Arguments

David Sanson


This page is about arguments. An argument, in the sense we care about here, is not a disagreement or a shouting match. An argument in the sense we care about here involves the articulation of a reason in support of a conclusion.

For example, some people believe that truth is relative. If you ask them what their reason is for believing that, they might say something like:

Different people believe different things. So each person has her own truth. So truth is relative.

This is an argument for the conclusion that truth is relative. It begins with the premise,

  1. Different people believe different things.

This is taken to support the conclusion that,

  1. Each person has her own truth.

And this is taken to support the conclusion that,

  1. Truth is relative.

Notice how the word ‘so’ helps indicate the structure of this argument. It is what tells us that the second sentence is meant to be supported by the first, and the third by the second. The word ‘so’ in English is used to mark conclusions—claims that are meant to follow from other claims.

We can also represent this argument using an argument map. An argument map is a graphical representation of the structure of an argument:

Here the green lines indicate support: the claim that truth is relative, at the top, is supported by the claim that each person has her own truth, below it. That claim is in turn supported by the claim that different people believe different things.

Now that we have the argument clearly articulated, we can ask whether or not it is a good argument. Does it provide us with a good reason to believe that truth is relative? There are two ways that an argument can go bad. So if we want to know whether or not an argument is good, we need to check whether or not is bad in either of these ways.

The first way that an argument can go bad is that it can begin from false premises. This argument begins with a single premise—the claim that different people believe different things. And that premise is obviously true. So the argument passes the first test: the premises it begins with are all true.

The other way an argument can go bad is more complicated: do the premises actually support the conclusion? This has to do with the relationships represented in the map with the green lines. Starting at the bottom, supposing it is true that different people have different beliefs, does it follow that each person has her own truth? And, continuing up the map, supposing that we were convinced that each person has her own truth, would it follow that truth is relative?

These are difficult questions. To get to the bottom of them, we would need to get clear about what is meant by “having her own truth” and what is meant by the claim that truth is “relative”. But these are topics for another time. So we will leave the question of whether or not this is a good argument unresolved.

In any case, this is just one argument for the claim that truth is relative—one articulated reason in support of the conclusion. There are other reasons to believe the conclusion, that can be articulated with other arguments. For example,

Since different people speak different languages, and truth depends on language, truth is relative.

This argument has the same conclusion, but it offers a different reason to believe it. It also has an interestingly different structure. The previous argument began with just one premise. This argument begins with two premises,

  1. Different people speak different languages.
  2. Truth depends on language.

These together are taken to support the conclusion that,

  1. Truth is relative.

Notice how the word ‘since’ helps indicate the structure of this argument. It is what tells us that (1) and (2) are considerations meant to support (3). The word ‘since’ in English is used to mark premises—claims that are meant to support other claims.

We can also represent this argument with an argument map.

At the top of the map, we have the same conclusion, the claim that truth is relative. But beneath it, we have a different reason in support of the conclusion. Notice that this time, our two premises are independent claims. The claim that different people speak different languages is not being offered as support for the claim that truth depends on language. The claim that truth depends on language is not being offered as support for the claim that different people speak different languages. Instead, the two claims together are being offered as support for the conclusion, that truth is relative.

This is a common feature of arguments. Often—usually!—it takes more than one premise, working together, to support a conclusion. Here is a hackneyed example from logic textbooks:

  1. All men are mortal.
  2. Socrates is a man.
  3. Therefore, Socrates is mortal.

The first premise alone does not support the conclusion—maybe Socrates is a god! The second premise alone does not support the conclusion—maybe some men are immortal! But the two premises together support the conclusion.

We call premises that work together like this co-premises. We represent this relationship in an argument map by putting both co-premises together under a green umbrella, beneath the claim that they support.

Argument maps allow us to represent more than one argument for the same conclusion. Distinct arguments will be represented by distinct green umbrellas. So, for example, here is a map that represents both of the arguments we have considered:

You know nothing
Knowledge requires certainty. So, if you are not 100% certain about something, then you can’t be said to know it. And you can’t be 100% certain about anything. So you don’t know anything.

Representing Reasoning

In Philosophy, we try to use reason as a tool for increasing our understanding of difficult problems. So we try to communicate our reasoning to each other as clearly and carefully as possible. And we try to evaluate our reasons, and the reasons of others, to see if they are good reasons.

