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Chapter: Invalid Logical Arguments

In mathematics, the ability to recognize invalid logical arguments is as crucial as the ability to construct a valid mathematical proof. Sometimes, invalid logical arguments are used by accident in a mathematical proof which makes the proof inaccurate and flawed, sometimes, they are constructed deliberately in order to deceive the audience.

In the following, we will become familiar with some examples of fallacies (lat. fallo "I deceive"), i.e. logical arguments, which are invalid, because the conclusion is false while all its premises are true. We will introduce the following common fallacies and actually prove that they are indeed invalid arguments:

• inductive reasoning,
• mixing-up the inclusive and exclusive disjunction,
• mixing-up the sufficient and necessary condition,
• affirming the consequent of an implication,
• denying the antecedent of an implication.

Table of Contents

Explanations: 1

1. Lemma: Mixing-up the Inclusive and Exclusive Disjunction
2. Lemma: Mixing-up the Sufficient and Necessary Conditions
3. Lemma: Affirming the Consequent of an Implication
4. Lemma: Denying the Antecedent of an Implication

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References

Bibliography

1. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016