What Is an Argument?

1. Logical Arguments

“Argument” is a word that has multiple distinct meanings, so it is important to be clear from the start about the sense of the word we mean in logic, how it differs from ordinary use of the word, and how those meanings relate to critical thinking. In one sense of the word, an argument is a heated exchange of differing views, as in the following:

Sally: I’m so sick of you dog people with your dogs running around off the leash. It’s so inconsiderate!

Bob: My dog is under voice command and is very well-trained. Don’t be so uptight!

Sally and Bob are having an argument in this exchange. That is, they are each expressing conflicting views in a heated manner. However, that is not the sense of “argument” in logic. In logic, an argument is a reason or set of reasons for thinking that a claim or conviction is true. For example:

Sally: Keeping your dog on a leash is necessary even if it is well-trained. It is for the animal’s safety more than anything; it keeps the dog safe from running into traffic or getting in a tussle with another dog that’s not so well-trained. Besides, it’s the law.

In the first example, Sally was simply yelling at Bob. In the second example, she is offering reasons for her position. She has evidence to support her conclusion. The conclusion of the argument is the first sentence, “Keeping your dog on a leash is necessary even if it is well-trained.” The evidence or premises for this conclusion are “It is for the animal’s safety” and “It’s the law.” If Bob accepts her premises (he doesn’t have to!), he will have to accept her conclusion, because she has made a valid argument. In fact, Bob might have a hard time refuting her argument.

This shows that there is not a complete distinction between formal logic and real-world arguments. In fact, effective real-world arguments should and often do have underlying logic to them: they present premises that are acceptable to the other person, then come to a logical conclusion based on the premises.

In formal logic, we are more interested in the structure of arguments than their content. Logical arguments are entirely composed of premises and conclusions, which are both types of declarative statements, which simply means they assert that something is true. The premises of the argument provide a reason for thinking that the conclusion is true. We can also call this type of logic sentential logic; the word “sentential” here means that it has to do with a sequencing of logical sentences, which are the same as statements. To keep things clear, we have three overlapping definitions of logic:

• Real-world arguments: Analyzing the successes and pitfalls of the content of everyday arguments. Unlike more formal logic, in more informal real-world argument analysis, we are interested in the content of arguments rather than their structure.
• Informal logic: Making and analyzing arguments in English that involves giving support for a conclusion. These sorts of arguments are usually unstructured and are found in paragraph form, in newspapers, tv broadcasts, and everyday life, but can be given more structure by putting them in premise/conclusion format. Informal logic bridges the gap between critical thinking and formal logic—it is interested in both content and structure.
• Formal logic: Formulating and analyzing arguments that are highly structured. Formal logic is focused on how the structure of an argument (how the premises relate to the conclusion) makes an argument good or bad.

Throughout this unit we will be moving from informal logic to formal logic, by learning how to translate statements and arguments into sentential form.

A standard way of capturing the structure of an argument is by numbering the premises and conclusion. For example, in Sally’s argument against dogs off the leash, we could write it out as:

1. An off-leash dog might run into traffic.
2. An off-leash dog might get in a tussle with another dog.
3. Therefore, it’s safer for the dog to use a leash.

By convention, the last numbered statement is the conclusion, and the earlier numbered statements are the premises. We call putting an argument into this format to be putting an argument into standard form. By this standard, we can define a logical argument as a set of statements, some of which (the premises) attempt to provide a reason for thinking that some other statement (the conclusion) is true. In subsequent tutorials, we will often refer to simply arguments, but specifically mean logical arguments.

brainstorm

Think of something you have a strong belief about. Write it as a formal argument with that belief as a conclusion, and the premises that support it. Now think about what premises might be unstated to accept the conclusion.

In real-world arguments, there are other effective ways to persuade somebody than logic. For example, Bob might explain that his dog had a bad experience with a previous owner that makes her now recoil at the sight of a leash. He might ask Sally rhetorically if she has ever seen or even heard of dogs off the leash attacking anyone in their neighborhood. He might simply tell her to mind her own business. These don’t address Sally’s premises and can’t be translated into a logical argument. That doesn’t mean they are not arguments in the broad sense of the term, and it doesn’t mean they are “bad” arguments or fallacies. It means that logic is only one part of persuasion, that there are several overlapping definitions of “argument,” and we are only dealing with one in formal logic. To take from this that our meaning of argument is the only valid meaning would itself be a fallacy.

think about it

Do you remember the name of the fallacy where we conflate two different meanings of a word?

Check Your Answer

The fallacy is called equivocation.

big idea

We are only concerned with the logical components of arguments, statements of fact, to which we can apply reasoning. While these are not the only elements of effective argument in the real world, they are the only ones which can be evaluated.

