4. Two kinds of argument

There are many ways premises can support their claims. In this post we’re going to look at two common forms widely used in academic and popular writing: inductive generalisations and arguments from authority. To begin, first read Sarah Graham’s short article “Effects of Smoking May Be Passed Down Through Generations”.

Look at the structure of each paragraph in Graham’s article. Paragraph 1 claims that the dangers of smoking for pregnant women may be greater than previously believed. The support for this claim is that research has found that the grandchildren of women who smoked when they were pregnant are more likely (double, in fact) to have asthma.

By the lights of logic, this is an informal but very common way of arguing: the writer tries to persuade you of the argument’s truth by citing an authority that you should believe: recent research. Hence, this kind of argument is called ‘Argument from authority’.

Other arguments from authority are

1. Jesus was the Son of God. How do I know? It says so in the Bible.
2. Darwin’s principle of natural selection is true for sure. It must be because it is accepted by modern science.
3. Pam is cheating on her boyfriend. How do I know? She told me so.
4. An argument’s definitely not the same as an explanation. I don’t know why, but that’s what it says in this text book.
5. Wittgenstein famously said that ‘the world is all that is the case’.
Therefore, we know that anything that isn’t the case in not part of the world.

Arguments from authority are only as good as the reliability of the authority being quoted. As an independent and critical thinker, you should never wholly accept a claim just on the basis of an argument from authority. If you do, you have to accept that others might disagree with you simply because they do not trust that authority. Good critical thinkers must judge an argument for themselves, and not believe it just because others tell them to.

Paragraph 2 of Graham’s article claims that if a woman smokes while she is pregnant, both her children and grandchildren may be more likely to have asthma as a result. The support for this claim comes from three premises:

Premise 1:

children of women who smoked while pregnant were 1.5 times as likely to develop asthma as the offspring of nonsmokers were.

Premise 2:

If both the mother and grandmother smoked during pregnancy, the risk increased to 2.6 times that of children of nonsmokers.

Premise 3:

Most surprising, even when a mother did not smoke while she was pregnant her child had nearly double the risk of developing asthma as a child from a smoke-free home if her mother had smoked during pregnancy.

This form of argument is known as ‘Argument from induction’. Inductive arguments are based on evidence, observation and past experience. Most scientific arguments are inductive. If the premises are true, you have good reason to believe the claim, but arguments from induction are never certain – they are only probable (look at the language used in the claim: ‘may be more likely’). It is possible that further evidence could undermine the argument (just check the history of science to see!).

Some philosophers have been so upset by this observation that they refuse to accept any argument based on induction. Referring to the problem of induction, the 18th Century Scottish philosopher David Hume famously complained that the past was not a reliable guide to the future.

While inductive reasoning cannot rule out the logical possibility that things might change, it remains true that, in practice, we could neither live our daily lives nor do science if we did not place regular faith in inductive generalisations.

Other arguments from induction are

1. Every swan we have ever seen is white. Therefore, all swans are white.
2. The sun always comes up in the morning. Therefore, the sun will come up tomorrow morning.

You will notice that 1 and 2, both contain universal statements. These are statements that have the logical form ‘All As are B’ (like “all swans are white” in 1), or which can easily be parsed into that form (as “The sun always comes up in the morning” can be rephrased as “All mornings are mornings with sunrises”).

Most universal statements are inductive generalisations, meaning we think that they are true because we have observed instances of them many times. Nonetheless, be careful because some universal statements are not generalisations based on evidence. Consider, for example,

‘All unicorns have only one horn.’

This universal statement is not an inductive generalisation. It is a semantic tautology; that is, a statement that is true by definition: the meanings of the terms make the proposition as a whole necessarily true (you may remember we saw another kind of tautology in post 1: What is an argument).

Other universal statements like this are

‘Every bachelor is an unmarried man.’
‘No object can be coloured both red and green all over at the same time.’ (this is a logical impossibility ruled out by the meanings of “coloured all over” and “at the same time”).

