conclusions; converting any rhetorical
questions; making explicit hidden premises; identifying intermediate conclusions and
listing them in a logical sequence (e.g. premise, premise, conclusion)
Statement: a sentence capable of being true or false (e.g. the sky is blue‘).
Statements are also known as propositions.
Strong/Weak: an inductive argument which provides a lot of evidence for the
conclusion is said to be strong while one which provides a small amount is said to be
weak. The terms strong and weak are necessarily relative. E.g., I have seen a
hundred cats with tails therefore all cats have tails‘ is a weaker argument than I have
seen a thousand cats with tails, therefore all cats have tails‘
Validity: a valid argument is one which would guarantee a true conclusion if the
premises were true. An invalid argument does not guarantee a true conclusion when
the premises are true.
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