Have you ever wanted to disagree with someone’s argument, but you couldn’t find any flaw in it? It’s possible you were facing a sound argument.
An argument is a series of statements that try to prove a point. The statement that the arguer tries to prove is called the conclusion. The statements that try to prove the conclusion are called premises.
Here’s a sample argument:
Premise 1: If it is raining, then the street is wet.
Premise 2: It is raining.
Conclusion: Therefore, the street is wet.
Above is an example of a series of statements that counts as an argument since it has a premise and conclusion. That’s all it takes for something to be an argument: it needs to have a premise and a conclusion.
A sound argument proves the arguer’s point by providing decisive evidence for the truth of their conclusion.
A sound argument has two features:
- The argument has a valid form, and
- All the premises are true.
I’m going to talk about these points in order. To understand the valid form, we need to understand the logical form of an argument and the logical form of a statement.
What Is an Argument’s Logical Form?
When we say an argument is valid, we are talking about an argument’s logical form. I wrote about valid arguments and logical forms in this piece here in detail.
Logical forms are like math formulas. Each comprises variables and operators. For example, the math formula “x + x = 2x” comprises a variable ‘x’ and an operator ‘+’. If we were to plug in the value 1 for x, then we would get “1+1 = 2.” Logical forms are similar. The difference is that instead of mathematical operators, logical forms use logical operators, and instead of variables that are filled in with numbers, the variables of logical forms are filled in with statements.
How do you get at the form of an argument? An argument is a series of statements, so to get at the form of an argument, you need to get at the form of the statements that compose it.
The Logical Form of a Statement
Here are a couple of examples of statements: “It is raining.”; “The street is wet.”
Statements can be combined using logical operators such as the following:
- Both… and…
- Either… or…
- If… then…
- … if and only if…
When we combine two or more statements using logical operators, the result is a compound statement.
For example, the statements, “It is raining,” and, “The street is wet,” can be combined by the logical operator ‘and’ to make a compound statement as follows: “It is raining, and the street is wet.” Or they can be combined using ‘if…then…’ as follows: “If it is raining, then the street is wet.”
Here are more examples of statements formed with logical operators: “It is not raining,” “James is tall, or Adam is fast,” “Either you can go straight, or you can make a right,” “Shawn can win the race if and only if he enters it.”
Now that we understand the logical form of a statement, let’s talk about the logical form of an argument. An argument is composed of statements. The premises and the conclusion of an argument are all statements. So if you want to know the logical form of an argument, you start by identifying the logical form of the statements composing it.
Here’s an example of an argument:
Premise 1: All mammals are animals.
Premise 2: All dogs are mammals.
Conclusion: Therefore, all dogs are animals.
Here’s the form of the argument:
All M are A
All D are M
Therefore, all D are A
Logicians have a name for this form of argument. It is a valid deductive argument called a categorical syllogism.
Now, an argument’s form is valid if and only if the truth of the argument’s premises guarantees the truth of its conclusion. If we plug in true premises, in other words, a valid form guarantees a true conclusion.
A valid form is similar to an accurate math formula. For example, in mathematics, if you want to get the area of a circle, you will first get the formula to calculate the area of a circle. In this case, the formula will be “A = π (r)^2.” At this point, all you need to do is plug in the radius r of the circle in the formula to get an accurate result. If you get the accurate radius, then you are guaranteed an accurate area.
The categorical syllogism is a valid form because if the two premises are true then the conclusion has to be true. In other words, if premises 1 and 2 are true, then the conclusion (All dogs are animals) has to be true–it’s impossible for it to be false.
Now that we’ve talked about forms of statements and arguments, let’s talk about what it means for an argument to be a sound argument.
What makes a valid argument into a sound argument?
Now that we understand what a valid argument is, it is easier to understand a sound argument. An argument is sound if and only if it is a valid argument and all the premises are true. Examples of sound arguments include categorical syllogisms whose premises are all true.
In order to determine whether an argument is sound, you need to ask the following two questions.
1. Does this argument have a valid form?
2. Are all the premises true?
Once the answer to both 1 and 2 is yes, then you know it’s a sound argument.
The following argument is another example of categorical syllogism:
Premise 1: All men are mortal.
Premise 2: Socrates is a man.
Conclusion: Therefore, Socrates is mortal.
Let’s look at the above example with two questions in mind to determine whether this argument is sound.
Does this argument has a valid form? Yes. The above form is called a categorical syllogism, and it is a valid form. Logicians have compiled a list of time-tested valid argument forms such as Modus ponens, Modus tollens, and Disjunctive syllogism. Categorical syllogism is one of the most popular forms, and it is a valid form because if the two premises are true then the conclusion has to be true.
Are all the premises true? Yes. Both of the premises above are true. Premises are statements. Statements can be either true or false. A statement is true when the world matches the statement. If I were to say, “2 plus 2 is 4,” then this statement is true since it matches how the world is. If I were to say, “2 plus 2 is 5,” then this statement is false since it doesn’t match how the world is.
If you can’t determine whether the premises are true or false, you can choose to withhold judgment. Withholding judgment means you don’t make a decision to accept or reject a claim. For example, suppose you don’t have decisive evidence for or against this claim: “There is life outside of the earth.” You don’t have to make a decision about whether or not the claim is true. You can withhold your judgment till you get more evidence for or against the claim.
If the answer to questions 1 and 2 is yes, then you know that the above argument is sound. You know that the argument actually proves its point. It actually proves that the conclusion is true.
However, if the answer to question 1 is yes, and you’re withholding judgment about question 2, then at least you know that the argument is a valid argument even if you don’t know whether the argument is sound.
Summary and Conclusion of Sound Argument
- An argument is a series of statements that try to prove a point. The statement that the arguer tries to prove is called the conclusion. The statements that try to prove the conclusion are called premises.
- Arguments are not true or false. Statements are true or false.
- When we say an argument is valid, we are talking about the form of an argument.
- An argument is valid if and only if the truth of the premises guarantees the truth of the conclusion.
- Validity is a feature of deductive arguments not inductive arguments.
- Logicians have tests for logical consequence and methods for constructing valid deductive arguments.
- An argument is sound if and only if it is a valid argument and all the premises are true.
- Unsound arguments either don’t have a valid form or they have at least one false premise.
- If the premises of an argument are false, then the argument doesn’t prove anything. An argument with even a single false premise doesn’t prove anything.
- Knowing how to identify sound arguments is essential to developing critical thinking skills.
- Not all invalid forms are fallacies. Inductive arguments are invalid arguments, but they aren’t fallacies. If inductive arguments have true premises, they still give us some reason to think their conclusions are true. They just don’t prove their conclusions. An inductive argument with true premises can still have a false conclusion; it’s just that the conclusion is probably true. An inductive argument with true premises is sometimes called a cogent argument.