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

As highlighted by German psychologist Gerd Gigerenzer in the paper “Heuristic Decision Making,” the term heuristic is of Greek origin, meaning “serving to find out or discover.” More precisely, a heuristic is a fast and accurate way to make decisions in the real world, which is driven by uncertainty.
The recognition heuristic is a psychological model of judgment and decision making. It is part of a suite of simple and economical heuristics proposed by psychologists Daniel Goldstein and Gerd Gigerenzer. The recognition heuristic argues that inferences are made about an object based on whether it is recognized or not.
The representativeness heuristic was first described by psychologists Daniel Kahneman and Amos Tversky. The representativeness heuristic judges the probability of an event according to the degree to which that event resembles a broader class. When queried, most will choose the first option because the description of John matches the stereotype we may hold for an archaeologist.
The take-the-best heuristic is a decision-making shortcut that helps an individual choose between several alternatives. The take-the-best (TTB) heuristic decides between two or more alternatives based on a single good attribute, otherwise known as a cue. In the process, less desirable attributes are ignored.
The concept of cognitive biases was introduced and popularized by the work of Amos Tversky and Daniel Kahneman since 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.
The bundling bias is a cognitive bias in e-commerce where a consumer tends not to use all of the products bought as a group, or bundle. Bundling occurs when individual products or services are sold together as a bundle. Common examples are tickets and experiences. The bundling bias dictates that consumers are less likely to use each item in the bundle. This means that the value of the bundle and indeed the value of each item in the bundle is decreased.
The Barnum Effect is a cognitive bias where individuals believe that generic information – which applies to most people – is specifically tailored for themselves.
Backward chaining, also called backward integration, describes a process where a company expands to fulfill roles previously held by other businesses further up the supply chain. It is a form of vertical integration where a company owns or controls its suppliers, distributors, or retail locations.
The Amazon Working Backwards Method is a product development methodology that advocates building a product based on customer needs. The Amazon Working Backwards Method gained traction after notable Amazon employee Ian McAllister shared the company’s product development approach on Quora. McAllister noted that the method seeks “to work backwards from the customer, rather than starting with an idea for a product and trying to bolt customers onto it.”
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.
Tim Brown, Executive Chair of IDEO, defined design thinking as “a human-centered approach to innovation that draws from the designer’s toolkit to integrate the needs of people, the possibilities of technology, and the requirements for business success.” Therefore, desirability, feasibility, and viability are balanced to solve critical problems.
The CATWOE analysis is a problem-solving strategy that asks businesses to look at an issue from six different perspectives. The CATWOE analysis is an in-depth and holistic approach to problem-solving because it enables businesses to consider all perspectives. This often forces management out of habitual ways of thinking that would otherwise hinder growth and profitability. Most importantly, the CATWOE analysis allows businesses to combine multiple perspectives into a single, unifying solution.

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