If a law firm’s employees can wear jeans to work, then it must casual Friday. Therefore, John’s superior is not concerned with his job performance. John’s superior did not call him into head office for a performance review. If John’s superior is concerned with his job performance, he is always called into head office for a performance review. 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. 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. If Frank works every Wednesday and Frank does not go to work today, then today cannot be Wednesday. Remember that modus tollens is a type of logical argument that uses deductive reasoning with two premises and a conclusion. To conclude, we’ll provide some modus tollens examples that are more related to business. If he does not wear sunglasses, it’s not sunny. The logic is if A and B are connected if A is not true, B also turns out as not true. In a Modus Tollens, if two facts are connected, and one is not true, then both are false. Modus Tollens concludes a deduction based on a fact with a denial. Modus Ponens concludes a deduction based on a fact with an affirmation. Since he’s not wearing an umbrella, it’s not raining outside. On a rainy day, Modus Ponens would reach such a conclusion: Take the example below to understand the difference. However, where Modus Tollens does that by removing or denying, Modus Ponens reaches a conclusion by affirming. Modus Ponens, like Modus Tollens, is a deductive way t form an argument and make conclusions from that argument. The first individual to describe modus pollens was Greek philosopher Theophrastus, successor to Aristotle in the Peripatetic school. Modus Ponens Modus ponens is a robust but simple conditional formulation that forms the basis of virtually all logical arguments. Therefore, no intruder was detected by the dog. If the dog detects an intruder, the dog will bark. Other examples of modus tollens arguments This assumption is a common fallacy known as denying the antecedent and is a trap many individuals fall into. It may just be a cloudy day where the sky is obscured. For example, a sky that is not blue does not necessarily mean it is raining. While P implies Q, it cannot be assumed that a false antecedent implies a false consequent in all instances. This same implication also means that if an argument fails to reach a true consequent then the antecedent must also be false. If the consequent is false, then it stands to reason that the antecedent is also false. In the previous section, we noted that P implies Q. “ The sky is blue” is the antecedent, while “ it is not raining” is the consequent. If the sky is blue, then it is not raining. 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. Here, the antecedent is the “if” statement. That is, the antecedent of the conditional claim P is also not the case. Here, the consequent is the “then” statement.īased on these two premises, a logical conclusion can be drawn. The second premise asserts that Q, the consequent of the conditional claim, is not the case. This is also known as an “if-then” claim. In deconstructing the argument, we can see that the first premise is a conditional claim such that P implies Q. 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. The first person to describe the rule in detail was Theophrastus, the successor to Aristotle in the Peripatetic school. Modus tollens as an inference rule dates back to late antiquity when it was taught as part of Aristotelian logic. Modus tollens argues that if P is true, then Q is also true. Modus tollens is a deductive argument form and a rule of inference used to make conclusions about arguments and sets of arguments.
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