Argument Analysis: Basic Concepts

David Sanson

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This short primer introduces several basic concepts used in argument analysis, including: argument, premise, conclusion; implicit premise; strength, validity, cogency, soundness; standard form; intermediate conclusion. For a similar short primer, with some differences in emphasis, I highly recommend:

• Dan Korman (2022), Learning from Arguments, Introduction §2–7 and Appendix A: Logic.

For a longer primer, I highly recommend

• Alex Rajczi (2022), Primer on the Methods of Philosophy.

Those are both free high-quality textbooks, and I have borrowed several of my examples from them. I also highly recommend this lovely paper by Dan Lowe, which offers an incisive illustration of the power of these tools for the clarification and evaluation of arguments:

• Dan Lowe (2016), “Common Arguments for the Moral Acceptablity of Eating Meat: A Discussion for Students”

Arguments

In philosophy, an argument is not a dispute or debate. Nor is it a thesis or position. An argument is an attempt to provide a reason in support of a thesis or position:

Argument

An attempt to support a conclusion by providing a reason.

Someone can offer more than one reason in support of the same conclusion. When they do, they are offering more than one argument in support of that conclusion. For example, someone might argue that eating meat is morally acceptable for humans because it is part of the order of nature, and also because it is an important part of a healthy diet. Those are two distinct reasons in support of the conclusion, and so two separate arguments.

A reason can be articulated into premises. Some reasons are simple, and can be articulated into a single premise:

1. Humans eating meat is part of the order of nature.
2. So, it is morally acceptable for humans to eat meat.

But usually, reasons are more complicated, and need to be articulated into two or more premises. Even this example is probably better articulated using two premises, not one. Think about it for a moment: what else must someone be assuming, if they take (1) to be a reason in support of (2)?

They must be assuming something like this: if something is natural, then it is morally acceptable. So here is a better representation of the argument, articulating the reason into two premises:

1. Humans eating meat is part of the order of nature.
2. If something is natural, it is morally acceptable.
3. So, it is morally acceptable for humans to eat meat.

A premise that is assumed but not mentioned is called a hidden premise or an implicit premise. Part of your job, when articulating a reason into premises, is to identify hidden premises.

When we articulate a reason into premises, we want each premise to express a complete independent claim or assumption. So make sure that each premise is a single complete sentence, not a sentence fragment, and not a paragraph. And make sure that your premises are not questions, since questions don’t express claims. And make sure you don’t overload your argument with several redundant premises—premises that make the same claim, perhaps in different words.

We also want the premises to link together in support of the conclusion. Notice how the two premises in the example above don’t quite link together? How does being “part of the order of nature” relate to being “natural”? We can sharpen the argument by fixing this:

1. Humans eating meat is part of the order of nature.
2. If something is part of the order of nature, it is morally acceptable.
3. So, it is morally acceptable for humans to eat meat.

See how, by using exactly the same phrase in premise (1) and premise (2), we make it clear how the two premises are meant to link together?

Exercises

1. Are there other things you can do to further sharpen the argument above?
2. Above, I mentioned another reason often offered in support of eating meat, namely, that is an important part of a healthy diet. Can you articulate the premises of that argument, following the example from above?
3. Can you come up with one or two other reasons in support of eating meat, and articulate them into premises, and present them as arguments?

Strength and Validity

When someone offers you an argument for a conclusion, the first question you should always ask is this:

Supposing we grant you that those premises are true, would they support your conclusion?

When we ask this, we are asking about the strength of the argument.

Strength

The strength of an argument is the degree to which the premises, if they were true, would support the conclusion.

Notice how the question of strength is not about whether the premises are actually true. It is about how well they would support the conclusion if they were true. It is important to settle the question of strength before you start worrying about the actual truth of the premises.

Here is a strong argument with a false premise:

1. Our best scientific theories tell us that the earth is flat.
2. So, the earth is flat.

The premise is false, but if it were true, then it would give us a good reason to believe that the earth is flat, so the argument is strong.

Here is a weak argument with true premises:

1. Ten-year-olds are not allowed to vote in US elections.
2. Valdimir Putin is not allowed to vote in US elections.
3. So, Validmir Putin is a ten-year-old.

The premises are true, but they simply do not support the conclusion, because there are so many other reasons Putin might not be allowed to vote in US elections.

Strength comes in degrees. The highest degree of strength is called validity:

Validity

An argument is valid if and only if it is absolutely impossible for the premises to be true but the conclusion false.

When an argument is valid, the premises, if true, would absolutely guarantee the truth of the conclusion.

Exercises

3. Come up with a few of your own examples of each of the following:

   1. Arguments that are strong, but have false premises;
   2. Arguments that are weak, but have true premises;
   3. Arguments that are valid, but have false premises;
   4. Arguments that are not valid, but have true premises.

Soundness and Cogency

Once you have decided that an argument is strong, you can move on to the next question:

Are the premises of this argument actually true?

If an argument is strong and all of its premises are true, we say that it is cogent:

Cogency

An argument is cogent iff (a) it is strong and (b) all of its premises are true.

If an argument is valid and all of its premises are true, we say that it is sound:

Soundness

An argument is sound iff (a) it is valid and (b) all of its premises are true.

