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 is a robust but simple conditional formulation that forms the basis of virtually all logical arguments. The first individual to describe modus pollens was Greek philosopher Theophrastus, successor to Aristotle in the Peripatetic school.
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.
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.
Leadership
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.
Trading hours
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.
Task delegation
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.
Leadership
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
The andon system alerts managerial, maintenance, or other staff of a production process problem. The alert itself can be activated manually with a button or pull cord, but it can also be activated automatically by production equipment. Most Andon boards utilize three colored lights similar to a traffic signal: green (no errors), yellow or amber (problem identified, or quality check needed), and red (production stopped due to unidentified issue).
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.
Convergent thinking occurs when the solution to a problem can be found by applying established rules and logical reasoning. Whereas divergent thinking is an unstructured problem-solving method where participants are encouraged to develop many innovative ideas or solutions to a given problem. Where convergent thinking might work for larger, mature organizations where divergent thinking is more suited for startups and innovative companies.
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and any eventuality. It also discourages the tendency for individuals to default to the most obvious choice.
Systems thinking is a holistic means of investigating the factors and interactions that could contribute to a potential outcome. It is about thinking non-linearly, and understanding the second-order consequences of actions and input into the system.
Vertical thinking, on the other hand, is a problem-solving approach that favors a selective, analytical, structured, and sequential mindset. The focus of vertical thinking is to arrive at a reasoned, defined solution.
First-principles thinking – sometimes called reasoning from first principles – is used to reverse-engineer complex problems and encourage creativity. It involves breaking down problems into basic elements and reassembling them from the ground up. Elon Musk is among the strongest proponents of this way of thinking.
The ladder of inference is a conscious or subconscious thinking process where an individual moves from a fact to a decision or action. The ladder of inference was created by academic Chris Argyris to illustrate how people form and then use mental models to make decisions.
The Six Thinking Hats model was created by psychologist Edward de Bono in 1986, who noted that personality type was a key driver of how people approached problem-solving. For example, optimists view situations differently from pessimists. Analytical individuals may generate ideas that a more emotional person would not, and vice versa.
Second-order thinking is a means of assessing the implications of our decisions by considering future consequences. Second-order thinking is a mental model that considers all future possibilities. It encourages individuals to think outside of the box so that they can prepare for every and eventuality. It also discourages the tendency for individuals to default to the most obvious choice.
Lateral thinking is a business strategy that involves approaching a problem from a different direction. The strategy attempts to remove traditionally formulaic and routine approaches to problem-solving by advocating creative thinking, therefore finding unconventional ways to solve a known problem. This sort of non-linear approach to problem-solving, can at times, create a big impact.
Moonshot thinking is an approach to innovation, and it can be applied to business or any other discipline where you target at least 10X goals. That shifts the mindset, and it empowers a team of people to look for unconventional solutions, thus starting from first principles, by leveraging on fast-paced experimentation.
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman in 1972. Biases are seen as systematic errors and flaws that make humans deviate from the standards of rationality, thus making us inept at making good decisions under uncertainty.
Bounded rationality is a concept attributed to Herbert Simon, an economist and political scientist interested in decision-making and how we make decisions in the real world. In fact, he believed that rather than optimizing (which was the mainstream view in the past decades) humans follow what he called satisficing.
The Dunning-Kruger effect describes a cognitive bias where people with low ability in a task overestimate their ability to perform that task well. Consumers or businesses that do not possess the requisite knowledge make bad decisions. What’s more, knowledge gaps prevent the person or business from seeing their mistakes.
The Mandela effect is a phenomenon where a large group of people remembers an event differently from how it occurred. The Mandela effect was first described in relation to Fiona Broome, who believed that former South African President Nelson Mandela died in prison during the 1980s. While Mandela was released from prison in 1990 and died 23 years later, Broome remembered news coverage of his death in prison and even a speech from his widow. Of course, neither event occurred in reality. But Broome was later to discover that she was not the only one with the same recollection of events.
