Episode 5 Modus Ponens and Modus Tollens
In the fifth episode of Critically Minded, Nick and Dave continue their discuss two common patterns of argument.
Nick: We’re back again with Critically Minded––Critical Thinking for 2nd Language Learners.
Dave: The podcast for English language learners who want to improve their critical thinking skills.
Nick: And we’re your hosts Nick-
Dave: And Dave. In this episode we’re going to discuss two kinds of basic argument forms. In the first episodes we talked a little about organizing an argument, and how logic connects premises and conclusions.
Nick: But what we haven’t talked about yet are patterns of logic. The first pattern we will look at is called Modus Ponens. A rule of reasoning which is often related to the conditional sentence.
The IF/THEN pattern. For example, “If the water is boiling, then the temperature of the water is 100℃.” There are two parts to this expression, “If the water is boiling.” and “The temperature of the water is 100℃.” So if we know for a fact that the water is boiling then we have to conclude that the water temperature is 100℃.
Dave: So what you are saying is that the logic of the Modus Ponens rule is actually quite simple. It says, that if the first part of the conditional sentence is true, then the second part must also be true.
p ->q: If the water is boiling, then the temperature of the water is 100℃.
p: The water is boiling.
q: The temperature of the water is 100℃.
Dave: Nick, do all examples of Modus Ponens follow the if/then pattern?
Nick: The pattern of logic, yes. But we don’t always need to use the words ‘if’ and ‘then’. For example, “The water is boiling so the temperature of the water is now at 100℃.” The words are different, but the relationship between the two parts is the same, and that’s what is important to us.
Dave: And for our listeners that is a very important point. As critical thinkers we have to look at the meaning and relationship between ideas, and not to be too worried about each and every word.
Nick: Right. And a good way to test the logic and relationship between two ideas is to try the Modus Tollens rule of reasoning. That is, make a conditional sentence with the two ideas, and then imagine that the second part is not true. For example, if we take the temperature of the water and it is NOT 100℃. It’s 55℃. Then we could safely conclude that the water is not boiling.
Dave: So, if the second part is false then the first part must also be false.
p -> q: If the water is boiling, then the temperature of the water is 100℃.
~q: The temperature of the water is not 100℃.
~p: The water is not boiling.
Nick: And why is this important?
Dave: Well, to be a critical thinker we have to look at the logical relationship between premises and conclusions. We need to be able to judge whether the premises are true, and that they lead to the most probable and logical conclusion.
Nick: Right. And that’s a very important point. When the premises are true and the conclusion is the most probable one we can think of, then we say the argument is sound. Here’s an example, “If Tom is human, then he will die.”
Dave: Okay, so let’s apply the Modus ponens rule to this. If the first part is true then so is the second. We can break it up like this: All humans die. We all know that is true. That’s common knowledge. So we have these two parts: Tom is human. Therefore, Tom will die . . .
Nick: And I think we can all agree that’s a sound argument. But that is only if the premise “ Tom is human.” is true. If Tom is actually a robot that looks exactly like a human, then this argument is not sound.
Dave: It’s unsound. It’s unsound, because even though the conclusion is true, the premise “Tom is human.” is false.
Nick: And I could test this. I could apply the Modus Tollens rule and we could watch him for a hundred and fifty years and wait for him to die.
Dave: Since no human has ever lived that long, then we could conclude that he is a robot.
Nick: And a robot with some awesome batteries.
Dave: So, remember, check that the premises lead logically to the conclusion. Test the argument.
Nick: And check the facts, and check we are talking about the same thing. Don’t assume.
Dave: So until next time, this is Critically Minded: Critical Thinking For 2nd Language Learners.
Episode 5 Modus Ponens and Modus Tollens