For some universal statements, it remains unclear whether they are semantic tautologies or inductive generalisations. For instance, are the universal statements

‘Every event has a cause.’ and  ‘Nothing can be in two places at the same time.’

inductive generalisations, or simply true because of the meaning of the terms in the sentence? Philosophers and quantum physicists seem unable to agree, but for now it is enough that we recognise that universal statements usually express either inductive generalisations or semantic tautologies.

• premises can provide different kinds of support for a claim. Two kinds of support are ‘argument from authority’ and ‘argument from induction’
• universal statements have the form ‘All As are B’. Some universal statements are true because of the meaning of ‘A’ and ‘B’, while others are inductive generalisations based on past experience

Try Exercise 4 to test your understanding of this post, or continue reading


3.1 Assessing arguments

Analysing an argument in terms of its claims and premises in itself tells us little. What it does do, however, is make it easier for us to judge or weigh the argument in at least two ways. First, we can examine each premise to decide whether it should be accepted. Second, we can begin to examine the relationship between the premises and the claim. In other words, we can question whether the premises which we are willing to accept make the claim believable or whether the premises could be accepted and the claim still rejected.

This second notion, the relationship between the premises and claim, is called ‘inference’, and we will be looking at it a lot more closely in subsequent posts. Although there are some specific techniques to help us examine inference, seeing it is, in large part, a natural skill of rational creatures, and we all do it unconsciously everyday in many ordinary ways. It is possible without any formal training whatsoever to make a judgment about whether you find a claim believable or not based on premises. What requires practice, and usually some degree of tuition, is the means by which to articulate our response.

To practice assessing an argument, re-read the argument in exercise 3 and your answers, then try exercise 3.1 here. Only after that should you engage with the answer key and notes.

Alternatively, continue reading the book…

3. More about claims and premises

We said earlier that an argument must have at least one claim and one premise. However, some arguments contain only hidden premises. Consider the argument:

8. The best way to avoid getting AIDS is to simply not have sex.

This is an argument with a single, hidden premise, namely, ‘having sex is the main way of getting AIDS.’ As we have said, when the premise is, or seems to be, uncontroversial, premises may not be stated. It is assumed in 8. that everyone agrees with the hidden premise and that the claim can be inferred from it. Whether you accept the conclusion or not will depend partly on whether you accept the hidden premise; however, you could accept the premise and still argue that there is a better way to avoid getting AIDS. As we shall see in later posts, words, like ‘best’ carry a lot of implicit content.

Be aware that sometimes something that looks like an argument is not an argument at all, but an explanation or description. You must be clear about the differences between these functions. As we have said, an argument must have a claim and at least one premise (even if hidden), but another way to characterise arguments is in terms of their function.

Thinking along these lines, we can think of an argument as a way of persuading someone that a statement is true or correct. Usually, an argument tries to convince someone to believe something new or different whereas a language function like explanation is an answer to a ‘Why?’ question – in other words, a request for further information or clarification. Explanations are commonly used to make something that is already accepted clearer or more understandable. Consider the difference between

9. Why does the Sun come up in the morning? (you already believe it, but you want to know how it happens). Explanation: The sun appears to come up in the morning because the Earth revolves around the Sun. If you are standing on the Earth, the Sun would appear to move in relation to your position.


10. Why should I believe that the Sun comes up in the morning? (You have lived your whole life in a cave and have never seen the sun). Argument: The sun comes up in the morning. If you were to go outside of your cave, you would observe a bright orange globe that rises over the horizon at the start of each day.

• An argument must have a claim and at least one premise
• One, more, or all the premises of an argument could be implicit
• Arguments whose premises are entirely implicit are usually uncontroversial
• Arguments can be distinguished from other language functions by thinking about their purpose: the purpose of an argument is to convince somebody of something they do not yet believe.

Try Exercise 3 to test your understanding of this and earlier posts, or continue reading

2. Hidden premises

Often, premises are implicit or hidden in an argument. This means they are not mentioned but are assumed – either knowingly or unknowingly – by the speaker or writer. Reconsider example 5 from the previous post:

5. Life on Earth is in deadly peril. If we had not burnt so much fossil fuel in the late 20th century, there would not have been so much carbon dioxide in the atmosphere. If there were less carbon dioxide in the atmosphere, the greenhouse effect would not be running out of control.

