Introduction to Logical Fallacies: Formal and Informal Errors in Reasoning

Logical Fallacies

Definition and Types of Fallacies

Logical fallacies are errors in reasoning that undermine the logical validity of an argument. They are commonly encountered in both academic and everyday discussions. Fallacies can be divided into two main categories: formal fallacies and informal fallacies.

• Formal fallacy: An error in reasoning that involves the explicit use of an invalid logical form. The argument is invalid due to its structure, regardless of the content of its premises.

• Informal fallacy: An error in reasoning that does not involve the explicit use of an invalid form, but rather issues with the content, ambiguity, or assumptions within the argument.

Formal Fallacies

Formal fallacies occur when the logical structure of an argument is invalid. The validity of the argument depends solely on its form, not the truth of its premises. If the form is invalid, the argument is always invalid.

• Arguments with invalid forms are always invalid, regardless of the premises.

• It is possible to generate substitution instances where all premises are true but the conclusion is false.

• Common types of formal fallacies include:

  • Affirming the consequent:

    1. If A, then B.

    2. B.

    3. Therefore, A.

  • Denying the antecedent:

    1. If A, then B.

    2. Not A.

    3. Therefore, not B.

  • Affirming a disjunct:

    1. A or B.

    2. A.

    3. Therefore, not B.

• All deductively invalid arguments are engaged in some type of formal fallacy, often called non sequiturs.

Informal Fallacies

Informal fallacies are errors in reasoning that arise from issues other than logical form, such as ambiguity, irrelevance, or unwarranted assumptions. These may have a deductively valid argument form but are flawed due to their content.

• To identify informal fallacies, examine the content of the premises and conclusion, not just the logical structure.

• Informal fallacies are often grouped into three broad categories:

Category	Description	Example
Fallacies of irrelevance	Argument contains information that is irrelevant to the conclusion.	"Ad hominem" attacks, where the character of the speaker is attacked rather than the argument.
Fallacies involving ambiguity	Ambiguous language or terms are used, leading to confusion or misinterpretation.	Equivocation, where a word is used in two different senses.
Fallacies involving unwarranted assumptions	Arguments rely on assumptions that are not supported by evidence.	Begging the question, where the conclusion is assumed in the premises.

Preliminary Notes on Fallacies

It is important to recognize that not every error in reasoning is a formal or informal fallacy. Some arguments may be weak or unsound without committing a specific fallacy. Additionally, the context of an argument may affect whether a statement is fallacious.

• Every fallacy will be either formal or informal, but not every invalid argument commits a named fallacy.

• Some statements may be fallacious depending on context.

• Arguments may be persuasive but still logically fallacious.

• Not all errors in reasoning are covered by the fallacies discussed.

• Do not assume that an argument with a fallacy must have a false conclusion. An invalid argument can still have a true conclusion.

Common Misconceptions

• Committing a fallacy does not guarantee the conclusion is false. This is known as the fallacy fallacy.

• An invalid argument might have a true conclusion.

• A weak argument might still have a true conclusion.

Examples and Applications

• Affirming the consequent: If it rains, the ground will be wet. The ground is wet. Therefore, it rained. (This is invalid; the ground could be wet for other reasons.)

• Ad hominem: Dismissing someone's argument because of their character rather than the merits of the argument.

• Equivocation: Using the word "bank" to mean both a financial institution and the side of a river in the same argument.

Additional info: Logical fallacies are a foundational topic in critical thinking and philosophy, and understanding them is essential for evaluating arguments in science, law, and everyday life.