The following argument is strong but not cogent, because its premise is false:

1. Our best scientific theories tell us that the earth is flat.
2. So, the earth is flat.

The argument for eating meat from above is a bit trickier:

1. Humans eating meat is part of the order of nature.
2. If something is part of the order of nature, it is morally acceptable.
3. So, it is morally acceptable for humans to eat meat.

Upon reflection, this is valid but not sound. Which premise is false? That depends a bit on what is meant by “part of the order of nature”. If it means “something many humans have done for a long time, and other animals do too”, then premise (1) is true, but premise (2) is false. On other interpretations, premise (1) is false, but (2) is true.

Exercises

For each of the following arguments:

1. If there are unstated implicit premises, add them to the argument.
2. Decide whether the argument is weak or strong.
3. If strong, is it also valid?
4. Is it cogent or sound?

Explain your answers.

1. People disagree about things.
2. So, truth is subjective.

1. Scientists disagree about whether global warming is real.
2. So, global warming isn’t real.

1. People disagree about what is morally right and wrong.
2. So, morality is subjective.

1. People disagree about whether the 2020 U.S. Presidential election was rigged.
2. So, it is impossible to know whether the U.S. Presidential election was rigged.

1. My hands are parts of me.
2. My hands are not parts of my brain.
3. I am not my brain.

1. Rihanna is a well-known pop star.
2. Robyn Fenty is not a well-known pop star.
3. So, Rihanna is not Robyn Fenty.

Standard Form

There are many ways of presenting and representing arguments. In reading and writing, arguments are usually presenting in prose:

We in the rich nations are like the occupants of a crowded lifeboat adrift in a sea full of drowning people. If we try to save the drowning by bringing them aboard, our boat will be overloaded and we shall all drown. Since it is better that some survive than none, we should leave the others to drown. In the world today, ‘lifeboat ethics’ apply. The rich should leave the poor to starve, for otherwise the poor will drag the rich down with them.

It’s clear that our mental powers wax and wane during the eleven-year sunspot cycle. All of the great discoveries of mankind were made during the occurrence of sunspots. The great discoveries of Einstein and Newton were made at the time of the greatest sunspot activity.

Recent increases in the Earth’s temperature are unlikely to lead to major human catastrophes. In the past, the Earth’s temperature has often fluctuated. This has never led to a major human catastrophe.

When an argument is presented like this, you need to do some work as a reader to identify the conclusion, work out what reason is being offered in support of that conclusion, and articulate that reason into premises.

Once you’ve done that work, how should you report your results? You could report them in prose:

This argument has two premises. They are…. These premises are supposed to support the conclusion that….

But when philosophers are thinking about arguments, they usually write them up in a somewhat more formal way, in what we call standard form. This is the form I have been using throughout this handout: a list of numbered claims, where the last claim in the list is the conclusion. For extra clarity, the conclusion also begins with ‘so’.

Exercises

Present each of the three arguments above in standard form.

Reasoning and intermediate conclusions

Sometimes, when authors give arguments, they include intermediate conclusions. Here is a simple example:

People should stop complaining that humans are destroying nature. Humans are natural animals, so anything we do is just as natural as what non-human animals do.

Think about that argument for a moment, and the structure of the reasoning. What is the conclusion? What reason is being offered in its support, and how does that reason support it?

Here is one stab at representing it:

1. Humans are natural animals.
2. So, anything humans do is just as natural as what non-human animals do. (from 1)
3. So, people should stop complaining that humans are destroying nature. (from 2)

Notice that both (2) and (3) are marked by ‘So’, indicating that they are both conclusions. (3) is the main conclusion—it is the claim that argument is trying to establish. (2) is an intermediate conclusion or subconclusion: a claim infered from another premise, which in turn is used to support the main conclusion.

An intermediate conclusion is not another premise. It is a step in the reasoning from the premises to the main conclusion, included to make it easier to see how the conclusion is meant to follow from the premises. Compare these three representations of the same argument:

1. Humans are natural animals.
2. So, people should stop complaining that humans are destroying nature.

1. Humans are natural animals.
2. So, anything humans do is just as natural as what non-human animals do. (from 1)
3. So, people should stop complaining that humans are destroying nature. (from 2)

1. Humans are natural animals.
2. So, anything humans do is just as natural as what non-human animals do. (from 1)
3. So, nothing humans do can count as destroying nature. (from 2)
4. So, people should stop complaining that humans are destroying nature. (from 3)

The first representation leaves it obscure how the premise is meant to support the conclusion. The second representation helps clarify this, by adding an intermediate conclusion. The third representation makes it even clearer, by adding a second intermediate conclusion.

Here is another example:

1. You cease to be conscious when you die.
2. If you cease to be conscious when you die, then being dead isn’t bad for you.
3. So, being dead isn’t bad for you. (from 1 and 2)
4. If being dead isn’t bad for you, then you shouldn’t fear death.
5. So, you shouldn’t fear death. (from 3 and 4)

(3) is not essential to the argument. But including (3) makes it easier for our reader to follow the reasoning. We also indicate about which lines are meant to support (3), and which are meant to support (5).

This way of extended standard form, by including intermediate conclusions, is limited. It cannot handle complicated forms of reasoning that involve making assumptions for the sake of argument, like conditional proof and reductio ad absurdum. In such cases, you can still present the argument in standard form, but you will need to present the reasoning in some other way, whether informally in prose, or by using the tools of natural deduction we teach in our logic class.