# 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 about 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 when it was taught as part of Aristotelian logic. The first person to describe the rule in detail was Theophrastus, the 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.

## Modus tollens examples in business

To conclude, we’ll provide some modus tollens examples that are more related to business.

Remember that modus tollens is a type of logical argument that uses deductive reasoning with two premises and a conclusion.

### Workplace attendance

If Frank works every Wednesday and Frank does not go to work today, then today cannot be Wednesday.

### Professional qualifications

If all accountants have Bachelor’s degrees in accounting, and Lucinda is not an accountant, then Lucinda does not possess a Bachelor’s degree in accounting.

### Sales presentation nerves

If Peter always wears a blue suit before delivering a sales presentation, and he is not wearing a blue suit, then today he is not delivering a sales presentation.

### Performance review

If John’s superior is concerned with his job performance, he is always called into head office for a performance review.

John’s superior did not call him into head office for a performance review. Therefore, John’s superior is not concerned with his job performance.

### Casual office attire

If a law firm’s employees can wear jeans to work, then it must casual Friday.

It is not casual Friday. Therefore, the law firm’s employees can’t wear jeans to work.

### Project management

If Mary is the project manager, then the project is the only one in the company concluded with a retrospective analysis.

The project is not concluded with a retrospective analysis. Therefore, Mary is not the project manager.

### Job interview

If Kate moves to the next phase of the recruitment process, then she will receive a call back from the recruiter.

Kate does not receive a call back from the recruiter. Therefore, she has not moved to the next phase of the recruitment process.

### Network access

If Peter has a password, he can access the company’s cloud infrastructure.

Peter cannot access the company’s cloud infrastructure. Therefore, he does not have a password.

### Supermarket ice cream

If the forecast temperature is above 35 degrees Celsius, the supermarket will place an extra order for ice cream.

The supermarket did not place an extra order for ice cream. Therefore, the forecast temperature did not exceed 35 degrees Celsius.

### Organizational structure

If the structure of the organization is hierarchical, then it has top-down command and several layers of management.

The organization does not have top-down command and several layers of management.

Therefore, the organization is not hierarchical.

### Education

If Mark has completed a diploma in education, then he is a teacher.

Mark is not a teacher. Therefore, he has not completed a diploma in education.

### Fortune 500 companies

If a company is among the 500 largest American companies by annual revenue, then it will feature on the Fortune 500 list.

The company does not feature on the Fortune 500 list. Therefore, it is not among the 500 largest American companies by annual revenue.

### Remote work

If an employee is considered a remote worker, they must have Zoom installed on their work laptop.

The employee does not have Zoom installed on their work laptop. Therefore, they are not considered a remote worker.

### Start-up company

If the start-up company is able to secure seed funding, then it will be able to hire three extra staff. The start-up company was not able to hire three extra staff. Therefore, it was not able to secure seed funding.

If Tony is a delegative leader, his subordinates will describe him as tolerant of their mistakes and preferring to focus on big-picture objectives.

Tony’s subordinates do not describe him as tolerant of their mistakes and preferring to focus on big-picture objectives. Therefore, Tony is not a delegative leader.

If a restaurant decides to trade on a public holiday, then it will have to pay its staff special penalty rates. The restaurant does not pay its staff special penalty rates. Therefore, the restaurant did not decide to trade on a public holiday.

### Unfair dismissal

If John is harassed at work and forced to resign from the company, he may have grounds for a wrongful termination suit.

John does not have grounds for a wrongful termination suit. Therefore, he was not harassed at work and forced to resign from the company.

### Constructive criticism

If Vincenzo delivers constructive criticism, employees subsequently feel motivated to correct their mistakes and improve their performance.

The employees do not subsequently feel motivated to correct their mistakes and improve their performance. Therefore, Vincenzo has not delivered constructive criticism.

### Lunchroom theft

If Susanne leaves her coffee mug at home, she borrows Kate’s coffee mug and leaves it dirty in the sink. Susanne does not borrow Kate’s coffee mug and leave it dirty in the sink. Therefore, Susanne did not leave her coffee mug at home.

### Company car

If a sales representative has 10 years of service with the firm, then they will receive a company car to visit clients. The sales representative does not receive a company car to visit clients. Therefore, they do not have 10 years of service with the firm.

### Supermarket proximity

If every consumer is less than 10 miles from the nearest Walmart store, then they must all reside in the United States. All consumers do not reside in the United States. Therefore, every consumer is not less than 10 miles from the nearest Walmart store.

### Promotion

If Rob is promoted ahead of Jack, then Rob will receive the corner office. Rob does not receive the corner office. Therefore, Rob has not been promoted ahead of Jack.

### Workplace hazards

If employees are forced to perform repetitive movements or lift heavy items without assistance from machines, then workplace safety manager Sandy will raise these issues in the next meeting.

Workplace safety manager Sandy does not raise these issues in the next meeting. Therefore, employees have not been forced to perform repetitive movements or left heavy items without assistance from machines.

### Lean manufacturing

If a company adopts the lean manufacturing philosophy, it will have specific procedures in place to minimize the eight forms of waste.

The company does not have specific procedures in place to minimize the eight forms of waste. Therefore, it does not adopt the lean manufacturing philosophy.

### Company revenue

If a company’s revenue decreases, then it must be losing customers.

The company is not losing customers. Therefore, the company’s revenue is not decreasing.

### Company expenses

If a company reduces its expenses, then profits will increase.

Profits are not increasing. Therefore, the company has not reduced its expenses.

### Work email

If Joe sends an email to his team, then Mary is one of the recipients.

Mary is not one of the recipients. Therefore, Joe has not sent an email to his team.

### Customer satisfaction

If the customer wants a refund on their product, they will contact a customer service representative.

The customer does not contact a customer service representative. Therefore, they do not want a refund on their product.

### Departmental management

If a department is well managed, then it should report high employee retention.

The department does not report high employee retention. Therefore, it is not well managed.

### Project outcomes

If a project is considered successful, it should meet or exceed five different KPIs.

The project does not meet or exceed five different KPIs. Therefore, it is not considered successful.

### Employee training

If the company invests in employee training, then its employees should become more skilled.

Employees do not become more skilled. Therefore, the company did not invest in employee training.

### Teams

If a software team is communicating effectively, the workplace will be characterized by collaboration and a lack of conflict.

The workplace is not characterized by collaboration and a lack of conflict. Therefore, the software team is not communicating effectively.

If Jack delegates project tasks effectively, then the project will be completed on time and within budget.

The project is not completed on time and within budget. Therefore, Jack has not delegated project tasks effectively.

If Peter is a laissez-faire leader, his employees possess some degree of decision-making authority and are held accountable for their work.

Employees do not possess some degree of decision-making authority and are not held accountable for their work. Therefore, Peter is not a laissez-faire leader.

### Andon system

If an automotive company employs the Andon system of lean manufacturing, its factories will incorporate color-coded lights that alert workers to various problem levels.

Factories do not incorporate color-coded lights that alert workers to various problem levels. Therefore, the automotive company does not employ the Andon system of lean manufacturing.

### Sales

If Jenny is an effective leader, then her team will exceed KPI targets related to annual contract value (AC), customer lifetime value (CLV), and conversion rate.

Jenny’s team does not exceed KPI targets related to annual contract value, customer lifetime value, and conversion rate. Therefore, Jenny is not an effective leader.

### AI chatbot

If an AI chatbot is helpful to the customer, it should be able to answer a range of questions and comments efficiently.

The AI chatbot is not able to answer a range of questions and comments efficiently. Therefore, it is not helpful to the customer.

## 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.

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