# 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.

## Modus Tollens vs. Modus Ponens

Modus Ponens, like Modus Tollens, is a deductive way t form an argument and make conclusions from that argument.

However, where Modus Tollens does that by removing or denying, Modus Ponens reaches a conclusion by affirming.

Take the example below to understand the difference.

On a rainy day, Modus Ponens would reach such a conclusion:

It’s rainy outside. Thus he needs an umbrella.

Whereas, Modus Tollens would say:

Since he’s not wearing an umbrella, it’s not raining outside.

Modus Ponens concludes a deduction based on a fact with an affirmation.

Modus Tollens concludes a deduction based on a fact with a denial.

## Modus Tollens Examples

In a Modus Tollens, if two facts are connected, and one is not true, then both are false.

The logic is if A and B are connected if A is not true, B also turns out as not true.

For instance, below are some examples:

• If it is a bike, it has wheels. It does not have a wheel. Thus it’s not a bike.
• If it rains, he wears an umbrella. If he does not wear an umbrella. It does not rain.
• If it’s sunny, he wears sunglasses. If he does not wear sunglasses, it’s not sunny.

## 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.

## What is the modus tollens argument?

Modus tollens is a deductive argument form used to make conclusions about arguments and sets of arguments. The very generalized structure of the argument reads as follows: if P, then Q. Not Q. Therefore, not P.

## What is modus tollens with example?

In a Modus Tollens, if two facts are connected, and one is not true, then both are false. The logic is if A and B are connected if A is not true, B also turns out as not true. For instance, If it is a bike, it has wheels. It does not have a wheel. Thus it’s not a bike.

## What is the opposite of modus tollens?

However, where Modus Tollens does that by removing or denying, Modus Ponens reaches a conclusion by affirming. Modus Ponens would reach such a conclusion: It’s rainy outside. Thus he needs an umbrella. Whereas, Modus Tollens would say: Since he’s not wearing an umbrella, it’s not raining outside.

First-Principles Thinking

Six Thinking Hats Model

Second-Order Thinking

Lateral Thinking

Moonshot Thinking

Biases

Bounded Rationality

Dunning-Kruger Effect

Occam’s Razor

Mandela Effect

Crowding-Out Effect

Bandwagon Effect

Read Next: BiasesBounded RationalityMandela EffectDunning-Kruger EffectLindy EffectCrowding Out EffectBandwagon Effect.

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