The Structure of Reasoning

When we reason, we reason from some given information to some new information. There are a few different ways to represent this. One way is with an “argument map”:

digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [label="given information", shape="box"];
   conclusion [label="new information", shape="box"];
   }

We will call the piece of reasoning itself an argument. We will call the information you reason from the premises of the argument, and the information you reason to the conclusion of the argument.

digraph G {
   premise -> conclusion:n;
   premise [label="premises", shape="box"];
   conclusion [label="conclusion", shape="box"];
   }

So, for example, given the information that Andrew is vegetarian, you might reason to the conclusion that Andrew does not eat chicken:

digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [label="Andrew is vegetarian", shape="box"];
   conclusion [label="Andrew does not eat chicken", shape="box"];
   }

But this argument map leaves a lot of important information out. When you reasoned from the premise to the conclusion, you relied on your background knowledge about vegetarians and chickens. This gave you additional information, and so additional premises. In day-to-day reasoning, we don’t bother to state premises when we think they are obvious. A premises that you rely on in your reasoning, but don’t bother to state, is called an implicit premise. Here is a more explicit representation of your reasoning:

digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [shape="record", label="Andrew\ is\ vegetarian | Vegetarians\ don't\ eat\ animals | Chickens\ are\ animals"];
   conclusion [shape="box", label="Andrew does not eat chicken"];
   }

Notice that the conclusion does not follow from any one of the premises taken by itself. It only follows from all the premises taken together. In a good argument, the premises, taken together, provide a reason in support of the conclusion.

You might have other independent reasons for believing that Andrew does not eat chicken. Those reasons can also be represented as arguments. Maybe you know that Andrew doesn’t like the way chicken tastes, and from this, you infer that he does not eat chicken:

digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [label="Andrew doesn't like the taste of chicken", shape="box"];
   conclusion [label="Andrew does not eat chicken", shape="box"];
   }

Here it seems that you relied on an implicit assumption about how people choose what to eat. Let’s make that assumption explicit:

digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [shape="record", label="Andrew\ doesn't\ like\ the\ taste\ of\ chicken | People\ don't\ eat\ things\ that\ don't\ taste\ good\ to\ them"]; conclusion [label="Andrew does not eat chicken", shape="box"];
   }

Again, the conclusion does not follow from either premise taken by itself. It only follows from all the premises taken together. So these premises, taken together, provide another reason in support of the same conclusion.

So the same conclusion can be supported by different premises. Also, the same premises can support several different conclusions:

digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [shape="record" label="Alice,\ Bob,\ and\ Christina\ are\ teammates
   | Alice\ is\ the\ tallest\ player\ on\ her\ team"];
   conclusion [shape="record", label="Alice\ is\ taller\ than\ Bob| Alice\ is\ taller\ than\ Christina"];
   } 

Notice that here each conclusion follows separately from the premises. What we have here is really two separate arguments, from the same premises, to different conclusions:

digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [shape="record" label="Alice,\ Bob,\ and\ Christina\ are\ teammates
   | Alice\ is\ the\ tallest\ player\ on\ her\ team"];
   conclusion [label="Alice is taller than Bob", shape="box"];
   } 
digraph G {
   graph [rankdir=UD]
   premise -> conclusion:n;
   premise [shape="record" label="Alice,\ Bob,\ and\ Christina\ are\ teammates
   | Alice\ is\ the\ tallest\ player\ on\ her\ team"];
   conclusion [label="Alice is taller than Christina", shape="box"];
   } 

Argument maps provide a nice visual way of representing arguments. They help to emphasize the basic structure of an argument: an argument is a piece of reasoning, from some given information, to a conclusion.

Argument maps are especially helpful as tools for argument development and argument analysis.

Argument Analysis and Argument Development

Argument analysis is what you do when you are trying to understand someone else’s argument. It is an essential part of careful reading. Argument development is what you do when you are trying to formulate your own argument. In both cases, constructing an argument map can help you clarify the conclusion and separate out the premises.

Argument mapping as a method for argument analysis and development is a topic typically taught in critical reasoning courses. For reasons of time, we won’t be covering it in this course. I encourage you to take a look at…

Premise-Conclusion Form

In practice, it is much easier to represent an argument as a simple list: first the premises, followed by the conclusion. So, for example, we can represent the argument above as,

  1. Alice, Bob, and Christina are teammates.
  2. Alice is the tallest player on her team.
  3. ∴ Alice is taller than Christina.

Here the premises are (1) and (2), and the conclusion is (3). We know that (3) is the conclusion because it is the last sentence in the list. We also know that it is the conclusion because it is marked by a special symbol, ‘∴’ which stands for “therefore”. We will always mark conclusions using ‘∴’.

When we represent arguments like this—as a list of premises, followed by the conclusion—we say that we have put the argument in premise-conclusion form. Putting arguments in premise-conclusion form is a common philosophical exercise. It forces you to clearly separate out the premises from each other, and from the conclusion.