In fact, this argument only works if we assume the truth of another premise, namely, that ‘When the greenhouse effect runs out of control, life on earth is in deadly peril’. Often, hidden or implicit premises like these are not mentioned simply because they are obvious.
Here’s another argument with an implicit premise:

6. H2O is abundant on Earth. 70% of the world’s surface area is water.

The implicit premise is that H2O and water are the same thing, but why mention something in an argument which no one finds controversial? It would be tiresome to have to mention everything presupposed by an argument’s conclusion when most of it is not in dispute. That being said, however, it is essential that the philosophy student realises that hidden premises are particularly important precisely because in complex arguments on controversial issues, there are often implicit premises that may not be recognised by one or more parties. What is more, it is these that often turn out to be the very premises which are responsible for the controversy. Here is a good example:

7. Murder is always wrong. Even though the state sanctions capital punishment, clearly capital punishment is wrong.

The claim in this argument cannot be established unless one agrees to the hidden premise that ‘capital punishment is murder’. Whether one agrees with the argument’s claim that ‘capital punishment is wrong’ will turn precisely on this hidden – and controversial – premise rather than on the two uncontroversial stated ones.

If you think carefully about any argument, you will almost always find a hidden premise. This is because speakers and writers usually have a common background with their audience, so that some information is unnecessary to mention. However, you should always think about hidden premises and weigh up whether they are significant or not. The argument in 7. has many implicit premises including, for example, ‘the State has the power to punish people’. However, this is not significant because it is irrelevant to establishing the claim – it makes no difference to the argument one way or the other.

• All philosophically-interesting arguments contain hidden premises
• Hidden premises need to be recognized and assessed as to their significance

Try Exercise 2 to test your understanding of this post, or continue reading

1. What is an argument?

Much of the business of philosophy is concerned with arguments – their construction, analysis, defence and refutation – but how do we determine exactly what is and what is not an argument? How do we distinguish arguments from other linguistic and logical functions such as explanations, descriptions, exhortations and the like? How do we assess whether any particular argument is worthy of assent or deserving of dismissal? How do we determine whether an argument’s acceptance amounts to something significant or is merely a nod to the trivial?

The answers to such questions lie in a loose body of techniques and skills called ‘critical thinking.’ They are ‘loose’ in the sense that although there are some very definite and universally accepted techniques involved in assessing the logical validity and soundness of arguments, there is a large dose of creative or imaginative skill involved too. In the 1960s, Edward de Bono coined the term ‘lateral thinking’ to refer to the ability to come up with novel ways of looking at and solving problems. Like other creative arts such as painting, writing, or playing musical instruments, skill at both logical and lateral thinking can be learned.

What is an argument?
In order to answer the questions posed above, it is necessary to first understand what makes a series of sentences an argument, rather than say an explanation, description or other language function. We can determine whether a passage contains an argument by asking whether it contains any claims that are being supported or defended. The sentences that provide – or are intended to provide – the support to a claim are called the premises of the argument. All arguments, by definition, must contain at least one premise and one claim.

Consider the following:

1. Tomorrow’s lecture will be on Kant. It’s the last lecture of the semester, and last year this professor chose Kant as his topic for his final lecture.

The speaker is making an ordinary prediction about what will happen at some future time (in this case, ‘tomorrow’). The prediction, however, takes the form of an argument, which is simply to say that the prediction amounts to a claim with some reason or evidence (a premise) given in support of it. Formally, it can be broken down in this way:

: Tomorrow’s lecture will be on Kant.
Premise: The same professor gave a lecture on Kant at the same point in time in last year’s course.

What links the claim to the premise is an inference. Inference in ordinary language is often signalled by a connecting word after the claim such as ‘because’, or if the premises are stated before the claim, ‘so’ or ‘therefore’:

i. Tomorrow’s lecture will be on Kant because it’s the last lecture of the semester and Dr Burke chose Kant as the topic for his final lecture last year.

ii. It’s the last lecture of the semester, and last year Dr Burke chose Kant as the topic for his final lecture. Therefore, tomorrow’s lecture will be on Kant.

