modus-tollens

What Is Modus Tollens? Modus Tollens In A Nutshell

Modus tollens is a deductive argument form and a rule of inference used to make conclusions of arguments and sets of arguments.  Modus tollens argues that if P is true then Q is also true. However, P is false. Therefore Q is also false. Modus tollens as an inference rule dates back to late antiquity where it was taught as part of Aristotelian logic. The first person to describe the rule in detail was Theophrastus, successor to Aristotle in the Peripatetic school.

Understanding modus tollens

The structure of a modus tollens argument resembles that of a syllogism, a type of logical argument using deductive reasoning to arrive at a conclusion based on two propositions that are assumed to be true.

More specifically:

If P, then Q

Not Q

Therefore, not P.

In deconstructing the argument, we can see that the first premise is a conditional claim such that P implies Q. This is also known as an “if-then” claim. The second premise asserts that Q, the consequent of the conditional claim, is not the case. Here, the consequent is the “then” statement.

Based on these two premises, a logical conclusion can be drawn. That is, the antecedent of the conditional claim P is also not the case. Here, the antecedent is the “if” statement. It’s important to note that P and Q can be anything – even completely made up words – so long as the construction of the argument makes logical sense.

Examples of modus tollens arguments

Consider the following argument: 

If the sky is blue, then it is not raining.

It is raining.

Therefore, the sky is not blue.

The sky is blue” is the antecedent, while “it is not raining” is the consequent. 

In the previous section, we noted that P implies Q. If the consequent is false, then it stands to reason that the antecedent is also false. This same implication also means that if an argument fails to reach a true consequent then the antecedent must also be false.

While P implies Q, it cannot be assumed that a false antecedent implies a false consequent in all instances. For example, a sky that is not blue does not necessarily mean it is raining. It may just be a cloudy day where the sky is obscured. This assumption is a common fallacy known as denying the antecedent and is a trap many individuals fall into.

Other examples of modus tollens arguments

If the dog detects an intruder, the dog will bark.

The dog did not bark.

Therefore, no intruder was detected by the dog.

One more example:

If it is a car, then it has wheels. 

It does not have wheels. 

Therefore, it is not a car.

Key takeaways:

  • Modus tollens is a deductive argument form used to make conclusions of arguments and sets of arguments. The rule dates back to late antiquity where it was taught as part of Aristotelian logic.
  • A modus tollens argument has two premises and a conclusion. The very generalized structure of the argument reads as follows: if P, then Q. Not Q. Therefore, not P.
  • A modus tollens argument is comprised of an antecedent (“if” statement) and consequent (“then”) statement. The antecedent and consequent can represent almost anything so long as the argument makes logical sense.

Connected Heuristics And Thinking Tools

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recognition-heuristic
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Gennaro Cuofano

Gennaro is the creator of FourWeekMBA which reached over a million business students, executives, and aspiring entrepreneurs in 2020 alone | He is also Head of Business Development for a high-tech startup, which he helped grow at double-digit rate | Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy | Visit The FourWeekMBA BizSchool | Or Get The FourWeekMBA Flagship Book "100+ Business Models"