In the next unit, we will learn some techniques of evaluating arguments (determining if they are valid), but for now the goal is to learn to understand the basic components of an argument, including its premises and conclusion(s). It is important to be able to identify arguments and understand their structure, whether or not you agree with the conclusion of the argument. In fact, it is important to be able to identify the logical components of your own arguments! Throughout this challenge we will learn how to identify the logical components of real-world arguments.

terms to know

Statement

A declarative sentence, one that asserts something is true.

Sentential Logic

Another term for formal logic, this name indicates the arrangement of sentences.

Standard Form

The way of organizing a logical argument with numbered premises and a conclusion. The sequencing of the statements shows how each premise leads to the conclusion.

Logical Argument

A set of statements, some of which (the premises) attempt to provide a reason for thinking that some other statement (the conclusion) is true.

---

2. How Formal Logic Aids Critical Thinking

As you’ve seen, we can translate both realistic, real-world arguments and completely hypothetical ones about hypothetical people and situations into formal logic. You may be wondering what the point is of the latter, especially when we proceed in the class and begin to translate arguments into a set of letters and symbols. We may also have examples that are false or absurd, such as this one by author and logician Lewis Carroll.

EXAMPLE

1. All babies are illogical.
2. Illogical persons are despised.
3. Nobody is despised who can manage a crocodile.
4. Therefore, no baby can manage a crocodile.

What do babies and crocodiles have to do with critical thinking?

2a. Analyzing Arguments

Logic is interested in how arguments are structured, and which structures make for better or worse arguments. In logic, we study characteristics of this form which can be studied independently of the content we might place in that form. For example, we will look at the role of sentences using the word “and,” and the conclusions we can draw (or not draw) from its use. In logic, the sentences ‘All babies are illogical’ and ‘all roads lead to Rome’ play the same role, despite their different contents. This is because they have the same form:

If X, then Y.

X might be, “is a baby,” or “is a road,” and Y might be “is illogical,” or “leads to Rome.” Either way, the truth of the statement doesn’t apply to the logic of the argument. The fundamental question in logic is whether the premises lead to the conclusion. For example, whatever the truth of the statement, we can say that if X is true, Y is true.

Of course, the kind of argument used in critical thinking is often written as an essay or given as a speech. Critical thinking is focused on the content of arguments—the relationships between the meanings of the sentences in the argument and their implications on our decisions. Critical thinking is aimed at enhancing our ability to create stronger and better arguments of this form, by being open-minded, not engaging in biases or fallacies, and interrogating our arguments for weaknesses and potential objections. These are about what is being said in an argument (not the form, or how the argument is structured). We emphasize the truthfulness of the facts, statistics, expert testimony, and first-hand testimony that support our conclusion; this is sometimes called evidentiary support.

think about it

What’s another example (hint: think about school subjects) in which content or meaning and structure are treated separately? How did this separation aid your learning?

However, every effective essay, op-ed, or speech does have the underlying form of a logical argument. Studying logic thus helps you learn to be a better critical thinker because it helps you learn about the underlying form of the arguments you make every day, or analyze the ones you encounter. When we don’t pay attention to the form of our arguments, even our everyday ones, we are prone to poor argumentative skills. We give arguments that fail to be clear, or concise, and are likely to fall prey to bad or incorrect argument structure. Noticing and relying on clear form for your arguments also helps you make clear decisions because you can see what evidence supports what decision and how to craft a compelling argument to defend the decision you do make.

2b. Cognitive Skills

Logic is an objective science, with objectively correct and incorrect answers to each question within the logical system. Critical thinking, on the other hand, is deeply subjective; the quality of the arguments and thinking process is evaluated subjectively by each individual. Some individuals will be more strongly persuaded by some arguments as opposed to others. Logic is more mathematical than psychological. Logic is about the evaluation of a formal argument on the basis of defined formal characteristics following a set of rules. The key to being effective in logic is being rigorous and disciplined, adhering to the rules, and being careful with your analysis.

On the other hand, critical thinking is about developing a particular kind of cognitive skill. To be a strong critical thinker is to have a set of abilities that let you create strong informal arguments for beliefs that you have, to be highly perceptive to weaknesses in your own and your opponents’ beliefs and biases, and to avoid fallacies (which we will discuss more in depth later). The key to being effective as a critical thinker is being creative and even courageous (challenging your own assumptions is brave!)

So you may again ask, why is formal logic helping me as a thinker? Is it going to help me create a budget, do my taxes, or solve today’s Wordle? If not, what’s the point?

The point, as we talked about in the last section, is to help you improve as a thinker by getting you to start paying attention to the structure of your thinking. What is the structure of my thoughts or my arguments? Is that structure valid? Is it good? Does it make sense? Do the premises support what I think they do? Are the premises strong or weak support for their conclusions? Is my argument form valid or invalid? Am I falling prey to fallacies? Thinking critically about and answering all of these questions thoroughly about your own thought processes is essential to becoming an articulate and clear thinker and writer.

term to know

Evidentiary Support

The facts, statistics, expert testimony, or anecdotal evidence that support the truth of a particular statement