The bandwagon effect tells us that the more a belief or idea has been adopted by more people within a group, the more the individual adoption of that idea might increase within the same group. This is the psychological effect that leads to herd mentality. What in marketing can be associated with social proof.
The Cynefin Framework gives context to decision making and problem-solving by providing context and guiding an appropriate response. The five domains of the Cynefin Framework comprise obvious, complicated, complex, chaotic domains and disorder if a domain has not been determined at all.
A SWOT Analysis is a framework used for evaluating the business’s Strengths, Weaknesses, Opportunities, and Threats. It can aid in identifying the problematic areas of your business so that you can maximize your opportunities. It will also alert you to the challenges your organization might face in the future.
The SWOT analysis is commonly used as a strategic planning tool in business. However, it is also well suited for personal use in addressing a specific goal or problem. A personal SWOT analysis helps individuals identify their strengths, weaknesses, opportunities, and threats.
The Pareto Analysis is a statistical analysis used in business decision making that identifies a certain number of input factors that have the greatest impact on income. It is based on the similarly named Pareto Principle, which states that 80% of the effect of something can be attributed to just 20% of the drivers.
A failure mode and effects analysis (FMEA) is a structured approach to identifying design failures in a product or process. Developed in the 1950s, the failure mode and effects analysis is one the earliest methodologies of its kind. It enables organizations to anticipate a range of potential failures during the design stage.
A Blindspot Analysis is a means of unearthing incorrect or outdated assumptions that can harm decision making in an organization. The term “blindspot analysis” was first coined by American economist Michael Porter. Porter argued that in business, outdated ideas or strategies had the potential to stifle modern ideas and prevent them from succeeding. Furthermore, decisions a business thought were made with care caused projects to fail because major factors had not been duly considered.
A comparable company analysis is a process that enables the identification of similar organizations to be used as a comparison to understand the business and financial performance of the target company. To find comparables you can look at two key profiles: the business and financial profile. From the comparable company analysis it is possible to understand the competitive landscape of the target organization.
A cost-benefit analysis is a process a business can use to analyze decisions according to the costs associated with making that decision. For a cost analysis to be effective it’s important to articulate the project in the simplest terms possible, identify the costs, determine the benefits of project implementation, assess the alternatives.
Agile Business Analysis (AgileBA) is certification in the form of guidance and training for business analysts seeking to work in agile environments. To support this shift, AgileBA also helps the business analyst relate Agile projects to a wider organizational mission or strategy. To ensure that analysts have the necessary skills and expertise, AgileBA certification was developed.
A SOAR analysis is a technique that helps businesses at a strategic planning level to:
Focus on what they are doing right.
Determine which skills could be enhanced.
Understand the desires and motivations of their stakeholders.
The STEEPLE analysis is a variation of the STEEP analysis. Where the step analysis comprises socio-cultural, technological, economic, environmental/ecological, and political factors as the base of the analysis. The STEEPLE analysis adds other two factors such as Legal and Ethical.
The PESTEL analysis is a framework that can help marketers assess whether macro-economic factors are affecting an organization. This is a critical step that helps organizations identify potential threats and weaknesses that can be used in other frameworks such as SWOT or to gain a broader and better understanding of the overall marketing environment.
A DESTEP analysis is a framework used by businesses to understand their external environment and the issues which may impact them. The DESTEP analysis is an extension of the popular PEST analysis created by Harvard Business School professor Francis J. Aguilar. The DESTEP analysis groups external factors into six categories: demographic, economic, socio-cultural, technological, ecological, and political.
A paired comparison analysis is used to rate or rank options where evaluation criteria are subjective by nature. The analysis is particularly useful when there is a lack of clear priorities or objective data to base decisions on. A paired comparison analysis evaluates a range of options by comparing them against each other.
Gennaro is the creator of FourWeekMBA, which reached about four million business people, comprising C-level executives, investors, analysts, product managers, and aspiring digital entrepreneurs in 2022 alone | He is also Director of Sales for a high-tech scaleup in the AI Industry | In 2012, Gennaro earned an International MBA with emphasis on Corporate Finance and Business Strategy.