Test Your Understanding

Research shows that it is easy to read something and feel like you understand it, even when you don’t. Most of us feel like we understand so long as we know what most of the words in a sentence mean, even if we don’t really grasp the ideas being communicated.

So, throughout these supplements, you will be provided with opportunities to stop and test your understanding. Please don’t skip this. If you get a question wrong, go back and re-read the preceding paragraphs with an eye to figuring out what you missed.

Arguments are everywhere. You can find them in blogs, magazine articles, textbooks, and newspaper editorials. They often pop up in conversations. But they are not usually found in premise-conclusion form, and important premises are often left unstated. Sometimes even the conclusion is left unstated, as in this example, from Confucius:

If there be righteousness in the heart, there will be beauty in the character. If there be beauty in the character, there will be harmony in the home. If there be harmony in the home, there will be order in the nation. If there be order in the nation, there will be peace in the world.1

Can you put this argument in premise-conclusion form? What is the conclusion? When you think you know the answer, click on the gray box below.

Presumably the conclusion is,

  • If there be righteousness in the heart, there will be peace in the world.

So the argument, in premise-conclusion form, would be,

  1. If there be righteousness in the heart, there will be beauty in the character.
  2. If there be beauty in the character, there will be harmony in the home.
  3. If there be harmony in the home, there will be order in the nation.
  4. If there be order in the nation, there will be peace in the world.
  5. ∴ If there be righteousness in the heart, there will be peace in the world.

Here is an argument:

Some pigs have wings. Everything with wings can fly. So, some pigs can fly.

What are the premises of this argument? What is its conclusion? Can you put it in premise-conclusion form? When you think you know the answer, click on the gray box below:

The premises are ‘Some pigs have wings’ and ‘Everything with wings can fly’. The conclusion is ‘Some pigs can fly’. In English, the words ‘so’ and ‘hence’ and ‘therefore’ are often used to indicate a conclusion. In this case, the fact that the last sentence begins with ‘So’ tells us that it is the conclusion.

  1. Some pigs have wings.
  2. Everything with wings can fly.
  3. ∴ Pigs can fly.

Here is another argument:

We need to raise the capital gains tax. We need to do this because a low capital gains tax provides a disproportionate benefit to the wealthiest citizens. It serves only to increase the gap between the super-wealthy and the rest of us, and we need to decrease that gap.

What are the premises of this argument? What is the conclusion?

The conclusion is, ‘We need to raise the capital gains tax.’ Notice that when people give arguments, they don’t always state the conclusion last, and they don’t always mark it with a word like ‘so’ or ‘therefore’.

The first premise is ‘A low capital gains tax provides a disproportionate benefit to the wealthiest citizens.’ Notice the way the word ‘because’ is used to indicate that this is a premise—a bit of information that helps support the conclusion. Another word that often indicates a premise is ‘since’.

Here is the argument in premise-conclusion form:

  1. A low capital gains tax provides a disproportionate benefit to the wealthiest citizens.
  2. A low capital gains tax serves only to increase the gap between the super-wealthy and the rest of us.
  3. We need to decrease the gap between the super-wealthy and the rest of us.
  4. ∴ We need to raise the capital gains tax.

Review and a Loose End

We’ve introduced three key terms: argument, premise, conclusion, They are defined in terms of each other:

Arguments, Premises, Conclusions
An argument is piece of reasoning that can be represented as a list of sentences, called the premises, followed by a sentence, called the conclusion.

And we’ve introduced a way of representing arguments, by putting them in premise-conclusion form.

We need to add one qualification to our definition of an argument. The sentences that play the role of premises or conclusions must be sentences that express information. So they have to be declarative sentences—the kinds of sentences that are true or false. They cannot be questions or commands, since questions and commands are not used to express information.

So this is not an argument:

  1. It is important to eat fruits and vegetables.
  2. ∴ Eat your fruits and vegetables!

Why not?

This is not an argument because the conclusion is an imperative sentence—a sentence used to give a command—rather than a declarative sentence—a sentence used to say something true or false.

It is possible to develop a logic that includes imperatives. Computer programming languages often involve imperatives. Consider:

  1. If the user clicks on the icon, then open the app!
  2. The user has clicked on the icon.
  3. ∴ Open the app!

We might think of this as an argument from one imperative—the command expressed by (1)—to another imperative—the command expressed by (3). But the logic of imperatives (like the logic of questions) is an advanced topic, to be considered after you have mastered the material of this course.

Done!

Head back to the table of contents.


  1. Borrowed from Pospesel, p. 76.