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Guías de estudio > Mathematics for the Liberal Arts Corequisite

Logical Fallacies in Common Language

Introduction

What you’ll learn to do: Identify logical inconsistencies in every day language found in social media, politics, advertising, etc.

In our current, social media-driven society, we are exposed to many ideas, opinions, and arguments, many of which are not based in fact nor logic.  It is important that, as consumers of information, we are able to sift through what is true and what is not as well as what constitutes a legitimate logical argument.  In this section, we investigate some of the more common logical fallacies.

Learning Outcomes

  • Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, correlation implies causation, and straw man arguments.
 

Logical Arguments and Fallacies

We begin with several key definitions.

Definitions

Logic is the study of the methods and formal principles of reasoning. An argument uses a set of facts or assumptions, called premises, to proceed toward a conclusion via logical inferences (or reasoning). A fallacy is a deceptive argument in which a conclusion is reached based on a faulty or insufficient premise or faulty reasoning.

A Note about Logical Fallacies

The ideas sampled on this page are classic and are often found in irresponsible advertising, politics, and in social media.  Many social media arguments appeal to emotion and sentiment.  Political candidates often (sometimes unintentionally) employ one or more of these fallacies to favorably manipulate situation.  A good way to understand them is to see as many examples of them in the world as you can.  Consider the example that follows each fallacy and try to identify why the statement is indeed an example of the given fallacy.  In many cases, a possible correction is offered.  Do any of these corrections introduce other possible fallacies?
   

Correlation implies causation

This fallacy assumes that just because two things are related one must have caused the other. Often there is a third variable not considered.

Example

Example “Months with high ice cream sales also have a high rate of deaths by drowning. Therefore ice cream must be causing people to drown.”

Answer: This argument is implying a causal relation, when really both are more likely dependent on the weather; that ice cream and drowning are both more likely during warm summer months.

 

Ad hominem

An ad hominem argument attacks the person making the argument, ignoring the argument itself.

Ad Hominem Fallacy

Example “Jane says that whales are fish, but she’s only in the second grade, so she can’t be right.”

Answer: Here the argument is attacking Jane, not the validity of her claim, so this is an ad hominem argument.

  Possible Correction “Jane says that whales are fish, but everyone knows that they’re really mammals—she doesn't know what she's talking about.”

Answer: This certainly isn’t very nice, but it is not ad hominem since a valid counterargument is made along with the personal insult.

 

Appeal to ignorance

An appeal to ignorance argument assumes something is true because it hasn’t been proven false.

Appeal to Ignorance

Example “Nobody has proven that photo isn’t Bigfoot, so it must be Bigfoot.”

Answer: There is no proof that it is or is not Bigfoot so no conclusion can be made.

  Possible Correction “After performing photo-enhancement and analysis, it was determined that the creature in the photograph is a large bear. Therefore, it cannot be Bigfoot.”

Answer: There is evidence to prove that the creature is a bear, therefore, it is logical to conclude that it is not Bigfoot.

 

Appeal to authority

Appeal to authority arguments attempt to use the authority of a person to prove a claim. While often authority can provide strength to an argument, problems can occur when the person’s opinion is not shared by other experts, or when the authority is irrelevant to the claim.

Appeal to authority

Example 1 “A diet high in bacon can be healthy – Dr. Atkins said so.”

Answer: Here, an appeal to the authority of a doctor is used for the argument. This generally would provide strength to the argument, except that the opinion that eating a diet high in saturated fat runs counter to general medical opinion. More supporting evidence would be needed to justify this claim.

  Example 2 “Jennifer Hudson lost weight with Weight Watchers, so their program must work.”

Answer: Here, there is an appeal to the authority of a celebrity. While her experience does provide evidence, it provides no more than any other person’s experience would and a single data point is insufficient to support the claim that the program works.

  Example 2 Possible Correction “According to Dr. Brunilda Nazario, Family Medicene Specialist and Lead Medical Director at WebMD, 'WW is one of the most well-researched weight loss programs available. And yes, it works. Many studies have shown that the plan can help you lose weight and keep it off. For instance, a study from The American Journal of Medicine showed that people doing WW lost more weight than those trying to drop pounds on their own. So the Weight Watcher program does work.”

Answer: Here, the appeal is to a medical authority who cites a study in a well-respected medical journal.

 

Appeal to Consequence

An appeal to consequence concludes that a premise is true or false based on whether the consequences are desirable or not.

Appeal to Consequence

Example “Humans will travel faster than light because faster-than-light travel would be beneficial for space travel.”

Answer: Although "faster-than-light" travel would certainly enhance our space travel, that does not guarantee that humans will be able to do it.

 

Straw man

A straw man argument involves misrepresenting the argument in a less favorable way to make it easier to attack.

Straw Man

Example “Senator Jones has proposed reducing military funding by 10%. Apparently he wants to leave us defenseless against attacks by terrorists”

Answer: Here the arguer has represented a 10% funding cut as equivalent to leaving us defenseless.  While this conclusion is a misrepresentation that does not logically follow, certainly most U.S. citizens would not want our country to be defenseless.  Thus, equating the two statements makes it easier to attack Senator Jones.

  Here are some examples for you to try:

Try It

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Try It

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Try It

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Licenses & Attributions

CC licensed content, Original

CC licensed content, Shared previously

  • Math in society. Authored by: Lippman, David. Located at: http://www.opentextbookstore.com/mathinsociety/. License: CC BY-SA: Attribution-ShareAlike.
  • Question ID 25481, 25482, 25483. Authored by: Lippman, David. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.