However, when we break down or analyse an argument’s structure, we usually leave the connecting words out. In part, this is because the strength of the inference, its validity, will be something that we want to test when we evaluate the argument, and it helps to reduce the argument to its simplest form in order to do this. We will be discussing inference and validity at length later on.

For now, compare 1 above, with 2 below:

2. I’m really bored. Every week is just the same. Study, study and more study.

Our teenage angst might well be used as a prelude to an argument – a persuasive appeal for a study break or extra allowance might easily follow – but barely stated, it offers nothing to trouble the disinterested parent simply because sentence 2 fails to amount to an argument. The speaker is not here trying to establish or support a claim of being bored. Rather, he is reporting that he is bored and offering an explanation for it.

One way to think of the difference between a claim and other language functions such as reports, descriptions and explanations is to say that a claim must, at least in principle, be capable of being either true or false. The statement ‘I’m really bored’, so long as it is not spoken in jest or insincerity, does not seem capable of being false in quite the same way that the claim in sentence 1 is capable of being false. That is to say, ordinarily, we would not expect a speaker to be mistaken or to turn out to be wrong or ignorant about their own immediate feelings.

The sentence in 3 below also fails to be an argument, but for a different reason:

3. If God exists, then atheism is false.

This kind of sentence is called a closed conditional. It is a statement of the relationship between a finite number of possibilities (in this case, two), where all the possibilities are covered, so the conditional sentence remains logically true no matter what is, as a matter of fact, the case. We say it is closed and remains logically true because even in a world where God were proven not to exist, it would still be true that if God had existed or ever would exist in that world, then atheism would be false. Thus, the sentence 3. is true regardless of whether God exists or not (later, we will learn that 3. is an example of a wider species of statements called ‘tautologies‘).

Open conditionals are ‘if…then’ statements that leave some options out of the statement:

4. If God exists, Jesus was the son of God.

It could be the case that God exists, but still false that Jesus was his son; hence, the conditional is said to be open. Even so, an open conditional barely stated does not amount to an argument if it contains no premise or supporting reason to justify its belief or acceptance. A claim without any premises or supporting reasons for its acceptance is called an assertion and is much like our report of teenage ennui in sentence 2, which is to say it fails to be philosophically interesting.

Conditionals, open or closed, do not on their own make arguments, but they can make claims and premises. Sentence 4 could be a claim if it were backed up with some supporting reason.

Here’s an example of an argument that use conditionals in both its premises:

5. Life on Earth is in peril. If we had not burned so much fossil fuel in the late 20th century, there would not have been so much carbon dioxide in the atmosphere. If there were less carbon dioxide in the atmosphere, the greenhouse effect would not be running out of control.

The form of the argument is:

Claim: Life on Earth is in peril.
Premise 1: If we had not burnt so much fossil fuel in the late 20th century, there would not have been so much carbon dioxide in the atmosphere.
Premise 2: If there were less carbon dioxide in the atmosphere, the greenhouse effect would not be running out of control.

• An argument must contain both a claim and one or more premises
• A claim without any premises is called an assertion

Try Exercise 1 to test your understanding of this post, or continue reading

Thinking – it hurts!

Well, it always used to hurt me. Actually, it still does. As some old philosopher must have said to someone with a headache ‘it wouldn’t be worth doing if it was easy’ (such adages are primarily aimed at stilling dissent rather than clearing the mind).

Well, easy things may not be worth doing, though I’ve always thought sleep was probably the most worthwhile activity, but in any case there’s certainly no harm in making things less difficult than they have to be. The posts in this blog are from the manuscript of my book on critical thinking*, and aimed at trying to give you a method for making difficult things easier to think about. It doesn’t mean you can get out of doing the thinking; it just means you don’t have to give yourself a headache while doing it.

Hope it helps.

*I’ll be publishing the entire book for free on this blog. Follow me on Twitter or get the RSS feed to find out when new posts go up..

Start reading the book

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