How Logical Fallacy Invalidates Any Argument

Understanding Defective Arguments

Woman and man on a bench in the park having an argument.

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Fallacies are defects that cause an argument to be invalid, unsound, or weak. Logical fallacies can be separated into two general groups: formal and informal. A formal fallacy is a defect which can be identified merely by looking at the logical structure of an argument, rather than at any specific statements. Informal fallacies are defects which can be identified only through an analysis of the actual content of the argument.

Formal Fallacies

Formal fallacies are found only in deductive arguments with identifiable forms. One of the things which makes them appear reasonable is the fact that they look like and mimic valid logical arguments, but are in fact invalid. Here is an example:

  1. Premise: All humans are mammals.
  2. Premise: All cats are mammals.
  3. Conclusion: All humans are cats.

Both premises in this argument are true, but the conclusion is false. The defect is a formal fallacy, and can be demonstrated by reducing the argument to its bare structure:

  1. All A are C
  2. All B are C
  3. All A are B

It does not matter what A, B, and C stand for. We could replace them with "wines," "milk," and "beverages." The argument would still be invalid for the exact same reason. It can be helpful to reduce an argument to its structure and ignore content in order to see if it is valid.

Informal Fallacies

Informal fallacies are defects which can be identified only through an analysis of the actual content of the argument, rather than through its structure. Here is an example:

  1. Premise: Geological events produce rock.
  2. Premise: Rock is a type of music.
  3. Conclusion: Geological events produce music.

The premises in this argument are true but clearly, the conclusion is false. Is the defect a formal fallacy or an informal fallacy? To see if this is actually a formal fallacy, we have to break it down to its basic structure:

  1. A = B
  2. B = C
  3. A = C

This structure is valid. Therefore, the defect cannot be a formal fallacy and must instead be an informal fallacy that is identifiable from the content. When we examine the content, we find that a key term ("rock") is being used with two different definitions.

Informal fallacies can work in several ways. Some distract the reader from what is really going on. Some, like in the above example, make use of ambiguity to cause confusion.

Defective Arguments

There are many ways to categorize fallacies. Aristotle was the first to try to systematically describe and categorize them, identifying 13 fallacies divided into two groups. Since then, many more have been described and the categorization has become more complicated. The categorization used here should prove useful, but it is not the only valid way of organizing fallacies.

  • Fallacies of Grammatical Analogy

Arguments with this defect have a structure that is grammatically close to arguments which are valid and make no fallacies. Because of this close similarity, a reader can be distracted into thinking that a bad argument is actually valid.

  • Fallacies of Ambiguity

With these fallacies, some sort of ambiguity is introduced either in the premises or in the conclusion itself. This way, an apparently false idea can be made to appear true so long as the reader does not notice the problematic definitions.

Examples:

These fallacies all make use of premises which are logically irrelevant to the final conclusion.

Examples:

Logical fallacies of presumption arise because the premises already assume what they are supposed to prove. This is invalid because there is no point in trying to prove something you already assume to be true. No one who needs to have something proven to them will accept a premise which already assumes the truth of that idea.

Examples:

With this type of fallacy, there may be an apparent logical connection between the premises and the conclusion. However, if that connection is real, then it is too weak to support the conclusion.

Examples:

Sources

Barker, Stephen F. "Elements of Logic." Hardcover — 1675, McGraw-Hill Publishing Co.

Curti, Gary N. "Weblog." Fallacy Files, March 31, 2019. 

Edwards, Paul (Editor). "The Encyclopedia of Philosophy." Hardcover, 1st edition, Macmillan/Collier, 1972.

Engel, S. Morris. "With Good Reason: An Introduction to Informal Fallacies." Sixth Edition, Bedford/St. Martin's, March 21, 2014.

Hurley, Patrick J. "A Concise Introduction to Logic." 12 Edition, Cengage Learning, January 1, 2014.

Salmon, Merrilee H. "Introduction to Logic and Critical Thinking." 6th Edition, Cengage Learning, January 1, 2012.

Vos Savant, Marilyn. "The Power of Logical Thinking: Easy Lessons in the Art of Reasoning...and Hard Facts About Its Absence in Our Lives." Hardcover, 1st edition, St Martins Press, March 1, 1996.