Modus Ponens

If P then Q P Therefore, Q ‘P’ and ‘Q’ are variables for statements, and ‘if...then…’ is a logical operator. Modus ponens is a valid form of argument.

Manuel: “If we are late, then the train will leave the station.” 

Pablo: “We are late.”  

Manuel: “The train will leave the station.”

Manuel and Pablo used modus ponens, a fundamental form of logical argument that shows up in everyday discussions. Modus ponens can help us understand others' arguments, and form our own arguments. 

In order to understand modus ponens, let’s go over the basic concepts of argument. 

What is an argument? 

An argument is a series of statements that try to prove a point. The statements can be either true or false. The statement that the arguer tries to prove is called the conclusion. The statements that try to prove the conclusion are called premises.

Difference between argument, and valid argument

If you put a series of statements together, then you make an argument.

Premise: P

Conclusion: Therefore, Q

Above is an example of something that counts as an argument since it has a premise and a conclusion. That’s all it takes for something to be an argument, but it doesn’t make it a valid argument. 

When we say an argument is valid, we are talking about an argument’s form. If we plug true premises into a valid form, it guarantees a true conclusion. A valid form is similar to an accurate math formula. For example, if you want to get the area of a circle, you will use the formula “A = π (r)^2.” Then, all you need to do is plug the accurate radius of the circle into the formula to get an accurate area.

The values we plug in for the variables in a math formula are numbers. By contrast, the values we plug in for the variables in a logic argument are statements. Let’s look at modus ponens’ form:

​​Premise 1: If P then Q

Premise 2: P

Conclusion: Therefore, Q

In the above form, ‘P’ and ‘Q’ are variables for statements, and ‘if...then…’ is a logical operator called a conditional. Modus ponens is a valid form of argument. 

Let’s plug statements into modus ponens to demonstrate that if the premises of a valid argument are true, then the argument is guaranteed a true conclusion. When an argument has a valid form(like modus ponens), and all the premises are true, it is called a sound argument. 

Let’s suppose P is “It is raining,” and Q is “The street is wet.” The result is the following argument: 

Premise 1: If it is raining, then the street is wet.

Premise 2: It is raining.

Conclusion: Therefore, the street is wet.

In our above example, if the premises of the argument are true, then it’s impossible for the conclusion of the argument to be false. 

How to detect modus ponens in conversations?

Often in conversations, modus ponens can look different than what we discussed above. Just like when you encounter a math problem, in order to solve it, you put it into an equation. Likewise, when you encounter an argument, in order to evaluate it, you put it into a valid form. Here are a couple of examples:

CEO using modus ponens: “I’ve said this before that if we increase our sales by 20% by the end of the year, everyone is going to get a bonus. And today, we have hit our sales target. Everyone gets a bonus”. 

Premise 1: If we increase our sales by 20% by the end of the year, then everyone gets a bonus. 

Premise 2: We increased our sales by 20% by the end of the year. 

Conclusion: Therefore, everyone gets a bonus. 

Your friend using modus ponens: “I’ll give you $100 if you can put this argument into modus ponens.”

Your response: 

Premise 1: If I put this argument into modus ponens, then I get $100. 

Premise 2: I put this argument into modus ponens. 

Conclusion: Therefore, I get $100. 

Modus ponens achieved. Where’s my money?

Recognizing modus ponens in conversation is a crucial skill for critical thinking. By mastering this form of reasoning, you can better analyze arguments, make informed decisions, and articulate your own ideas well.